enhance logical and critical thinking

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3 Simple Habits to Improve Your Critical Thinking

Helen Lee Bouygues

But simple doesn’t mean easy.

Too many business leaders are simply not reasoning through pressing issues, and it’s hurting their organizations. The good news is that critical thinking is a learned behavior. There are three simple things you can do to train yourself to become a more effective critical thinker: question assumptions, reason through logic, and diversify your thought and perspectives. They may sound obvious, but deliberately cultivating these three key habits of mind go a long way in helping you become better at clear and robust reasoning.

A few years ago, a CEO assured me that his company was the market leader. “Clients will not leave for competitors,” he added. “It costs too much for them to switch.” Within weeks, the manufacturing giant Procter & Gamble elected not to renew its contract with the firm. The CEO was shocked — but he shouldn’t have been.

HB Helen Lee Bouygues is the president of the Paris-based Reboot Foundation . A former partner at McKinsey & Company, she has served as interim CEO, CFO, or COO for more than one dozen companies.

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Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Publisher: Matthew J. Van Cleave

Language: English

Formats Available

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Reviewed by "yusef" Alexander Hayes, Professor, North Shore Community College on 6/9/21

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness. read more

Comprehensiveness rating: 5 see less

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness.

Content Accuracy rating: 5

The book is accurate.

Relevance/Longevity rating: 5

While many modern examples are used, and they are helpful, they are not necessarily needed. The usefulness of logical principles and skills have proved themselves, and this text presents them clearly with many examples.

Clarity rating: 5

It is obvious that the author cares about their subject, audience, and students. The text is comprehensible and interesting.

Consistency rating: 5

The format is easy to understand and is consistent in framing.

Modularity rating: 5

This text would be easy to adapt.

Organization/Structure/Flow rating: 5

The organization is excellent, my one suggestion would be a concluding chapter.

Interface rating: 5

I accessed the PDF version and it would be easy to work with.

Grammatical Errors rating: 5

The writing is excellent.

Cultural Relevance rating: 5

This is not an offensive text.

Reviewed by Susan Rottmann, Part-time Lecturer, University of Southern Maine on 3/2/21

Comprehensiveness rating: 4 see less

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it fits better for a general critical thinking course than for a true logic course. I'm not sure that I'd agree. I have been using Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," and I think that book is a better introduction to critical thinking for non-philosophy majors. However, the latter is not open source so I will figure out how to get by without it in the future. Overall, the book seems comprehensive if the subject is logic. The index is on the short-side, but fine. However, one issue for me is that there are no page numbers on the table of contents, which is pretty annoying if you want to locate particular sections.

Content Accuracy rating: 4

I didn't find any errors. In general the book uses great examples. However, they are very much based in the American context, not for an international student audience. Some effort to broaden the chosen examples would make the book more widely applicable.

Relevance/Longevity rating: 4

I think the book will remain relevant because of the nature of the material that it addresses, however there will be a need to modify the examples in future editions and as the social and political context changes.

Clarity rating: 3

The text is lucid, but I think it would be difficult for introductory-level students who are not philosophy majors. For example, in Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," the sub-headings are very accessible, such as "Experts cannot rescue us, despite what they say" or "wishful thinking: perhaps the biggest single speed bump on the road to critical thinking." By contrast, Van Cleave's "Introduction to Logic and Critical Thinking" has more subheadings like this: "Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form" or "Propositional logic and the four basic truth functional connectives." If students are prepared very well for the subject, it would work fine, but for students who are newly being introduced to critical thinking, it is rather technical.

It seems to be very consistent in terms of its terminology and framework.

Modularity rating: 4

The book is divided into 4 chapters, each having many sub-chapters. In that sense, it is readily divisible and modular. However, as noted above, there are no page numbers on the table of contents, which would make assigning certain parts rather frustrating. Also, I'm not sure why the book is only four chapter and has so many subheadings (for instance 17 in Chapter 2) and a length of 242 pages. Wouldn't it make more sense to break up the book into shorter chapters? I think this would make it easier to read and to assign in specific blocks to students.

Organization/Structure/Flow rating: 4

The organization of the book is fine overall, although I think adding page numbers to the table of contents and breaking it up into more separate chapters would help it to be more easily navigable.

Interface rating: 4

The book is very simply presented. In my opinion it is actually too simple. There are few boxes or diagrams that highlight and explain important points.

The text seems fine grammatically. I didn't notice any errors.

The book is written with an American audience in mind, but I did not notice culturally insensitive or offensive parts.

Overall, this book is not for my course, but I think it could work well in a philosophy course.

Reviewed by Daniel Lee, Assistant Professor of Economics and Leadership, Sweet Briar College on 11/11/19

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument read more

Comprehensiveness rating: 3 see less

To the best of my ability, I regard this content as accurate, error-free, and unbiased

The book is broadly relevant and up-to-date, with a few stray temporal references (sydney olympics, particular presidencies). I don't view these time-dated examples as problematic as the logical underpinnings are still there and easily assessed

Clarity rating: 4

My only pushback on clarity is I didn't find the distinction between argument and explanation particularly helpful/useful/easy to follow. However, this experience may have been unique to my class.

To the best of my ability, I regard this content as internally consistent

I found this text quite modular, and was easily able to integrate other texts into my lessons and disregard certain chapters or sub-sections

The book had a logical and consistent structure, but to the extent that there are only 4 chapters, there isn't much scope for alternative approaches here

No problems with the book's interface

The text is grammatically sound

Cultural Relevance rating: 4

Perhaps the text could have been more universal in its approach. While I didn't find the book insensitive per-se, logic can be tricky here because the point is to evaluate meaningful (non-trivial) arguments, but any argument with that sense of gravity can also be traumatic to students (abortion, death penalty, etc)

No additional comments

Reviewed by Lisa N. Thomas-Smith, Graduate Part-time Instructor, CU Boulder on 7/1/19

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text,... read more

The content is excellent. The text is thorough and accurate with no errors that I could discern. The terminology and exercises cover the material nicely and without bias.

The text should easily stand the test of time. The exercises are excellent and would be very helpful for students to internalize correct critical thinking practices. Because of the logical arrangement of the text and the many sub-sections, additional material should be very easy to add.

The text is extremely clearly and simply written. I anticipate that a diligent student could learn all of the material in the text with little additional instruction. The examples are relevant and easy to follow.

The text did not confuse terms or use inconsistent terminology, which is very important in a logic text. The discipline often uses multiple terms for the same concept, but this text avoids that trap nicely.

The text is fairly easily divisible. Since there are only four chapters, those chapters include large blocks of information. However, the chapters themselves are very well delineated and could be easily broken up so that parts could be left out or covered in a different order from the text.

The flow of the text is excellent. All of the information is handled solidly in an order that allows the student to build on the information previously covered.

The PDF Table of Contents does not include links or page numbers which would be very helpful for navigation. Other than that, the text was very easy to navigate. All the images, charts, and graphs were very clear

I found no grammatical errors in the text.

Cultural Relevance rating: 3

The text including examples and exercises did not seem to be offensive or insensitive in any specific way. However, the examples included references to black and white people, but few others. Also, the text is very American specific with many examples from and for an American audience. More diversity, especially in the examples, would be appropriate and appreciated.

Reviewed by Leslie Aarons, Associate Professor of Philosophy, CUNY LaGuardia Community College on 5/16/19

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an argument and an explanation; validity; soundness; and the distinctions between an inductive and a deductive argument in accessible terms in the first chapter. It also does a good job introducing and discussing informal fallacies (Chapter 4). The incorporation of opportunities to evaluate real-world arguments is also very effective. Chapter 2 also covers a number of formal methods of evaluating arguments, such as Venn Diagrams and Propositional logic and the four basic truth functional connectives, but to my mind, it is much more thorough in its treatment of Informal Logic and Critical Thinking skills, than it is of formal logic. I also appreciated that Van Cleave’s book includes exercises with answers and an index, but there is no glossary; which I personally do not find detracts from the book's comprehensiveness.

Overall, Van Cleave's book is error-free and unbiased. The language used is accessible and engaging. There were no glaring inaccuracies that I was able to detect.

Van Cleave's Textbook uses relevant, contemporary content that will stand the test of time, at least for the next few years. Although some examples use certain subjects like former President Obama, it does so in a useful manner that inspires the use of critical thinking skills. There are an abundance of examples that inspire students to look at issues from many different political viewpoints, challenging students to practice evaluating arguments, and identifying fallacies. Many of these exercises encourage students to critique issues, and recognize their own inherent reader-biases and challenge their own beliefs--hallmarks of critical thinking.

As mentioned previously, the author has an accessible style that makes the content relatively easy to read and engaging. He also does a suitable job explaining jargon/technical language that is introduced in the textbook.

Van Cleave uses terminology consistently and the chapters flow well. The textbook orients the reader by offering effective introductions to new material, step-by-step explanations of the material, as well as offering clear summaries of each lesson.

This textbook's modularity is really quite good. Its language and structure are not overly convoluted or too-lengthy, making it convenient for individual instructors to adapt the materials to suit their methodological preferences.

The topics in the textbook are presented in a logical and clear fashion. The structure of the chapters are such that it is not necessary to have to follow the chapters in their sequential order, and coverage of material can be adapted to individual instructor's preferences.

The textbook is free of any problematic interface issues. Topics, sections and specific content are accessible and easy to navigate. Overall it is user-friendly.

I did not find any significant grammatical issues with the textbook.

The textbook is not culturally insensitive, making use of a diversity of inclusive examples. Materials are especially effective for first-year critical thinking/logic students.

I intend to adopt Van Cleave's textbook for a Critical Thinking class I am teaching at the Community College level. I believe that it will help me facilitate student-learning, and will be a good resource to build additional classroom activities from the materials it provides.

Reviewed by Jennie Harrop, Chair, Department of Professional Studies, George Fox University on 3/27/18

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters that are dense with statistical analyses and critical vocabulary. These topics are likely better broached in manageable snippets rather than hefty single chapters.

The ideas addressed in Introduction to Logic and Critical Thinking are accurate but at times notably political. While politics are effectively used to exemplify key concepts, some students may be distracted by distinct political leanings.

The terms and definitions included are relevant, but the examples are specific to the current political, cultural, and social climates, which could make the materials seem dated in a few years without intentional and consistent updates.

While the reasoning is accurate, the author tends to complicate rather than simplify -- perhaps in an effort to cover a spectrum of related concepts. Beginning readers are likely to be overwhelmed and under-encouraged by his approach.

Consistency rating: 3

The four chapters are somewhat consistent in their play of definition, explanation, and example, but the structure of each chapter varies according to the concepts covered. In the third chapter, for example, key ideas are divided into sub-topics numbering from 3.1 to 3.10. In the fourth chapter, the sub-divisions are further divided into sub-sections numbered 4.1.1-4.1.5, 4.2.1-4.2.2, and 4.3.1 to 4.3.6. Readers who are working quickly to master new concepts may find themselves mired in similarly numbered subheadings, longing for a grounded concepts on which to hinge other key principles.

Modularity rating: 3

The book's four chapters make it mostly self-referential. The author would do well to beak this text down into additional subsections, easing readers' accessibility.

The content of the book flows logically and well, but the information needs to be better sub-divided within each larger chapter, easing the student experience.

The book's interface is effective, allowing readers to move from one section to the next with a single click. Additional sub-sections would ease this interplay even further.

Grammatical Errors rating: 4

Some minor errors throughout.

For the most part, the book is culturally neutral, avoiding direct cultural references in an effort to remain relevant.

Reviewed by Yoichi Ishida, Assistant Professor of Philosophy, Ohio University on 2/1/18

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic, this textbook does not cover suppositional arguments, such as conditional proof and reductio ad absurdum. But other standard argument forms are covered. Chapter 3 covers inductive logic, and here this textbook introduces probability and its relationship with cognitive biases, which are rarely discussed in other textbooks. Chapter 4 introduces common informal fallacies. The answers to all the exercises are given at the end. However, the last set of exercises is in Chapter 3, Section 5. There are no exercises in the rest of the chapter. Chapter 4 has no exercises either. There is index, but no glossary.

The textbook is accurate.

The content of this textbook will not become obsolete soon.

The textbook is written clearly.

The textbook is internally consistent.

The textbook is fairly modular. For example, Chapter 3, together with a few sections from Chapter 1, can be used as a short introduction to inductive logic.

The textbook is well-organized.

There are no interface issues.

I did not find any grammatical errors.

This textbook is relevant to a first semester logic or critical thinking course.

Reviewed by Payal Doctor, Associate Professro, LaGuardia Community College on 2/1/18

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner book, but seems to be a good text for a course that needs a foundation for arguments. There are exercises on creating truth tables and proofs, so it could work as a logic primer in short sessions or with the addition of other course content.

The books is accurate in the information it presents. It does not contain errors and is unbiased. It covers the essential vocabulary clearly and givens ample examples and exercises to ensure the student understands the concepts

The content of the book is up to date and can be easily updated. Some examples are very current for analyzing the argument structure in a speech, but for this sort of text understandable examples are important and the author uses good examples.

The book is clear and easy to read. In particular, this is a good text for community college students who often have difficulty with reading comprehension. The language is straightforward and concepts are well explained.

The book is consistent in terminology, formatting, and examples. It flows well from one topic to the next, but it is also possible to jump around the text without loosing the voice of the text.

The books is broken down into sub units that make it easy to assign short blocks of content at a time. Later in the text, it does refer to a few concepts that appear early in that text, but these are all basic concepts that must be used to create a clear and understandable text. No sections are too long and each section stays on topic and relates the topic to those that have come before when necessary.

The flow of the text is logical and clear. It begins with the basic building blocks of arguments, and practice identifying more and more complex arguments is offered. Each chapter builds up from the previous chapter in introducing propositional logic, truth tables, and logical arguments. A select number of fallacies are presented at the end of the text, but these are related to topics that were presented before, so it makes sense to have these last.

The text is free if interface issues. I used the PDF and it worked fine on various devices without loosing formatting.

1. The book contains no grammatical errors.

The text is culturally sensitive, but examples used are a bit odd and may be objectionable to some students. For instance, President Obama's speech on Syria is used to evaluate an extended argument. This is an excellent example and it is explained well, but some who disagree with Obama's policies may have trouble moving beyond their own politics. However, other examples look at issues from all political viewpoints and ask students to evaluate the argument, fallacy, etc. and work towards looking past their own beliefs. Overall this book does use a variety of examples that most students can understand and evaluate.

My favorite part of this book is that it seems to be written for community college students. My students have trouble understanding readings in the New York Times, so it is nice to see a logic and critical thinking text use real language that students can understand and follow without the constant need of a dictionary.

Reviewed by Rebecca Owen, Adjunct Professor, Writing, Chemeketa Community College on 6/20/17

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current events, funny scenarios, or other interesting ways to evaluate argument structure and validity. The third section, which deals with logical fallacies, is very clear and comprehensive. My only critique of the material included in the book is that the middle section may be a bit dense and math-oriented for learners who appreciate the more informal, informative style of the first and third section. Also, the book ends rather abruptly--it moves from a description of a logical fallacy to the answers for the exercises earlier in the text.

The content is very reader-friendly, and the author writes with authority and clarity throughout the text. There are a few surface-level typos (Starbuck's instead of Starbucks, etc.). None of these small errors detract from the quality of the content, though.

One thing I really liked about this text was the author's wide variety of examples. To demonstrate different facets of logic, he used examples from current media, movies, literature, and many other concepts that students would recognize from their daily lives. The exercises in this text also included these types of pop-culture references, and I think students will enjoy the familiarity--as well as being able to see the logical structures behind these types of references. I don't think the text will need to be updated to reflect new instances and occurrences; the author did a fine job at picking examples that are relatively timeless. As far as the subject matter itself, I don't think it will become obsolete any time soon.

The author writes in a very conversational, easy-to-read manner. The examples used are quite helpful. The third section on logical fallacies is quite easy to read, follow, and understand. A student in an argument writing class could benefit from this section of the book. The middle section is less clear, though. A student learning about the basics of logic might have a hard time digesting all of the information contained in chapter two. This material might be better in two separate chapters. I think the author loses the balance of a conversational, helpful tone and focuses too heavily on equations.

Consistency rating: 4

Terminology in this book is quite consistent--the key words are highlighted in bold. Chapters 1 and 3 follow a similar organizational pattern, but chapter 2 is where the material becomes more dense and equation-heavy. I also would have liked a closing passage--something to indicate to the reader that we've reached the end of the chapter as well as the book.

I liked the overall structure of this book. If I'm teaching an argumentative writing class, I could easily point the students to the chapters where they can identify and practice identifying fallacies, for instance. The opening chapter is clear in defining the necessary terms, and it gives the students an understanding of the toolbox available to them in assessing and evaluating arguments. Even though I found the middle section to be dense, smaller portions could be assigned.

The author does a fine job connecting each defined term to the next. He provides examples of how each defined term works in a sentence or in an argument, and then he provides practice activities for students to try. The answers for each question are listed in the final pages of the book. The middle section feels like the heaviest part of the whole book--it would take the longest time for a student to digest if assigned the whole chapter. Even though this middle section is a bit heavy, it does fit the overall structure and flow of the book. New material builds on previous chapters and sub-chapters. It ends abruptly--I didn't realize that it had ended, and all of a sudden I found myself in the answer section for those earlier exercises.

The simple layout is quite helpful! There is nothing distracting, image-wise, in this text. The table of contents is clearly arranged, and each topic is easy to find.

Tiny edits could be made (Starbuck's/Starbucks, for one). Otherwise, it is free of distracting grammatical errors.

This text is quite culturally relevant. For instance, there is one example that mentions the rumors of Barack Obama's birthplace as somewhere other than the United States. This example is used to explain how to analyze an argument for validity. The more "sensational" examples (like the Obama one above) are helpful in showing argument structure, and they can also help students see how rumors like this might gain traction--as well as help to show students how to debunk them with their newfound understanding of argument and logic.

The writing style is excellent for the subject matter, especially in the third section explaining logical fallacies. Thank you for the opportunity to read and review this text!

Reviewed by Laurel Panser, Instructor, Riverland Community College on 6/20/17

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as... read more

Competing with Hurley is difficult with respect to comprehensiveness. For example, Van Cleave’s book is comprehensive to the extent that it probably covers at least two-thirds or more of what is dealt with in most introductory, one-semester logic courses. Van Cleave’s chapter 1 provides an overview of argumentation including discerning non-arguments from arguments, premises versus conclusions, deductive from inductive arguments, validity, soundness and more. Much of Van Cleave’s chapter 1 parallel’s Hurley’s chapter 1. Hurley’s chapter 3 regarding informal fallacies is comprehensive while Van Cleave’s chapter 4 on this topic is less extensive. Categorical propositions are a topic in Van Cleave’s chapter 2; Hurley’s chapters 4 and 5 provide more instruction on this, however. Propositional logic is another topic in Van Cleave’s chapter 2; Hurley’s chapters 6 and 7 provide more information on this, though. Van Cleave did discuss messy issues of language meaning briefly in his chapter 1; that is the topic of Hurley’s chapter 2.

Van Cleave’s book includes exercises with answers and an index. A glossary was not included.

Reviews of open source textbooks typically include criteria besides comprehensiveness. These include comments on accuracy of the information, whether the book will become obsolete soon, jargon-free clarity to the extent that is possible, organization, navigation ease, freedom from grammar errors and cultural relevance; Van Cleave’s book is fine in all of these areas. Further criteria for open source books includes modularity and consistency of terminology. Modularity is defined as including blocks of learning material that are easy to assign to students. Hurley’s book has a greater degree of modularity than Van Cleave’s textbook. The prose Van Cleave used is consistent.

Van Cleave’s book will not become obsolete soon.

Van Cleave’s book has accessible prose.

Van Cleave used terminology consistently.

Van Cleave’s book has a reasonable degree of modularity.

Van Cleave’s book is organized. The structure and flow of his book is fine.

Problems with navigation are not present.

Grammar problems were not present.

Van Cleave’s book is culturally relevant.

Van Cleave’s book is appropriate for some first semester logic courses.

Chapter 1: Reconstructing and analyzing arguments

1.1 What is an argument?
1.2 Identifying arguments
1.3 Arguments vs. explanations
1.4 More complex argument structures
1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form
1.6 Validity
1.7 Soundness
1.8 Deductive vs. inductive arguments
1.9 Arguments with missing premises
1.10 Assuring, guarding, and discounting
1.11 Evaluative language
1.12 Evaluating a real-life argument

Chapter 2: Formal methods of evaluating arguments

2.1 What is a formal method of evaluation and why do we need them?
2.2 Propositional logic and the four basic truth functional connectives
2.3 Negation and disjunction
2.4 Using parentheses to translate complex sentences
2.5 “Not both” and “neither nor”
2.6 The truth table test of validity
2.7 Conditionals
2.8 “Unless”
2.9 Material equivalence
2.10 Tautologies, contradictions, and contingent statements
2.11 Proofs and the 8 valid forms of inference
2.12 How to construct proofs
2.13 Short review of propositional logic
2.14 Categorical logic
2.15 The Venn test of validity for immediate categorical inferences
2.16 Universal statements and existential commitment
2.17 Venn validity for categorical syllogisms

Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies

3.1 Inductive arguments and statistical generalizations
3.2 Inference to the best explanation and the seven explanatory virtues
3.3 Analogical arguments
3.4 Causal arguments
3.5 Probability
3.6 The conjunction fallacy
3.7 The base rate fallacy
3.8 The small numbers fallacy
3.9 Regression to the mean fallacy
3.10 Gambler's fallacy

Chapter 4: Informal fallacies

4.1 Formal vs. informal fallacies
4.1.1 Composition fallacy
4.1.2 Division fallacy
4.1.3 Begging the question fallacy
4.1.4 False dichotomy
4.1.5 Equivocation
4.2 Slippery slope fallacies
4.2.1 Conceptual slippery slope
4.2.2 Causal slippery slope
4.3 Fallacies of relevance
4.3.1 Ad hominem
4.3.2 Straw man
4.3.3 Tu quoque
4.3.4 Genetic
4.3.5 Appeal to consequences
4.3.6 Appeal to authority

Answers to exercises Glossary/Index

Ancillary Material

About the book.

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.”

About the Contributors

Matthew Van Cleave , PhD, Philosophy, University of Cincinnati, 2007. VAP at Concordia College (Moorhead), 2008-2012. Assistant Professor at Lansing Community College, 2012-2016. Professor at Lansing Community College, 2016-

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Critical Thinking

Critical thinking is a widely accepted educational goal. Its definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. Conceptions differ with respect to the scope of such thinking, the type of goal, the criteria and norms for thinking carefully, and the thinking components on which they focus. Its adoption as an educational goal has been recommended on the basis of respect for students’ autonomy and preparing students for success in life and for democratic citizenship. “Critical thinkers” have the dispositions and abilities that lead them to think critically when appropriate. The abilities can be identified directly; the dispositions indirectly, by considering what factors contribute to or impede exercise of the abilities. Standardized tests have been developed to assess the degree to which a person possesses such dispositions and abilities. Educational intervention has been shown experimentally to improve them, particularly when it includes dialogue, anchored instruction, and mentoring. Controversies have arisen over the generalizability of critical thinking across domains, over alleged bias in critical thinking theories and instruction, and over the relationship of critical thinking to other types of thinking.

2.1 Dewey’s Three Main Examples

2.2 dewey’s other examples, 2.3 further examples, 2.4 non-examples, 3. the definition of critical thinking, 4. its value, 5. the process of thinking critically, 6. components of the process, 7. contributory dispositions and abilities, 8.1 initiating dispositions, 8.2 internal dispositions, 9. critical thinking abilities, 10. required knowledge, 11. educational methods, 12.1 the generalizability of critical thinking, 12.2 bias in critical thinking theory and pedagogy, 12.3 relationship of critical thinking to other types of thinking, other internet resources, related entries.

Use of the term ‘critical thinking’ to describe an educational goal goes back to the American philosopher John Dewey (1910), who more commonly called it ‘reflective thinking’. He defined it as

active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it, and the further conclusions to which it tends. (Dewey 1910: 6; 1933: 9)

and identified a habit of such consideration with a scientific attitude of mind. His lengthy quotations of Francis Bacon, John Locke, and John Stuart Mill indicate that he was not the first person to propose development of a scientific attitude of mind as an educational goal.

In the 1930s, many of the schools that participated in the Eight-Year Study of the Progressive Education Association (Aikin 1942) adopted critical thinking as an educational goal, for whose achievement the study’s Evaluation Staff developed tests (Smith, Tyler, & Evaluation Staff 1942). Glaser (1941) showed experimentally that it was possible to improve the critical thinking of high school students. Bloom’s influential taxonomy of cognitive educational objectives (Bloom et al. 1956) incorporated critical thinking abilities. Ennis (1962) proposed 12 aspects of critical thinking as a basis for research on the teaching and evaluation of critical thinking ability.

Since 1980, an annual international conference in California on critical thinking and educational reform has attracted tens of thousands of educators from all levels of education and from many parts of the world. Also since 1980, the state university system in California has required all undergraduate students to take a critical thinking course. Since 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions in conjunction with the divisional meetings of the American Philosophical Association (APA). In 1987, the APA’s Committee on Pre-College Philosophy commissioned a consensus statement on critical thinking for purposes of educational assessment and instruction (Facione 1990a). Researchers have developed standardized tests of critical thinking abilities and dispositions; for details, see the Supplement on Assessment . Educational jurisdictions around the world now include critical thinking in guidelines for curriculum and assessment.

For details on this history, see the Supplement on History .

2. Examples and Non-Examples

Before considering the definition of critical thinking, it will be helpful to have in mind some examples of critical thinking, as well as some examples of kinds of thinking that would apparently not count as critical thinking.

Dewey (1910: 68–71; 1933: 91–94) takes as paradigms of reflective thinking three class papers of students in which they describe their thinking. The examples range from the everyday to the scientific.

Transit : “The other day, when I was down town on 16th Street, a clock caught my eye. I saw that the hands pointed to 12:20. This suggested that I had an engagement at 124th Street, at one o’clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o’clock.” (Dewey 1910: 68–69; 1933: 91–92)

Ferryboat : “Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river is a long white pole, having a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere on the boat two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

“I then tried to imagine all possible purposes of the pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

“In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot’s position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly.” (Dewey 1910: 69–70; 1933: 92–93)

Bubbles : “In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat, or by decrease of pressure, or both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside. But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse” (Dewey 1910: 70–71; 1933: 93–94).

Dewey (1910, 1933) sprinkles his book with other examples of critical thinking. We will refer to the following.

Weather : A man on a walk notices that it has suddenly become cool, thinks that it is probably going to rain, looks up and sees a dark cloud obscuring the sun, and quickens his steps (1910: 6–10; 1933: 9–13).

Disorder : A man finds his rooms on his return to them in disorder with his belongings thrown about, thinks at first of burglary as an explanation, then thinks of mischievous children as being an alternative explanation, then looks to see whether valuables are missing, and discovers that they are (1910: 82–83; 1933: 166–168).

Typhoid : A physician diagnosing a patient whose conspicuous symptoms suggest typhoid avoids drawing a conclusion until more data are gathered by questioning the patient and by making tests (1910: 85–86; 1933: 170).

Blur : A moving blur catches our eye in the distance, we ask ourselves whether it is a cloud of whirling dust or a tree moving its branches or a man signaling to us, we think of other traits that should be found on each of those possibilities, and we look and see if those traits are found (1910: 102, 108; 1933: 121, 133).

Suction pump : In thinking about the suction pump, the scientist first notes that it will draw water only to a maximum height of 33 feet at sea level and to a lesser maximum height at higher elevations, selects for attention the differing atmospheric pressure at these elevations, sets up experiments in which the air is removed from a vessel containing water (when suction no longer works) and in which the weight of air at various levels is calculated, compares the results of reasoning about the height to which a given weight of air will allow a suction pump to raise water with the observed maximum height at different elevations, and finally assimilates the suction pump to such apparently different phenomena as the siphon and the rising of a balloon (1910: 150–153; 1933: 195–198).

Diamond : A passenger in a car driving in a diamond lane reserved for vehicles with at least one passenger notices that the diamond marks on the pavement are far apart in some places and close together in others. Why? The driver suggests that the reason may be that the diamond marks are not needed where there is a solid double line separating the diamond lane from the adjoining lane, but are needed when there is a dotted single line permitting crossing into the diamond lane. Further observation confirms that the diamonds are close together when a dotted line separates the diamond lane from its neighbour, but otherwise far apart.

Rash : A woman suddenly develops a very itchy red rash on her throat and upper chest. She recently noticed a mark on the back of her right hand, but was not sure whether the mark was a rash or a scrape. She lies down in bed and thinks about what might be causing the rash and what to do about it. About two weeks before, she began taking blood pressure medication that contained a sulfa drug, and the pharmacist had warned her, in view of a previous allergic reaction to a medication containing a sulfa drug, to be on the alert for an allergic reaction; however, she had been taking the medication for two weeks with no such effect. The day before, she began using a new cream on her neck and upper chest; against the new cream as the cause was mark on the back of her hand, which had not been exposed to the cream. She began taking probiotics about a month before. She also recently started new eye drops, but she supposed that manufacturers of eye drops would be careful not to include allergy-causing components in the medication. The rash might be a heat rash, since she recently was sweating profusely from her upper body. Since she is about to go away on a short vacation, where she would not have access to her usual physician, she decides to keep taking the probiotics and using the new eye drops but to discontinue the blood pressure medication and to switch back to the old cream for her neck and upper chest. She forms a plan to consult her regular physician on her return about the blood pressure medication.

Candidate : Although Dewey included no examples of thinking directed at appraising the arguments of others, such thinking has come to be considered a kind of critical thinking. We find an example of such thinking in the performance task on the Collegiate Learning Assessment (CLA+), which its sponsoring organization describes as

a performance-based assessment that provides a measure of an institution’s contribution to the development of critical-thinking and written communication skills of its students. (Council for Aid to Education 2017)

A sample task posted on its website requires the test-taker to write a report for public distribution evaluating a fictional candidate’s policy proposals and their supporting arguments, using supplied background documents, with a recommendation on whether to endorse the candidate.

Immediate acceptance of an idea that suggests itself as a solution to a problem (e.g., a possible explanation of an event or phenomenon, an action that seems likely to produce a desired result) is “uncritical thinking, the minimum of reflection” (Dewey 1910: 13). On-going suspension of judgment in the light of doubt about a possible solution is not critical thinking (Dewey 1910: 108). Critique driven by a dogmatically held political or religious ideology is not critical thinking; thus Paulo Freire (1968 [1970]) is using the term (e.g., at 1970: 71, 81, 100, 146) in a more politically freighted sense that includes not only reflection but also revolutionary action against oppression. Derivation of a conclusion from given data using an algorithm is not critical thinking.

What is critical thinking? There are many definitions. Ennis (2016) lists 14 philosophically oriented scholarly definitions and three dictionary definitions. Following Rawls (1971), who distinguished his conception of justice from a utilitarian conception but regarded them as rival conceptions of the same concept, Ennis maintains that the 17 definitions are different conceptions of the same concept. Rawls articulated the shared concept of justice as

a characteristic set of principles for assigning basic rights and duties and for determining… the proper distribution of the benefits and burdens of social cooperation. (Rawls 1971: 5)

Bailin et al. (1999b) claim that, if one considers what sorts of thinking an educator would take not to be critical thinking and what sorts to be critical thinking, one can conclude that educators typically understand critical thinking to have at least three features.

It is done for the purpose of making up one’s mind about what to believe or do.
The person engaging in the thinking is trying to fulfill standards of adequacy and accuracy appropriate to the thinking.
The thinking fulfills the relevant standards to some threshold level.

One could sum up the core concept that involves these three features by saying that critical thinking is careful goal-directed thinking. This core concept seems to apply to all the examples of critical thinking described in the previous section. As for the non-examples, their exclusion depends on construing careful thinking as excluding jumping immediately to conclusions, suspending judgment no matter how strong the evidence, reasoning from an unquestioned ideological or religious perspective, and routinely using an algorithm to answer a question.

