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## Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

## Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
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• Pythagoras and Trigonometry
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## Probability and statistics

• Handling, Processing and Representing Data
• Probability

## Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

## For younger learners

• Early Years Foundation Stage

• Decision Mathematics and Combinatorics

Published 2011

## Co-operative Problem Solving: Pieces of the Puzzle Approach

What is the pieces of a puzzle approach.

• You are responsible for your own work and behaviour
• You must be willing to help any group member who asks
• You may only ask the teacher for help if everyone in the group has the same question
• Risk taking - pupils are more likely ask questions of each other and put forward ideas in a small group situation, particularly with Rule 2 in place.
• Mathematical language development - usually the clues for the tasks are communicated with words. The group needs to negotiate their interpretation of the mathematical vocabulary. They also must talk to each other, listen to others and explain their ideas clearly.
• Peer coaching - pupils are able to clarify their understanding of mathematical concepts, correct misconceptions and test out ideas during the process of finding a collective solution to the problem.
• Teacher's role as a facilitator and observer - the independence of the groups gives the teacher freedom to move around the class, observe language and strategies, interact with groups as required and assess their progress.
• Effective learning - the tasks generally incorporate the manipulation of physical objects to produce a final product, which promotes the linking of verbal knowledge with visual imagery.
• Mixed ability class teaching - the features listed above combine to make this approach particularly suited to use with mixed ability classes. Every child should be able to make a contribution to the problem solving process, learn from the activity and have received attention from the teacher when needed.

## Forming the Groups

There are, of course, many ways to organise children into groups. Unless the teacher has specific reasons for doing otherwise, a random mix method is best for this type of co-operative problem solving.

Random Mix by the Cards

Here is one way to achieve a random mix of pupils using a pack of ordinary playing cards. To form seven groups of four children, use all four card suits from one (Ace) to seven. Shuffle this pack and have each child choose a card. All the sevens form a group, all the sixes form a group and so on.

• Diamonds - team manager - responsible for assisting teacher to get group's attention at specified signal and reminding the group of the 'rules';
• Spades - equipment manager - responsible for collecting and returning materials, and ensuring all group members have access to the materials;
• Hearts - recorder - noting significant information, steps in solution, or preparation of finished product (such as the model, drawing or chart);
• Clubs - spokesperson - responsible for reporting the group's efforts and/or solutions

## Lesson Structure

Introduction: This type of problem solving activity is well suited to developing and clarifying mathematical ideas that have already been introduced in other lessons. Therefore, in introducing the task to the class, the teacher can make links to previous work. If the mathematical vocabulary contained in the problem is of particular concern, then key terms should be revised.

Group work: The groups are formed and each child in a group is given one clue card. To maintain 'ownership' of the piece of information, the child may not physically give away the clue-card, but must be responsible for communicating the content to the group. Each pupil's role is now to work within his/her group to solve the puzzle, following the set of work rules. The teacher must also take care to follow these rules, and not take back responsibility for the task by interfering with the problem-solving processes or offering help before being asked by the whole group.

As always, it is advisable to have an extension question ready for a group that finishes before the others. It is also useful to have one or two 'extra' clues ready. These can be used to allow the inclusion of an extra group member, to give help to a group that is 'stuck', or to assist 'checking' when a group thinks it has finished the task.

Plenary - It is important for groups to report on their problem-solving processes as well as confirming the correctness of their end product. The teacher can use questions focus on particular issues and highlight points that have been observed during the session. For example:

## Examples of Problems

 PETER'S NUMBER PETER'S NUMBER PETER'S NUMBER PETER'S NUMBER PETER'S NUMBER PETER'S NUMBER

(More than one answer is possible until Clues E & F are incorporated)

Stick Figures

Each group needs a handful of sticks, all of the same length - such as matches, ice-cream or lolly sticks, or drinking straws. The aim is to arrange some of the sticks to make either a single shape or shapes-combinations (depending on the level of complexity).

 STICK FIGURE 3 STICK FIGURE 3 STICK FIGURE 3 STICK FIGURE 3 STICK FIGURE 3 STICK FIGURE 3

Fractured Shapes

The clues in this type of problem are non-verbal. In the example below, the squares are cut up by the teacher and each member of a group-of-four is given three pieces marked with the same letter. The aim is for the group to make four complete squares.