If the core of critical thinking is careful goal-directed thinking, conceptions of it can vary according to its presumed scope, its presumed goal, one’s criteria and threshold for being careful, and the thinking component on which one focuses. As to its scope, some conceptions (e.g., Dewey 1910, 1933) restrict it to constructive thinking on the basis of one’s own observations and experiments, others (e.g., Ennis 1962; Fisher & Scriven 1997; Johnson 1992) to appraisal of the products of such thinking. Ennis (1991) and Bailin et al. (1999b) take it to cover both construction and appraisal. As to its goal, some conceptions restrict it to forming a judgment (Dewey 1910, 1933; Lipman 1987; Facione 1990a). Others allow for actions as well as beliefs as the end point of a process of critical thinking (Ennis 1991; Bailin et al. 1999b). As to the criteria and threshold for being careful, definitions vary in the term used to indicate that critical thinking satisfies certain norms: “intellectually disciplined” (Scriven & Paul 1987), “reasonable” (Ennis 1991), “skillful” (Lipman 1987), “skilled” (Fisher & Scriven 1997), “careful” (Bailin & Battersby 2009). Some definitions specify these norms, referring variously to “consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey 1910, 1933); “the methods of logical inquiry and reasoning” (Glaser 1941); “conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication” (Scriven & Paul 1987); the requirement that “it is sensitive to context, relies on criteria, and is self-correcting” (Lipman 1987); “evidential, conceptual, methodological, criteriological, or contextual considerations” (Facione 1990a); and “plus-minus considerations of the product in terms of appropriate standards (or criteria)” (Johnson 1992). Stanovich and Stanovich (2010) propose to ground the concept of critical thinking in the concept of rationality, which they understand as combining epistemic rationality (fitting one’s beliefs to the world) and instrumental rationality (optimizing goal fulfillment); a critical thinker, in their view, is someone with “a propensity to override suboptimal responses from the autonomous mind” (2010: 227). These variant specifications of norms for critical thinking are not necessarily incompatible with one another, and in any case presuppose the core notion of thinking carefully. As to the thinking component singled out, some definitions focus on suspension of judgment during the thinking (Dewey 1910; McPeck 1981), others on inquiry while judgment is suspended (Bailin & Battersby 2009, 2021), others on the resulting judgment (Facione 1990a), and still others on responsiveness to reasons (Siegel 1988). Kuhn (2019) takes critical thinking to be more a dialogic practice of advancing and responding to arguments than an individual ability.

In educational contexts, a definition of critical thinking is a “programmatic definition” (Scheffler 1960: 19). It expresses a practical program for achieving an educational goal. For this purpose, a one-sentence formulaic definition is much less useful than articulation of a critical thinking process, with criteria and standards for the kinds of thinking that the process may involve. The real educational goal is recognition, adoption and implementation by students of those criteria and standards. That adoption and implementation in turn consists in acquiring the knowledge, abilities and dispositions of a critical thinker.

Conceptions of critical thinking generally do not include moral integrity as part of the concept. Dewey, for example, took critical thinking to be the ultimate intellectual goal of education, but distinguished it from the development of social cooperation among school children, which he took to be the central moral goal. Ennis (1996, 2011) added to his previous list of critical thinking dispositions a group of dispositions to care about the dignity and worth of every person, which he described as a “correlative” (1996) disposition without which critical thinking would be less valuable and perhaps harmful. An educational program that aimed at developing critical thinking but not the correlative disposition to care about the dignity and worth of every person, he asserted, “would be deficient and perhaps dangerous” (Ennis 1996: 172).

Dewey thought that education for reflective thinking would be of value to both the individual and society; recognition in educational practice of the kinship to the scientific attitude of children’s native curiosity, fertile imagination and love of experimental inquiry “would make for individual happiness and the reduction of social waste” (Dewey 1910: iii). Schools participating in the Eight-Year Study took development of the habit of reflective thinking and skill in solving problems as a means to leading young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18, 81). Harvey Siegel (1988: 55–61) has offered four considerations in support of adopting critical thinking as an educational ideal. (1) Respect for persons requires that schools and teachers honour students’ demands for reasons and explanations, deal with students honestly, and recognize the need to confront students’ independent judgment; these requirements concern the manner in which teachers treat students. (2) Education has the task of preparing children to be successful adults, a task that requires development of their self-sufficiency. (3) Education should initiate children into the rational traditions in such fields as history, science and mathematics. (4) Education should prepare children to become democratic citizens, which requires reasoned procedures and critical talents and attitudes. To supplement these considerations, Siegel (1988: 62–90) responds to two objections: the ideology objection that adoption of any educational ideal requires a prior ideological commitment and the indoctrination objection that cultivation of critical thinking cannot escape being a form of indoctrination.

Despite the diversity of our 11 examples, one can recognize a common pattern. Dewey analyzed it as consisting of five phases:

suggestions , in which the mind leaps forward to a possible solution;
an intellectualization of the difficulty or perplexity into a problem to be solved, a question for which the answer must be sought;
the use of one suggestion after another as a leading idea, or hypothesis , to initiate and guide observation and other operations in collection of factual material;
the mental elaboration of the idea or supposition as an idea or supposition ( reasoning , in the sense on which reasoning is a part, not the whole, of inference); and
testing the hypothesis by overt or imaginative action. (Dewey 1933: 106–107; italics in original)

The process of reflective thinking consisting of these phases would be preceded by a perplexed, troubled or confused situation and followed by a cleared-up, unified, resolved situation (Dewey 1933: 106). The term ‘phases’ replaced the term ‘steps’ (Dewey 1910: 72), thus removing the earlier suggestion of an invariant sequence. Variants of the above analysis appeared in (Dewey 1916: 177) and (Dewey 1938: 101–119).

The variant formulations indicate the difficulty of giving a single logical analysis of such a varied process. The process of critical thinking may have a spiral pattern, with the problem being redefined in the light of obstacles to solving it as originally formulated. For example, the person in Transit might have concluded that getting to the appointment at the scheduled time was impossible and have reformulated the problem as that of rescheduling the appointment for a mutually convenient time. Further, defining a problem does not always follow after or lead immediately to an idea of a suggested solution. Nor should it do so, as Dewey himself recognized in describing the physician in Typhoid as avoiding any strong preference for this or that conclusion before getting further information (Dewey 1910: 85; 1933: 170). People with a hypothesis in mind, even one to which they have a very weak commitment, have a so-called “confirmation bias” (Nickerson 1998): they are likely to pay attention to evidence that confirms the hypothesis and to ignore evidence that counts against it or for some competing hypothesis. Detectives, intelligence agencies, and investigators of airplane accidents are well advised to gather relevant evidence systematically and to postpone even tentative adoption of an explanatory hypothesis until the collected evidence rules out with the appropriate degree of certainty all but one explanation. Dewey’s analysis of the critical thinking process can be faulted as well for requiring acceptance or rejection of a possible solution to a defined problem, with no allowance for deciding in the light of the available evidence to suspend judgment. Further, given the great variety of kinds of problems for which reflection is appropriate, there is likely to be variation in its component events. Perhaps the best way to conceptualize the critical thinking process is as a checklist whose component events can occur in a variety of orders, selectively, and more than once. These component events might include (1) noticing a difficulty, (2) defining the problem, (3) dividing the problem into manageable sub-problems, (4) formulating a variety of possible solutions to the problem or sub-problem, (5) determining what evidence is relevant to deciding among possible solutions to the problem or sub-problem, (6) devising a plan of systematic observation or experiment that will uncover the relevant evidence, (7) carrying out the plan of systematic observation or experimentation, (8) noting the results of the systematic observation or experiment, (9) gathering relevant testimony and information from others, (10) judging the credibility of testimony and information gathered from others, (11) drawing conclusions from gathered evidence and accepted testimony, and (12) accepting a solution that the evidence adequately supports (cf. Hitchcock 2017: 485).

Checklist conceptions of the process of critical thinking are open to the objection that they are too mechanical and procedural to fit the multi-dimensional and emotionally charged issues for which critical thinking is urgently needed (Paul 1984). For such issues, a more dialectical process is advocated, in which competing relevant world views are identified, their implications explored, and some sort of creative synthesis attempted.

If one considers the critical thinking process illustrated by the 11 examples, one can identify distinct kinds of mental acts and mental states that form part of it. To distinguish, label and briefly characterize these components is a useful preliminary to identifying abilities, skills, dispositions, attitudes, habits and the like that contribute causally to thinking critically. Identifying such abilities and habits is in turn a useful preliminary to setting educational goals. Setting the goals is in its turn a useful preliminary to designing strategies for helping learners to achieve the goals and to designing ways of measuring the extent to which learners have done so. Such measures provide both feedback to learners on their achievement and a basis for experimental research on the effectiveness of various strategies for educating people to think critically. Let us begin, then, by distinguishing the kinds of mental acts and mental events that can occur in a critical thinking process.

Observing : One notices something in one’s immediate environment (sudden cooling of temperature in Weather , bubbles forming outside a glass and then going inside in Bubbles , a moving blur in the distance in Blur , a rash in Rash ). Or one notes the results of an experiment or systematic observation (valuables missing in Disorder , no suction without air pressure in Suction pump )
Feeling : One feels puzzled or uncertain about something (how to get to an appointment on time in Transit , why the diamonds vary in spacing in Diamond ). One wants to resolve this perplexity. One feels satisfaction once one has worked out an answer (to take the subway express in Transit , diamonds closer when needed as a warning in Diamond ).
Wondering : One formulates a question to be addressed (why bubbles form outside a tumbler taken from hot water in Bubbles , how suction pumps work in Suction pump , what caused the rash in Rash ).
Imagining : One thinks of possible answers (bus or subway or elevated in Transit , flagpole or ornament or wireless communication aid or direction indicator in Ferryboat , allergic reaction or heat rash in Rash ).
Inferring : One works out what would be the case if a possible answer were assumed (valuables missing if there has been a burglary in Disorder , earlier start to the rash if it is an allergic reaction to a sulfa drug in Rash ). Or one draws a conclusion once sufficient relevant evidence is gathered (take the subway in Transit , burglary in Disorder , discontinue blood pressure medication and new cream in Rash ).
Knowledge : One uses stored knowledge of the subject-matter to generate possible answers or to infer what would be expected on the assumption of a particular answer (knowledge of a city’s public transit system in Transit , of the requirements for a flagpole in Ferryboat , of Boyle’s law in Bubbles , of allergic reactions in Rash ).
Experimenting : One designs and carries out an experiment or a systematic observation to find out whether the results deduced from a possible answer will occur (looking at the location of the flagpole in relation to the pilot’s position in Ferryboat , putting an ice cube on top of a tumbler taken from hot water in Bubbles , measuring the height to which a suction pump will draw water at different elevations in Suction pump , noticing the spacing of diamonds when movement to or from a diamond lane is allowed in Diamond ).
Consulting : One finds a source of information, gets the information from the source, and makes a judgment on whether to accept it. None of our 11 examples include searching for sources of information. In this respect they are unrepresentative, since most people nowadays have almost instant access to information relevant to answering any question, including many of those illustrated by the examples. However, Candidate includes the activities of extracting information from sources and evaluating its credibility.
Identifying and analyzing arguments : One notices an argument and works out its structure and content as a preliminary to evaluating its strength. This activity is central to Candidate . It is an important part of a critical thinking process in which one surveys arguments for various positions on an issue.
Judging : One makes a judgment on the basis of accumulated evidence and reasoning, such as the judgment in Ferryboat that the purpose of the pole is to provide direction to the pilot.
Deciding : One makes a decision on what to do or on what policy to adopt, as in the decision in Transit to take the subway.

By definition, a person who does something voluntarily is both willing and able to do that thing at that time. Both the willingness and the ability contribute causally to the person’s action, in the sense that the voluntary action would not occur if either (or both) of these were lacking. For example, suppose that one is standing with one’s arms at one’s sides and one voluntarily lifts one’s right arm to an extended horizontal position. One would not do so if one were unable to lift one’s arm, if for example one’s right side was paralyzed as the result of a stroke. Nor would one do so if one were unwilling to lift one’s arm, if for example one were participating in a street demonstration at which a white supremacist was urging the crowd to lift their right arm in a Nazi salute and one were unwilling to express support in this way for the racist Nazi ideology. The same analysis applies to a voluntary mental process of thinking critically. It requires both willingness and ability to think critically, including willingness and ability to perform each of the mental acts that compose the process and to coordinate those acts in a sequence that is directed at resolving the initiating perplexity.

Consider willingness first. We can identify causal contributors to willingness to think critically by considering factors that would cause a person who was able to think critically about an issue nevertheless not to do so (Hamby 2014). For each factor, the opposite condition thus contributes causally to willingness to think critically on a particular occasion. For example, people who habitually jump to conclusions without considering alternatives will not think critically about issues that arise, even if they have the required abilities. The contrary condition of willingness to suspend judgment is thus a causal contributor to thinking critically.

Now consider ability. In contrast to the ability to move one’s arm, which can be completely absent because a stroke has left the arm paralyzed, the ability to think critically is a developed ability, whose absence is not a complete absence of ability to think but absence of ability to think well. We can identify the ability to think well directly, in terms of the norms and standards for good thinking. In general, to be able do well the thinking activities that can be components of a critical thinking process, one needs to know the concepts and principles that characterize their good performance, to recognize in particular cases that the concepts and principles apply, and to apply them. The knowledge, recognition and application may be procedural rather than declarative. It may be domain-specific rather than widely applicable, and in either case may need subject-matter knowledge, sometimes of a deep kind.

Reflections of the sort illustrated by the previous two paragraphs have led scholars to identify the knowledge, abilities and dispositions of a “critical thinker”, i.e., someone who thinks critically whenever it is appropriate to do so. We turn now to these three types of causal contributors to thinking critically. We start with dispositions, since arguably these are the most powerful contributors to being a critical thinker, can be fostered at an early stage of a child’s development, and are susceptible to general improvement (Glaser 1941: 175)

8. Critical Thinking Dispositions

Educational researchers use the term ‘dispositions’ broadly for the habits of mind and attitudes that contribute causally to being a critical thinker. Some writers (e.g., Paul & Elder 2006; Hamby 2014; Bailin & Battersby 2016a) propose to use the term ‘virtues’ for this dimension of a critical thinker. The virtues in question, although they are virtues of character, concern the person’s ways of thinking rather than the person’s ways of behaving towards others. They are not moral virtues but intellectual virtues, of the sort articulated by Zagzebski (1996) and discussed by Turri, Alfano, and Greco (2017).

On a realistic conception, thinking dispositions or intellectual virtues are real properties of thinkers. They are general tendencies, propensities, or inclinations to think in particular ways in particular circumstances, and can be genuinely explanatory (Siegel 1999). Sceptics argue that there is no evidence for a specific mental basis for the habits of mind that contribute to thinking critically, and that it is pedagogically misleading to posit such a basis (Bailin et al. 1999a). Whatever their status, critical thinking dispositions need motivation for their initial formation in a child—motivation that may be external or internal. As children develop, the force of habit will gradually become important in sustaining the disposition (Nieto & Valenzuela 2012). Mere force of habit, however, is unlikely to sustain critical thinking dispositions. Critical thinkers must value and enjoy using their knowledge and abilities to think things through for themselves. They must be committed to, and lovers of, inquiry.

A person may have a critical thinking disposition with respect to only some kinds of issues. For example, one could be open-minded about scientific issues but not about religious issues. Similarly, one could be confident in one’s ability to reason about the theological implications of the existence of evil in the world but not in one’s ability to reason about the best design for a guided ballistic missile.

Facione (1990a: 25) divides “affective dispositions” of critical thinking into approaches to life and living in general and approaches to specific issues, questions or problems. Adapting this distinction, one can usefully divide critical thinking dispositions into initiating dispositions (those that contribute causally to starting to think critically about an issue) and internal dispositions (those that contribute causally to doing a good job of thinking critically once one has started). The two categories are not mutually exclusive. For example, open-mindedness, in the sense of willingness to consider alternative points of view to one’s own, is both an initiating and an internal disposition.

Using the strategy of considering factors that would block people with the ability to think critically from doing so, we can identify as initiating dispositions for thinking critically attentiveness, a habit of inquiry, self-confidence, courage, open-mindedness, willingness to suspend judgment, trust in reason, wanting evidence for one’s beliefs, and seeking the truth. We consider briefly what each of these dispositions amounts to, in each case citing sources that acknowledge them.

Attentiveness : One will not think critically if one fails to recognize an issue that needs to be thought through. For example, the pedestrian in Weather would not have looked up if he had not noticed that the air was suddenly cooler. To be a critical thinker, then, one needs to be habitually attentive to one’s surroundings, noticing not only what one senses but also sources of perplexity in messages received and in one’s own beliefs and attitudes (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
Habit of inquiry : Inquiry is effortful, and one needs an internal push to engage in it. For example, the student in Bubbles could easily have stopped at idle wondering about the cause of the bubbles rather than reasoning to a hypothesis, then designing and executing an experiment to test it. Thus willingness to think critically needs mental energy and initiative. What can supply that energy? Love of inquiry, or perhaps just a habit of inquiry. Hamby (2015) has argued that willingness to inquire is the central critical thinking virtue, one that encompasses all the others. It is recognized as a critical thinking disposition by Dewey (1910: 29; 1933: 35), Glaser (1941: 5), Ennis (1987: 12; 1991: 8), Facione (1990a: 25), Bailin et al. (1999b: 294), Halpern (1998: 452), and Facione, Facione, & Giancarlo (2001).
Self-confidence : Lack of confidence in one’s abilities can block critical thinking. For example, if the woman in Rash lacked confidence in her ability to figure things out for herself, she might just have assumed that the rash on her chest was the allergic reaction to her medication against which the pharmacist had warned her. Thus willingness to think critically requires confidence in one’s ability to inquire (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
Courage : Fear of thinking for oneself can stop one from doing it. Thus willingness to think critically requires intellectual courage (Paul & Elder 2006: 16).
Open-mindedness : A dogmatic attitude will impede thinking critically. For example, a person who adheres rigidly to a “pro-choice” position on the issue of the legal status of induced abortion is likely to be unwilling to consider seriously the issue of when in its development an unborn child acquires a moral right to life. Thus willingness to think critically requires open-mindedness, in the sense of a willingness to examine questions to which one already accepts an answer but which further evidence or reasoning might cause one to answer differently (Dewey 1933; Facione 1990a; Ennis 1991; Bailin et al. 1999b; Halpern 1998, Facione, Facione, & Giancarlo 2001). Paul (1981) emphasizes open-mindedness about alternative world-views, and recommends a dialectical approach to integrating such views as central to what he calls “strong sense” critical thinking. In three studies, Haran, Ritov, & Mellers (2013) found that actively open-minded thinking, including “the tendency to weigh new evidence against a favored belief, to spend sufficient time on a problem before giving up, and to consider carefully the opinions of others in forming one’s own”, led study participants to acquire information and thus to make accurate estimations.
Willingness to suspend judgment : Premature closure on an initial solution will block critical thinking. Thus willingness to think critically requires a willingness to suspend judgment while alternatives are explored (Facione 1990a; Ennis 1991; Halpern 1998).
Trust in reason : Since distrust in the processes of reasoned inquiry will dissuade one from engaging in it, trust in them is an initiating critical thinking disposition (Facione 1990a, 25; Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001; Paul & Elder 2006). In reaction to an allegedly exclusive emphasis on reason in critical thinking theory and pedagogy, Thayer-Bacon (2000) argues that intuition, imagination, and emotion have important roles to play in an adequate conception of critical thinking that she calls “constructive thinking”. From her point of view, critical thinking requires trust not only in reason but also in intuition, imagination, and emotion.
Seeking the truth : If one does not care about the truth but is content to stick with one’s initial bias on an issue, then one will not think critically about it. Seeking the truth is thus an initiating critical thinking disposition (Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001). A disposition to seek the truth is implicit in more specific critical thinking dispositions, such as trying to be well-informed, considering seriously points of view other than one’s own, looking for alternatives, suspending judgment when the evidence is insufficient, and adopting a position when the evidence supporting it is sufficient.

Some of the initiating dispositions, such as open-mindedness and willingness to suspend judgment, are also internal critical thinking dispositions, in the sense of mental habits or attitudes that contribute causally to doing a good job of critical thinking once one starts the process. But there are many other internal critical thinking dispositions. Some of them are parasitic on one’s conception of good thinking. For example, it is constitutive of good thinking about an issue to formulate the issue clearly and to maintain focus on it. For this purpose, one needs not only the corresponding ability but also the corresponding disposition. Ennis (1991: 8) describes it as the disposition “to determine and maintain focus on the conclusion or question”, Facione (1990a: 25) as “clarity in stating the question or concern”. Other internal dispositions are motivators to continue or adjust the critical thinking process, such as willingness to persist in a complex task and willingness to abandon nonproductive strategies in an attempt to self-correct (Halpern 1998: 452). For a list of identified internal critical thinking dispositions, see the Supplement on Internal Critical Thinking Dispositions .

Some theorists postulate skills, i.e., acquired abilities, as operative in critical thinking. It is not obvious, however, that a good mental act is the exercise of a generic acquired skill. Inferring an expected time of arrival, as in Transit , has some generic components but also uses non-generic subject-matter knowledge. Bailin et al. (1999a) argue against viewing critical thinking skills as generic and discrete, on the ground that skilled performance at a critical thinking task cannot be separated from knowledge of concepts and from domain-specific principles of good thinking. Talk of skills, they concede, is unproblematic if it means merely that a person with critical thinking skills is capable of intelligent performance.

Despite such scepticism, theorists of critical thinking have listed as general contributors to critical thinking what they variously call abilities (Glaser 1941; Ennis 1962, 1991), skills (Facione 1990a; Halpern 1998) or competencies (Fisher & Scriven 1997). Amalgamating these lists would produce a confusing and chaotic cornucopia of more than 50 possible educational objectives, with only partial overlap among them. It makes sense instead to try to understand the reasons for the multiplicity and diversity, and to make a selection according to one’s own reasons for singling out abilities to be developed in a critical thinking curriculum. Two reasons for diversity among lists of critical thinking abilities are the underlying conception of critical thinking and the envisaged educational level. Appraisal-only conceptions, for example, involve a different suite of abilities than constructive-only conceptions. Some lists, such as those in (Glaser 1941), are put forward as educational objectives for secondary school students, whereas others are proposed as objectives for college students (e.g., Facione 1990a).

The abilities described in the remaining paragraphs of this section emerge from reflection on the general abilities needed to do well the thinking activities identified in section 6 as components of the critical thinking process described in section 5 . The derivation of each collection of abilities is accompanied by citation of sources that list such abilities and of standardized tests that claim to test them.

Observational abilities : Careful and accurate observation sometimes requires specialist expertise and practice, as in the case of observing birds and observing accident scenes. However, there are general abilities of noticing what one’s senses are picking up from one’s environment and of being able to articulate clearly and accurately to oneself and others what one has observed. It helps in exercising them to be able to recognize and take into account factors that make one’s observation less trustworthy, such as prior framing of the situation, inadequate time, deficient senses, poor observation conditions, and the like. It helps as well to be skilled at taking steps to make one’s observation more trustworthy, such as moving closer to get a better look, measuring something three times and taking the average, and checking what one thinks one is observing with someone else who is in a good position to observe it. It also helps to be skilled at recognizing respects in which one’s report of one’s observation involves inference rather than direct observation, so that one can then consider whether the inference is justified. These abilities come into play as well when one thinks about whether and with what degree of confidence to accept an observation report, for example in the study of history or in a criminal investigation or in assessing news reports. Observational abilities show up in some lists of critical thinking abilities (Ennis 1962: 90; Facione 1990a: 16; Ennis 1991: 9). There are items testing a person’s ability to judge the credibility of observation reports in the Cornell Critical Thinking Tests, Levels X and Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). Norris and King (1983, 1985, 1990a, 1990b) is a test of ability to appraise observation reports.

Emotional abilities : The emotions that drive a critical thinking process are perplexity or puzzlement, a wish to resolve it, and satisfaction at achieving the desired resolution. Children experience these emotions at an early age, without being trained to do so. Education that takes critical thinking as a goal needs only to channel these emotions and to make sure not to stifle them. Collaborative critical thinking benefits from ability to recognize one’s own and others’ emotional commitments and reactions.

Questioning abilities : A critical thinking process needs transformation of an inchoate sense of perplexity into a clear question. Formulating a question well requires not building in questionable assumptions, not prejudging the issue, and using language that in context is unambiguous and precise enough (Ennis 1962: 97; 1991: 9).

Imaginative abilities : Thinking directed at finding the correct causal explanation of a general phenomenon or particular event requires an ability to imagine possible explanations. Thinking about what policy or plan of action to adopt requires generation of options and consideration of possible consequences of each option. Domain knowledge is required for such creative activity, but a general ability to imagine alternatives is helpful and can be nurtured so as to become easier, quicker, more extensive, and deeper (Dewey 1910: 34–39; 1933: 40–47). Facione (1990a) and Halpern (1998) include the ability to imagine alternatives as a critical thinking ability.

Inferential abilities : The ability to draw conclusions from given information, and to recognize with what degree of certainty one’s own or others’ conclusions follow, is universally recognized as a general critical thinking ability. All 11 examples in section 2 of this article include inferences, some from hypotheses or options (as in Transit , Ferryboat and Disorder ), others from something observed (as in Weather and Rash ). None of these inferences is formally valid. Rather, they are licensed by general, sometimes qualified substantive rules of inference (Toulmin 1958) that rest on domain knowledge—that a bus trip takes about the same time in each direction, that the terminal of a wireless telegraph would be located on the highest possible place, that sudden cooling is often followed by rain, that an allergic reaction to a sulfa drug generally shows up soon after one starts taking it. It is a matter of controversy to what extent the specialized ability to deduce conclusions from premisses using formal rules of inference is needed for critical thinking. Dewey (1933) locates logical forms in setting out the products of reflection rather than in the process of reflection. Ennis (1981a), on the other hand, maintains that a liberally-educated person should have the following abilities: to translate natural-language statements into statements using the standard logical operators, to use appropriately the language of necessary and sufficient conditions, to deal with argument forms and arguments containing symbols, to determine whether in virtue of an argument’s form its conclusion follows necessarily from its premisses, to reason with logically complex propositions, and to apply the rules and procedures of deductive logic. Inferential abilities are recognized as critical thinking abilities by Glaser (1941: 6), Facione (1990a: 9), Ennis (1991: 9), Fisher & Scriven (1997: 99, 111), and Halpern (1998: 452). Items testing inferential abilities constitute two of the five subtests of the Watson Glaser Critical Thinking Appraisal (Watson & Glaser 1980a, 1980b, 1994), two of the four sections in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), three of the seven sections in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), 11 of the 34 items on Forms A and B of the California Critical Thinking Skills Test (Facione 1990b, 1992), and a high but variable proportion of the 25 selected-response questions in the Collegiate Learning Assessment (Council for Aid to Education 2017).

Experimenting abilities : Knowing how to design and execute an experiment is important not just in scientific research but also in everyday life, as in Rash . Dewey devoted a whole chapter of his How We Think (1910: 145–156; 1933: 190–202) to the superiority of experimentation over observation in advancing knowledge. Experimenting abilities come into play at one remove in appraising reports of scientific studies. Skill in designing and executing experiments includes the acknowledged abilities to appraise evidence (Glaser 1941: 6), to carry out experiments and to apply appropriate statistical inference techniques (Facione 1990a: 9), to judge inductions to an explanatory hypothesis (Ennis 1991: 9), and to recognize the need for an adequately large sample size (Halpern 1998). The Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) includes four items (out of 52) on experimental design. The Collegiate Learning Assessment (Council for Aid to Education 2017) makes room for appraisal of study design in both its performance task and its selected-response questions.

Consulting abilities : Skill at consulting sources of information comes into play when one seeks information to help resolve a problem, as in Candidate . Ability to find and appraise information includes ability to gather and marshal pertinent information (Glaser 1941: 6), to judge whether a statement made by an alleged authority is acceptable (Ennis 1962: 84), to plan a search for desired information (Facione 1990a: 9), and to judge the credibility of a source (Ennis 1991: 9). Ability to judge the credibility of statements is tested by 24 items (out of 76) in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) and by four items (out of 52) in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). The College Learning Assessment’s performance task requires evaluation of whether information in documents is credible or unreliable (Council for Aid to Education 2017).

Argument analysis abilities : The ability to identify and analyze arguments contributes to the process of surveying arguments on an issue in order to form one’s own reasoned judgment, as in Candidate . The ability to detect and analyze arguments is recognized as a critical thinking skill by Facione (1990a: 7–8), Ennis (1991: 9) and Halpern (1998). Five items (out of 34) on the California Critical Thinking Skills Test (Facione 1990b, 1992) test skill at argument analysis. The College Learning Assessment (Council for Aid to Education 2017) incorporates argument analysis in its selected-response tests of critical reading and evaluation and of critiquing an argument.

Judging skills and deciding skills : Skill at judging and deciding is skill at recognizing what judgment or decision the available evidence and argument supports, and with what degree of confidence. It is thus a component of the inferential skills already discussed.

Lists and tests of critical thinking abilities often include two more abilities: identifying assumptions and constructing and evaluating definitions.

In addition to dispositions and abilities, critical thinking needs knowledge: of critical thinking concepts, of critical thinking principles, and of the subject-matter of the thinking.

We can derive a short list of concepts whose understanding contributes to critical thinking from the critical thinking abilities described in the preceding section. Observational abilities require an understanding of the difference between observation and inference. Questioning abilities require an understanding of the concepts of ambiguity and vagueness. Inferential abilities require an understanding of the difference between conclusive and defeasible inference (traditionally, between deduction and induction), as well as of the difference between necessary and sufficient conditions. Experimenting abilities require an understanding of the concepts of hypothesis, null hypothesis, assumption and prediction, as well as of the concept of statistical significance and of its difference from importance. They also require an understanding of the difference between an experiment and an observational study, and in particular of the difference between a randomized controlled trial, a prospective correlational study and a retrospective (case-control) study. Argument analysis abilities require an understanding of the concepts of argument, premiss, assumption, conclusion and counter-consideration. Additional critical thinking concepts are proposed by Bailin et al. (1999b: 293), Fisher & Scriven (1997: 105–106), Black (2012), and Blair (2021).

According to Glaser (1941: 25), ability to think critically requires knowledge of the methods of logical inquiry and reasoning. If we review the list of abilities in the preceding section, however, we can see that some of them can be acquired and exercised merely through practice, possibly guided in an educational setting, followed by feedback. Searching intelligently for a causal explanation of some phenomenon or event requires that one consider a full range of possible causal contributors, but it seems more important that one implements this principle in one’s practice than that one is able to articulate it. What is important is “operational knowledge” of the standards and principles of good thinking (Bailin et al. 1999b: 291–293). But the development of such critical thinking abilities as designing an experiment or constructing an operational definition can benefit from learning their underlying theory. Further, explicit knowledge of quirks of human thinking seems useful as a cautionary guide. Human memory is not just fallible about details, as people learn from their own experiences of misremembering, but is so malleable that a detailed, clear and vivid recollection of an event can be a total fabrication (Loftus 2017). People seek or interpret evidence in ways that are partial to their existing beliefs and expectations, often unconscious of their “confirmation bias” (Nickerson 1998). Not only are people subject to this and other cognitive biases (Kahneman 2011), of which they are typically unaware, but it may be counter-productive for one to make oneself aware of them and try consciously to counteract them or to counteract social biases such as racial or sexual stereotypes (Kenyon & Beaulac 2014). It is helpful to be aware of these facts and of the superior effectiveness of blocking the operation of biases—for example, by making an immediate record of one’s observations, refraining from forming a preliminary explanatory hypothesis, blind refereeing, double-blind randomized trials, and blind grading of students’ work. It is also helpful to be aware of the prevalence of “noise” (unwanted unsystematic variability of judgments), of how to detect noise (through a noise audit), and of how to reduce noise: make accuracy the goal, think statistically, break a process of arriving at a judgment into independent tasks, resist premature intuitions, in a group get independent judgments first, favour comparative judgments and scales (Kahneman, Sibony, & Sunstein 2021). It is helpful as well to be aware of the concept of “bounded rationality” in decision-making and of the related distinction between “satisficing” and optimizing (Simon 1956; Gigerenzer 2001).

Critical thinking about an issue requires substantive knowledge of the domain to which the issue belongs. Critical thinking abilities are not a magic elixir that can be applied to any issue whatever by somebody who has no knowledge of the facts relevant to exploring that issue. For example, the student in Bubbles needed to know that gases do not penetrate solid objects like a glass, that air expands when heated, that the volume of an enclosed gas varies directly with its temperature and inversely with its pressure, and that hot objects will spontaneously cool down to the ambient temperature of their surroundings unless kept hot by insulation or a source of heat. Critical thinkers thus need a rich fund of subject-matter knowledge relevant to the variety of situations they encounter. This fact is recognized in the inclusion among critical thinking dispositions of a concern to become and remain generally well informed.

Experimental educational interventions, with control groups, have shown that education can improve critical thinking skills and dispositions, as measured by standardized tests. For information about these tests, see the Supplement on Assessment .

What educational methods are most effective at developing the dispositions, abilities and knowledge of a critical thinker? In a comprehensive meta-analysis of experimental and quasi-experimental studies of strategies for teaching students to think critically, Abrami et al. (2015) found that dialogue, anchored instruction, and mentoring each increased the effectiveness of the educational intervention, and that they were most effective when combined. They also found that in these studies a combination of separate instruction in critical thinking with subject-matter instruction in which students are encouraged to think critically was more effective than either by itself. However, the difference was not statistically significant; that is, it might have arisen by chance.

Most of these studies lack the longitudinal follow-up required to determine whether the observed differential improvements in critical thinking abilities or dispositions continue over time, for example until high school or college graduation. For details on studies of methods of developing critical thinking skills and dispositions, see the Supplement on Educational Methods .

12. Controversies

Scholars have denied the generalizability of critical thinking abilities across subject domains, have alleged bias in critical thinking theory and pedagogy, and have investigated the relationship of critical thinking to other kinds of thinking.

McPeck (1981) attacked the thinking skills movement of the 1970s, including the critical thinking movement. He argued that there are no general thinking skills, since thinking is always thinking about some subject-matter. It is futile, he claimed, for schools and colleges to teach thinking as if it were a separate subject. Rather, teachers should lead their pupils to become autonomous thinkers by teaching school subjects in a way that brings out their cognitive structure and that encourages and rewards discussion and argument. As some of his critics (e.g., Paul 1985; Siegel 1985) pointed out, McPeck’s central argument needs elaboration, since it has obvious counter-examples in writing and speaking, for which (up to a certain level of complexity) there are teachable general abilities even though they are always about some subject-matter. To make his argument convincing, McPeck needs to explain how thinking differs from writing and speaking in a way that does not permit useful abstraction of its components from the subject-matters with which it deals. He has not done so. Nevertheless, his position that the dispositions and abilities of a critical thinker are best developed in the context of subject-matter instruction is shared by many theorists of critical thinking, including Dewey (1910, 1933), Glaser (1941), Passmore (1980), Weinstein (1990), Bailin et al. (1999b), and Willingham (2019).

McPeck’s challenge prompted reflection on the extent to which critical thinking is subject-specific. McPeck argued for a strong subject-specificity thesis, according to which it is a conceptual truth that all critical thinking abilities are specific to a subject. (He did not however extend his subject-specificity thesis to critical thinking dispositions. In particular, he took the disposition to suspend judgment in situations of cognitive dissonance to be a general disposition.) Conceptual subject-specificity is subject to obvious counter-examples, such as the general ability to recognize confusion of necessary and sufficient conditions. A more modest thesis, also endorsed by McPeck, is epistemological subject-specificity, according to which the norms of good thinking vary from one field to another. Epistemological subject-specificity clearly holds to a certain extent; for example, the principles in accordance with which one solves a differential equation are quite different from the principles in accordance with which one determines whether a painting is a genuine Picasso. But the thesis suffers, as Ennis (1989) points out, from vagueness of the concept of a field or subject and from the obvious existence of inter-field principles, however broadly the concept of a field is construed. For example, the principles of hypothetico-deductive reasoning hold for all the varied fields in which such reasoning occurs. A third kind of subject-specificity is empirical subject-specificity, according to which as a matter of empirically observable fact a person with the abilities and dispositions of a critical thinker in one area of investigation will not necessarily have them in another area of investigation.

The thesis of empirical subject-specificity raises the general problem of transfer. If critical thinking abilities and dispositions have to be developed independently in each school subject, how are they of any use in dealing with the problems of everyday life and the political and social issues of contemporary society, most of which do not fit into the framework of a traditional school subject? Proponents of empirical subject-specificity tend to argue that transfer is more likely to occur if there is critical thinking instruction in a variety of domains, with explicit attention to dispositions and abilities that cut across domains. But evidence for this claim is scanty. There is a need for well-designed empirical studies that investigate the conditions that make transfer more likely.

It is common ground in debates about the generality or subject-specificity of critical thinking dispositions and abilities that critical thinking about any topic requires background knowledge about the topic. For example, the most sophisticated understanding of the principles of hypothetico-deductive reasoning is of no help unless accompanied by some knowledge of what might be plausible explanations of some phenomenon under investigation.

Critics have objected to bias in the theory, pedagogy and practice of critical thinking. Commentators (e.g., Alston 1995; Ennis 1998) have noted that anyone who takes a position has a bias in the neutral sense of being inclined in one direction rather than others. The critics, however, are objecting to bias in the pejorative sense of an unjustified favoring of certain ways of knowing over others, frequently alleging that the unjustly favoured ways are those of a dominant sex or culture (Bailin 1995). These ways favour:

reinforcement of egocentric and sociocentric biases over dialectical engagement with opposing world-views (Paul 1981, 1984; Warren 1998)
distancing from the object of inquiry over closeness to it (Martin 1992; Thayer-Bacon 1992)
indifference to the situation of others over care for them (Martin 1992)
orientation to thought over orientation to action (Martin 1992)
being reasonable over caring to understand people’s ideas (Thayer-Bacon 1993)
being neutral and objective over being embodied and situated (Thayer-Bacon 1995a)
doubting over believing (Thayer-Bacon 1995b)
reason over emotion, imagination and intuition (Thayer-Bacon 2000)
solitary thinking over collaborative thinking (Thayer-Bacon 2000)
written and spoken assignments over other forms of expression (Alston 2001)
attention to written and spoken communications over attention to human problems (Alston 2001)
winning debates in the public sphere over making and understanding meaning (Alston 2001)

A common thread in this smorgasbord of accusations is dissatisfaction with focusing on the logical analysis and evaluation of reasoning and arguments. While these authors acknowledge that such analysis and evaluation is part of critical thinking and should be part of its conceptualization and pedagogy, they insist that it is only a part. Paul (1981), for example, bemoans the tendency of atomistic teaching of methods of analyzing and evaluating arguments to turn students into more able sophists, adept at finding fault with positions and arguments with which they disagree but even more entrenched in the egocentric and sociocentric biases with which they began. Martin (1992) and Thayer-Bacon (1992) cite with approval the self-reported intimacy with their subject-matter of leading researchers in biology and medicine, an intimacy that conflicts with the distancing allegedly recommended in standard conceptions and pedagogy of critical thinking. Thayer-Bacon (2000) contrasts the embodied and socially embedded learning of her elementary school students in a Montessori school, who used their imagination, intuition and emotions as well as their reason, with conceptions of critical thinking as

thinking that is used to critique arguments, offer justifications, and make judgments about what are the good reasons, or the right answers. (Thayer-Bacon 2000: 127–128)

Alston (2001) reports that her students in a women’s studies class were able to see the flaws in the Cinderella myth that pervades much romantic fiction but in their own romantic relationships still acted as if all failures were the woman’s fault and still accepted the notions of love at first sight and living happily ever after. Students, she writes, should

be able to connect their intellectual critique to a more affective, somatic, and ethical account of making risky choices that have sexist, racist, classist, familial, sexual, or other consequences for themselves and those both near and far… critical thinking that reads arguments, texts, or practices merely on the surface without connections to feeling/desiring/doing or action lacks an ethical depth that should infuse the difference between mere cognitive activity and something we want to call critical thinking. (Alston 2001: 34)

Some critics portray such biases as unfair to women. Thayer-Bacon (1992), for example, has charged modern critical thinking theory with being sexist, on the ground that it separates the self from the object and causes one to lose touch with one’s inner voice, and thus stigmatizes women, who (she asserts) link self to object and listen to their inner voice. Her charge does not imply that women as a group are on average less able than men to analyze and evaluate arguments. Facione (1990c) found no difference by sex in performance on his California Critical Thinking Skills Test. Kuhn (1991: 280–281) found no difference by sex in either the disposition or the competence to engage in argumentative thinking.

The critics propose a variety of remedies for the biases that they allege. In general, they do not propose to eliminate or downplay critical thinking as an educational goal. Rather, they propose to conceptualize critical thinking differently and to change its pedagogy accordingly. Their pedagogical proposals arise logically from their objections. They can be summarized as follows:

Focus on argument networks with dialectical exchanges reflecting contesting points of view rather than on atomic arguments, so as to develop “strong sense” critical thinking that transcends egocentric and sociocentric biases (Paul 1981, 1984).
Foster closeness to the subject-matter and feeling connected to others in order to inform a humane democracy (Martin 1992).
Develop “constructive thinking” as a social activity in a community of physically embodied and socially embedded inquirers with personal voices who value not only reason but also imagination, intuition and emotion (Thayer-Bacon 2000).
In developing critical thinking in school subjects, treat as important neither skills nor dispositions but opening worlds of meaning (Alston 2001).
Attend to the development of critical thinking dispositions as well as skills, and adopt the “critical pedagogy” practised and advocated by Freire (1968 [1970]) and hooks (1994) (Dalgleish, Girard, & Davies 2017).

A common thread in these proposals is treatment of critical thinking as a social, interactive, personally engaged activity like that of a quilting bee or a barn-raising (Thayer-Bacon 2000) rather than as an individual, solitary, distanced activity symbolized by Rodin’s The Thinker . One can get a vivid description of education with the former type of goal from the writings of bell hooks (1994, 2010). Critical thinking for her is open-minded dialectical exchange across opposing standpoints and from multiple perspectives, a conception similar to Paul’s “strong sense” critical thinking (Paul 1981). She abandons the structure of domination in the traditional classroom. In an introductory course on black women writers, for example, she assigns students to write an autobiographical paragraph about an early racial memory, then to read it aloud as the others listen, thus affirming the uniqueness and value of each voice and creating a communal awareness of the diversity of the group’s experiences (hooks 1994: 84). Her “engaged pedagogy” is thus similar to the “freedom under guidance” implemented in John Dewey’s Laboratory School of Chicago in the late 1890s and early 1900s. It incorporates the dialogue, anchored instruction, and mentoring that Abrami (2015) found to be most effective in improving critical thinking skills and dispositions.

What is the relationship of critical thinking to problem solving, decision-making, higher-order thinking, creative thinking, and other recognized types of thinking? One’s answer to this question obviously depends on how one defines the terms used in the question. If critical thinking is conceived broadly to cover any careful thinking about any topic for any purpose, then problem solving and decision making will be kinds of critical thinking, if they are done carefully. Historically, ‘critical thinking’ and ‘problem solving’ were two names for the same thing. If critical thinking is conceived more narrowly as consisting solely of appraisal of intellectual products, then it will be disjoint with problem solving and decision making, which are constructive.

Bloom’s taxonomy of educational objectives used the phrase “intellectual abilities and skills” for what had been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others (Bloom et al. 1956: 38). Thus, the so-called “higher-order thinking skills” at the taxonomy’s top levels of analysis, synthesis and evaluation are just critical thinking skills, although they do not come with general criteria for their assessment (Ennis 1981b). The revised version of Bloom’s taxonomy (Anderson et al. 2001) likewise treats critical thinking as cutting across those types of cognitive process that involve more than remembering (Anderson et al. 2001: 269–270). For details, see the Supplement on History .

As to creative thinking, it overlaps with critical thinking (Bailin 1987, 1988). Thinking about the explanation of some phenomenon or event, as in Ferryboat , requires creative imagination in constructing plausible explanatory hypotheses. Likewise, thinking about a policy question, as in Candidate , requires creativity in coming up with options. Conversely, creativity in any field needs to be balanced by critical appraisal of the draft painting or novel or mathematical theory.

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Critical Thinking Definition, Instruction, and Assessment: A Rigorous Approach
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The Nature of Critical Thinking: An Outline of Critical Thinking Dispositions and Abilities , by Robert H. Ennis

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Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

Developing technical and problem-solving skills
Engaging in more active listening
Actively questioning their assumptions and beliefs
Seeking out more diversity of thought
Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

What information should be included?
Which information resources should the author look to?
What degree of technical knowledge should the report assume its audience has?
What is the most effective way to show information?
How should the report be organized?
How should it be designed?
What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

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Critical Thinking and Effective Communication: Enhancing Interpersonal Skills for Success

In today’s fast-paced world, effective communication and critical thinking have become increasingly important skills for both personal and professional success. Critical thinking refers to the ability to analyze situations, gather information, and make sound judgments, while effective communication involves not only conveying ideas clearly but also actively listening and responding to others. These two crucial abilities are intertwined, as critical thinking often mediates information processing, leading to a more comprehensive understanding and ultimately enhancing communication.

The importance of critical thinking and effective communication cannot be overstated, as they are essential in various aspects of life, including problem-solving, decision-making, and relationship-building. Additionally, these skills are indispensable in the workplace, as they contribute to overall productivity and foster a positive and collaborative environment. Developing and nurturing critical thinking and effective communication abilities can significantly improve both personal and professional experiences, leading to increased success in various realms of life.

Key Takeaways

Critical thinking and effective communication are essential skills for personal and professional success.
These abilities play a vital role in various aspects of life, including problem-solving, decision-making, and relationship-building.
Developing and honing critical thinking and communication skills can lead to increased productivity and a more positive, collaborative environment.

Critical Thinking Fundamentals

Skill and knowledge.

Critical thinking is an essential cognitive skill that individuals should cultivate in order to master effective communication. It is the ability to think clearly and rationally, understand the logical connections between ideas, identify and construct arguments, and evaluate information to make better decisions in personal and professional life [1] . A well-developed foundation of knowledge is crucial for critical thinkers, as it enables them to analyze situations, evaluate arguments, and draw, inferences from the information they process.

Analysis and Evidence

A key component of critical thinking is the ability to analyze information, which involves breaking down complex problems or arguments into manageable parts to understand their underlying structure [2] . Analyzing evidence is essential in order to ascertain the validity and credibility of the information, which leads to better decision-making. Critical thinkers must consider factors like the source’s credibility, the existence of potential biases, and any relevant areas of expertise before forming judgments.

Clarity of Thought

Clarity of thought is an integral element of critical thinking and effective communication. Being able to articulate ideas clearly and concisely is crucial for efficient communication [3] . Critical thinkers are skilled at organizing their thoughts and communicating them in a structured manner, which is vital for ensuring the transmission of accurate and relevant information.

In summary, mastering critical thinking fundamentals, including skill and knowledge, analysis of evidence, and clarity of thought, is essential for effective communication. Cultivating these abilities will enable individuals to better navigate their personal and professional lives, fostering stronger, more efficient connections with others.

Importance of Critical Thinking

Workplace and leadership.

Critical thinking is a vital skill for individuals in the workplace, particularly for those in leadership roles. It contributes to effective communication, enabling individuals to articulate their thoughts clearly and understand the perspectives of others. Furthermore, critical thinking allows leaders to make informed decisions by evaluating available information and considering potential consequences. Developing this skill can also empower team members to solve complex problems by exploring alternative solutions and applying rational thinking.

Decisions and Problem-Solving

In both personal and professional contexts, decision-making and problem-solving are crucial aspects of daily life. Critical thinking enables individuals to analyze situations, identify possible options, and weigh the pros and cons of each choice. By employing critical thinking skills, individuals can arrive at well-informed decisions that lead to better outcomes. Moreover, applying these skills can help to identify the root cause of a problem and devise innovative solutions, thereby contributing to overall success and growth.

Confidence and Emotions

Critical thinking plays a significant role in managing one’s emotions and cultivating self-confidence. By engaging in rational and objective thinking, individuals can develop a clearer understanding of their own beliefs and values. This awareness can lead to increased self-assurance and the ability to effectively articulate one’s thoughts and opinions. Additionally, critical thinking can help individuals navigate emotionally-charged situations by promoting logical analysis and appropriate emotional responses. Ultimately, honing critical thinking skills can establish a strong foundation for effective communication and emotional intelligence.

Effective Communication

Effective communication is essential in building strong relationships and achieving desired outcomes. It involves the exchange of thoughts, opinions, and information so that the intended message is received and understood with clarity and purpose. This section will focus on three key aspects of effective communication: Verbal Communication, Nonverbal Communication, and Visual Communication.

Verbal Communication

Verbal communication is the use of spoken or written words to convey messages. It is vital to choose the right words, tone, and structure when engaging in verbal communication. Some elements to consider for effective verbal communication include:

Being clear and concise: Focus on the main points and avoid unnecessary information.
Active listening: Give full attention to the speaker and ask questions for clarification.
Appropriate language: Use language that is easily understood by the audience.
Emotional intelligence: Understand and manage emotions during communication.

Nonverbal Communication

Nonverbal communication involves gestures, body language, facial expressions, and other visual cues that complement verbal messages. It plays a crucial role in conveying emotions and intentions, and can often have a significant impact on the effectiveness of communication. Some key aspects of nonverbal communication are:

Eye contact: Maintaining eye contact shows that you are attentive and engaged.
Posture: Good posture indicates confidence and credibility.
Gestures and facial expressions: Use appropriate gestures and facial expressions to support your message.
Proximity: Maintain a comfortable distance from your audience to establish rapport.

Visual Communication

Visual communication involves the use of visual aids such as images, graphs, charts, and diagrams to support or enhance verbal messages. It can help to make complex information more understandable and engaging. To maximize the effectiveness of visual communication, consider the following tips:

Relevance: Ensure that the visual aids are relevant to the message and audience.
Simplicity: Keep the design and content simple for easy comprehension.
Consistency: Use a consistent style, format, and color scheme throughout the presentation.
Accessibility: Make sure that the visual aids are visible and clear to all audience members.

In conclusion, understanding and implementing verbal, nonverbal, and visual communication skills are essential for effective communication. By combining these elements, individuals can establish strong connections, and successfully relay their messages to others.

Critical Thinking Skills in Communication

Listening and analyzing.

Developing strong listening and analyzing skills is crucial for critical thinking in communication. This involves actively paying attention to what others are saying and sifting through the information to identify key points. Taking a step back to analyze and evaluate messages helps ensure a clear understanding of the topic.

By improving your listening and analyzing abilities, you become more aware of how people communicate their thoughts and ideas. Active listening helps you dig deeper and discover the underlying connections between concepts. This skill enhances your ability to grasp the core meaning and identify any ambiguities or inconsistencies.

Biases and Perspective

Recognizing biases and considering different perspectives are essential components of critical thinking in communication. Everyone has preconceived notions and beliefs that can influence their understanding of information. By being aware of your biases and actively questioning them, you can strengthen your ability to communicate more effectively.

Considering other people’s perspectives allows you to view an issue from multiple angles, eventually leading to a more thorough understanding. Approaching communications with an open and receptive mind gives you a greater ability to relate and empathize with others, which in turn enhances the overall effectiveness of communication.

Problem-Solving and Questions

Critical thinking is intrinsically linked to problem-solving and asking questions. By incorporating these skills into the communication process, you become more adept at identifying issues, formulating solutions, and adapting the way you communicate to different situations.

Asking well-crafted questions helps you uncover valuable insights and points of view that may be hidden or not immediately apparent. Inquiring minds foster a more dynamic and interactive communication; promoting continuous learning, growth, and development.

Ultimately, enhancing your critical thinking skills in communication leads to better understanding, stronger connections, and more effective communication. By combining active listening, awareness of biases and perspectives, and problem-solving through questioning, you can significantly improve your ability to navigate even the most complex communications with confidence and clarity.

Improving Critical Thinking and Communication

Methods and techniques.

One approach to improve critical thinking and communication is by incorporating various methods and techniques into your daily practice. Some of these methods include:

Asking open-ended questions
Analyzing information from multiple perspectives
Employing logical reasoning

By honing these skills, individuals can better navigate the complexities of modern life and develop more effective communication capabilities.

Problem-Solving Skills

Developing problem-solving skills is also essential for enhancing critical thinking and communication. This involves adopting a systematic framework that helps in identifying, analyzing, and addressing problems. A typical problem-solving framework includes:

Identifying the problem
Gathering relevant information
Evaluating possible solutions
Choosing the best solution
Implementing the chosen solution
Assessing the outcome and adjusting accordingly

By mastering this framework, individuals can tackle problems more effectively and communicate their solutions with clarity and confidence.

Staying on Point and Focused

Staying on point and focused is a critical aspect of effective communication. To ensure that your message is concise and clear, it is crucial to:

Determine the main purpose of your communication
Consider the needs and expectations of your audience
Use precise language to convey your thoughts

By maintaining focus throughout your communication, you can improve your ability to think critically and communicate more effectively.

In summary, enhancing one’s critical thinking and communication skills involves adopting various techniques, honing problem-solving skills, and staying focused during communication. By incorporating these practices into daily life, individuals can become more confident, knowledgeable, and capable communicators.

Teaching and Training Critical Thinking

Content and curriculum.

Implementing critical thinking in educational settings requires a well-designed curriculum that challenges learners to think deeply on various topics. To foster critical thinking, the content should comprise of complex problems, real-life situations, and thought-provoking questions. By using this type of content , educators can enable students to analyze, evaluate, and create their own understandings, ultimately improving their ability to communicate effectively.

Instructors and Teachers

The role of instructors and teachers in promoting critical thinking cannot be underestimated. They should be trained and equipped with strategies to stimulate thinking, provoke curiosity, and encourage students to question assumptions. Additionally, they must create a learning environment that supports the development of critical thinking by being patient, open-minded, and accepting of diverse perspectives.

Engaging Conversations

Conversations play a significant role in the development of critical thinking and effective communication skills. Instructors should facilitate engaging discussions, prompt students to explain their reasoning, and ask open-ended questions that promote deeper analysis. By doing so, learners will be able to refine their ideas, understand various viewpoints, and build their argumentation skills, leading to more effective communication overall.

Critical thinking and effective communication are two interrelated skills that significantly contribute to personal and professional success. Through the application of critical thinking , individuals can create well-structured, clear, and impactful messages.

Clarity of Thought : Critical thinking helps in organizing thoughts logically and coherently. When engaging in communication, this clarity provides a strong foundation for conveying ideas and opinions.
Active Listening : A crucial aspect of effective communication involves actively listening to the messages from others. This allows for better understanding and consideration of multiple perspectives, strengthening the critical thinking process.
Concise and Precise Language : Utilizing appropriate language and avoiding unnecessary jargon ensures that the message is easily understood by the target audience.

Individuals who excel in both critical thinking and communication are better equipped to navigate complex situations and collaborate with others to achieve common goals. By continuously honing these skills, one can improve their decision-making abilities and enhance their relationships, both personally and professionally. In a world where effective communication is paramount, mastering critical thinking is essential to ensuring one’s thoughts and ideas are received and understood by others.

Frequently Asked Questions

What are the essential aspects of critical thinking.

Critical thinking involves the ability to analyze, evaluate, and synthesize information in order to make sound decisions and solve problems. Essential aspects of critical thinking include asking better questions , identifying and challenging assumptions, understanding different perspectives, and recognizing biases.

How do communication skills impact problem-solving?

Effective communication skills are crucial in problem-solving, as they facilitate the exchange of information, ideas, and perspectives. Clear and concise communication helps ensure that all team members understand the problem, the proposed solutions, and their roles in the process. Additionally, strong listening skills enable better comprehension of others’ viewpoints and foster collaboration.

How does language influence critical thinking?

Language plays a key role in critical thinking, as it shapes the way we interpret and express information. The choice of words, phrases, and structures can either clarify or obscure meaning. A well-structured communication promotes a better understanding of complex ideas, making it easier for individuals to think critically and apply the concepts to problem-solving.

What strategies can enhance communication in critical thinking?

To enhance communication during critical thinking, individuals should be clear and concise in expressing their thoughts, listen actively to others’ perspectives, and use critical thinking skills to analyze and evaluate the information provided. Encouraging open dialogue, asking probing questions, and being receptive to feedback can also foster a conducive environment for critical thinking.

What are the benefits of critical thinking in communication?

Critical thinking enhances communication by promoting clarity, objectivity, and logical reasoning. When we engage in critical thinking, we question assumptions, consider multiple viewpoints, and evaluate the strength of arguments. As a result, our communication becomes more thoughtful, persuasive, and effective at conveying the intended message .

How do critical thinking skills contribute to effective communication?

Critical thinking skills contribute to effective communication by ensuring that individuals are able to analyze, comprehend, and interpret the information being shared. This allows for more nuanced understanding of complex ideas and helps to present arguments logically and coherently. Additionally, critical thinking skills can aid in identifying any underlying biases or assumptions in the communicated information, thus enhancing overall clarity and effectiveness.

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Using the power of debate to enhance critical thinking

Asking students to analyse, defend and counterargue a contentious issue has proved an engaging way to teach reasoning and communication skills in organisational behaviour courses

M. C. Zhang

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The role of debate in the learning process is paramount. As a teacher of organisational behaviour (OB), an interdisciplinary field that probes the intricacies of human actions in organisational settings, I have realised the immense potential of an intellectual tug of war. It nurtures essential skills such as critical thinking and logical reasoning in students.

OB itself draws on myriad concepts, theories and principles from psychology, sociology and anthropology, creating a broad understanding of human behaviour in the workplace. Given the diversity of this field, its students require high levels of critical thinking and logical reasoning to master the concepts. And so to foster these academic and real-world skills, debate sessions have become an integral part of my OB course.

Debaters in class at Macau University of Science and Technology

To create a lively learning environment and enhance critical-thinking skills among my students, I introduced a “super debaters” competition. The engaging activity has been met with exuberance and active participation and has become a much-anticipated feature of my OB course. The students research and gather supporting evidence for their respective positions, fuelling dynamic and rigorous analysis, interpretation and evaluation of the topic at hand.

Before they participate in the debate, students need basic skills such as critical thinking, research skills and how to formulate a sound argument. They should understand the structure of a debate and how to respect and respond to opposing viewpoints. Public-speaking skills – such as articulation, voice modulation, body language and using eye contact – are important, too.

I aim to set aside class time to explain these skills and let students practise. However, the beauty of debate is that it is also a process of learning by doing. As students participate, they start developing these skills.

Collection: Teaching critical thinking
Using affective learning to foster engagement and critical thinking
Harness human and artificial intelligence to improve classroom debates

Super debaters is no ordinary debating competition. It is a platform for students to delve into contentious issues related to the course content, express their opinions, challenge opposing views and defend their stance. It encourages them to interrogate an issue, scrutinise evidence and construct logical arguments, thereby honing their critical-thinking and logical-reasoning skills.

When choosing a topic for a debate, I consider the following factors:

Relevance: I choose topics that are related to the course content, students’ lives or hot topics in society.
Controversial aspect: Each topic should have the capacity to generate an effective debate.
Student interest: If the topic is stimulating to students, they are more likely to immerse themselves in discussion and go deeper into understanding the topic.
Compatibility with students’ comprehension level: The topic shouldn’t be too difficult or obscure for students to understand and discuss in depth.
Enhance students’ critical-thinking skills: Suitable topics encourage students to view problems from different perspectives. They have a high relevance to the teaching objectives and can engage the students, provoking their thinking.

Each debate session begins with the introduction of a relevant topic – a recent question was “Is emotional intelligence more important than cognitive intelligence in the workplace?” – and the class is divided into teams of four to six students. Each group is assigned a position to defend, sparking off an intellectual tug of war.

After each team has presented, you could have an open-floor debate where members of each team can question the other’s arguments. It’s essential when setting up the debate that the rules and expectations are explained clearly to the students in terms of time allocation, order of speakers and respect for each other’s speaking times.

During these debates, students are encouraged to maintain the decorum of a healthy debate, present their arguments effectively, challenge their opponents logically and respond to counterarguments critically. The exercise promotes a deep understanding of the course content and fosters a spirit of enquiry among students.

At the end of each session, the entire class votes to decide the “best” debaters. The process ensures a fair and democratic selection. The winning group is presented with a bouquet of flowers (see below), further fuelling the competitive spirit and boosting the students’ confidence.

The super debaters format not only allows students to engage with the course content in a practical and interactive manner, it also bridges the gap between theoretical knowledge and its real-world application. The students have expressed their fondness for this engaging and inclusive method of learning, which has significantly enhanced their knowledge, critical thinking and communication skills.

According to one student, debates enhance their knowledge in an engaging and practical way. The format requires students to refine their ideas, scrutinise their beliefs and articulate their opinions in a cogent manner. Another student emphasised that debates led to a deeper comprehension of theories.

Moreover, this exercise improves the students’ communication skills, as they learn to express their views logically and convincingly, a skill highly valued in both academic and professional realms.

Debates have proved to be an effective pedagogical tool in my OB course. The power of debate is something that educators across disciplines can harness to stimulate intellectual growth among students. It not only enriches the academic journey of students but also prepares them for real-world challenges in the professional sphere.

M. C. Zhang is assistant professor at the School of Liberal Arts at Macau University of Science and Technology.

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11 Activities That Promote Critical Thinking In The Class

52 Critical Thinking Flashcards for Problem Solving

Critical thinking activities encourage individuals to analyze, evaluate, and synthesize information to develop informed opinions and make reasoned decisions. Engaging in such exercises cultivates intellectual agility, fostering a deeper understanding of complex issues and honing problem-solving skills for navigating an increasingly intricate world. Through critical thinking, individuals empower themselves to challenge assumptions, uncover biases, and constructively contribute to discourse, thereby enriching both personal growth and societal progress.

Critical thinking serves as the cornerstone of effective problem-solving, enabling individuals to dissect challenges, explore diverse perspectives, and devise innovative solutions grounded in logic and evidence. For engaging problem solving activities, read our article problem solving activities that enhance student’s interest.

What is Critical Thinking?

Critical thinking is a 21st-century skill that enables a person to think rationally and logically in order to reach a plausible conclusion. A critical thinker assesses facts and figures and data objectively and determines what to believe and what not to believe. Critical thinking skills empower a person to decipher complex problems and make impartial and better decisions based on effective information.

Importance of Acquiring Critical Thinking Skills

Acquiring critical thinking skills was never as valuable as it is today because of the prevalence of the modern knowledge economy. Today, information and technology are the driving forces behind the global economy. To keep pace with ever-changing technology and new inventions, one has to be flexible enough to embrace changes swiftly.

Read our article: How to Foster Critical Thinking Skills in Students? Creative Strategies and Real-World Examples

Today critical thinking skills are one of the most sought-after skills by the companies. In fact, critical thinking skills are paramount not only for active learning and academic achievement but also for the professional career of the students. The lack of critical thinking skills catalyzes memorization of the topics without a deeper insight, egocentrism, closed-mindedness, reduced student interest in the classroom and not being able to make timely and better decisions.

Benefits of Critical Thinking Skills in Education

Certain strategies are more eloquent than others in teaching students how to think critically. Encouraging critical thinking in the class is indispensable for the learning and growth of the students. In this way, we can raise a generation of innovators and thinkers rather than followers. Some of the benefits offered by thinking critically in the classroom are given below:

It allows a student to decipher problems and think through the situations in a disciplined and systematic manner
Through a critical thinking ability, a student can comprehend the logical correlation between distinct ideas
The student is able to rethink and re-justify his beliefs and ideas based on facts and figures
Critical thinking skills make the students curious about things around them
A student who is a critical thinker is creative and always strives to come up with out of the box solutions to intricate problems
Critical thinking skills assist in the enhanced student learning experience in the classroom and prepares the students for lifelong learning and success
The critical thinking process is the foundation of new discoveries and inventions in the world of science and technology
The ability to think critically allows the students to think intellectually and enhances their presentation skills, hence they can convey their ideas and thoughts in a logical and convincing manner
Critical thinking skills make students a terrific communicator because they have logical reasons behind their ideas

Critical Thinking Lessons and Activities

11 Activities that Promote Critical Thinking in the Class

We have compiled a list of 11 activities that will facilitate you to promote critical thinking abilities in the students. We have also covered problem solving activities that enhance student’s interest in our another article. Click here to read it.

1. Worst Case Scenario

Divide students into teams and introduce each team with a hypothetical challenging scenario. Allocate minimum resources and time to each team and ask them to reach a viable conclusion using those resources. The scenarios can include situations like stranded on an island or stuck in a forest. Students will come up with creative solutions to come out from the imaginary problematic situation they are encountering. Besides encouraging students to think critically, this activity will enhance teamwork, communication and problem-solving skills of the students.

Read our article: 10 Innovative Strategies for Promoting Critical Thinking in the Classroom

2. If You Build It

It is a very flexible game that allows students to think creatively. To start this activity, divide students into groups. Give each group a limited amount of resources such as pipe cleaners, blocks, and marshmallows etc. Every group is supposed to use these resources and construct a certain item such as building, tower or a bridge in a limited time. You can use a variety of materials in the classroom to challenge the students. This activity is helpful in promoting teamwork and creative skills among the students.

It is also one of the classics which can be used in the classroom to encourage critical thinking. Print pictures of objects, animals or concepts and start by telling a unique story about the printed picture. The next student is supposed to continue the story and pass the picture to the other student and so on.

4. Keeping it Real

In this activity, you can ask students to identify a real-world problem in their schools, community or city. After the problem is recognized, students should work in teams to come up with the best possible outcome of that problem.

5. Save the Egg

Make groups of three or four in the class. Ask them to drop an egg from a certain height and think of creative ideas to save the egg from breaking. Students can come up with diverse ideas to conserve the egg like a soft-landing material or any other device. Remember that this activity can get chaotic, so select the area in the school that can be cleaned easily afterward and where there are no chances of damaging the school property.

6. Start a Debate

In this activity, the teacher can act as a facilitator and spark an interesting conversation in the class on any given topic. Give a small introductory speech on an open-ended topic. The topic can be related to current affairs, technological development or a new discovery in the field of science. Encourage students to participate in the debate by expressing their views and ideas on the topic. Conclude the debate with a viable solution or fresh ideas generated during the activity through brainstorming.

7. Create and Invent

This project-based learning activity is best for teaching in the engineering class. Divide students into groups. Present a problem to the students and ask them to build a model or simulate a product using computer animations or graphics that will solve the problem. After students are done with building models, each group is supposed to explain their proposed product to the rest of the class. The primary objective of this activity is to promote creative thinking and problem-solving skills among the students.

8. Select from Alternatives

This activity can be used in computer science, engineering or any of the STEM (Science, Technology, Engineering, Mathematics) classes. Introduce a variety of alternatives such as different formulas for solving the same problem, different computer codes, product designs or distinct explanations of the same topic.

Form groups in the class and ask them to select the best alternative. Each group will then explain its chosen alternative to the rest of the class with reasonable justification of its preference. During the process, the rest of the class can participate by asking questions from the group. This activity is very helpful in nurturing logical thinking and analytical skills among the students.

9. Reading and Critiquing

Present an article from a journal related to any topic that you are teaching. Ask the students to read the article critically and evaluate strengths and weaknesses in the article. Students can write about what they think about the article, any misleading statement or biases of the author and critique it by using their own judgments.

In this way, students can challenge the fallacies and rationality of judgments in the article. Hence, they can use their own thinking to come up with novel ideas pertaining to the topic.

10. Think Pair Share

In this activity, students will come up with their own questions. Make pairs or groups in the class and ask the students to discuss the questions together. The activity will be useful if the teacher gives students a topic on which the question should be based.

For example, if the teacher is teaching biology, the questions of the students can be based on reverse osmosis, human heart, respiratory system and so on. This activity drives student engagement and supports higher-order thinking skills among students.

11. Big Paper – Silent Conversation

Silence is a great way to slow down thinking and promote deep reflection on any subject. Present a driving question to the students and divide them into groups. The students will discuss the question with their teammates and brainstorm their ideas on a big paper. After reflection and discussion, students can write their findings in silence. This is a great learning activity for students who are introverts and love to ruminate silently rather than thinking aloud.

Read our next article: 10 Innovative Strategies for Promoting Critical Thinking in the Classroom

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Critical Thinking, Logic & Problem Solving: (4 Books in 1) The Definitive Guide to Make Smarter Decisions and Creatively Solve Complex Problems and Challenges Autonomously

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Critical Thinking, Logic & Problem Solving: (4 Books in 1) The Definitive Guide to Make Smarter Decisions and Creatively Solve Complex Problems and Challenges Autonomously Paperback – April 9, 2024

Purchase options and add-ons, unlock your potential: master the art of decision-making and creative problem solving.

As you probably already know, in a world overwhelmed by fake news , rapid technological shifts, and information overload, the need to master critical thinking, logic, and problem-solving has never been more urgent . These skills are your armor against confusion and your toolkit for clear, impactful decision-making.

Whether you're tackling personal dilemmas or professional obstacles , with this book you'll learn to cut through complexities with precision, challenge flawed reasoning, and merge creativity with analysis to make sound decisions.

Inside, you’ll discover a treasure trove of strategies and real-world examples that set the stage for a smarter and more decisive YOU . Here’s what you’ll gain:

Critical Foundations : Navigate through complex arguments and spot inconsistencies with ease.
Adaptive Mindset : Cultivate a philosophy of continuous improvement to excel in a dynamic world.
Informed Decision-Making : Develop robust methods to make and sustain informed choices.
Emotional Intelligence : Enhance your understanding and management of emotions to influence outcomes positively.
Strategic Problem-Solving : Elevate your ability to devise innovative solutions and think outside the box.
Effective Communication : Learn to express your ideas with clarity and persuade others through powerful storytelling techniques.
Logical Precision : Harness logical strategies to dissect problems and craft clear, compelling solutions.

Don’t let hesitation or faulty logic undermine your potential. Become the epitome of intellect and innovation. Start your transformation into a decision-making genius and a master of problem resolution.

Empower your intellect—make the smart choice of grabbing your copy now!

Print length 145 pages
Language English
Publication date April 9, 2024
Dimensions 6 x 0.33 x 9 inches
ISBN-13 979-8322270393
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ASIN ‏ : ‎ B0D17ZR2H9
Publisher ‏ : ‎ Independently published (April 9, 2024)
Language ‏ : ‎ English
Paperback ‏ : ‎ 145 pages
ISBN-13 ‏ : ‎ 979-8322270393
Item Weight ‏ : ‎ 9.8 ounces
Dimensions ‏ : ‎ 6 x 0.33 x 9 inches
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With a sharp focus on pioneering authors and innovative formats, from interactive eBooks to augmented reality narratives, Vanguard Nova seeks to redefine the reading experience. It champions a diverse array of voices, especially those exploring the intersections of technology, society, and human emotion, making it a haven for readers and writers fascinated by the potential of the digital age.

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16 Best Free Online Critical Thinking Courses

Written by Argumentful

Critical thinking is one of the most fundamental skills you could focus on. In fact, these skills are so important that many educational institutions have listed them among their central goals. Critical thinking helps you sort the true from the false.

The bad news is that not many people own these skills. Einstein famously said:

“Only two things are infinite, the universe and human stupidity, and I’m not sure about the former.”

The good news though is that you can improve your thinking and you can do it without breaking the bank.

Below are listed 16 of the best free online critical thinking courses with details regarding their contents.

Go on, choose your preferred course and take action today! (You can thank me later😉!)

P.S. Apart from the general critical thinking courses, I’ve included 5 specific ones which focus on today’s burning issues- fake news and climate change , as well as correctly interpreting randomized clinical trials and screening trials. See numbers 12 to 16 below.

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Critical reasoning for beginners, critical thinking classes at fayetteville state university, logical and critical thinking, critical thinking: fundamentals of good reasoning, philosophy and critical thinking, critical thinking & problem solving, introduction to critical thinking and logic, teaching critical thinking through art with the national gallery of art.

Critical thinking: Reasoned Decision Making

The Science of Everyday Thinking

Critical thinking at university: an introduction, making sense of news, sorting truth from fiction: civic online reasoning, making sense of climate science denial, thinking critically: interpreting randomized clinical trials, thinking critically series: interpreting screening trials.

Offered by : University of Oxford

Description :

4 hours, 6 modules

1: The Nature of Arguments

How to recognise arguments and what the nature of an argument is

2: Different Types of Arguments

Different types of arguments, in particular deductive and inductive arguments

3: Setting Out Arguments Logic Book Style

How to identify and analyse arguments, and how to set arguments out logic book-style to make them easier to evaluate

4: What is a Good Argument? Validity and Truth

How to evaluate arguments and how to tell whether an argument is good or bad, focusing specifically on inductive arguments

5: Evaluating Arguments Part One

Evaluation of arguments – this time deductive arguments – focusing in particular on the notion of validity

6: Evaluating Arguments Part Two

Fallacies: bad arguments that can easily be mistaken for good arguments

Also available on YouTube and iTunes

Offered by : Fayetteville State University

24 videos, 24 hours

Lectures from Spring 2011 Critical Thinking classes at Fayetteville State University held by Gregory B. Sadler. The textbook used was Moore And Parker’s Critical Thinking 9th edition .

Issues, claims, arguments
Arguments and non-arguments
Value Judgments
Complex arguments, unstated premises
Deductive and inductive arguments with implicit premises
Deductive and inductive arguments
Information sources
Experts and appeal to authority
Critical thinking and advertising
Rhetorical devices

Offered by : University Of Auckland

8 Weeks of study, 4 hours weekly

Identify common flaws in belief construction
Recognise and reconstruct arguments
Evaluate arguments as being good or bad
Analyse arguments using basic logical tools
Apply basic logical strategies in areas such as science, moral theories and law

Offered by : IsraelX

9 weeks, 4-6 hours per week

You can create a free account on edx.org and have access to the course for 2 months. After 2 months, you can pay £37 to get unlimited access to the course.

The objective of the course is to improve the student’s ability in the basic skills of critical thinking:

how to recognize arguments,
how to interpret them,
how to evaluate them,
how to construct them.

Lesson 1. What’s “Critical Thinking?” Lesson 2. What are Arguments Made Of? Lesson 3. From Premises to Conclusions Lesson 4. Recognizing Arguments: Introduction Lesson 5. Argument vs. The Text Containing It Lesson 6. Recognizing Conclusions Lesson 7. Arguments vs. Explanations Lesson 8. Argument Diagrams: Introduction Lesson 9. More about Argument Diagrams Lesson 10. Argument Diagrams: Examples Lesson 11. Hedges Lesson 12. Disclaimers Lesson 13. Examples Lesson 14. Rhetorical Language Lesson 15. Referential Attribution Lesson 16. Principles of Interpretation Lesson 17. Implicit Premises Lesson 18. What’s a Good Argument? Lesson 19. More Virtues of Arguments Lesson 20. Argument Ad Hominem Lesson 21. Argument Ad Verecundiam Lesson 22. Argument Ad Populum Lesson 23. Argument Ad Ignorantiam Lesson 24. Argument Ad Baculum and Ad Misericordiam Lesson 25. Venn Diagrams Lesson 26. Beyond Venn Lesson 27. Modus Ponens Lesson 28. Modus Tollens Lesson 29. Conditionals Lesson 30. Reductio Ad Absurdum Lesson 31. Process of Elimination Lesson 32. Separation of Cases Lesson 33. Truth Trees: An Example Lesson 34. How to Grow Truth Trees Lesson 35. Truth Trees: Another Example Lesson 36. Reflexive Relations Lesson 37. Symmetric Relations Lesson 38. Transitive Relations Lesson 39. Inductive Generalization Lesson 40. What’s a Good Sample? Lesson 41. The New Riddle of Induction Lesson 42. From Induction to Causation Lesson 43. Evaluating Causal Generalizations Lesson 44. Argument from Analogy: Basics Lesson 45. Argument from Analogy: Examples Lesson 46. Who Needs Analogues? Lesson 47. Inference to the Best Explanation Lesson 48. Experimentation Lesson 49. Building an Argument Lesson 50. Writing Up an Argument

Offered by : The University of Queensland

6 weeks, 1-4 hours per week

How to think with clarity and rigour
How to identify, analyse and construct cogent arguments
How to think of solutions to the central problems of philosophy
How to engage in philosophical conversations with others about topics that matter

Offered by : Rochester Institute of Technology

3 weeks, 4-6 hours per week

How to perform strategic analysis and assessment
How to perceive and assess a critical need and design a tailored solution
How to identify key stakeholders and ensure their needs are met
How to employ adaptive problem-solving
How to work through obstacles collaboratively
How to analyse failure to improve future performance

Offered by : Saylor.org Academy

This course will introduce you to critical thinking, informal logic, and a small amount of formal logic. Its purpose is to provide you with the basic tools of analytical reasoning, which will give you a distinctive edge in a wide variety of careers and courses of study. While many university courses focus on the presentation of content knowledge, the emphasis here is on learning how to think effectively. Although the techniques and concepts covered here are classified as philosophical, they are essential to the practice of nearly every major discipline, from the physical sciences and medicine to politics, law, and the humanities.

Unit 1: Introduction and Meaning Analysis
Unit 2: Argument Analysis
Unit 3: Basic Sentential Logic
Unit 4: Venn Diagrams
Unit 5: Fallacies
Unit 6: Scientific Reasoning
Unit 7: Strategic Reasoning and Creativity

Offered by : Smithsonian Institution

16 weeks, 3-4 hours per week

How to use Artful Thinking Routines to strengthen thinking.
How to facilitate meaningful conversations in your classroom using art for artful learning and artful teaching.
How to help learners of all levels develop more discerning descriptions, evidence-based reasoning, and meaningful questioning habits.
Key strategies for using content information to push original thinking deeper.
Exciting, immersive activities for any type of classroom.
How to use online teaching resources from the National Gallery of Art, including downloadable Artful Thinking lesson plans
Unit 0: Welcome (2 hours)
Unit 1: Diving into Thinking Routines (3-4 hours)
Unit 2: Observing and Describing (3-4 hours)
Unit 3: Reasoning with Evidence (3-4 hours)
Unit 4: Questioning and Investigating (3-4 hours)

Critical thinking: reasoned decision making

Offered by : Tecnológico de Monterrey

4 weeks, 5-8 hours per week

Identify the theories that support critical thinking
Employ a methodology for the application of critical thinking
Relate the elements that make up the stages of critical thinking
Analyse the standards of critical thinking practice
Assess the responsibility of perpetuating the intellectual values of the resolution analysis
Distinguish the vices of thought in decision making
Apply critical thinking to groups

1. Thinking according to our times

1.1 Why critical thinking?

1.2 The exciting world of thinking and criticism

2. Evaluating our modes of thought

2.1 Intellectual values of a good thinker

2.2 Evaluating our critical thinking skills. Avoiding vices and biased thinking

3. Elements and standards of critical thinking

3.1 Elements of a critical thinking process

3.2 Standards to apply to our thinking modes

4. Articulating our decisions making process

4.1 The logic of our decisions and the behaviour derived from them

4.2 How to improve our critical thinking skills and become a fair-minded thinker

12 weeks, 2-3 hours per week

The course explores the psychology of our everyday thinking: why people believe weird things, how we form and change our opinions, why our expectations skew our judgments, and how we can make better decisions. We’ll discuss and debate topics such as placebos, the paranormal, medicine, miracles, and more.

You will use the scientific method to evaluate claims, make sense of evidence, and understand why we so often make irrational choices. You will begin to rely on slow, effortful, deliberative, analytic, and logical thinking rather than fast, automatic, instinctive, emotional, and stereotypical thinking.

tools for how to think independently, how to be skeptical, and how to value data over personal experience.
examining the mental shortcuts that people use and misuse, and apply this knowledge to help make better decisions, and improve critical thinking.

Offered by : University of Leeds

2 weeks, 4 hours weekly

What is critical thinking?
A model for critical thinking
Why is critical thinking important at university?
Challenges to thinking critically at university
How can you improve your critical thinking?
How will critical thinking help you at university?

Offered by : University of Hong Kong

4 weeks, 2-3 hours per week

This course will help you identify reliable information in news reports and become better informed about the world we live in. A discussion on journalism from the viewpoint of the news audience.

What makes news? The blurred lines between news, promotion and entertainment.
Why does news matter? Social sharing and the dynamics of the news cycles.
Who provides information? How to evaluate sources in news reports.
Where is the evidence? The process of verification.
When should we act? Recognizing our own biases.
How do we know what we know? Becoming an active news audience.

You’ll learn to:

Distinguish news from opinion; media bias from audience bias; assertion from verification
Apply critical thinking skills to examine the validity of information
Contextualize the knowledge gained from news report
Respond quickly to daily news events and make an informed decision

Offered by : Massachusetts Institute of Technology

9 weeks, 2-4 hours per week

Course aimed at fighting fake news and misinformation

Educators—from teachers to librarians—will learn about:

New knowledge that can be applied in your lessons and resources for your own students.
How to shift from ineffective information literacy practices towards the kinds of strategies employed by professional fact-checkers.

Unit 1: Search Like a Fact Checker

Unit 2: The Two Big Fact Checker Moves: Lateral Reading & Click Restraint

Unit 3: Evaluating Different Types of Evidence

Unit 4: Adapting Civic Online Reasoning

7 weeks, 2-4 hours per week

WEEK 1: Understanding The Climate Controversy During the first week of the course, we introduce the course content, interact with each other and complete an introductory survey. The week continues with an exploration of political consensus, the drivers and psychology of climate science denial and an overview of the controversy surrounding this topic.

WEEK 2: Global Warming Is Happening In week two, we will look at the indicators of global warming and myths related to temperature and glaciers.

WEEK 3: We Are Causing Global Warming Week three focuses on the ways in which humans cause climate change and the myths associated with the greenhouse effect and the rise in carbon dioxide.

WEEK 4: The Past Tells Us About The Future This week looks at the history of climate change in order to model future climate change. We also address myths related to models.

WEEK 5: We Are Feeling The Impacts Of Climate Change Week five covers climate feedbacks and the impacts of climate change on the environment, society and the weather.

WEEK 6 and 7: Responding to Denial The final weeks of the course look more closely at the psychology of science denial and debunking techniques. We also complete a peer assessment that asks students to practice debunking strategies on real myths that can be found in today’s media.

Approach: mini-lectures, video interviews, quizzes, activities, a peer assessed writing assignment, and readings.

Offered by : Stanford University

1 week, 2-3 hours

This course seeks to fulfil the clinical community’s need to improve skills in the critical evaluation of clinical research papers. Competency in critical appraisal skills can have a significant impact by improving clinical practice, quality of research projects, and peer-review of manuscripts and grants. The course will utilize efficient and engaging videos with relevant clinical examples to cover essential research methodology principles.

Analyse the concepts of randomization and blinding in reducing bias.
Develop strategies to critically appraise randomized clinical trials and determine if study results are valid.
Analyse the key design features of screening studies.
Develop strategies to critically appraise screening studies and determine if study results are valid.

The Importance of Critical Thinking when Using ChatGPT (and Other Large Language Models)

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Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors

Clio cresswell.

1 School of Mathematics and Statistics, The University of Sydney, Sydney, Australia

Craig P. Speelman

2 School of Arts and Humanities, Edith Cowan University, Joondalup, Australia

Associated Data

All relevant data are within the paper and its Supporting Information files.

Mathematics is often promoted as endowing those who study it with transferable skills such as an ability to think logically and critically or to have improved investigative skills, resourcefulness and creativity in problem solving. However, there is scant evidence to back up such claims. This project tested participants with increasing levels of mathematics training on 11 well-studied rational and logical reasoning tasks aggregated from various psychological studies. These tasks, that included the Cognitive Reflection Test and the Wason Selection Task, are of particular interest as they have typically and reliably eluded participants in all studies, and results have been uncorrelated with general intelligence, education levels and other demographic information. The results in this study revealed that in general the greater the mathematics training of the participant, the more tasks were completed correctly, and that performance on some tasks was also associated with performance on others not traditionally associated. A ceiling effect also emerged. The work is deconstructed from the viewpoint of adding to the platform from which to approach the greater, and more scientifically elusive, question: are any skills associated with mathematics training innate or do they arise from skills transfer?

Introduction

Mathematics is often promoted as endowing those who study it with a number of broad thinking skills such as: an ability to think logically, analytically, critically and abstractly; having capacity to weigh evidence with impartiality. This is a view of mathematics as providing transferable skills which can be found across educational institutions, governments and corporations worldwide. A view material to the place of mathematics in curricula.

Consider the UK government’s commissioned inquiry into mathematics education “Making Mathematics Count” ascertaining the justification that “mathematical training disciplines the mind, develops logical and critical reasoning, and develops analytical and problem-solving skills to a high degree” [ 1 p11]. The Australian Mathematical Sciences Institute very broadly states in its policy document “Vision for a Maths Nation” that “Not only is mathematics the enabling discipline, it has a vital productive role planning and protecting our well-being” (emphasis in original) [ 2 ]. In Canada, British Columbia’s New 2016 curriculum K-9 expressly mentions as part of its “Goals and Rationale”: “The Mathematics program of study is designed to develop deep mathematical understanding and fluency, logical reasoning, analytical thought, and creative thinking.” [ 3 ]. Universities, too, often make such specific claims with respect to their teaching programs. “Mathematics and statistics will help you to think logically and clearly, and apply a range of problem-solving strategies” is claimed by The School of Mathematical Sciences at Monash University, Australia [ 4 ]. The School of Mathematics and Statistics at The University of Sydney, Australia, directly attributes as part of particular course objectives and outcomes skills that include “enhance your problem-solving skills” as part of studies in first year [ 5 ], “develop logical thinking” as part of studies in second year, which was a statement drafted by the lead author in fact [ 6 ], and “be fluent in analysing and constructing logical arguments” as part of studies in third year [ 7 ]. The University of Cambridge’s Faculty of Mathematics, UK, provides a dedicated document “Transferable Skills in the Mathematical Tripos” as part of its undergraduate mathematics course information, which again lists “analytic ability; creativity; initiative; logical and methodical reasoning; persistence” [ 8 ].

In contrast, psychological research, which has been empirically investigating the concept of transferability of skills since the early 1900s, points quite oppositely to reasoning skills as being highly domain specific [ 9 ]. Therefore, support for claims that studying mathematics engenders more than specific mathematics knowledge is highly pertinent. And yet it is largely absent. The 2014 Centre for Curriculum Redesign (CCR) four part paper “Mathematics for the 21st Century: What Should Students Learn?” concludes in its fourth paper titled “Does mathematics education enhance higher-order thinking skills?” with a call to action “… there is not sufficient evidence to conclude that mathematics enhances higher order cognitive functions. The CCR calls for a much stronger cognitive psychology and neuroscience research base to be developed on the effects of studying mathematics” [ 10 ].

Inglis and Simpson [ 11 ], bringing up this very issue, examined the ability of first-year undergraduate students from a high-ranking UK university mathematics department, on the “Four Cards Problem” thinking task, also known as the Wason Selection Task. It is stated as follows.

Each of the following cards have a letter on one side and a number on the other.

Here is a rule: “if a card has a D on one side, then it has a 3 on the other”. Your task is to select all those cards, but only those cards, which you would have to turn over in order to find out whether the rule is true or false. Which cards would you select?

This task involves understanding conditional inference, namely understanding the rule “If P then Q” and with this, deducing the answer as “P and not Q” or “D and 7”. Such logical deduction indeed presents as a good candidate to test for a potential ability of the mathematically trained. This task has also been substantially investigated in the domain of the psychology of reasoning [ 12 p8] revealing across a wide range of publications that only around 10% of the general population reach the correct result. The predominant mistake being to pick “D and 3”; where in the original study by Wason [ 13 ] it is suggested that this was picked by 65% of people. This poor success rate along with a standard mistake has fuelled interest in the task as well as attempts to understand why it occurs. A prevailing theory being the so named matching bias effect; the effect of disproportionately concentrating on items specifically mentioned in the situation, as opposed to reasoning according to logical rules.

Inglis and Simpson’s results isolated mathematically trained individuals with respect to this task. The participants were under time constraint and 13% of the first-year undergraduate mathematics students sampled reached the correct response, compared to 4% of the non-mathematics (arts) students that was included. Of note also was the 24% of mathematics students as opposed to 45% of the non-mathematics students who chose the standard mistake. The study indeed unveiled that mathematically trained individuals were significantly less affected by the matching bias effect with this problem than the individuals without mathematics training. However, the achievement of the mathematically trained group was still far from masterful and the preponderance for a non-standard mistake compared with non-mathematically trained people is suggestive. Mathematical training appears to engender a different thinking style, but it remains unclear what the difference is.

Inglis, Simpson and colleagues proceeded to follow up their results with a number of studies concentrated on conditional inference in general [ 14 , 15 ]. A justification for this single investigatory pathway being that if transfer of knowledge is present, something subtle to test for in the first place, a key consideration should be the generalisation of learning rather than the application of skills learned in one context to another (where experimenter bias in the choice of contexts is more likely to be an issue). For this they typically used sixteen “if P then Q” comprehension tasks, where their samples across a number of studies have included 16-year-old pre-university mathematics students (from England and Cyprus), mathematics honours students in their first year of undergraduate university study, third year university mathematics students, and associated control groups. The studies have encompassed controls for general intelligence and thinking disposition prior to training, as well as follows ups of up to two years to address the issue of causation. The conclusive thinking pattern that has emerged is a tendency of the mathematical groups towards a greater likelihood of rejecting the invalid denial of the antecedent and affirmation of the consequent inferences. But with this, and this was validated by a second separate study, the English mathematics group actually became less likely to endorse the valid modus tollens inference. So again, mathematical training appears to engender a different thinking style, but there are subtleties and it remains unclear what the exact difference is.

This project was designed to broaden the search on the notion that mathematics training leads to increased reasoning skills. We focused on a range of reasoning problems considered in psychological research to be particularly insightful into decision making, critical thinking and logical deduction, with their distinction in that the general population generally struggles with answering them correctly. An Australian sample adds diversity to the current enquiries that have been European focussed. Furthermore, in an effort to identify the impact of mathematics training through a possible gradation effect, different levels of mathematically trained individuals were tested for performance.

Well-studied thinking tasks from a variety of psychological studies were chosen. Their descriptions, associated success rates and other pertinent details follows. They were all chosen as the correct answer is typically eluded for a standard mistake.

The three-item Cognitive Reflection Test (CRT) was used as introduced by Frederick [ 16 ]. This test was devised in line with the theory that there are two general types of cognitive activity: one that operates quickly and without reflection, and another that requires not only conscious thought and effort, but also an ability to reflect on one’s own cognition by including a step of suppression of the first to reach it. The three items in the test involve an incorrect “gut” response and further cognitive skill is deemed required to reach the correct answer (although see [ 17 ] for evidence that correct responses can result from “intuition”, which could be related to intelligence [ 18 ]).

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

Bat and ball

A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?

The solutions are: 47 days for the Lily Pads problem, 5 minutes for the Widgets problem and 5 cents for the Bat and Ball problem. The considered intuitive, but wrong, answers are 24 days, 100 minutes and 10 cents, respectively. These wrong answers are attributed to participants becoming over focused on the numbers so as to ignore the exponential growth pattern in the Lily Pads problem, merely complete a pattern in numbers in the Widgets problem, and neglect the relationship “more than” in the Bat and Ball problem [ 19 ]. The original study by Frederick [ 16 ] provides a composite measure of the performance on these three items, with only 17% of those studied (n = 3428) reaching the perfect score. The CRT has since been studied extensively [ 19 – 21 ]. Research using the CRT tends not to report performance on the individual items of the test, but rather a composite measure of performance. Attridge and Inglis [ 22 ] used the CRT as a test for thinking disposition of mathematics students as one way to attempt to disentangle the issue of filtering according to prior thinking styles rather than transference of knowledge in successful problem solving. They repeat tested 16-year old pre-university mathematics students and English literature students without mathematics subjects at a one-year interval and found no difference between groups.

Three problems were included that test the ability to reason about probability. All three problems were originally discussed by Kahneman and Tversky [ 23 ], with the typically poor performance on these problems explained by participants relying not on probability knowledge, but a short-cut method of thinking known as the representativeness heuristic. In the late 1980s, Richard Nisbett and colleagues showed that graduate level training in statistics, while not revealing any improvement in logical reasoning, did correlate with higher-quality statistical answers [ 24 ]. Their studies lead in particular to the conclusion that comprehension of, what is known as the law of large numbers, did show improvement with training. The first of our next three problems targeted this law directly.

A certain town is served by two hospitals. In the larger hospital, about 45 babies are born each day, and in the smaller hospital, about 15 babies are born each day. As you know, about 50 percent of all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of one year, each hospital recorded the number of days on which more than 60 percent of the babies born were boys. Which hospital do you think recorded more such days? (Circle one letter.)

(a) the larger hospital
(b) the smaller hospital
(c) about the same (that is, within 5 percent of each other)

Kahneman and Tversky [ 23 ] reported that, of 50 participants, 12 chose (a), 10 chose (b), and 28 chose (c). The correct answer is (b), for the reason that small samples are more likely to exhibit extreme events than large samples from the same population. The larger the sample, the more likely it will exhibit characteristics of the parent population, such as the proportion of boys to girls. However, people tend to discount or be unaware of this feature of sampling statistics, which Kahneman and Tversky refer to as the law of large numbers. Instead, according to Kahneman and Tversky, people tend to adhere to a fallacious law of small numbers, where even small samples are expected to exhibit properties of the parent population, as illustrated by the proportion of participants choosing the answer (c) in their 1972 study. Such thinking reflects use of the representativeness heuristic, whereby someone will judge the likelihood of an uncertain event based on how similar it is to characteristics of the parent population of events.

Birth order

All families of six children in a city were surveyed. In 72 families the exact order of births of boys and girls was GBGBBG.

(a) What is your estimate of the number of families surveyed in which the exact order of births was BGBBBB?
(b) In the same survey set, which, if any, of the following two sequences would be more likely: BBBGGG or GBBGBG?

All of the events listed in the problem have an equal probability, so the correct answer to (a) is 72, and to (b) is “neither is more likely”. Kahneman and Tversky [ 23 ] reported that 75 of 92 participants judged the sequence in (a) as less likely than the given sequence. A similar number (unspecified by Kahneman and Tversky, but the statistical effect was reported to be of the same order as in (a)) reported that GBBGBG was the more likely sequence. Again, Kahneman and Tversky suggested that these results reflected use of the representativeness heuristic. In the context of this problem, the heuristic would have taken the following form: some birth orders appear less patterned than others, and less patterned is to be associated with the randomness of birth order, making them more likely.

Coin tosses

In a sequence of coin tosses (the coin is fair) which of the following outcomes would be most likely (circle one letter):

(a) H T H T H T H T
(b) H H H H T T T T
(c) T T H H T T H H
(d) H T T H T H H T
(e) all of the above are equally likely

The correct answer in this problem is (e). Kahneman and Tversky [ 23 ] reported that participants tend to choose less patterned looking sequences (e.g., H T T H T H H T) as more likely than more systematic looking sequences (e.g., H T H T H T H T). This reasoning again reflects the representativeness heuristic.

Three further questions from the literature were included to test problem solving skill.

Two drivers

Two drivers set out on a 100-mile race that is marked off into two 50-mile sections. Driver A travels at exactly 50 miles per hour during the entire race. Driver B travels at exactly 45 mph during the first half of the race (up to the 50-mile marker) and travels at exactly 55 mph during the last half of the race (up to the finish line). Which of the two drivers would win the race? (Circle one letter.)

(a) Driver A would win the race
(b) Driver B would win the race
(c) the two drivers would arrive at the same time (within a few seconds of one another)

This problem was developed by Pelham and Neter [ 25 ]. The correct answer is (a), which can be determined by calculations of driving times for each Driver, using time = distance/velocity. Pelham and Neter argue, however, that (c) is intuitively appealing, on the basis that both drivers appear to have the same overall average speed. Pelham and Neter reported that 67% of their sample gave this incorrect response to the problem, and a further 13% selected (b).

Petrol station

Imagine that you are driving along the road and you notice that your car is running low on petrol. You see two petrol stations next to each other, both advertising their petrol prices. Station A’s price is 65c/litre; Station B’s price is 60c/litre. Station A’s sign also announces: “5c/litre discount for cash!” Station B’s sign announces “5c/litre surcharge for credit cards.” All other factors being equal (for example, cleanliness of the stations, number of cars waiting at each etc), to which station would you choose to go, and why?

This problem was adapted from one described by Galotti [ 26 ], and is inspired by research reported by Thaler [ 27 ]. According to Thaler’s research, most people prefer Station A, even though both stations are offering the same deal: 60c/litre for cash, and 65c/litre for credit. Tversky and Kahneman [ 28 ] explain this preference by invoking the concept of framing effects. In the context of this problem, such an effect would involve viewing the outcomes as changes from some initial point. The initial point frames the problem, and provides a context for viewing the outcome. Thus, depending on the starting point, outcomes in this problem can be viewed as either a gain (in Station A, you gain a discount if you use cash) or a loss (in Station B, you are charged more (a loss) for using credit). Given that people are apparently more concerned about a loss than a gain [ 29 ], the loss associated with Station B makes it the less attractive option, and hence the preference for Station A. The correct answer, though, is that the stations are offering the same deal and so no station should be preferred.

And finally, a question described by Stanovich [ 30 , 31 ] as testing our predisposition for cognitive operations that require the least computational effort.

Jack looking at Anne

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person? (Circle one letter.)

Stanovich reported that over 80% of people choose the “lazy” answer (c). The correct answer is (a).

The above questions survey, in a clear problem solving setting, an ability to engage advanced cognitive processing in order to critically evaluate and possibly override initial gut reasoning, an ability to reason about probability within the framework of the law of large numbers and the relationship between randomness and patterning, an ability to isolate salient features of a problem and, with the last question in particular, an ability to map logical relations. It might be hypothesised that according to degrees of mathematical training, in line with the knowledge base provided and the claims of associated broad and enhanced problem-solving abilities in general, that participants with greater degrees of such training would outperform others on these questions. This hypothesis was investigated in this study. In addition, given that no previous study on this issue has examined the variety of problems used in this study, we also undertook an exploratory analysis to investigate whether there exist any associations between the problems in terms of their likelihood of correct solution. Similarities between problems might indicate which problem solving domains could be susceptible to the effects of mathematics training.

A questionnaire was constructed containing the problems described in the previous sections plus the Four Cards Problem as tested by Inglis and Simpson [ 11 ] for comparison. The order of the problems was as follows: 1) Lily Pads; 2) Hospitals; 3) Widgets; 4) Four Cards; 5) Bat and Ball; 6) Birth Order; 7) Petrol Station; 8) Coin Tosses; 9) Two Drivers; 10) Jack looking at Anne. It was administered to five groups distinctive in mathematics training levels chosen from a high-ranking Australian university, where the teaching year is separated into two teaching semesters and where being a successful university applicant requires having been highly ranked against peers in terms of intellectual achievement:

Introductory—First year, second semester, university students with weak high school mathematical results, only enrolled in the current unit as a compulsory component for their chosen degree, a unit not enabling any future mathematical pathway, a typical student may be enrolled in a Biology or Geography major;
Standard—First year, second semester, university students with fair to good high school mathematical results, enrolled in the current mathematics unit as a compulsory component for their chosen degree with the possibility of including some further mathematical units in their degree pathway, a typical student may be enrolled in an IT or Computer Science major;
Advanced1—First year, second semester, university mathematics students with very strong interest as well as background in mathematics, all higher year mathematical units are included as possible future pathway, a typical student may be enrolled in a Mathematics or Physics major;
Advanced2—Second year, second semester, university mathematics students with strong interest as well as background in mathematics, typically a direct follow on from the previously mentioned Advanced1 cohort;
Academic—Research academics in the mathematical sciences.

Participants

123 first year university students volunteered during “help on demand” tutorial times containing up to 30 students. These are course allocated times that are supervised yet self-directed by students. This minimised disruption and discouraged coercion. 44 second year university students completed the questionnaire during a weekly one-hour time slot dedicated to putting the latest mathematical concepts to practice with the lecturer (whereby contrast to what occurs in tutorial times the lecturer does most of the work and all students enrolled are invited). All these university students completed the questionnaire in normal classroom conditions; they were not placed under strict examination conditions. The lead author walked around to prevent discussion and coercion and there was minimum disruption. 30 research academics responded to local advertising and answered the questionnaire in their workplace while supervised.

The questionnaires were voluntary, anonymous and confidential. Participants were free to withdraw from the study at any time and without any penalty. No participant took this option however. The questionnaires gathered demographic information which included age, level of education attained and current qualification pursued, name of last qualification and years since obtaining it, and an option to note current speciality for research academics. Each problem task was placed on a separate page. Participants were not placed under time constraint, but while supervised, were asked to write their start and finish times on the front page of the survey to note approximate completion times. Speed of completion was not incentivised. Participants were not allowed to use calculators. A final “Comments Page” gave the option for feedback including specifically if the participants had previously seen any of the questions. Questionnaires were administered in person and supervised to avoid collusion or consulting of external sources.

The responses were coded four ways: A) correct; B) standard error (the errors discussed above in The Study); C) other error; D) left blank.

The ethical aspects of the study were approved by the Human Research Ethics Committee of the University of Sydney, protocol number [2016/647].

The first analysis examined the total number of correct responses provided by the participants as a function of group. Scores ranged from 1 to 11 out of a total possible of 11 (Problem 6 had 2 parts) ( Fig 1 ). An ANOVA of this data indicated a significant effect of group (F(4, 192) = 20.426, p < .001, partial η 2 = .299). Pairwise comparisons using Tukey’s HSD test indicated that the Introductory group performed significantly worse than the Advanced1, Advanced2 and Academic groups. There were no significant differences between the Advanced1, Advanced2 and Academic groups.

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Error bars are one standard error of the mean.

Overall solution time, while recorded manually and approximately, was positively correlated with group, such that the more training someone had received, the longer were these solution times (r(180) = 0.247, p = .001). However, as can be seen in Fig 2 , this relationship is not strong.

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A series of chi-squared analyses, and their Bayesian equivalents, were performed on each problem, to determine whether the distribution of response types differed as a function of group. To minimise the number of cells in which expected values in some of these analyses were less than 5, the Standard Error, Other Error and Blank response categories were collapsed into one category (Incorrect Response). For three of the questions, the expected values of some cells did fall below 5, and this was due to most people getting the problem wrong (Four Cards), or most people correctly responding to the problem (Bat and Ball, Coin Tosses). In these cases, the pattern of results was so clear that a statistical analysis was barely required. Significant chi-squared results were examined further with pairwise posthoc comparisons (see Table 1 ).

Superscripts label the groups (e.g., Introductory = a). Within the table, these letters refer to which other group a particular group was significantly different to according to a series of pairwise post hoc chi squared analyses (Bonferroni corrected α = .005) (e.g., ‘d’ in the Introductory column indicates the Introductory and the Advanced2 (d) group were significantly different for a particular problem).

The three groups with the least amount of training in mathematics were far less likely than the other groups to give the correct solution (χ 2 (4) = 31.06, p < .001; BF 10 = 45,045) ( Table 1 ). People in the two most advanced groups (Advanced2 and Academic) were more likely to solve the card problem correctly, although it was still less than half of the people in these groups who did so. Further, these people were less likely to give the standard incorrect solution, so that most who were incorrect suggested some more cognitively elaborate answer, such as turning over all cards. The proportion of people in the Advanced2 and Academic groups (39 and 37%) who solved the problem correctly far exceeded the typical proportion observed with this problem (10%). Of note, also, is the relatively high proportion of those in the higher training groups who, when they made an error, did not make the standard error, a similar result to the one reported by Inglis and Simpson [ 11 ].

The cognitive reflection test

In the Lily Pads problem, although most people in the Standard, Advanced1, Advanced2 and Academic groups were likely to select the correct solution, it was also the case that the less training someone had received in mathematics, the more likely they were to select an incorrect solution (χ 2 (4) = 27.28, p < .001; BF 10 = 15,554), with the standard incorrect answer being the next most prevalent response for the two lower ability mathematics groups ( Table 1 ).

Performance on the Widgets problem was similar to performance on the Lily Pads problem in that most people in the Standard, Advanced1, Advanced2 and Academic groups were likely to select the correct solution, but that the less training someone had received in mathematics, the more likely they were to select an incorrect solution (χ 2 (4) = 23.76, p< .001; BF 10 = 516) ( Table 1 ). As with the Lily Pads and Widget problems, people in the Standard, Advanced1, Advanced2 and Academic groups were highly likely to solve the Bat and Ball problem (χ 2 (4) = 35.37, p < .001; BF 10 = 208,667). Errors were more likely from the least mathematically trained people (Introductory, Standard) than the other groups ( Table 1 ).

To compare performance on the CRT with previously published results, performance on the three problems (Lily Pads, Widgets, Bat and Ball) were combined. The number of people in each condition that solved 0, 1, 2, or 3 problems correctly is presented in Table 2 . The Introductory group were evenly distributed amongst the four categories, with 26% solving all three problems correctly. Around 70% of the rest of the groups solved all 3 problems correctly, which is vastly superior to the 17% reported by Frederick [ 16 ].

Responses to the Hospitals problem were almost universally split between correct and standard errors in the Standard, Advanced1, Advanced2 and Academic groups. Although this pattern of responses was also evident in the Introductory group, this group also exhibited more non-standard errors and non-responses than the other groups. However, the differences between the groups were not significant (χ 2 (4) = 4.93, p = .295; BF 10 = .068) ( Table 1 ). Nonetheless, the performance of all groups exceeds the 20% correct response rate reported by Kahneman and Tversky [ 23 ].

The two versions of the Birth Order problem showed similar results, with correct responses being more likely in the groups with more training (i.e., Advanced1, Advanced2 and Academic), and responses being shared amongst the various categories in the Introductory and Standard groups (χ a 2 (4) = 24.54, p < .001; BF 10 = 1,303; χ b 2 (4) = 25.77, p < .001; BF 10 = 2,970) ( Table 1 ). Nonetheless, performance on both versions of the problem in this study was significantly better than the 82% error rate reported by Kahneman and Tversky [ 23 ].

The Coin Tosses problem was performed well by all groups, with very few people in any condition committing errors. There were no obvious differences between the groups (χ 2 (4) = 3.70, p = .448; BF 10 = .160) ( Table 1 ). Kahneman and Tversky [ 23 ] reported that people tend to make errors on this type of problem by choosing less patterned looking sequences, but they did not report relative proportions of people making errors versus giving correct responses. Clearly the sample in this study did not perform like those in Kahneman and Tversky’s study.

Responses on the Two Drivers problem were clearly distinguished by a high chance of error in the Introductory and Standard groups (over 80%), and a fairly good chance of being correct in the Advanced1, Advanced2 and Academic groups (χ 2 (4) = 46.16, p < .001; BF 10 = 1.32 x 10 8 ) ( Table 1 ). Academics were the standout performers on this problem, although over a quarter of this group produced an incorrect response. Thus, the first two groups performed similarly to the participants in the Pelham and Neter [ 25 ] study, 80% of whom gave an incorrect response.

Responses on the Petrol Station problem were marked by good performance by the Academic group (73% providing a correct response), and just over half of each of the other groups correctly solving the problem. This difference was not significant (χ 2 (4) = 4.68, p = .322: BF 10 = .059) ( Table 1 ). Errors were fairly evenly balanced between standard and other, except for the Academic group, who were more likely to provide a creative answer if they made an error. Thaler [ 27 ] reported that most people get this problem wrong. In this study, however, on average, most people got this problem correct, although this average was boosted by the Academic group.

Responses on the Jack looking at Anne problem generally were standard errors, except for the Advanced2 and Academic groups, which were evenly split between standard errors and correct responses (χ 2 (4) = 18.03, p = .001; BF 10 = 46) ( Table 1 ). Thus, apart from these two groups, the error rate in this study was similar to that reported by Stanovich [ 30 ], where 80% of participants were incorrect.

A series of logistic regression analyses were performed in order to examine whether the likelihood of solving a particular problem correctly could be predicted on the basis of whether other problems were solved correctly. Each analysis involved selecting performance (correct or error) on one problem as the outcome variable, and performance on the other problems as predictor variables. Training (amount of training) was also included as a predictor variable in each analysis. A further logistic regression was performed with training as the outcome variable, and performance on all of the problems as predictor variables. The results of these analyses are summarised in Table 3 . There were three multi-variable relationships observed in these analyses, which can be interpreted as the likelihood of solving one problem in each group being associated with solving the others in the set. These sets were: (1) Lily Pads, Widgets and Petrol Station; (2) Hospitals, Four Cards and Two Drivers; (3) Birth Order and Coin Tosses. Training also featured in each of these sets, moderating the relationships as per the results presented above for each problem.

P = Problem (1 = Four Cards; 2 = Lily Pads; 3 = Widgets; 4 = Bat & Ball; 5 = Hospitals; 6a = Birth Order (a); 6b = Birth Order (b); 7 = Coin Tosses; 8 = Two Drivers; 9 = Petrol Station; 10 = Jack looking at Anne).

training = Amount of training condition.

p = significance level of logistic regression model.

% = percentage of cases correctly classified by the logistic regression model.

✓ = significant predictor, α < .05.

* = logistic regression for the training outcome variable is multinomial, whereas all other logistic regressions are binomial.

The final “Comments Page” revealed the participants as overwhelmingly enjoying the questions. Any analysis of previous exposure to the tasks proved impossible as there was little to no alignment on participant’s degree of recall, if any, and even perceptions of what exposure entailed. For example, some participants confused being exposed to the particular tasks with being habitually exposed to puzzles, or even mathematics problems, more broadly.

In general, the amount of mathematics training a group had received predicted their performance on the overall set of problems. The greater the training, the more problems were answered correctly, and the slower the recorded response times. There was not an obvious difference between the Advanced1, Advanced2 and Academic groups on either of these measures, however there were clear differences between this group and the Introductory and Standard groups, with the former exhibiting clearly superior accuracy. While time records were taken approximately, so as to avoid adding time pressure as a variable, that the Advanced1, Advanced2 and Academic groups recorded more time in their consideration of the problems, may suggest a “pause and consider” approach to such problems is a characteristic of the advanced groups. This is in line with what was suggested by an eye-movement tracking study of mathematically trained students attempting the Four Cards Problem; where participants that had not chosen the standard error had spent longer considering the card linked to the matching bias effect [ 14 ]. It is important to note, however, that longer response times may reflect other cognitive processes than deliberation [ 32 ].

Performance on some problems was associated with performance on other problems. That is, if someone correctly answered a problem in one of these sets, they were also highly likely to correctly answer the other problems in the set. These sets were: (1) Lily Pads, Widgets and Petrol Station; (2) Hospitals, Four Cards and Two Drivers; (3) Birth Order and Coin Tosses. This is different with how these problems have been typically clustered a priori in the research literature: (I) Lily Pads, Widgets and Bat and Ball (CRT); (II) Hospitals and Two Drivers (explained below); (III) Hospitals, Birth Order and Coin Tosses (representativeness heuristic); (IV) Birth Order and Coin Tosses (probability theory). Consideration of these problem groupings follows.

Correctly answering all three problems in (I) entailed not being distracted by particular pieces of information in the problems so as to stay focused on uncovering the real underlying relationships. The Lily Pads and Widget problems can mislead if attention is over focused on the numbers, and conversely, the Petrol Station problem can mislead if there is too much focus on the idea of a discount. While the Lily Pads and Widget problems are traditionally paired with the Bat and Ball problem in the CRT, it may be that performance on the Bat and Ball problem did not appear as part of this set due to an added level of difficulty. With the problems in (I), avoiding being distracted by certain parts of the questions at the expense of others almost leads directly to the correct answer. However, with the Bat and Ball problem, further steps in mathematical reasoning still need to occur in answering which two numbers add together to give a result while also subtracting one from the other for another.

With the problems in (II) it is of interest that the Two Drivers problem was created specifically to be paired with the Hospitals problem to test for motivation in problem solving [ 23 ]. Within this framework further transparent versions of these problems were successfully devised to manipulate for difficulty. The Two Drivers problem was amended to have Driver B travelling at exactly 5 mph during the first half of the race and at exactly 95 mph during the last half of the race. The Hospitals problem was amended so the smaller hospital would have “only 2” babies born each day and where for a period of one year the hospitals recorded the number of days on which all of the babies born were boys. Could the association in (II) be pointing to how participants overcome initial fictitious mathematical rules? Maybe they reframe the question in simpler terms to see the pattern. The Four Cards Problem also elicited a high number of incorrect answers where, associated with mathematical training, the standard incorrect solution was avoided for more cognitively elaborate ones. Indeed, a gradation effect appeared across the groups where the standard error of the “D and 3” cards becomes “D only” ( Table 4 ). Adrian Simpson and Derrick Watson found a comparable result across their two groups [14 p61]. This could again be pointing to having avoided an initial fictitious rule of simply concentrating on items directly found in the question, participants then seek to reframe the question to unearth the logical rule to be deduced. An added level of difficulty with this question may be why participants become trapped in a false answer. The eye-movement tracking study mentioned above supports this theory.

The problems in (III) fit naturally together as part of basic probability theory, a topic participants would have assimilated, or not, as part of various education curricula. While the equal likelihood of all possible outcomes with respect to a coin toss may be culturally assimilated, the same may not be as straightforward for birth gender outcomes where such assumptions could be swayed by biological hypothesis or folk wisdom [ 33 ]. The gradation of the results in terms of mathematical training does not support this possibility.

The effect of training on performance accuracy was more obvious in some problems compared to others, and to some extent, this was related to the type of problem. For instance, most of the problems in which performance was related to training (Four Cards, CRT [Lily Pads, Widgets, Bat and Ball], Two Drivers, Jack looking at Anne) could be classed as relying on logical and/or critical thinking. The one exception was the Birth Order problems, which are probability related.

In contrast, two of the three problems in which training did not appear to have much impact on performance (Hospitals and Coin Tosses) require domain-specific knowledge. The Hospitals problem requires a degree of knowledge about sampling statistics. This is a topic of quite distinct flavour that not all mathematically trained individuals gain familiarity with. On the other hand, all groups having performed well on the Coin Tosses problem is in line with a level of familiarity with basic probability having been originally presented at high school. While the questioning of patterning as negatively correlated with randomness is similar to that appearing in the Birth Order question, in the Birth Order question this aspect is arguably more concealed. These results and problem grouping (III) could be pointing to an area for improvement in teaching where the small gap in knowledge required to go from answering the Coin Tosses problem correctly to achieving similarly with the Birth Order problem could be easily addressed. A more formal introduction to sampling statistics in mathematical training could potentially bridge this gap as well as further be extended towards improvement on the Hospitals problem.

The other problem where performance was unrelated to training, the Petrol Station problem, cannot be characterised similarly. It is more of a logical/critical thinking type problem, where there remains some suggestion that training may have impacted performance, as the Academic group seemed to perform better than the rest of the sample. An alternate interpretation of this result is therefore that this problem should not be isolated but grouped with the other problems where performance is affected by training.

Although several aspects of the data suggest mathematics training improves the chances that someone will solve problems of the sort examined here, differences in the performance of participants in the Advanced1, Advanced2 and Academic groups were not obvious. This is despite the fact that large differences exist in the amount of training in these three groups. The first two groups were undergraduate students and the Academic group all had PhDs and many were experienced academic staff. One interpretation of this result is current mathematics training can only take someone so far in terms of improving their abilities with these problems. There is a point of demarcation to consider in terms of mathematical knowledge between the Advanced1, Advanced2 and Academic groups as compared to the Introductory and Standard groups. In Australia students are able to drop mathematical study at ages 15–16 years, or choose between a number of increasingly involved levels of mathematics. For the university in this study, students are filtered upon entry into mathematics courses according to their current knowledge status. All our groups involved students who had opted for post-compulsory mathematics at high school. And since our testing occurred in second semester, some of the mathematical knowledge shortfalls that were there upon arrival were bridged in first semester. Students must pass a first semester course to be allowed entry into the second semester course. A breakdown of the mathematics background of each group is as follows:

The Introductory group’s mathematics high school syllabus studied prior to first semester course entry covered: Functions, Trigonometric Functions, Calculus (Introduction to Differentiation, Applications of the Derivative, Antiderivatives, Areas and the Definite Integral), Financial Mathematics, Statistical Analysis. The Introductory group then explored concepts in mathematical modelling with emphasis on the importance of calculus in their first semester of mathematical studies.
The Standard group’s mathematics high school syllabus studied prior to first semester course entry covered: Functions, Trigonometric Functions, Calculus (Rates of Change, Integration including the method of substitution, trigonometric identities and inverse trigonometric functions, Areas and Volumes of solids of revolution, some differential equations), Combinatorics, Proof (with particular focus on Proof by Mathematical Induction), Vectors (with application to projectile motion), Statistical Analysis. In first semester their mathematical studies then covered a number of topics the Advanced1 group studied prior to gaining entrance at university; further details on this are given below.
The Advanced1 group’s mathematics high school syllabus studied prior to first semester course entry covered: the same course content the Standard group covered at high school plus extra topics on Proof (develop rigorous mathematical arguments and proofs, specifically in the context of number and algebra and further develop Proof by Mathematical Induction), Vectors (3 dimensional vectors, vector equations of lines), Complex Numbers, Calculus (Further Integration techniques with partial fractions and integration by parts), Mechanics (Application of Calculus to Mechanics with simple harmonic motion, modelling motion without and with resistance, projectiles and resisted motion). The Standard group cover these topics in their first semester university studies in mathematics with the exclusion of further concepts of Proof or Mechanics. In first semester the Advanced1 group have built on their knowledge with an emphasis on both theoretical and foundational aspects, as well as developing the skill of applying mathematical theory to solve practical problems. Theoretical topics include a host of theorems relevant to the study of Calculus.

In summary, at the point of our study, the Advanced1 group had more knowledge and practice on rigorous mathematical arguments and proofs in the context of number and algebra, and more in-depth experience with Proofs by Induction, but the bulk of extra knowledge rests with a much deeper knowledge of Calculus. They have had longer experience with a variety of integration techniques, and have worked with a variety of applications of calculus to solve practical problems, including a large section on mechanics at high school. In first semester at university there has been a greater focus on theoretical topics including a host of theorems and associated proofs relevant to the topics studied. As compared to the Introductory and Standard groups, the Advanced1 group have only widened the mathematics knowledge gap since their choice of post-compulsory mathematics at high school. The Advanced2 group come directly from an Advanced1 cohort. And the Academics group would have reached the Advanced1 group’s proficiency as part of their employment. So, are specific reasoning skills resulting from this level of abstract reasoning? Our findings suggest this should certainly be an area of investigation and links in interestingly with other research work. In studying one of the thinking tasks in particular (the Four Cards Problem) and its context of conditional inference more specifically, Inglis and Simpson [ 15 ] found a clear difference between undergraduates in mathematics and undergraduates in other university disciplines, yet also showed a lack of development over first-year university studies on conditional inference measures. A follow up study by Attridge and Inglis [ 22 ] then zeroed in on post-compulsory high school mathematical training and found that students with such training did develop their conditional reasoning to a greater extent than their control group over the course of a year, despite them having received no explicit tuition in conditional logic. The development though, whilst demonstrated as not being the result of a domain-general change in cognitive capacity or thinking disposition, and most likely associated with the domain-specific study of mathematics, revealed a complex pattern of endorsing more of some inferences and less of others. The study here focused on a much broader problem set associated with logical and critical thinking and it too is suggestive of a more complex picture in how mathematics training may be contributing to problem solving styles. A more intricate pattern to do with the impact of mathematical training on problem solving techniques is appearing as required for consideration.

There is also a final interpretation to consider: that people in the Advanced 1, Advanced2 and Academic groups did not gain anything from their mathematics training in terms of their ability to solve these problems. Instead, with studies denying any correlation of many of these problems with what is currently measured as intelligence [ 30 ], they might still be people of a particular intelligence or thinking disposition to start with, who have been able to use that intelligence to not only solve these problems, but also survive the challenges of their mathematics training.

That the CRT has been traditionally used as a measure of baseline thinking disposition and that performance has been found to be immutable across groups tested is of particular interest since our results show a clear possible training effect on these questions. CRT is tied with a willingness to engage in effortful thinking which presents as a suitable ability for training. It is beyond the scope of this study, but a thorough review of CRT testing is suggestive of a broader appreciation and better framework to understand thinking disposition, ability and potential ability.

Mathematical training appears associated with certain thinking skills, but there are clearly some subtleties that need to be extricated. The thinking tasks here add to the foundational results where the aim is for a firmer platform on which to eventually base more targeted and illustrative inquiry. If thinking skills can be fostered, could first year university mathematics teaching be improved so that all samples from that group reach the Advanced1 group level of reasoning? Do university mathematics courses become purely about domain-specific knowledge from this point on? Intensive training has been shown to impact the brain and cognition across a number of domains from music [ 34 ], to video gaming [ 35 ], to Braille reading [ 36 ]. The hypothesis that mathematics, with its highly specific practice, fits within this list remains legitimate, but simply unchartered. With our current level of understanding it is worth appreciating the careful wording of the NYU Courant Institute on ‘Why Study Math?’ where there is no assumption of causation: “Mathematicians need to have good reasoning ability in order to identify, analyze, and apply basic logical principles to technical problems.” [ 37 ].

Limitations

One possible limitation of the current study is that the problems may have been too easy for the more advanced people, and so we observed a ceiling effect (i.e., some people obtained 100% correct on all problems). This was most obvious in the Advanced1, Advanced2 and Academic groups. It is possible that participants in these groups had developed logical and critical thinking skills throughout their mathematical training that were sufficient to cope with most of the problems used in this study, and so this would support the contention that training in mathematics leads to the development of logical and critical thinking skills useful in a range of domains. Another interpretation is that participants in these groups already possessed the necessary thinking skills for solving the problems in this study, which is why they are able to cope with the material in the advanced units they were enrolled in, or complete a PhD in mathematics and hold down an academic position in a mathematics department. This would then suggest that training in mathematics had no effect on abstract thinking skills—people in this study possessed them to varying extents prior to their studies. This issue might be settled in a future study that used a greater number of problems of varying difficulties to maximise the chances of finding a difference between the three groups with the most amount of training. Alternatively, a longitudinal study that followed people through their mathematics training could determine whether their logical and critical thinking abilities changed throughout their course.

A further limitation of the study may be that several of the reasoning biases examined in this study were measured by only one problem each (i.e., Four Cards Problem, Two Drivers, Petrol Station, Jack looking at Anne). A more reliable measure of these biases could be achieved by including more problems that tap into these biases. This would, however, increase the time required of participants during data collection, and in the context of this study, would mean a different mode of testing would likely be required.

Broad sweeping intuitive claims of the transferable skills endowed by a study of mathematics require evidence. Our study uniquely covers a wide range of participants, from limited mathematics training through to research academics in the mathematical sciences. It furthermore considered performance on 11 well-studied thinking tasks that typically elude participants in psychological studies and on which results have been uncorrelated with general intelligence, education levels and other demographic information [ 15 , 16 , 30 ]. We identified different performances on these tasks with respect to different groups, based on level of mathematical training. This included the CRT which has developed into a method of measuring baseline thinking disposition. We identified different distributions of types of errors for the mathematically trained. We furthermore identified a performance threshold that exists in first year university for those with high level mathematics training. This study then provides insight into possible changes and adjustments to mathematics courses in order for them to fulfil their advertised goal of reaching improved rational and logical reasoning for a higher number of students.

It is central to any education program to have a clear grasp of the nature of what it delivers and how, but arguably especially so for the core discipline that is mathematics. In 2014 the Office of The Chief Scientist of Australia released a report “Australia’s STEM workforce: a survey of employers” where transferable skills attributed to mathematics were also ones that employers deemed as part of the most valuable [ 38 ]. A better understanding of what mathematics delivers in this space is an opportunity to truly capitalise on this historical culture-crossing subject.

Supporting information

Acknowledgments.

The authors would like to thank Jacqui Ramagge for her proof reading and input, as well as support towards data collection.

Funding Statement

The authors received no specific funding for this work.

Data Availability

PLoS One. 2020; 15(7): e0236153.

Decision Letter 0

17 Mar 2020

PONE-D-20-01159

Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors

Dear Professor Speelman,

Thank you for submitting your manuscript to PLOS ONE. I have sent it to two expert reviewers and have received their comments back. As you can see at the bottom of this email, both reviewers are positive about your manuscript but raise some issues that you would need to address before the manuscript can be considered for publication. Notably, reviewer #1 points out that the manuscript should include a discussion on the reasons why individuals with math training may have improved reasoning skills (e.g., logical intuitions versus deliberate thinking). The reviewer also rightly mentions that your sample sizes are limited, notably for the most advanced groups. This should be discussed and acknowledged. Reviewer #2 has a number of conceptual and methodological points that you will also have to address. The reviewer provides very thorough comments and I will not reiterate the points here. However, note that both reviewers suggest that you need to improve the figures and I agree with them.

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Reviewers' comments:

Reviewer #1: I think this is a very good and interesting manuscript trying to answer an important research question. I propose some changes that I believe should be applied before publication.

1. Each reasoning bias is measured with only one problem. In reasoning research, it is rather common to measure each type of reasoning problem with a series of structurally equivalent reasoning problems, so the results will be independent of contexts effects and will be generalizable to that type of problem. Here, the authors only measured each reasoning bias with one single problem and this might be problematic (see, for example: Fiedler & Hertel, 1994). I think this can be addressed by simply discussing it in the limitation section.

2. This is rather a minor issue, but the discussion on the CRT problems is not up-to-date (page 7). Most recent experiments on dual process theory suggest that people who are able to correctly solve these reasoning problems (including the CRT) do so intuitively, and not because they engaged in careful deliberation (Bago & De Neys, 2019). Intelligence made people have better intuitive responses (Thompson, Pennycook, Trippas & Evans, 2018). Similarly, this problems persists in the discussion about reaction times (page 25). Longer reaction times does not necessarily mean that people engaged in deliberation (see: Evans, Kyle, Dillon & Rand, 2015). Response time might be driven by decision conflict or response rationalization. These issues could be clarified with some changes in the wording or some footnotes on page 7 and 25. Furthermore, it would be interesting to have a discussion on how mathematical education helps people overcome their biases. Is it because it creates better intuition, or helps people engage in deliberation? An interesting question this manuscript does not discuss. It’s on the authors whether or not they discuss this latter point now, but the changes on page 7 and 25 should be made.

3. A more serious problem is the rather small sample size (especially in the more advanced groups). This small sample size makes the appearance of both false negatives and false positives more likely. Perhaps, the authors could compute the Bayes Factors for the chi-square or logistic regression test, so we can actually see how strong the evidence is for or against the null. This is especially important as the authors run a great number of explorative analysis (Table 3), and some of those results might need to be interpreted with great caution (depending on the Bayes Factor).

The graphs are not looking good, they should comply with APA formatting. At the very least, the axis titles should be meaningful and measure units should be written there.

The presentation order of the problems is quite unusual; why isn’t it random? Why did the authors decide on this order?

Reviewer #2: The study reported in this paper compared five groups of participants with varying levels of mathematical expertise on a set of reasoning tasks. The study is interesting and informative. It extends the current literature on this topic (which is reviewed very nicely in the introduction). However, there are some issues with the current analysis and interpretation that should be resolved prior to publication. I have therefore recommended major revisions. My comments are organised in the order in which they came up in the paper and they explain my responses to the questions above.

1. Line 114 – “general population” a bit misleading – they were also students but from other disciplines.

2. Line 124 onwards reads:

“The ultimate question to consider here is: are any skills associated with mathematics training innate or do they arise from skills transfer? Though to investigate how mathematical training affects reasoning skills, randomised sampling and randomised intervention to reveal causal relationships are clearly not viable. With so many possible confounding variables and logistical issues, it is even questionable what conclusions such studies might provide. Furthermore, a firm baseline from which to propose more substantive investigations is still missing.”

I find this paragraph slightly problematic because the current study doesn’t inform us on this ultimate question, so it makes the outline of the current study in the following paragraph feel unsatisfactory. I think the current study is important but prefacing it with this paragraph underplays that importance. And I think a randomised controlled study, although not viable, would give the answers we need because the random allocation to groups would allow us to rule out any confounding variables. Finally, the last sentence in this paragraph is unclear to me.

3. In the descriptions of the five participants groups the authors refer to the group’s level of interest in mathematics, but this seems like an overgeneralisation to me. Surely the introductory group could contain a biology student who also happens to be good at mathematics and very much enjoy it? I would be more comfortable with the descriptions if the parts about interest level were removed.

4. How many of the 123 first year students were in each of the three first year groups?

5. Line 313 – the standard group is referred to as “university mathematics students”, but they are not taking mathematics degreed.

6. Line 331 - what is a practice class?

7. Were the data collection settings quiet? From the description it sounds like groups of participants were completing the study at the same time in the same room, but the authors should make this explicit for the sake of the method being reproducible. E.g. how many students were in the room at the time?

8. Line 355-356 – the authors should not use the term “marginally worse” because this is statistically inappropriate – in a frequentist approach results are either significant or non-significant.

9. Line 340 – “approximate completion times were noted.”

This doesn’t sound rigorous enough to justify analysing them. Their analysis is interesting, but the authors should remind readers clearly whenever the response times are analysed or discussed that their recording was only manual and approximate.

10. I suggest replacing Figure 1 with a bar chart showing standard error of the mean on the error bars. A table with mean score out of 11 and the standard deviation for each group may also be useful. Figure 2 should be a scatterplot rather than a box and whisker plot.

11. Was the 0-11 total correct score approximately normally distributed across the full sample?

12. Chi square analysis requires at least 5 cases in each cell, was this met? It seems not since Table 1 shows lots of cells in the “no response” row having 0% of cases.

13. The chi-square analyses should be followed up with post hoc tests to see exactly where the differences between groups are. The descriptions as they stand aren’t that informative (as readers can just look at Table 1) without being backed up by post hoc tests.

14. For each chi square analysis in the text, I would find it easier to read if the test statistics came at the top of the paragraph, before the description.

15. Line 381-383 – “Of note, also, is the relatively low proportion of those in the higher training groups who, when they made an error, did not make the standard error, a similar result to the one reported by Inglis and Simpson [11]."

I think this is supposed to say that a low proportion did make the standard error or that a high proportion did not make the standard error.

16. Line 403 - p values this small should be reported as p < .001 rather than p = .000 since they aren’t actually 0.

17. Line 476 – “…if a particular outcome variable was predicted significantly by a particular predictor variable, the converse relationship was also observed”

Isn’t that necessarily the case with regression analyses, like with correlations?

18. I don’t think the logistic regression analyses add much to the paper and at the moment they come across as potential p-hacking since they don’t clearly relate to the research question. To me they make the paper feel less focused. Having said that, there is some interesting discussion of them in the Discussion section. I’d recommend adding some justification to the introduction for why it is interesting to look at the relationships among tasks (without pretending to have made any specific hypotheses about the relationships, of course).

19. Line 509 would be clearer if it read “between these groups and the introductory and standard groups”

20. Lines 597 – 620 - This is an interesting discussion, especially the suggestion that advanced calculus may be responsible for the development. No development in reasoning skills from the beginning of a mathematics degree onwards was also found by Inglis and Simpson (2009), who suggested that the initial difference between mathematics and non-mathematics undergraduates could have been due to pre-university study of mathematics. Attridge & Inglis (2013) found evidence that this was the case (they found no difference between mathematics and non-mathematics students at age 16 but a significant difference at the end of the academic year, where the mathematics students had improved and the non-mathematics students had not).

Could the authors add some discussion of whether something similar may have been the case with their Australian sample? E.g. do students in Australia choose whether, or to what extent, to study mathematics towards the end of high school? If not, the description of the groups suggests that there were at least differences in high school mathematics attainment between groups 1-3, even if they studied the same mathematics curriculum. Do the authors think that this difference in attainment could have led to the differences between groups in the current study?

21. Line 617 – “Intensive training has been shown to impact the brain and cognition across a number of domains from music, to video gaming, to Braille reading [31].”

Reference 31 appears to only relate to music. Please add references for video gaming and Braille reading.

22. I recommend editing the figures from SPSS’s default style or re-making them in Excel or DataGraph to look more attractive.

23. I cannot find the associated datafile anywhere in the submission. Apologies if this is my mistake.

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Author response to Decision Letter 0

20 Apr 2020

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Decision Letter 1

11 Jun 2020

PONE-D-20-01159R1

Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors.

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Reviewer #2: The manuscript has improved but there are still a few issues that should be resolved prior to publication.

1. On lines 96, 97, 100 and 102, the references to “general population” should be changed to reflect the fact that these participants were non-mathematics (arts) students.

2. Line 306 – change “mathematics students” to “university students”.

3. The method section doesn’t specify the gender split and mean age of the sample.

4. Table 3 - values the p values listed as .000 should be changed to <.001.

5. Table 3 - I suggest repeating the list of problem numbers and names in the legend. It may make for a long legend but would make it much easier for the reader to interpret the table.

6. I am not sure what the new post hoc tests are comparing. What I expected was to see group 1 compared to groups 2, 3, 4 and 5, and so on. This would tell us which groups are statistically different from each other. At the moment we only know from the overall chi square tests whether there are any differences among the groups or not, we don’t know specifically which groups are statistically different from each other and which ones are not. We only have the authors’ interpretations based on the observed counts.

7. Line 584 - change “performance was correlated with training” to “performance was related to training” to avoid any confusion since a correlation analysis was not performed.

8. Data file – I had expected the data file to give the raw data rather than summary data, i.e. with each participant in a separate row, and a column indicating their group membership, a column giving their age, a column for sex etc (including all the demographics mentioned in the method), and a column for each reasoning question. This would allow other researchers to replicate the regression analyses and look at other relationships within the dataset. Without being able to replicate all analyses in the paper, the data file does not meet the minimal data set definition for publication in PLOS journals: https://journals.plos.org/plosone/s/data-availability .

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Author response to Decision Letter 1

16 Jun 2020

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Logic Ab Initio: A Functional Approach to Improve Law Students’ Critical Thinking Skills

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While certainly not suggesting that formal logic training would remedy all that ails legal education or even that it could enhance critical thinking for all students, this article asserts that law schools should make the process of legal reasoning more transparent and explicit from the outset, and proposes techniques that can be adopted quickly with minimal institutional costs or upheaval. Part I examines possible reasons that law-school matriculants increasingly lack critical-thinking skills needed for success. Part II maps out three basic components of informal logic training: deductive reasoning, inductive reasoning, and fallacy. It then identifies related law-school competencies that could be enhanced through training in these areas. Part III proposes a relatively painless method of incorporating functional logic training across the law-school curriculum. Given the breadth and depth of the critical thinking deficit, this approach presents a pragmatic—though admittedly imperfect—solution to the problem.

“Logic!” said the Professor half to himself. “Why don’t they teach logic at these schools?” ― C.S. Lewis , The Lion, the Witch, and the Wardrobe

Law professors and legal employers alike lament a modern trend of diminishing critical-thinking skills among law students and new graduates. [1] These concerns are not imaginary: a recent study that followed thousands of undergraduates through college concluded that large proportions of college graduates lacked critical thinking, complex reasoning, and written communication skills once thought to be the foundation of university education. [2] This means that law schools are increasingly enrolling students who lack the skill set traditionally associated with law-school success. [3] To complicate matters, this critical-thinking crisis comes at a time when law schools face stricter and more detailed accreditation standards than ever before. [4]

The concept of “critical thinking” has many overlapping definitions. [5] It’s been described as an “intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, [] or evaluating information.” [6] In cognitive terms, critical thinking is “problem solving in situations where ‘solutions’ cannot be verified empirically.” [7] In the specific context of legal education, critical thinking can be broadly described as “questioning knowledge.” [8] It requires students to remember, understand, and apply both law and facts, and then analyze, evaluate, and integrate that knowledge to determine “what is important, what is missing, and what is vague.” [9] In this respect, critical thinking is the “foundation for the ‘key intellectual tasks’ associated with the sophisticated higher order thinking required in law school.” [10]

We are all born with the ability to think, but critical thinking generally requires considerable training and hard work. [11] The ancient philosophers excelled at critical thinking because most formal learning involved—to a greater or lesser extent—the mastery of logic. [12] Classical philosophers like Aristotle practiced “formal” logic, so named because of its emphasis on the “form,” or structure, of the argument. [13] To formal logicians, whether the substance of an argument was true or false was unimportant. Their focus was on the argument’s logical structure and whether the form itself was reliable. [14] Those ancient philosophers spent considerable time thinking about how they were thinking and, were, perhaps, the first true metacognitive [15] thinkers.

But formal logic was and remains a discipline requiring rigorous training—an impractical detour on the path to critical thinking in law school. Therefore, requiring a course in formal logic in law school is much like using a sledgehammer to crack a nut: the benefit is outweighed by the collateral damage. What’s needed is a practical method harnessing the metacognitive benefits of logic that fits unobtrusively into existing law-school curricula. By introducing informal or “functional” logic into the curriculum, law schools can not only enhance students’ comprehension of individual lessons, but make them better overall thinkers.

The late Judge Ruggero Aldisert was an outspoken proponent of teaching logic to law students. In 1989, he published Logic for Lawyers: A Guide to Clear Legal Thinking , [16] a text that cogently explained that the basics of legal reasoning, including the use of precedent, are merely variations of deductive and inductive reasoning—the building blocks of logic. Logic for Lawyers coincided with a late-20 th and early-21 st century burst of legal scholarship exploring the relationship between law and classical logic and rhetoric. [17] In 2007, Judge Aldisert published the article Logic for Law Students: How to Think Like a Lawyer , [18] a more streamlined version of his earlier work, “explain[ing], in broad strokes, the core principles of logic and how they apply in the law-school classroom.” [19]

This article builds on Judge Aldisert’s premise that “thinking like a lawyer”—critical thinking—means “employing logic to construct arguments.” [20] It goes a step further, however, proposing that training law students to use logic would not only provide professors and students a common language to identify specific deficiencies in analysis, it could actually increase students’ cognitive capacity for critical thinking.

While certainly not suggesting that such training would remedy all that ails legal education or even that it could enhance critical thinking for all students, this article asserts that law schools should make the process of legal reasoning more transparent and explicit from the outset, and proposes techniques that can be adopted quickly with minimal institutional costs or upheaval. Part I examines possible reasons that law-school matriculants increasingly lack critical-thinking skills needed for success. Part II maps out three basic components of informal logic training: deductive reasoning, inductive reasoning, and fallacy. It then identifies related law-school competencies that could be enhanced through training in these areas. Part III proposes a relatively painless method of incorporating functional logic training across the law-school curriculum. Given the breadth and depth of the critical thinking deficit (detailed below), this approach presents a pragmatic—though admittedly imperfect—solution to the problem.

Part I: A Lack Of Critical-Thinking Skills And (Some) Reasons For It

Success in law school (as opposed to success in most undergraduate disciplines) requires skills beyond mastery of facts, dates, formulas, and established theories and positions of academics. It requires independent reasoning. [21] And that reasoning cannot be theoretical or abstract: it must comport with societal norms of justice, fairness, and overall propriety. [22] Furthermore, that reasoning must be drawn from—and remain consistent with—numerous sources of law. Legal reasoning must be sound and valid; in other words, it must be logical. But increasingly, students come to law school ill-equipped for this type of rigor. [23] In recent years, law student credentials have decreased across the board: between 2010 and 2013, the median score of the Law School Admission Test (“LSAT”), which purports to measure critical-thinking skills, declined from 157 to 155. [24] In fact, nearly ninety percent of law schools had a lower median LSAT score in 2013 than in 2010. [25]

As to the cause, there is no shortage of finger pointing. Professor Jay Sterling Silver has opined that primary education—often undertaken in overcrowded public schools, where learning is geared toward mastery of standardized tests—teaches students not to think. [26] Professors Susan Stuart and Ruth Vance blame federal law, specifically noting that the current generation of law-school matriculants has been almost wholly educated under No Child Left Behind, which, since enactment in 2001, has shifted primary education focus towards mandatory achievement of minimum skill. [27] Others point to systematic grade inflation at the undergraduate level as contributing to students’ inflated opinion of their competency. [28] Still others suggest that institutional use of student evaluations as part of tenure decisions contributes to lower teaching standards. [29] Moreover, there appears to be no end in sight to the decline, given educational, social, and technological trends.

It’s likely impossible to identify the contributing factors exhaustively. But, as explained below, trends in undergraduate education and technology partly explain why students generally seem to have adopted a more shallow, heuristic method of thinking. This is particularly true of the Millennial generation, whose unique cultural characteristics make them all the more prone to such thinking shortcuts.

a. The Changing Nature of Undergraduate Education

Undergraduate education has changed over the last fifty years. [30] Some scholars theorize that modern law students lack adequate thinking skills partly because undergraduates no longer receive the benefit of a classical liberal-arts education. [31] A foundation in the liberal arts was long presumed to prepare students “to become civic and professional leaders, to prepare them for lifelong learning and inquiry.” [32] These students were well versed in the humanities, logic, and rhetoric, and developed “communication skills through a variety of oral and written exercises.” [33] This liberal education, focused on flexibility, creativity, critical thinking, analysis, and written communication, [34] would, unsurprisingly, prepare a college graduate to successfully participate in and benefit from the rigors of a law-school classroom. [35]

But while classic liberal-arts education did indeed mold creative and well-rounded learners for many decades, colleges and universities—along with students and their parents—have, over time, become increasingly dubious of its practical value. Knowledge of classical literature, arts, and natural sciences does not provide specific, marketable competencies for a defined entry-level job. [36] Some presume that a broad, liberal-arts education is unlikely to lead to the same level of monetary reward as, for example, a Master’s degree in Business Administration [37] or Engineering. [38] As a result, undergraduate institutions in the United States have, since the 1970s, shifted curricular emphasis from liberal arts to more professionally-oriented or vocational training. [39]

Colleges and universities now promise to prepare students for specific careers. But a classic liberal-arts program used classic literature, history, the arts, and natural sciences (as opposed to applied sciences) to shape thinkers who could, presumably, succeed in any number of careers. “The essential paradox, or one might even say the miracle of liberal education, is that by being evidently impractical, it equips a student for life far more richly and completely, and across a far wider expanse of time and space, than does education whose sole aim is to be useful.” [40]

Whether caused by an institutional shift away from liberal arts or some other phenomenon, the decrease in critical-thinking skills in undergraduates is well documented. In 2011, two researchers, Richard Arum and Josipa Roksa, collected empirical evidence of a downward trend in critical-thinking skills in undergraduates. Their book, Academically Adrift , proposed that undergraduates are overwhelmingly distracted by work, social lives, and an educational culture that puts learning low on the priority list. [41] Arum and Roksa collected data using the Collegiate Learning Assessment (“CLA”), a test comparing similarly situated students from a wide variety of colleges and universities. [42] The test measured critical thinking, analytical reasoning, problem solving, and writing skills, all of which are essential during the first year of law school. [43] The study tracked the academic progress of 2,322 students, scoring them once in their first semester of college and again at the end of their fourth semester (half-way through college). The study found that forty-five percent of students gained virtually no critical thinking, complex reasoning, or writing skills over the assessment period:

While these students may have developed subject-specific skills . . . , in terms of general analytical competencies assessed, large numbers of U.S. college students can be accurately described as academically adrift. They might graduate, but they are failing to develop the higher-order cognitive skills that it is widely assumed college students should master. [44]

Other studies have painted an equally grim picture of college graduates’ critical-thinking skills. The Wabash National Study of Liberal Arts Education, [45] conducted in 2006-2007, concluded that thirty percent of undergraduates tested showed no growth—or even declined—in critical-thinking skills after completing four years of college. [46] These results confirmed those of earlier studies, which also suggested a long-term decline in skills acquisition among undergraduates. [47]

Arum & Roksa’s study revealed another disturbing problem: universities participating in the assessment were not closing the achievement gap experienced by socioeconomically disadvantaged students. [48] In the initial, freshman-year CLA assessments, minorities and students from less-educated families scored significantly lower in critical thinking, complex reasoning, and writing than white students from more-educated families. [49] According to the study, this “achievement gap” between privileged students and their less-advantaged peers only increased after the first year of college. In other words, “[t]he results of the CLA ‘suggest higher education . . . reproduces social inequality,’” [50] insofar as it correlates to lack of critical thinking skills. Accordingly, the critical thinking necessary for law school is likely foreign to students who lack that privilege. [51] Law schools that purport to promote diversity and equal opportunity in learning simply cannot ignore such data.

The effect of this achievement gap is brought into sharper focus by the recent, colossal downturn in law-school applications. Higher-tier schools made up for the deficit in applications by accepting students they previously would never have considered. [52] Those students were effectively pilfered from middle-tier schools, which made up for their own losses by accepting students who they, in turn, would previously have rejected. [53] But this left many lower-tier schools, particularly those created to provide opportunities for minorities or other at-risk students, with an existential crisis: disappear, or continue the valuable mission with less-qualified and, presumably, less-prepared students. At the end of the day, nearly every law school has been left with a student cohort less likely than previous ones to pass the bar exam. [54]

The ostensible decrease in critical thinking in college graduates across socioeconomic spectrums impacts more than just individual students. A first-year law student who has never had the opportunity to disagree with a professor or to independently form opinions about cultures based on their art, literature, or music will almost certainly struggle to synthesize seemingly inconsistent judicial opinions into a cogent legal principle. But a critical mass of students struggling on the same level will fundamentally change the dynamic of a law-school classroom and prevent the purposeful exchange of ideas.

b. The Effect of Technology on Students’ Ability to Think

The effect of the digital age and the ubiquity of technology in nearly every detail of daily life cannot be understated when considering the reasons for waning critical thinking. “The Internet has made so much information available to us, more than we could possibly retain in our brains, that we are more often ‘handing off the job of remembering’ things to technology.” [55] But technology causes problems more worrisome than just intellectual laziness: technology is changing the way students learn.

Learning can be described as any “relatively permanent change in a neuron.” [56] Neurons are simply the brain’s cells which, when activated, release chemicals called neurotransmitters. Neurotransmitters connect neurons to other neurons, creating electrochemical pathways in the brain that form our thoughts, memories, emotions, and sensations. [57] When confronted with challenges, the human brain adapts by modifying existing neural connections. [58] This is known as brain plasticity or neuroplasticity. The brain can “efficiently reorganize allocation of its resources to meet demands and compensate for deficits.” [59] “Evolution has given us a brain that can literally change its mind—over and over again.” [60] This means humans “can form bad neurological habits as well as good ones.” [61]

In The Shallows: What the Internet is Doing to Our Brains , author Nicholas Carr describes the subtle—yet ultimately profound—effects the Internet and other technological advances are having on human brains. Just as we can strengthen our mental capabilities through use of technology, Carr explains that human brains are subject to “intellectual decay.” [62] His collected research suggests that information and communication technologies are changing humans at a neurological level. [63]

For example, Carr posits that the Internet has supplanted reading as the primary source of information gathering (as did television, to some extent, before it). In terms of neurological development, the emergence of reading—particularly the “deep reading” necessary to consume literature and other book-length works—rewired and optimized the human brain for “deep thinking.” [64] The ability to read not only expanded one’s knowledge; it allowed previously unattainable levels of comparison to thoughts and experiences of others. [65] To fully appreciate the written word, one would have to discipline one’s mind to “follow a line of argument or narrative through a succession of printed pages.” [66]

The Internet, in contrast, features small chunks of information punctuated with distracting hyperlinks, multimedia, and ads. These features activate the prefrontal cortex, overtaxing the brain, making online reading a “cognitively strenuous act.” [67] In response to this stress, Carr suggests, our brains’ plasticity kicks in, rewiring and optimizing neural connections (and pruning unnecessary ones) for this new, rapid method of information gathering. [68] His research shows that as little as five hours of Internet use can significantly rewire the neural circuitry of the prefrontal cortex. [69]

The triumph of the Internet as a single medium for communication and information gathering may, therefore, also be its greatest danger. Just as computers have evolved to function simultaneously as typewriters, encyclopedias, phones, televisions, and social gathering spaces, their users have, unsurprisingly, become skillful multi-taskers. [70] And the same plasticity that, over millennia, had optimized our brains for deep thinking is now strengthening the neural circuitry customized for “rapid and incisive spurts of directed attention” that enable multitasking. [71] Unfortunately, quick shifts of attention and multitasking are quite useless in a typical 1L classroom. The reasoned analysis necessary in law school is not achievable without focused attention for a sustained time period. [72] Thus, critical thinking takes another hit thanks to technology.

One last insult to critical thinking occurs as a result of “The Google Effect.” [73] This phenomenon describes the automatic forgetting of information that can be found online. [74] Neuropsychologists know that, to maintain efficiency, our brains constantly—and subconsciously–prune memories. [75] Since there is less need to preserve information that can be readily retrieved, facts and ideas are more often pruned when the brain perceives that the information will be archived. [76] For law students faced with hundred-page reading assignments and looming deadlines, this phenomenon would appear rational and advantageous. Sometimes, “the effort needed to acquire knowledge outweighs the advantage of having it.” [77] The Google Effect could, therefore, be further eroding law students’ capacity for successful legal analysis. For example, a student accustomed to efficient and fruitful Internet searches will have little success using those techniques to brief a case before class. In the context of legal research, the wide-cast net of a Google search will yield poor results in comparison to a systematic, linear exploration of legal sources made possible by understanding jurisdictional structure. [78] Rule-based subjects, such as Civil Procedure and Evidence, which require memorization of rules as building-blocks of greater concepts, [79] could be challenging for a student whose brain is unaccustomed to storing large amounts of data. As technology rapidly pushes aside millennia of neurological refinements allowing for deep thinking and logical reasoning, legal education will likely have to adapt.

c. Millennial Zeitgeist and Beyond

Shifts in undergraduate education and technology may indeed be the two main ingredients for the collective deficits in critical-thinking skills of matriculating law students. But the culture and attitudes of the 21 st Century could be the seasoning that makes those deficits so unpalatable in the context of law-school learning. It’s all too easy to blast the Millennial generation [80] for its (real or imagined) lack of intellectualism, [81] perfunctory knowledge of history, [82] or narcissism. [83] But Millennials are also more socially conscious and idealistic than previous generations. [84] Their early exposure to computers and the Internet make them “the most technologically savvy and resourceful generation yet to hit the law school scene.” [85] They are “education-oriented, career-minded, motivated, connected, and self-confident.” [86] These same characteristics have led some scholars to brand Millennials as overconfident and entitled. [87]

In the context of legal education, overconfidence should be distinguished from confidence. Students who matriculate to law school have generally achieved much: They have completed a Bachelor’s degree—at least—with enough success to be accepted into a graduate-level program. [88] They have succeeded on the LSAT to the extent that their scores have earned them a place in an entering law-school class. Non-traditional students entering law school as a second or third career may have already achieved business success. As a result of this widely varied success, many students come to law school overestimating their intellectual abilities. [89] Often, students “express high academic expectations and professional ambitions but fail to realistically appreciate the necessary steps to achieve their goals.” [90]

This pattern is consistent with a fascinating psychological phenomenon known as the Dunning-Kruger Effect. The Dunning-Kruger Effect [91] was proposed in 1999 by David Dunning and Justin Kruger, cognitive psychologists at Cornell University. Their study concluded that unskilled people generally hold overly favorable views of their intellectual abilities. This overestimation of ability increases as actual ability decreases. In other words, incompetence “robs [the incompetent] of the metacognitive ability to realize” they are incompetent: [92]

[S]kills that engender competence in a particular domain are often the very same skills necessary to evaluate competence in that domain—one’s own or anyone else’s. Because of this, incompetent individuals lack what cognitive psychologists variously term metacognition, metamemory, metacomprehension , or self-monitoring skills. These terms refer to the ability to know how well one is performing, when one is likely to be accurate in judgment, and when one is likely to be in error. [93]

Dunning and Kruger’s study is particularly interesting considering that the researchers used logical reasoning skills—in the form of LSAT questions—as one of the metrics for measuring the effect. [94] Overall, subjects (forty-five Cornell undergraduates) overestimated their logical reasoning skills relative to their peers. [95] But bottom quartile subjects overestimated their performance by a staggering degree: although they scored at the 12th percentile on average, they nevertheless estimated that their general logical reasoning ability fell at the 68th percentile. [96] In other words, the poorest performers considered themselves significantly above average.

The point, of course, is not that law-school matriculants are incompetent. But the existence of the Dunning-Kruger effect may shed light on why those students most lacking in critical-thinking skills are either unaware of their deficits or are unable to rectify them. [97] More importantly, it suggests that students would benefit from learning specific metacognitive skills at an early stage in law school so that they can evaluate their own analytical competence before and after graduation.

Whatever the reasons for the (real or perceived) lack of critical thinking skills, a more appropriate discussion is what law schools can do to address any real deficits. There is no definite etiology for dwindling reasoning skills, nor is there any real need to articulate one. But if legal educators sense that “things are not as they were,” and that observation is coupled with increasing attrition rates or decreasing bar exam success, [98] then we must take corrective measures.

Part II: The Basics of Logic and Related Law-School Competencies

Law schools purport to teach students to “think like lawyers.” [99] But despite the need for clear and logical reasoning in the legal profession, law schools do not teach principles of logic. [100] Or do they?

The fact is that modern law curricula do use principles of logic—without denominating them as such. Law-school competencies—identifying issues, articulating rules and exceptions, comparing precedent to new facts, understanding public policy, addressing counterarguments—all require some form of logical reasoning. When law students apply a general legal rule to a specific legal issue on an exam, they engage in deductive reasoning. When students synthesize precedent into a general legal principle in legal writing class, they engage in inductive reasoning. When students argue in a brief or oral argument that a particular precedent should be followed, they engage in reasoning by analogy. [101]

But often, students see these law-school learning methods as nothing more than their professors’ personal methodological preferences. [102] They fail to appreciate that these techniques have been tested over thousands of years by history’s greatest thinkers. Hence the need for basic logic training: exposing neophyte law students to the basic principles of logic could provide them and their professors a common language to identify and correct deficits in reasoning and critical thinking. In addition, such training could—through the magic of brain plasticity—remediate deficiencies in cognitive analytical ability and foster better learning.

The principles of logic that could benefit a law-school curriculum in this way represent only a fraction of the discipline of formal logic. It would be impractical and counterproductive to teach a comprehensive additional discipline in the already-crowded list of required subjects. Sufficient metacognitive benefits can be achieved through exposure to three fundamental principles of logic: deductive reasoning, inductive reasoning, and fallacy. [103] While philosophers may cringe at such attenuation of the Art of Aristotle, Aquinas, and Wittgenstein, [104] the goal is not to teach logic for its own sake. It is to provide students with a practical—perhaps heuristic—method for evaluating the quality of their reasoning. In short, one “familiar with the basics of logical thinking is more likely to argue effectively than one who is not.” [105]

a. Deductive Reasoning and Rule Application

Perhaps the easiest logic principle to teach law students is deduction, a lawyer’s most fundamental skill. [106] This process of reflective thinking [107] moves from general truth to specific conclusion. [108] In its simplest form, deduction involves two propositions which, if true, taken together lead undeniably to a third proposition. The classic tool of deductive reasoning is the syllogism, [109] demonstrated by this ubiquitous example:

All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

The reliability of a syllogism comes from the objective certainty that the conclusion follows from the truth of the first two propositions, or “premises.” [110] The first, the “major premise,” represents a universal truth. The second, the “minor premise,” represents a specific and more narrowly applicable fact. The third, the conclusion, is a new idea that follows inferentially from the truth of the first two premises. It is this progression of thought, based on the relationship between known truths, that instills confidence in the resulting conclusion. [111]

Logicians test the validity of a syllogism by analyzing the patterns of the terms within each premise. [112] Each of the three premises is made up of two terms: a subject term (e.g., “All humans”) and a predicate term (“are mortal”). The specific idea contained in each of these terms appears twice in the syllogism. The “major term” appears in the major premise and the conclusion. The “minor term” appears in the minor premise and the conclusion. The “middle term” appears in the major and minor premises but not the conclusion. [113] So, in the Socrates example, “mortal” is the major term, “human” is the middle term, and “Socrates” is the minor term. [114]

All humans are mortal. Middle Term , Major Term

Socrates is a human . Minor Term , Middle Term

Therefore, Socrates is mortal. Minor Term, Major Term

Each term can further be described as “distributed” or “undistributed.” A subject term is distributed if it represents all members of the class and is undistributed if it represents only part of a class. [115] A predicate term is distributed if it is a negative statement and undistributed if it is a positive statement. [116] Only certain patterns of distributed and undistributed terms can be valid syllogistic forms. [117]

In the legal context, the syllogism involves taking a legal premise (an enacted or judicially created “rule”) and applying it to a factual premise (the facts of a case) to reach an objectively sound result (the conclusion). Judge Aldisert used a generic template, which he called the “prosecutor’s model,” to illustrate this fundamental “categorical syllogism” of legal reasoning:

Major premise: [Doing something] [violates the law] Minor premise: [The defendant] [did something] Conclusion: [The defendant] [violated the law]. [118]

The benefits of presenting legal ideas in this structured way are manifest. The structure promotes clarity and consistency and prevents many analytical errors. [119] It allows one to test the accuracy of individual arguments by observing each step of the analytical process. For lawyers, who must routinely debunk opponents’ arguments, this reasoning skill is critical. [120] Another helpful structure is the conditional (or hypothetical) syllogism, which takes an “if-then” format. The “if” term is known as the “antecedent” and the “then” term is known as the “consequent.” To be valid, a conditional syllogism must take one of two forms. [121] One such form, known as modus ponens , [122] is structured,

If p , then q ; p , therefore q.

The syllogism is valid when the antecedent is “affirmed” as existing or being true. For example,

If a non-competition clause is not in writing, then it is unenforceable. The defendant’s agreement not to compete was oral. Therefore, it is unenforceable.

When the minor premise of a conditional syllogism negates the consequent of the major premise, the form is called modus tollens . [123]

If p , then q ; Not q , then therefore not p .

These conditional syllogism forms appeared in a recent Florida First District Court of Appeals case, Madison v. Florida. [124] In Madison , the majority reversed the defendant’s conviction on the grounds that the trial court had abused its discretion in failing to properly consider and grant the defendant’s motion for a continuance. [125] The deferential standard of review for abuse of discretion required “affirmance of the trial court order unless no reasonable judge could have reached the decision challenged on appeal.” [126] But, in his dissent, Judge T. Kent Wetherell pointed out that, when broken down into a modus tollens syllogism, the majority’s decision demonstrated flawed logic: If reasonable judges could disagree as to the propriety of the trial court’s ruling, then the trial court did not abuse its discretion.

The trial court abused its discretion. Therefore, reasonable judges could not disagree as to the propriety of the trial court’s ruling. [127]

If the majority’s conclusion that the trial court had abused its discretion were true, then the antecedent (reasonable judges could not disagree as to the propriety of the trial court’s ruling) would also have to be true. But Judge Wetherell—presumably a reasonable judge— did disagree. The syllogism, according to Judge Wetherell, revealed the majority’s illogic. [128] He then demonstrated that, because the antecedent was true, the consequent (the trial court did not abuse its discretion) must be true as well under modus ponens . [129] Alas, deductive logic did not carry the day in Madison . But the case cogently demonstrates the utility of breaking an argument into its fundamental parts: doing so reveals illogic and, simultaneously, suggests the better outcome.

This greatly attenuated description of deductive reasoning would be enough to start students on the path to recognizing syllogisms in judicial opinions and, more importantly, to “shoehorning” [130] their own arguments into the illuminating pattern of syllogistic thought. By thinking meaningfully about their thought processes in this way, students gain metacognitive skills that could improve overall learning.

b. Inductive Reasoning and Precedent

In areas where the law is unsettled, deductive logic is an insufficient reasoning tool. [131] If there is no universal “rule,” there can be no material for the major premise in syllogistic thinking. [132] In such cases, rules must be extracted from many specific outcomes. [133] This is the process of inductive reasoning. [134]

“Induction is the inference from the observed to the unobserved, occasionally, and rather loosely, termed inferring the general from the specific.” [135] Unlike deductive reasoning, where the conclusion follows absolutely from the premises, inductive reasoning does not produce conclusions guaranteed to be correct. [136] However, if one examines enough similar, specific outcomes, one can ascertain with some confidence the resulting new principle. [137]

Consider scientific research. A scientist conducts enough trials of an experiment to be able to observe a pattern in the results. Numerous similar results can then suggest a general hypothesis: if A, B, and C all have result X, then D (which is similar to A, B, and C) will probably also have result X. As long as the scientist conducts enough trials, he or she can have confidence in the accuracy of the hypothesis. [138] It is unlikely, however, that a scientist would suggest that simply repeating results consistently creates scientific proof or absolute certainty in the result. [139] The process of induction as applied to legal reasoning is no different.

Inductive reasoning generally takes one of two forms: inductive generalization (or enumeration) or reasoning by analogy. [140] The process of inductive generalization lies at the heart of common law: in the absence of codified law, the accumulation of many specific holdings in individual cases has led, over time, to common acceptance—and formal articulation—of generalized legal precepts or principles. [141] The common law, therefore, “is but the accumulated expressions of the various judicial tribunals in their efforts to ascertain what is right and just . . . .” [142] Again, this inductive process does not provide certainty. It yields probabilities and generalities—but often extremely reliable ones.

One instructive example of inductive generalization is found in Justice Cardozo’s opinion in the early products liability case of MacPherson v. Buick Motor Co. [143] The case involved an injury from a collapsed wooden wheel of an automobile. [144] At the time, lack of privity of contract between the automobile’s owner and the manufacturer would have prevented the injured owner from collecting damages from the manufacturer. [145] Rather than decide the case on established contract principles (as the dissent suggested), [146] Justice Cardozo used inductive reasoning to fashion a rule that avoided the unjust result existing law seemed to require. Cardozo compared the results of sixteen factually diverse products liability cases. [147] He identified relevant similar or divergent features between the cases, such as whether the defendant was a manufacturer and whether there was a near certainty of injury, should the product be defective. [148] By analyzing a large enough number of specific circumstances of liability and comparing relevant resemblances between them, Cardozo was able to derive a new (and yet, not new) principle: A manufacturer who constructs an automobile using defective component parts may be liable to a remote purchaser of the automobile for injuries resulting from those parts. [149] Cardozo’s rule has withstood the test of time. [150] Its longevity can be attributed to the large number of cases Cardozo compared and the significance of the common features he analyzed. In other words, Cardozo used enough relevant particulars to generalize a reliable statement of the law.

Analogical reasoning is also a form of induction. It’s arguably one of the most crucial skills in the study and practice of law. [151] Analogy is simply the comparison of similarities between things with the attendant expectation that, if they resemble each other in several ways, then they will likely share some other property. [152] In the law, analogical reasoning involves comparing precedent—with established facts and outcome—to a new set of facts to determine the likely outcome of the new case. The more relevant similarities between the cases, the more likely their outcomes will be similar as well. Unlike inductive generalization, analogy’s reliability is not dependent on presenting a large number of particulars. [153] Rather, it is the quality of the comparison of the cases that makes the analogy reliable:

The success of the analogy depends on how significant the reader perceives the factual similarities between the two cases and whether any differences strike the reader as even more significant. An analogy can fail as much because an advocate ignores significant differences between two cases as because of a dearth of similarities. [154]

One could rightly state that our system of jurisprudence is built on a foundation of analogy. Stare decisis , the doctrine that underlies our case law system, requires that courts compare pending cases to existing precedent such that similar facts lead to similar legal consequences. Accordingly, students with a healthy working knowledge of induction (both inductive generalization and analogy) will not only better understand our legal system’s foundational principles but will be equipped to mold and manipulate legal ideas in useful ways.

c. Fallacy and the Quality of Arguments

If an argument can be defined as an attempt to establish the truth, a fallacy can be described as an argument that appears to do so–but doesn’t. [155] The ability to recognize fallacy allows law students to meaningfully evaluate judicial opinions and question outcomes in cases. As a result, it improves the quality of students’ argumentation and assessment of opponents’ counter-arguments.

Unfortunately, much like the public at large, students entering law school have been so inundated with arguments undermined by logical fallacies [156] that they are psychologically predisposed to accept logical fallacy as a substitute for sound reasoning. [157] People routinely “make logical mistakes, ignore logic altogether, or actually prefer certain illogical argument patterns.” [158] Essentially, audiences are conditioned to pick up on cues embedded in an argument that hint at the desired conclusions. These thinking shortcuts, known as “superficial heuristics,” often take the place of actual analysis. [159]

Of course, superficial heuristics and faulty reasoning should be avoided at all costs in law school. Exposing these thinking shortcuts and their attendant risk of error is the gateway to avoiding them. Therefore, learning a bit about common logical fallacies would help law students and law professors alike: When a student makes a faulty argument in class, the professor can describe the problem using the common language of functional logic.

A formal fallacy describes an error in the structure of an argument. [160] In a formal fallacy, a conclusion could be false even if all of the premises are true. [161] For example, using the classic “Socrates” syllogism:

All humans are mortal Socrates is mortal Therefore, Socrates is human.

This syllogism is fallacious because it is entirely possible that Socrates is the name of the neighbor’s cat. The formal error is the swapping of the minor term (in the minor premise) with the major term (in the conclusion). As with all formal logic, recognizing a formal fallacy requires familiarity with the patterns of distributed or undistributed terms. Again, this level of knowledge is beyond what’s needed for our limited goal of improving critical thinking. Nonetheless, it’s important to recognize that formal fallacy and formal deductive logic are two sides of the same coin.

Informal fallacies, also known as material fallacies, [162] are harder to spot. Informal fallacies could be described as mistakes in “the content (and possibly the intent) of the reasoning.” [163] Logicians have identified hundreds of distinct types of informal fallacies; [164] therefore, a comprehensive list of them is unworkable here. But some are so common—and so effective—that learning to recognize them should be considered a critical law-school skill. The following common fallacies demonstrate the potential deceptiveness of otherwise appealing arguments:

Ad Hominem : This fallacy is committed by abusing the proponent of an argument or by dismissing the proponent’s position on the grounds of the proponent’s appearance, circumstances, or background. [165] An advocate can cross the line from identifying weakness in an opponent’s argument into an improper attack on the opponent’s character. In Bauer v. Yellen , [166] the Second Circuit admonished counsel (and reduced its award of attorney fees) for the following ad hominem attack on its opponent, a pro se litigant: “Ms. Bauer has pursued this case blindly, recklessly, vindictively, maliciously and without a shred of evidence to support her wild and deluded claim of copyright infringement. . . . Ms. Bauer’s opposition papers mirror the nasty, mean-spirited approach she has taken in prosecuting this matter.” [167]

Bandwagon Fallacy : Also known as the ad populum fallacy, this type of fallacious argument suggests that, because a great number of people believe something, it must be objectively true. This fallacy occurs when a party argues that a court should adopt a rule because of “near universal agreement among . . . courts that have confronted [the] issue,” [168] rather than because of the merits of the rule.

Begging the Question : This fallacy assumes as true what is to be proved. [169] It can be as simple as a single step of faulty reasoning (e.g., “The hospital was negligent because it failed to use ordinary care”) or it can be buried in several steps of circular reasoning (e.g., An indigent prisoner claims a right to a free trial transcript because he wishes to argue ineffective assistance of counsel on appeal. There is no requirement to furnish an indigent prisoner with a free transcript unless he is unable to show that he has a non-frivolous claim. Because the prisoner cannot show that he has a non-frivolous claim, he has no right to a free trial transcript).

Fallacy of Accident : This fallacy, also known as dicto simpliciter , occurs when one applies a general rule to exceptional circumstances or facts. [170] For example, an Internet pornographer arguing that his website’s content is “Free Speech” may be committing the fallacy of accident by not acknowledging that limitations on obscenity and commercial speech exceptions likely apply—and must be analyzed—in his case.

Hasty Generalization : Essentially “jumping to conclusions.” A Hasty Generalization fallacy occurs when a conclusion is induced from too few particulars. [171] The reliability of any inductive generalization depends on having considered enough specific instances with identical outcomes to eliminate doubt as to the likelihood of non-conforming outcomes. But drawing a conclusion from only a few particular instances lacks that reliability. For example, in O’Conner v. Commonwealth Edison Co. , [172] an expert witness committed the fallacy when he testified that a plaintiff’s cataracts were caused by exposure to radiation at a nuclear plant where he worked. [173] His opinion was based on previously observing five patients with similar cataracts, all of which had been radiation-induced. [174]

Post Hoc : Any argument that suggests causation simply because one event preceded another is guilty of the post hoc ergo propter hoc fallacy. [175] It’s also known as the false cause fallacy, and it is tricky. The danger of presuming a causal connection between events when none exists is obvious. But in a legal context, it’s often rational to conclude that when a legally significant event is followed by a result, that result probably flowed from the event. [176] For example, a criminal defendant could claim her medication prevented her guilty plea from being knowingly and voluntarily made. [177] It sounds reasonable, but absent evidence that the medication affected the defendant’s cognitive function, it’s spurious. Despite the fallacy, post hoc arguments are an effective tool for litigators since they are so enticing to jurors. [178] Straw Man : This is a fallacious argument in which one “creates the illusion of having refuted a solid proposition by substituting a similar, weaker proposition for it and refuting the substitute instead.” [179] By exaggerating or misrepresenting an opposing argument, one can more easily present one’s own position as reasonable. Consider the statement by former presidential candidate Bernie Sanders, who, during a Democratic Presidential Candidates Forum, suggested that opponents of gun control “think they should have a missile launcher in their backyard as a Constitutional right . . . .” [180]

These—and the scores of other known fallacies—all have the common attribute of obscuring the truth. But fallacies are often highly persuasive and can be used to manipulate—intentionally or otherwise. [181] And to properly represent clients and fulfill one’s professional responsibilities, lawyers must, if not pursue the truth, at least be aware of when it is being obscured. Knowing how to recognize fallacies is, in itself, a tool for honing critical thinking, and should be considered a fundamental lawyering skill.

Part III: Integrating Functional Logic Training Across the Law-School Curriculum

Regardless of how theoretically beneficial logic training may be, students cannot be expected to distill the principles of logic on their own. [182] Integrating basic, informal logic training into the law-school curriculum could be relatively painless and cost-effective and, most importantly, could begin to bridge the ever-widening gap between how students think and how academics expect them to think.

a. Logic During Orientation

The obvious moment to begin exposing students to a paradigmatic system of thinking is during orientation. Orientation varies in length, depth, and purpose from school to school. Schools use orientation for everything from registering parking passes and assigning study carrels to presenting more substantive programs that introduce the cohort to systems of law and the Socratic Method. Schools with more in-depth programs could introduce basic principles of logic in a two-to-three hour session, incorporating outside reading and a formative (perhaps online) assessment.

Orientation programs introducing logic should be straightforward and unintimidating. The goal is to build a solid foundation upon which to build the thinking processes students will encounter in the first weeks of law school and beyond. The classic categorical syllogism is a perfect starting point. [183] After introducing the basic form of a syllogism, the professor should provide numerous real-world examples of valid syllogisms:

Lack of sleep makes one drowsy during the day . Joe Law Student stayed up all night . Joe Law Student will be drowsy during the day . [184]

When we finish this orientation session, it will be time for lunch. We have not yet finished this orientation session. Therefore, it is not time for lunch. [185]

Once the basic form is clear, students should see examples of legal syllogisms: the basic application of rules to facts, along with their consequent conclusions. A formative assessment at this point could test students’ ability to distinguish rules from facts.

Students with innately sound reasoning skills (or, perhaps, previous training in logical reasoning) would recognize the deductive pattern at once and organize their thinking about legal issues accordingly. But for students who lack critical-thinking skills, this breakdown of the basic syllogistic form would provide a step-by-step process upon which to structure analysis. Armed with an effective process of reflective thinking, these students could avoid analytical missteps, which often go unnoticed until mid-term or final exams—in other words, too late.

In addition to basic deduction, Orientation should present the basic principles of inductive reasoning. Simple but engaging exercises in a “what do all these cases tell you about the law” model—presented as “induction”—would not only prepare students for the progressive integration of law that will happen once classes begin, but would give a name to the process they will be expected to use and, eventually, master. Professors involved in Orientation can enhance this benefit by preparing exercises specifically engineered to call out invalid induction. For example, a set of cases that seem to induce an obvious answer, save one anomalous result, tempts students to commit the fallacy of hasty generalization. [186] The fruits of the endeavor would be enduring: students who take the time to consider why their answers are good or bad are thinking like lawyers.

Introducing deductive and inductive reasoning during Orientation would, therefore, likely bear fruit once classes begin. By repeating these processes in different contexts as classes progress, students will naturally strengthen their brains’ neural networks responsible for critical thinking. [187]

b. Logic in Doctrinal Classes

Merely knowing the principles that distinguish good and bad reasoning is not enough. To enhance critical thinking, law students should replicate the process of putting analytical components together in multiple contexts. In other words, students should be encouraged to use syllogistic logic across the curriculum.

But herein lies the greatest difficulty: changing the way law students think means a change in the way law professors think and teach. Law professors, however, are not generally known for their great desire to implement teaching innovations. [188] Fortunately, simple adjustments to existing instructional models might yield unexpected mutual benefits and ease frustration for both professors and students.

In nearly every American law-school class, students read appellate decisions in casebooks and answer professors’ questions about the holdings and principles of law contained in the cases. This “Case Law” or “Socratic” [189] method of instruction remains the standard teaching method in law schools, despite concerns about its effectiveness and recommendations against its widespread use. [190] But despite its prevalence, law schools generally fail at explaining the process and goals of the Socratic Method. [191] Many professors assume that students implicitly recognize these goals. [192] There is generally no explanation of the underlying thought process that gets the students to the “right” answer. [193] Many students eventually work out that professors are not simply “hiding the ball,” but are, rather, drawing out reasoned analysis. Others however, may stumble through law school never quite understanding the reason for the trauma and humiliation that the Socratic Method engenders. [194]

The frustration is mutual. First-year professors complain that students’ exam answers are missing analysis. [195] Students jump from identifying a rule to stating a conclusion with no significant application of the rule to facts in between. What is missing in those answers, logically speaking, is the syllogistic minor premise. [196] On an exam, many students struggle to even articulate the accurate legal issue.

Consider a scenario where a defendant is charged with aggravated battery for using a deadly weapon. The facts state that the defendant sloshed household bleach in the victim’s face. [197] The rule is that any object can be a deadly weapon if it is used in such a way as to make it likely to cause great bodily harm. [198] It may seem obvious to an experienced lawyer that the precise legal issue is “whether bleach, sloshed in a victim’s face, is likely to cause great bodily harm.” But a student with poor analytical skills might begin by stating the issue as “whether the defendant used a deadly weapon” or even more obtuse, “whether defendant committed aggravated battery.” With this as a starting point, it’s no wonder that students resort to incomplete, heuristic thinking in place of reasoned analysis.

Now, imagine if every professor began requiring students to express arguments in the form of a syllogism. Certainly, the process would be a struggle, if not downright ugly, in the first weeks or even months of law school. But with repetition, students would quickly become proficient at identifying the proper components of the syllogistic process—thereby clarifying their reasoning. A simple approach to achieve these benefits in nearly any law-school classroom is to require students to articulate rules as “if-then” statements. [199] By reframing rules in this way, students are forced to critically examine the constituent elements of the rule: its requirements and its consequences. [200] Consider the following basic rules in Torts, Constitutional Law, and Civil Procedure:

If the plaintiff proves elements X, Y, and Z, then tort liability is established. If the state deprives a citizen of notice and opportunity to be heard, then the right to Due Process is violated. If a party currently resides in the state and intends to remain there indefinitely, then he or she qualifies as a “citizen” for diversity jurisdiction purposes.

Note that these simple rules are structured so as to force the rule’s requirement (the “if”) and consequence (the “then”) into plain view. This skill alone is beneficial for students because it not only trains the brain to recognize the pattern of rules, it transfers to skills necessary for legal writing and drafting: coherence and clarity. More importantly, however, these if-then rules form the major premise of a conditional syllogism. In such a major premise, the “if” clause is the middle term and the “then” clause is the major term.

Once students are comfortable articulating rules as the major premise of a syllogism, the next step is to present the facts of a case—whether a hypothetical presented by the professor or an assigned case reading—as the minor premise. Here are the minor premises that correlate to the major premises above:

Defendant did facts A B C. The state imposed a fine without affording the party an opportunity for a hearing. Plaintiff owns a houseboat that is moored in the state.

The subject of each minor premise is the minor term. The predicate of each minor premise is the middle term—or at least it would be, if the syllogism were complete. In a complete syllogism, of course, the middle terms would match exactly. Here, the middle terms do not match—yet. This is the advantage of this syllogistic exercise: students can immediately spot the precise legal issue in a case by joining the two middle term positions (in bold):

The issues revealed in this way are:

Do facts A B C —> satisfy elements X Y Z? Did the state’s imposing a fine without affording the party an opportunity for a hearing —> deprive the citizen of notice and opportunity to be heard? (YES) Does merely owning a houseboat currently moored in the state —> mean that a party currently resides in the state and intends to remain there indefinitely? (NO)

In this way, the analysis can be tested for accuracy. And in the first weeks and months of law school, the reliability of students’ analyses is of paramount importance.

These functional logic exercises, repeated in various contexts across the curriculum, would undoubtedly have at least some metacognitive benefits. And professors might find that the process improves not only students’ preparation, but also the quality of dialogue between them and their students.

c. Logic in Legal Writing and Analysis Courses

There is no question that legal writing professors are on the front lines of recognizing—and attempting to mitigate—shortcomings in law students’ reasoning. Legal writing assignments force students to reveal their thought processes on paper. [201] In grading their memos and briefs, we see that students’ “confusing prose reflects their confused thinking.” [202] Moreover, legal writing courses bridge a curricular gap between doctrine and skills. Students learn theory in their doctrinal courses and learn to apply it in a meaningful way toward the resolution of a client’s legal issue in legal writing classes. These courses help students integrate material across curriculum “because they do not separate the learning of theory from its application.” [203] Naturally, this setting is ideal for reinforcing functional logic skills.

Most law students are exposed to fundamental logical reasoning in their first-year research and writing course. They just don’t know it. Basic IRAC structure (Issue, Rule, Analysis, Conclusion)—the hallmark of legal writing organization—represents a deductive syllogistic process. [204] But written legal analysis involves induction as well. [205] Virtually no analysis is complete without incorporating analogical reasoning by comparing the facts of one’s case to precedent. And when a factual scenario presents novel or troublesome facts that seem not to fit established law, students are taught to engage in rule synthesis. [206] In other words, the legal writing classroom is rich with opportunities to practice deduction and induction in ways that incorporate both theory and practical application. What’s critical, however, is for legal writing professors to use logic terminology (i.e., deduction, induction, analogy, fallacy) when teaching these skills. It’s not that IRAC , synthesis , case illustration , or application are bad terms: legal writing professors have had great success using these and other labels for parts of analysis and should continue to do so. [207] Rather, it’s the additional benefit of reinforcing the concepts of logical thought in various contexts that will strengthen those skills across the board. [208] Accordingly, during the writing-instruction phase of a typical first-year legal-writing course, professors should take every opportunity to point out deductive and inductive analysis wherever it can be found. The professor should demonstrate that the Rule Synthesis section (the “R” of IRAC) has, overall, the same function as the major premise of a syllogism: as a unit, it represents a universal truth against which the facts of the case must be tested. Ideally, students should be exposed to several such deductive (or “rule-based” [209] ) analyses during their first legal-writing class session. Doing so connects legal writing not only to the deduction they learned about in Orientation, but also to the deductive processes used in their doctrinal courses. It also serves as a jumping-off point for the next step: the inductive process of applying precedent to new facts.

New law students learning predictive writing [210] are often confounded by the concept of analogizing facts of a case to established precedent. [211] It’s not that students don’t understand analogy: they’ve likely mastered the “head is to hat as foot is to shoe” analogy prevalent on the LSAT. [212] Rather, it’s the fact that using multiple (and often seemingly contradictory) analogies to reach a conclusion is a foreign concept to most non-lawyers. Moreover, even the conclusions reached by such a process can be less than satisfying, since they lack certainty. [213]

In drafting their first memos, rookie law students often make the mistake of analogizing a single precedent case to the facts of the memo problem. Despite having described several precedent cases, they default to choosing “the closest” single case to apply to the untested facts without endeavoring to reconcile other precedent or, much less, the law as a whole. The result is a superficial conclusion and inadequate prediction. To combat this tendency, legal-writing professors should reinforce that the two inductive forms, (1) inductive generalization and (2) analogy, should feature in the application (the “A” of IRAC) section of a memo.

In inductive generalization, a legal writer extracts multiple, often intersecting, points of similarity among a representative group of precedent cases to reach a working standard. [214] Say a legal writing professor includes four precedent cases in a closed-universe memo assignment. The professor undoubtedly chose those cases because they represent basic concepts relevant to the expected analysis. Case 1 has characteristics A and B ; Case 2 has characteristics A and C ; Case 3 has characteristics similar to A , B , and C , but mostly hinges on D ; and Case 4 falls short on A , B , C , and D (and, accordingly, fails to meet the legal standard at issue). Again, a student may be tempted to base his or her application simply on which of these cases most closely resembles the untested set of facts. But a professor can avoid this dangerous shortcut by taking time in class to break down each case conceptually, identifying and describing characteristics A , B , C , and D , and, where possible, articulating a formula describing characteristics necessary for the standard to be met.

Disorderly conduct provides a good example. In Florida, disorderly conduct is rather abstractly defined by Florida Statute section 877.03 as conduct that “corrupt[s] the public morals,” “outrage[s] the sense of public decency,” or “affect[s] the peace and quiet of persons who may witness [it].” [215] This mushy definition makes pure deduction difficult. Precedent, however, provides more helpful concepts. In one case, a defendant’s loud verbal conduct attracted a crowd of curious onlookers, but it was his physical act of interfering with the police officer’s lawful duties that made his conduct disorderly. [216] In another case, the defendant’s verbal conduct attracted a crowd, and he was physically aggressive toward an officer; this was also sufficient to constitute disorderly conduct. [217] In a third case, the defendant’s verbal conduct attracted a crowd that became hostile toward the officer, and this too was considered disorderly conduct. [218] But in a case where a defendant’s loud verbal conduct merely attracted a crowd of annoyed onlookers, the conduct was not considered disorderly. [219]

From these cases, at least three conceptual points of comparison arise: (A) conduct that draws a crowd; (B) conduct that interferes with an officer’s lawful duties; and (C) conduct that puts the officer in danger. In the cases where the disorderly conduct standard was met, there was some combination of (A) attracting a crowd and either (B) interfering with the officer’s duties or (C) putting the officer in danger. In the one case where the standard was not met, only (A) was present. Therefore, even from this limited selection of precedent, an implicit working standard can be extracted: Where (A)+(B) or (A)+(C) are present, conduct will be considered disorderly. If the formula is reliable, it should explain the results in all cases.

What’s happened here is induction: a general principle has been extracted from a number of particulars based on relevant similarities. [220] That general principle would then be applied to the untested facts of a new case. Admittedly, four cases may be a small sample from which to extract a general standard. But if the chosen cases are highly representative of all the cases on point, then the standard is likely to be highly reliable. [221] Nonetheless, because the conclusion reached by this process is uncertain, further substantiation is needed. That’s where analogy comes in.

Using analogical reasoning, the legal writer justifies his or her conclusion in terms of the chosen precedent. [222] Our typical “rookie” law student tried analogy, but failed to connect it to the law as a whole; therefore, it was superficial and analytically flimsy. But analogy coupled with the application of the inductive working standard demonstrates that a predicted outcome is consistent not only with an individual case, but also with the entire body of law on that issue. Thus, instead of describing random or disconnected similarities and distinctions between precedent cases and a set of untested facts, students can think of analogical reasoning as “proof” that the inductive formula was reliable.

Back to the disorderly conduct example. Suppose a memo fact pattern described a suspect—a witness to a shooting—who was loudly insisting that an officer take his statement, despite the fact that the officer was busy arresting the shooter. The suspect’s antics of yelling at the officer attracted a crowd of onlookers. The suspect, perhaps fueled by having an audience, put his face within two inches of the officer’s face, causing the officer to push him away with a free hand. The issue, of course, is whether the suspect can be charged with disorderly conduct.

In applying the law to these facts (the “A” of IRAC), a writer may initially want to point out that the statute does not provide concrete enough concepts upon which to base a purely deductive analysis. [223] Therefore, the analysis would be inductive. First, the writer should articulate the inductive generalization that the charge is generally supported by evidence that the defendant’s conduct (A) caused a crowd to form and either (B) interfered with an officer’s lawful duties or (C) put the officer in danger. Based on that working standard, the writer can state that the facts satisfy the inductive standard: the suspect both attracted a crowd and interfered with the officer making the arrest.

Next, it’s time to analogize the precedent cases. Because analogy compares cases with the expectation that, if they resemble each other in several relevant ways, then they will likely share the same outcome, [224] the writer must demonstrate that the specific relevant similarities between the chosen precedent and the untested facts support the stated conclusion. Because the relevant characteristics ( A , B , C , or D ) have already been described in the inductive generalization, it’s sufficient to briefly connect them to the specific facts of the memo problem. Analogy, in this sense, further substantiates the reliability of the inductive process.

What I’ve described above does not differ significantly from analytical processes taught by the average legal writing professor. But I believe there’s a significant additional benefit gained from reinforcing basic logic processes and terminology along the way.

d. Logic in Oral Advocacy

One final golden opportunity to reinforce basic logic is during the oral argument component of a first-year persuasive-writing class. Besides being a blood-curdlingly terrifying event forever etched in students’ memories and an important rite of passage, the appellate oral argument is fertile ground for using and recognizing informal fallacy. Generally, the lead-up to the oral argument is preceded by several weeks of instruction on oral persuasion and, ideally, in-class practice. Students already exposed to the concept of informal fallacy would be more adept at responding to their opponents’ positions, perhaps even identifying faulty logic by name. A student’s argument that “opposing counsel asserts X, but that is without merit because (restate original premise for the ninth time)” can become “opposing counsel asserts X, which falls into the logical fallacy of hasty generalization and is, therefore, not a reliable result.”

One way to achieve this benefit is to use class time to brainstorm every possible fallacious (but compelling) argument that could be made in the context of an appellate-brief fact pattern. Do the facts of the case allow for an improper appeal to authority? Can an ad hominem argument be made against an unsympathetic witness? This exercise not only reinforces the meaning of individual fallacies in a practical way; it challenges students to test how far advocacy can stretch before it becomes no longer persuasive.

Introducing basic logic into the legal writing classroom, therefore, requires little substantive change to existing pedagogy. But if students learn that the familiar paradigms of legal writing are exactly the same logic principles introduced in orientation and reinforced in doctrinal classes, their ability to critically think about legal issues—and their overall comprehension—could significantly increase.

Legal education in the United States has evolved over time in response to economic and social change. But the social, educational, and technological changes of recent decades, which have noticeably altered students’ ability to think critically, merit at least an adjustment in the way law schools teach. The time-tested methods of logic—even when pared down to their most practical and functional components—could begin to remediate some of the problems students face in the modern law-school classroom.

See generally Paul Douglas Callister, Beyond Training: Law Librarianship’s Quest for the Pedagogy of Legal Research Education , 95 L. Lib. J. 7, 9 (2003) (discussing legal employers’ frustration with new graduates’ poor legal research skills); Rebecca C. Flanagan, The Kids Aren’t Alright: Rethinking the Law Student Skills Deficit , 2015 BYU Educ. & L.J. 135, 138 (2015) (discussing possible reasons for law students’ decreasing critical-thinking skills); Courtney G. Lee, Changing Gears to Meet the “New Normal” in Legal Education , 53 Duq. L. Rev. 39 , 67 (2015) (decreased critical-thinking skills of many law schools’ entering classes is likely to continue for years to come); Karen Sloan, Practice Ready? Law Students and Practitioners Disagree , Nat’l L.J . (March 6, 2015), https://www.law.com/nationallawjournal/almID/1202719928678/?slreturn=20171030205801 (last visited Nov. 30, 2017) (discussing a survey by BarBri finding that only 23% of practitioners felt that graduating law students were ready to practice law); James Etienne Viator, Legal Education’s Perfect Storm: Law Students’ Poor Writing and Legal Analysis Skills Collide with Dismal Employment Prospects, Creating the Urgent Need to Reconfigure the First-Year Curriculum , 61 Cath. U. L. Rev. 735, 740—41 (2012) (discussing law-school “education-to-profession” disjunction).

Richard Arum & Josipa Roksa, Academically Adrift: Limited Learning on College Campuses 35—36 (2011).

Flanagan, supra note 1, at 144—45.

Changes needed to implement innovative curriculum changes have been “hampered,” in part, by American Bar Association regulations. Kristen K. Tiscione, How the Disappearance of Classical Rhetoric and the Decision to Teach Law as a “Science” Severed Theory from Practice in Legal Education , 51 Wake Forest L. Rev. 385 (2016); see also ABA Sec. Leg. Educ. & Admissions to the Bar , Managing Director’s Guidance Memo: Standard 316, Bar Passage (Aug. 2016), http://www.americanbar.org/content/dam/aba/administrative/legal_education_and_admissions_to_the_bar/governancedocuments/2016_august_guidance_memo_S316.authcheckdam.pdf (last visited Dec. 12, 2017).

Michael Scriver & Richard Paul , Defining Critical Thinking, The Critical Thinking Community , http://www.criticalthinking.org/pages/defining-critical-thinking/766 (last visited Dec. 12, 2017).

Joanne G. Kurfiss, Critical Thinking: Theory, Research, Practice, and Possibilities , ASHE-ERIC Higher Educ. Rep. 1, 5 (1988).

Flanagan, supra note 1, at 144.

Id. (quoting Judith Welch Wegner, Reframing Legal Education’s "Wicked Problems ," 61 Rutgers L. Rev. 867, 871 (2009)).

Henry Ford is reported to have said, “Thinking is hard work, and that’s why so few people do it.”

See Kurfiss, supra note 7, at 14.

Stephen M. Rice, Indiscernible Logic: Using the Logical Fallacies of the Illicit Major Term and the Illicit Minor Term as Litigation Tools , 47 Willamette L. Rev. 101, 108 (2010).

Cheryl B. Preston et al., Teaching “Thinking Like a Lawyer”: Metacognition and Law Students , 2014 BYU L. Rev. 1053, 1057 (2014) (defining metacognition as “thinking about thinking”).

Ruggero J. Aldisert, Logic for Lawyers: A Guide to Clear Legal Thinking , 28—29 (Nat’l Inst. for Trial Advo. 3d Ed. 1997); Edwin W. Patterson, Logic in the Law , 90 U. Pa. L. Rev. 875 (1942).

See, e.g. , Michael R. Smith, Rhetoric Theory and Legal Writing: An Annotated Bibliography , 3 J. ALWD 129 (2006) (listing dozens of scholarly works discussing logic and rhetoric in the discipline of legal writing); Richard D. Friedman, Logic and Elements (Symposium: Premises and Conclusions: Symbolic Logic for Legal Analysis), 73 Notre Dame L. Rev. 575 (1998).

Ruggero J. Aldisert et al., Logic for Law Students: How to Think Like a Lawyer , 69 U. Pitt. L. Rev. 1, 2 (2007).

Paula Lustbader, Construction Sites, Building Types, and Bridging Gaps: A Cognitive Theory of the Learning Progression of Law Students , 33 Willamette L. Rev. 315, 338 (1997) (“What is expected of students at the undergraduate level is vastly different from what is expected in law school. Prior to law school, learning mainly involved memorizing and regurgitating predigested, prepackaged, and organized information obtained from textbooks, lectures, and the media. Consequently, they are ill-prepared to read critically, synthesize rules, or analyze material to the extent required in law school.”).

Jesse Franklin Brumbaugh, Legal Reasoning and Briefing: Logic Applied to the Preparation, Trial and Appeal of Cases, with Illustrative Briefs and Forms 59 (1917) (“Ordinary logical theory requires but truthfulness only in the materials of the syllogism and form, but legal logic adds the social elements of justice and equity . . . .”); James R. Maxeiner, Thinking Like A Lawyer Abroad: Putting Justice into Legal Reasoning , 11 Wash. U. Global Stud. L. Rev . 55, 60 (2012) (“It is elementary learning that law seeks justice.”).

Ruth Vance & Susan Stuart, Of Moby Dick and Tartar Sauce: The Academically Underprepared Law Student and the Curse of Overconfidence , 53 Duq. L. Rev. 133, 134 (2015) (“[M]any matriculating law students arrive at law school woefully underprepared at the same time legal educators are challenged with the task of producing practice-ready graduates.”).

Aaron N. Taylor, Diversity as a Law School Survival Strategy , 59 St. Louis U.L.J 321, 329 (2015).

Id . While not the only predictor of law-school success, the LSAT measures “natural skill or reasoning,” skills that law schools and state bars consider essential to lawyering. Robert Steinbuch & Kim Love, Color-Blind-Spot: The Intersection of Freedom of Information Law and Affirmative Action in Law School Admissions , 20 Tex. Rev. L. & Pol. 181, 201 (2016) (citing Nicholas Georgakopoulos, Bar Passage: GPA and LSAT, Not Bar Reviews (Indiana University Robert H. McKinney School of Law Research Paper No. 2013-30 Sept. 19, 2013), http://bit.ly/20Ar8aB [ perma.cc/62MU-JRR7 ]).

Jay Sterling Silver, Responsible Solutions: Reply to Tamanaha and Campos , 2 Tex. A&M L. Rev . 215, 229—30 (2014).

Vance & Stuart, supra note 23, at 137. A full discussion of the deficiencies of K-12 and undergraduate educations is beyond the scope of the article.

“Despite a dramatic decrease in hours spent studying, college students are receiving higher grades.” Flanagan, supra note 1, at 139 (citing Kevin Carey, ‘Trust Us’ Won’t Cut It Anymore , Chron. Higher Educ. , Jan. 18, 2011, http://chronicle.com/article/Trust-Us-Wont-Cut-It/125978/ (last visited Dec. 12, 2017). (“Yes, there’s been grade inflation. A-minus is the new C.”); Lee, supra note 1, at 66; see also Rebecca C. Flanagan, Do Med Schools Do It Better? Improving Law School Admissions by Adopting a Medical School Admissions Model , 53 Duq. L. Rev . 75, 81 (2015) (“Many students can earn above-average grades throughout their undergraduate years by artfully selecting courses and majors.”).

Lee, supra note 1, at 66.

Flanagan, supra note 1, at 135—36.

Viator, supra note 1, at 753 (“From the late seventeenth century through the end of the nineteenth century, all levels of American schooling were dedicated to the study of classical literature and history.”).

Flanagan, supra note 1, at 148; see also Marilyn R. Walter, Erasing the Lines Between the Law School and the Liberal Arts Curricula: A Comment on “A Liberal Education in Law,” 1 J. Alwd. 153, 154 (2002) (discussing that familiarity with the classical authors and with principles of oratory was viewed, pre-Civil War, as essential to a lawyer’s excellence).

Tiscione, supra note 4, at 400.

Carol T. Christ, Myth: A Liberal Arts Education Is Becoming Irrelevant , Am. Council on Educ. (Spring 2012), http://www.acenet.edu/the-presidency/columns-and-features/Pages/Myth-A-Liberal-Arts-Education-Is-Becoming-Irrelevant.aspx (last visited Dec. 12, 2017).

“[T]he best preparation for the intense phase of the apprenticeship we call ‘going to law school’ is a broad-based liberal arts education.” Patricia Sayre, “Socrates is Mortal”: Formal Logic and the Pre-Law Undergraduate , 73 Notre Dame L. Rev . 689, 703 (1998).

Flanagan, supra note 1, at 148.

Doug Mataconis, College Students Lack Critical Thinking Skills, But Who’s To Blame? , Outside The Beltway (Jan. 18, 2011), http://www.outsidethebeltway.com/college-students-lack-critical-thinking-skills-but-whos-to-blame/ (last visited Dec. 12, 2017).

“Most of the top earners in the liberal arts end up matching only the bottom earners in science, technology, engineering and mathematics — known as the STEM fields — and some will earn less than high school graduates who have vocational skills, like welders and mechanics.” Patricia Cohen, A Rising Call to Promote STEM Education and Cut Liberal Arts Funding , N.Y. Times (Feb. 21, 2016), https://www.nytimes.com/2016/02/22/business/a-rising-call-to-promote-stem-education-and-cut-liberal-arts-funding.html (last visited Dec. 12, 2017).

Id. ; Michael Delucchi, “Liberal Arts” Colleges and the Myth of Uniqueness , 68(4) J. of Higher Educ. 414, 414 (1997) (“[T]he curricular trend in higher education since about 1970 has been toward studies related to work . . . . Enrollment concerns in recent years have compelled many liberal arts colleges to abandon or sharply scale back their arts and sciences curriculum in order to accommodate student preoccupation with the immediate job market.”); see also Mark Yates, The Carnegie Effect: Elevating Practical Training over Liberal Education in Curricular Reform , 17 Legal Writing 233, 243 (2011) (“Since the 1970s, undergraduate institutions in the United States have been shifting their curricular emphasis from liberal arts to more professionally oriented education. This shift is due largely to enrollment concerns caused by changes in the labor market and corresponding changes in the expectations of entering students.”); Judith T. Younger, Legal Education: An Illusion , 75 Minn. L. Rev. 1037, 1043 (1991) (arguing that, in attempting to democratize higher education, colleges and universities abandoned the liberal arts in favor of specialization and vocationalism).

Nicholas Lemann, Liberal Education and Professionals , 90 Liberal Educ. 14 (Spring 2004), http://www.aacu.org/liberaleducation/le-sp04/le-sp04feature1.cfm (last visited Dec. 12, 2017).

Arum & Roksa , supra note 2, at 96—98.

See Flanagan, supra note 1, at 140 (describing Collegiate Learning Assessment test subjects as similarly situated students from wide variety of colleges and universities).

Id . (characterizing critical thinking, analytical reasoning, problem solving, and writing skills as essential skills during the first year of law school).

Arum & Roksa, supra note 2, at 121.

Center of Inquiry in the Liberal Arts at Wabash College, Wabash National Study of Liberal Arts Education , http://www.liberalarts.wabash.edu/study-research/ (last visited Dec. 12, 2017).

Center of Inquiry in the Liberal Arts at Wabash College, Wabash National Study of Liberal Arts Education, Fourth Year Change Summary , http://static1.1.sqspcdn.com/static/f/333946/10418206/1296073333850/4-year-change-summary-website.pdf?token=ZVEVCl3%2ButHXke%2Fk0YqlLCJCYMo%3D (last visited Dec. 12, 2017).

“[S]tudies have not found positive evidence of broad-based skills acquisition by college students since the 1990s.” Flanagan, supra note 1, at 142.

Id. at 143.

Id. (quoting Arum & Roksa, supra note 2, at 40).

Elizabeth Olsen, Study Cites Lower Standards in Law School Admissions , N.Y. TIMES, Oct. 27, 2015, at B1; Jennifer M. Cooper, Smarter Law Learning: Using Cognitive Science to Maximize Law Learning , 44 Cap. U.L. Rev. 551, 552 (2016).

See generally Taylor, supra note 24.

Jeremy Berke, Law-School Grads are Bombing the Bar and It’s a Sign of Trouble for Legal Education , Business Insider , http://www.businessinsider.com/bar-passage-exam-rates-have-dropped-in-several-key-states-2015-11 (last visited Dec. 12, 2017).

Shailini Jandial George, Teaching the Smartphone Generation: How Cognitive Science Can Improve Learning in Law School , 66 Me. L. Rev. 163, 169 (2013).

Id. at 172.

Id. at 172–73.

Sara Bernard, Neuroplasticity: Learning Physically Changes the Brain , EDUTOPIA (Dec. 1, 2010), http://www.edutopia.org/neuroscience-brain-based-learning-neuroplasticity (Dec. 12, 2017).

Nicholas Carr, The Shallows: What the Internet is Doing to our Brains 31, 34 (2011).

Id. at 120.

Jennie Bricker, Where No One Has Gone Before: Practicing Law in the Digital Age , 72 J. Mo. B. 18 (2016).

Carr, supra note 60, at 65.

See id. at 72.

Id . at 75.

Id. at 122.

Id. at 141—42.

Id . at 121.

A slightly exaggerated, but not-all-too-unrealistic multi-tasking scenario is described at the outset of George, supra note 55, at 164.

Carr , supra note 60, at 140.

Vance & Stuart, supra note 22, at 141.

Daniel M. Wegner & Adrian F. Ward, The Internet Has Become the External Hard Drive for our Memories , Sci. Am. (Dec. 1, 2013), http://www.scientificamerican.com/article/the-internet-has-become-the-external-hard-drive-for-our-memories/ (last visited Dec. 12, 2017).

Patrick Meyer, The Google Effect, Multitasking, and Lost Linearity: What We Should Do , 42 Ohio N.U. L. Rev. 705, 716 (2016).

William Poundstone, The Internet Isn’t Making Us Dumber — It’s Making Us More “Meta-Ignorant,” N.Y. Mag. (July 27, 2016) , http://nymag.com/scienceofus/2016/07/the-internet-isnt-making-us-dumber-its-making-us-more-meta-ignorant.html (last visited Dec. 12, 2017).

Meyer, supra note 74, at 712—13.

Gabriel H. Teninbaum, Spaced Repetition: A Method for Learning More Law in Less Time , 17 J. High Tech. L. 273, 302 (2017).

Neil Howe & William Strauss , Millennials Rising: The Next Great Generation 4 (2000) (defining a Millennial as anyone born during or after 1982).

Data suggests that Millennials do not read print newspapers, watch television news, or purposely visit news websites, instead receiving information on selected stories through social media. The Media Insight Project, How Millenials Get News: Inside the Habits of American’s First Digital Generation , http://www.mediainsight.org/Pages/how-millennials-get-news-inside-the-habits-of-americas-first-digital-generation.aspx (last visited Dec. 12, 2017).

Poundstone, supra note 77 (“Most — more than 50 percent — of millennials can’t name anyone who shot a U.S. president or discovered a planet; they don’t know the ancient city celebrated for its hanging gardens, the one destroyed by Mount Vesuvius, or the emperor said to have fiddled while Rome burned; and most millennials can’t name the single word uttered by the raven in Edgar Allan Poe’s poem.”).

“The incidence of narcissistic personality disorder is nearly three times as high for people in their 20s as for the generation that’s now 65 or older, according to the National Institutes of Health; 58% more college students scored higher on a narcissism scale in 2009 than in 1982.” Joel Stein, Millennials: The Me Me Me Generation , Time Magazine (May 20, 2013) http://time.com/247/millennials-the-me-me-me-generation/ ; see also Vance & Stuart, supra note 22, at 134—35.

Kari Mercer Dalton, Bridging the Digital Divide and Guiding the Millennial Generation’s Research and Analysis , 18 Barry L. Rev . 167, 173—74 (2012).

Eric A. DeGroff, Training Tomorrow’s Lawyers: What Empirical Research Can Tell Us About the Effect of Law School Pedagogy on Law Student Learning Styles , 36 S. Ill. U.L.J. 251 (2012).

Vance & Stuart, supra note 22, at 134—35.

Anthony Niedwiecki, Teaching for Lifelong Learning: Improving the Metacognitive Skills of Law Students Through More Effective Formative Assessment Techniques , 40 Cap. U. L. Rev. 149, 160 (2012); Cooper, supra note 53, at 556.

Cooper, supra note 52, at 556.

See generally Justin Kruger & David Dunning, Unskilled and Unaware of It: How Difficulties in Recognizing One’s Own Incompetence Lead to Inflated Self-Assessments , 77 J. Personality & Soc. Psychology 1121 (1999).

Id . at 1121.

Id . (citations omitted).

Id. at 1124.

Participants placed themselves in the 66th percentile relative to others, significantly higher than the actual mean of 50. Id . at 1123.

Id . at 1125.

Legal Writing guru Bryan Garner linked the Dunning-Kruger effect to the legal profession. He suggested that attorneys overestimate their writing skills and, therefore, fail to take steps to improve it, even when doing so would be beneficial. Bryan A. Garner, Why Lawyers Can’t Write: Science Has Something to Do with It, and Law Schools Are Partly to Blame , 99- Mar. A.B.A. J. 24 (2013).

See 2016 MBE Statistics, Nat’l Conf. Bar Examiners, http://www.ncbex.org/publications/statistics/mbe-statistics/ (last visited Sept. 29, 2017) (showing a decline in MBE National Mean Scaled Scores from 2007 to 2016).

“Thinking like a lawyer” has been described as “employing logic to construct arguments.” Aldisert et al., supra note 18, at 1.

Jack L. Landau, Logic for Lawyers , 13 Pac. L.J. 59, 60 (1981); Aldisert et al., supra note 18, at 2; Stephen M. Rice, False Persuasion, Superficial Heuristics, and the Power of Logical Form to Test the Integrity of Legal Argument , 34 Pace L. Rev. 76, 76 (2014).

Aldisert, supra note 16, at 28—29; see Patterson, supra note 16, at 903 — 04 (describing types of analogies).

Professors often hear, “I know the material; I just didn’t present it the way you wanted it.”

The Honorable Jack L. Landau, Justice of the Supreme Court of Oregon, proposed essentially the same in 1981, when he was an Instructor of Law at Northwestern School of Law of Lewis and Clark College:

Much of what is currently taught in logic classes is entirely too cumbersome for analysis. However, there are certain techniques, namely deduction, induction and analogy, and the avoidance of informal fallacies, that can easily be taught to first-year students, that do have a direct bearing on the legal reasoning process, and that can definitely improve the quality of reasoning and critical thinking skills exhibited by students and lawyers alike.

Landau, supra note 100, at 60.

Judge Aldisert expressed similar unease at possibly offending logicians and mathematicians. Aldisert et al., supra note 18, at 2. But it is, perhaps, the greatest approbation to demonstrate Logic’s utility even in such a highly diluted form.

“Deductive reasoning is a mental operation that a student, lawyer or judge must employ every working day.” Aldisert, supra note 16, at 45.

See, e.g. , id. at 48—49.

There are three basic types of syllogisms:

Conditional Syllogism: If A is true then B is true (If A then B). Categorical Syllogism: If A is in C (and B is in A) then B is in C. Disjunctive Syllogism: If A is true, then B must be false (A or B).

See id . at 145.

This is true, of course, only if the syllogism is valid.

Aldisert et al., supra note 18, at 4.

See generally Aldisert, supra note 16.

Aldisert et al., supra note 18, at 6.

For beginners, it may be easier to remember that the major term represents the broad or universal class, the middle term represents a portion of that class, and the minor term represents the narrowest or most specific component.

Aldisert, supra note 16, at 57—58.

The informal or practical logic envisioned in this article does not necessarily require students to understand these patterns or, for that matter, to create exclusively valid syllogisms. Rather, it is the process of forcing ideas into a syllogism—whether revealing an objective “truth” or not—that is likely to improve students’ critical-thinking skills. A secondary effect of this approach may be that some students become interested in more formal logic and pursue it further.

Aldisert, supra note 16, at 237.

“[Formal logic] structure allows legal thinkers to comparatively analyze legal argument, by comparing and contrasting it to necessarily valid or invalid logical structures, and reach conclusive logical decisions about the validity or invalidity of the form of the argument.” Stephen M. Rice, Conspicuous Logic: Using the Logical Fallacy of Affirming the Consequent as a Litigation Tool , 14 Barry L. Rev . 1, 13 (2010).

Andrew Jay McClurg, Logical Fallacies and the Supreme Court: A Critical Examination of Justice Rehnquist’s Decisions in Criminal Procedure Cases , 59 U . Colo. L. Rev . 741, 774 (1988).

Rice, supra note 120, at 9.

132 So. 3d 237 (Fla. Dist. Ct. App. 2013).

Id. at 245.

Id. at 247 (quoting Clark v. State, 95 So. 3d 986, 987 (Fla. Dist. Ct. App. 2012)).

Id. at 247 n. 16.

Naturally, it is possible that, in this particular judgment on this particular issue, Judge Wetherell was not reasonable. Nonetheless, his use of conditional syllogism to compare the facts (judges disagreed about the ruling) to the legal standard (no abuse of discretion if reasonable judges could disagree) was effective, in theory.

Id . at 12.

See Aldisert , supra note 16, at 48.

Kent Sinclair Jr., Comment, Legal Reasoning: In Search of an Adequate Theory of Argument , 59 Calif. L. Rev. 821, 827 (1971), http://scholarship.law.berkeley.edu/californialawreview/vol59/iss3/13 (last visited Dec. 12, 2017).

Aldisert et al., supra note 18, at 13.

Anita Schnee, Legal Reasoning "Obviously ," 3 Legal Writing 105, 112 (1997), http://www.legalwritingjournal.org/wp-content/uploads/2015/06/volume3.pdf (last visited Dec. 12, 2017).

Aldisert, supra note 16, at 92—93.

Carlo Rovelli, Science is not Certainty , NEW REPUBLIC (July 11, 2014), https://newrepublic.com/article/118655/theoretical-phyisicist-explains-why-science-not-about-certainty (“Science is extremely reliable; it’s not certain.”) (last visited Dec. 12, 2017).

Mary Massaron Ross, A Basis for Legal Reasoning: Logic on Appeal , 3 J. Ass’n Legal Writing Directors 179, 182 (2006).

Aldisert, supra note 16, at 50, 92.

Kansas v. Colorado , 206 U.S. 46, 97 (1907).

111 N.E. 1050 (N.Y. 1916); see Schnee, supra note 137, at 113.

MacPherson , 111 N.E. at 1051.

Id . at 1055 (commenting that “defendant was not absolved from a duty of inspection” because it bought the wheels from a third party manufacturer); Schnee, supra note 137, at 113.

Id. at 1055 (Bartlett, J., dissenting) (opining that the majority’s opinion extended vendor liability further than any case the court previously approved).

Id. at 1051—53 (majority opinion); Schnee, supra note 137, at 113.

Aldisert, supra note 16, at 100—01.

MacPherson , 111 N.E. at 1055.

Schnee, supra note 137, at 113.

See Aldisert , supra note 16, at 91 (“Inductive generalization is used in all aspects of the legal profession – in studying law, in practicing law and in judging cases. Thus, it looms large in the common-law tradition in the development of legal precepts in the case by case experience.”).

Ross, supra note 140, at 185 (“Typically, deductive reasoning proceeds from a general proposition to a conclusion that is either a particular proposition or another general proposition.”).

Kristen K. Robbins, Paradigm Lost: Recapturing Classical Rhetoric to Validate Legal Reasoning , 27 Vt. L. Rev . 483, 532 (2003).

Bruce Weinstein, How Trump and Friends Could Learn a Few Things From Mr. Spock , Fortune Magazine Online (March 8, 2016), http://fortune.com/2016/03/08/fallacious-arguments-logic-trump/ (discussing fallacies in recent presidential campaign speeches).

Consider some pop-culture examples of blatant fallacy: Advertisements in the “Four out of five dentists approve” variety (demonstrating appeal to authority fallacy); talking head debates over whether ISIS militants are or are not “genuine Muslims” (no true Scotsman fallacy); political candidates stating their opponents are in the pocket of special interests, hate the middle class, are socialist, are racist, etc. (ad hominem argument); arguments against the theory of evolution using a picture of a chimpanzee and asking, “Is this really your ancestor?” (straw-man fallacy).

Indeed, use of fallacy is so prevalent that television and commercial writers have found it a ripe target for satire: A Simpsons episode where Homer concludes that a rock is capable of repelling tigers because, while the rock was present, no tigers were about ( post hoc fallacy), Simpson- I want to buy your rock , https://www.youtube.com/watch?v=g3U6IUMTDHY (last visited Sept. 28, 2017); a Direct TV commercial suggesting, “Don’t wake up in a roadside ditch: Get rid of cable” (slippery slope fallacy).

Rice, supra note 100, at 79—80.

Id . at 82.

Id. at 82—83.

Ross, supra note 140, at 189 (“Formal fallacies are based on a mistake in the form or logic of the argument.”).

Aldisert, supra note 16, at 141.

Aldisert , supra note 16, at 143.

Cory S. Clements, Perception and Persuasion in Legal Argumentation: Using Informal Fallacies and Cognitive Biases to Win the War of Words , 2013 BYU L. Rev . 319, 332 (2013).

LOGICALLY FALLACIOUS: THE ULTIMATE COLLECTION OF OVER 300 LOGICAL FALLACIES , https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies (last visited Sept. 28, 2017).

Michael Sean Quinn, “Scholarly Ethics”: A Response , 46 J. Legal Educ. 110, 112 (1996).

375 Fed. App’x 154, 157 (2d Cir. 2010) (unpublished).

375 F. App’x at 156 n.2.

Scheck v. Burger King Corp ., 798 F. Supp. 692, 698 n10 (S.D. Fla. 1992).

Aldisert , supra note 16, at 208.

Id. at 193.

Id . at 195.

807 F. Supp. 1376 (C.D. Ill. 1992).

Id . at 1391.

Aldisert , supra note 16, at 199.

Eugene Volokh, The Mechanisms of the Slippery Slope , 116 Harv. L. Rev . 1026, 1102 (2003)

See State v. Brown , 305 P.3d 48 (Kan. App. 2013).

See generally Neal R. Feigenson, The Rhetoric of Torts: How Advocates Help Jurors Think About Causation, Reasonableness, and Responsibility , 47 Hastings L.J. 61, 165 n 154 (1995).

Gabriel H. Teninbaum, Reductio Ad Hitlerum: Trumping the Judicial Nazi Card , 2009 Mich. St. L. Rev. 541, 554 (2009)

Weinstein, supra note 155.

Doing so would be “like asking them to design a rocket without teaching them the rules of physics.” Aldisert et al., supra note 18, at 2.

Id . at 6. Judge Aldisert describes the prosecutor’s syllogism as a useful template for most legal problems:

Major premise: [Doing something] [violates the law] Minor premise: [The defendant] [did something] Conclusion: [The defendant] [violated the law].

A basic categorical syllogism.

A modus tollens conditional syllogism.

Aldisert , supra note 16, at 195.

“The more times a network is stimulated, the stronger and more efficient it becomes.” Bernard J. Luskin, “If I Had a Better Brain!” Brain Health, Plasticity, Media, and Learning Can be a Perfect Storm , Psychology Today (Aug. 20, 2013), https://www.psychologytoday.com/blog/the-media-psychology-effect/201308/if-i-had-better-brain (last visited Dec. 12, 2017).

See Michael Hunter Schwartz, Teaching Law by Design: How Learning Theory and Instructional Design Can Inform and Reform Law Teaching , 38 San Diego L. Rev . 347, 360 (2001) (law schools’ emphasis on scholarship and publication, the criteria by which law schools measure professors’ performance for tenure purposes, discourages teaching innovation); Samantha A. Moppett, Control-Alt-Incomplete? Using Technology to Assess “Digital Natives” , 12 Chi.-Kent J. Intell. Prop . 77, 86 (2013) (law professors fear change because of concern about academic freedom, resistance to changing status quo, and hesitation over increasing workload).

The Case Law method, introduced by Christopher Columbus Langdell at Harvard Law School in 1870, has been commonly labeled the “Socratic Method.” This is, somewhat, a misnomer. Ruta K. Stropus, Mend It, Bend It, and Extend It: The Fate of Traditional Law School Methodology in the 21st Century , 27 Loy. U. Chi. L.J. 449, 453 (1996) (“Unlike Socrates, who focused purely on the questioning process, Langdell sought to combine both the substance of the law and the process of the law into the legal classroom.”) Despite this technical difference, I refer to the typical law-school instructional method as “Socratic.”

See, e.g., William M. Sullivan et al., educating Lawyers: Preparation for the Profession of Law 56—60, 75—78 (The Carnegie Foundation for the Advancement of Teaching, Preparation for the Professions Program, 2007); A.B.A. Section of Legal Educ. & Admissions to the Bar , Legal Education and Professional Development–an Educational Continuum, Report of The Task Force on Law Schools and the Profession: Narrowing the Gap 233—36 (1992) [MacCrate Report].

Tiscione, supra note 4, at 399—400

Niedwiecki, supra note 89, at 168.

Id. at 169.

See generally Jennifer L. Rosato, The Socratic Method and Women Law Students: Humanize, Don’t Feminize , 7 S. Cal. Rev. L. & Women’s Stud. 37 (1997) (discussing students’ humiliation as an integral part of the Socratic Method).

Timothy R. Zinnecker, Syllogisms, Enthymemes and Fallacies: Mastering Secured Transactions Through Deductive Reasoning , 56 Wayne L. Rev. 1581, 1589 (2010) (quoting James M. Boland, Legal Writing Programs and Professionalism: Legal Writing Professors Can Join the Academic Club , 18 St. Thomas L. Rev. 711, 726 (2006)).

State v. Smith , 969 So. 2d 452, 453 (Fla. Dist. Ct. App. 2007).

Id. at 454.

I am indebted to my colleague, Professor Brendan Beery, for this pragmatic and tested approach for using conditional syllogisms to promote what he terms “right thinking.” Professor Beery conducts voluntary logic workshops that not only teach the syllogistic process using functional terminology, but which enhance students’ ability to express their reasoning on exams.

See generally Kevin H. Smith, Practical Jurisprudence: Deconstructing and Synthesizing the Art and Science of Thinking Like a Lawyer , 29 U. Mem. L. Rev . 1, 49 (1998).

Carol McCrehan Parker, Writing Throughout the Curriculum: Why Law Schools Need It and How to Achieve It , 76 Neb. L. Rev . 561, 571 (1997).

Viator, supra note 1, at 742.

David S. Romantz, The Truth About Cats and Dogs: Legal Writing Courses and the Law School Curriculum , 52 U. Kan. L. Rev. 105, 139 (2003).

Schnee, supra note 137, at 106.

Laura P. Graham, Why-Rac? Revisiting the Traditional Paradigm for Writing About Legal Analysis , 63 U. Kan. L. Rev. 681, 688 (2015) (citing Kristin Konrad Robbins-Tiscione, Rhetoric for Legal Writers: The Theory and Practice of Analysis and Persuasion 111—13 (2009)).

See generally Jane Kent Gionfriddo, Thinking Like A Lawyer: The Heuristics of Case Synthesis , 40 Tex. Tech L. Rev . 1 (2007).

But see Terrill Pollman, Building A Tower of Babel or Building A Discipline? Talking About Legal Writing , 85 Marq. L. Rev. 887, 924–25 (2002) (discussing the need for consistent legal-writing terminology, or “jargon,” to effectively communicate about writing and about the substance of the academic discipline of legal writing).

Some writing texts already approach legal analysis using logic terminology. See generally Deborah A. Schmedemann & Christina L. Kunz , Synthesis: Legal Reading, Reasoning, and Writing (3d ed. 2007); Teresa J. Reid Rambo & Leanne J. Pflaum, Legal Writing by Design (2d ed. 2013).

See Laurel Currie Oates & Anne Enquist , Just Memos (3d ed. 2011).

Predictive writing is nearly always taught before persuasive writing. Kathy Stanchi, Teaching Students to Present Law Persuasively Using Techniques From Psychology , 19 Perspectives: Teaching Legal Res. & Writing 142, 142 (2011).

See, e.g ., Dan Hunter, Teaching and Using Analogy in Law , 2 J. Ass’n. Legal Writing Directors 151, 151 (2004).

Cass R. Sunstein, On Analogical Reasoning , 106 Harv. L. Rev. 741, 745 (1993).

Ross, supra note 140, at 180.

Fla. Stat. § 877.03 (2016).

C.L.B. v. State , 689 So. 2d 1171, 1172 (Fla. Dist. Ct. App. 1997).

Wiltzer v. State, 756 So. 2d 1063, 1065 (Fla. Dist. Ct. App. 2000).

W.M. v. State, 491 So. 2d 335, 336 (Fla. Dist. Ct. App. 1986).

Fields v. State, 24 So. 3d 646, 648 (Fla. Dist. Ct. App. 2009).

See Aldisert et al., supra note 18, at 12.

“If the analysis is based on a complete set, then the conclusion will be strong. But if a complete set is not used for the analysis, the conclusion may be weak. The advocate must test the strength of the conclusion by examining the sample’s size and its representativeness.” Ross, supra note 140, at 181.

Dan Hunter, Reason Is Too Large: Analogy and Precedent in Law , 50 Emory L.J. 1197, 1246 (2001).

In reality, Fla. Stat. § 877.03 provides one concrete example of disorderly conduct: “brawling or fighting.” However, in a “closed universe” memo, that part of the statute can be left out for pedagogical purposes.

Aldisert , supra note 16, at 93.

Logic models used to enhance critical thinking

Affiliation.

1 University of Hawaii at Manoa, School of Nursing and Dental Hygiene, Honolulu, Hawaii, USA. [email protected]
PMID: 16780010
DOI: 10.3928/01484834-20060601-06

Over time, various methods have been used to stimulate critical thinking in undergraduate nursing students, and although many have been successful in helping students integrate the essential knowledge, experiences, and clinical reasoning that support practice, it is also useful to explore new methods. Faculty at the University of Hawaii at Manoa, School of Nursing and Dental Hygiene have taken an innovative approach of using logic models to further enhance critical thinking. This article presents an application of varying experiences and methods of using logic models to support the development of critical thinking and reasoning skills in nursing students. The processes in which logic models are used in the curriculum are described. The models are used to connect concepts from concrete to abstract levels in diverse and often nonlinear diagrams, guided discourse, and written assignments. The specific instructional methods used include concept mapping, concept papers, conceptual linking, and substruction.

Publication types

Evaluation Study
Attitude of Health Personnel
Clinical Competence
Concept Formation
Data Collection
Education, Nursing, Baccalaureate / organization & administration*
Health Knowledge, Attitudes, Practice
Models, Educational
Models, Nursing*
Models, Psychological
Nursing Assessment
Nursing Diagnosis
Nursing Education Research
Nursing Methodology Research
Nursing Process / organization & administration*
Problem Solving
Program Evaluation
Psychology, Educational
Students, Nursing / psychology*

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3 critical thinking skills you need in 2024.

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Critical thinking skills help you improve diversity and inclusion within your team

In 2018, a Hart survey revealed that out of over 500 business executives interviewed, 78% agreed that critical thinking is the most essential skill they desire to see demonstrated in their employees. However, astonishingly, a mere 34% of college graduates were equipped with this in-demand skill.

Today, critical thinking remains one of the most essential skill sets you need to succeed in today's workforce and experience a thriving career. The World Economic Forum's Future of Jobs 2023 report confirmed just how essential critical thinking and analytical reasoning skills are in 2024, placing this skill set at the top of its list.

In an earlier report from the Forum, it most notably pointed out:

“Skills gaps continue to be high as in-demand skills across jobs change in the next five years. The top skills and skill groups which employers see as rising in prominence in the lead up to 2025, include groups such as critical thinking and analysis as well as problem-solving."

This is hardly surprising, given the fact that we continue to be bombarded with the spread of misinformation everyday, from social media, to conspiracy groups, to the prevalent usage of AI which can generate misleading and potentially harmful information if not developed and used ethically. This makes it of the utmost important that we take deliberate effort to develop the habit of critically analysis, everything instead of taking at face value and accepting things for what they are.

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Through developing critical thinking skills, you can prevent the advancement of misinformation, become a trusted an reliable source within your network and industry, and gain access to exciting career opportunities including promotions.

But how can you develop critical thinking and analysis skills?

First, let's unpack what critical thinking actually is.

What Is Critical Thinking?

Critical thinking, in simple terms, is the process of objectively analyzing data, and using your reflections and observations from multiple sources to arrive at conclusions, decisions, or judgements.

What Are Some Critical Thinking Skills?

To develop critical thinking for your career success, consider building the following skills:

1. Curiosity

Innovation comes through being curious enough to keep probing and digging for information. Challenge your own assumptions, and those of others. As you do this, you will notice that it will help pave the way for the removal of unconscious bias within the workplace. When never you do receive information, regardless of the source or format, seek clarification before accepting it as fact.

2. Evaluation

To evaluate others' conclusions and supporting arguments, research their background, credentials, reputation, possible influencing factors, and experience. This will help you assess just how reliable, relevant, and credible they are.

3. Diversity

Last but not least, it's essential to keep an open mind to a wide variety of sources. The greater the variety, the higher the quality of your conclusion. For example, as a leader or manager, you should seek to foster inclusivity and diversity within your team by creating processes whereby all team members can feel involved in your decision-making or policy creation process.

This helps to ensure that the final solution is reflective of those it is intended to serve and is well adapted to everyone's needs and preferences.

Through developing critical thinking skills, you can help stay the spread of misinformation and be ... [+] recognized as a credible industry expert

Practice these three essential critical thinking skills every time you read a new item of information online, when browsing through social media, watching the news, in a meeting, or when studying for your professional development. The more you practice, the more you'll refine and strengthen your critical thinking skills over time.

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