Each group needs a set of digit cards (two or three copies of the digits 0-9) and a template of the algorithm, in this example a two-column sum

 FIND THE SUM 1 FIND THE SUM 1 FIND THE SUM 1 FIND THE SUM 1 FIND THE SUM 1 FIND THE SUM 1
 MODEL VIEWS 2 MODEL VIEWS 2 looks like this. MODEL VIEWS 2 looks like this. MODEL VIEWS 2 looks like this. MODEL VIEWS 2 MODEL VIEWS 2

Burns, M. (1992) About Teaching Mathematics , Maths Solution Publications: California Erickson, T. (1989) Get It Together, EQUALS: University of California.

Gould, P. (1993) Co-operative Problem Solving in Mathematics , Mathematical Association of N.S.W. Australia. ISBN 0-7310-1371-9 (Available through the Australian Association of Mathematics Teachers Catalogue code MAN466 - http://www.aamt.edu.au/ )

## Collaborative Problem Solving: What It Is and How to Do It

What is collaborative problem solving, how to solve problems as a team, celebrating success as a team.

Problems arise. That's a well-known fact of life and business. When they do, it may seem more straightforward to take individual ownership of the problem and immediately run with trying to solve it. However, the most effective problem-solving solutions often come through collaborative problem solving.

As defined by Webster's Dictionary , the word collaborate is to work jointly with others or together, especially in an intellectual endeavor. Therefore, collaborative problem solving (CPS) is essentially solving problems by working together as a team. While problems can and are solved individually, CPS often brings about the best resolution to a problem while also developing a team atmosphere and encouraging creative thinking.

Because collaborative problem solving involves multiple people and ideas, there are some techniques that can help you stay on track, engage efficiently, and communicate effectively during collaboration.

• Set Expectations. From the very beginning, expectations for openness and respect must be established for CPS to be effective. Everyone participating should feel that their ideas will be heard and valued.
• Provide Variety. Another way of providing variety can be by eliciting individuals outside the organization but affected by the problem. This may mean involving various levels of leadership from the ground floor to the top of the organization. It may be that you involve someone from bookkeeping in a marketing problem-solving session. A perspective from someone not involved in the day-to-day of the problem can often provide valuable insight.
• Communicate Clearly.  If the problem is not well-defined, the solution can't be. By clearly defining the problem, the framework for collaborative problem solving is narrowed and more effective.
• Expand the Possibilities.  Think beyond what is offered. Take a discarded idea and expand upon it. Turn it upside down and inside out. What is good about it? What needs improvement? Sometimes the best ideas are those that have been discarded rather than reworked.
• Encourage Creativity.  Out-of-the-box thinking is one of the great benefits of collaborative problem-solving. This may mean that solutions are proposed that have no way of working, but a small nugget makes its way from that creative thought to evolution into the perfect solution.
• Provide Positive Feedback. There are many reasons participants may hold back in a collaborative problem-solving meeting. Fear of performance evaluation, lack of confidence, lack of clarity, and hierarchy concerns are just a few of the reasons people may not initially participate in a meeting. Positive public feedback early on in the meeting will eliminate some of these concerns and create more participation and more possible solutions.
• Consider Solutions. Once several possible ideas have been identified, discuss the advantages and drawbacks of each one until a consensus is made.
• Assign Tasks.  A problem identified and a solution selected is not a problem solved. Once a solution is determined, assign tasks to work towards a resolution. A team that has been invested in the creation of the solution will be invested in its resolution. The best time to act is now.
• Evaluate the Solution. Reconnect as a team once the solution is implemented and the problem is solved. What went well? What didn't? Why? Collaboration doesn't necessarily end when the problem is solved. The solution to the problem is often the next step towards a new collaboration.

The burden that is lifted when a problem is solved is enough victory for some. However, a team that plays together should celebrate together. It's not only collaboration that brings unity to a team. It's also the combined celebration of a unified victory—the moment you look around and realize the collectiveness of your success.

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Given the robust nature of learning sciences research, this website is best viewed on tablets and computers. A small screen experience is coming in the future.

## Cooperative Problem Solving

As learners work together to solve problems, they learn new strategies and practice Communication skills as they express their academic thinking. This communal process can help students reflect on their problem-solving strategies and adjust their approaches to support future learning, consider others' perspectives, and support Critical Thinking and Collaboration skills. When classrooms scaffold and implement cooperative problem solving as part of the culture of learning, learners are better prepared to come together to achieve classroom and community goals, core to Civic Mindedness. Showcasing problem-solving as a collaborative effort and allowing learners to experience the process of trial and error can help to strengthen Learner Mindset. Working together to analyze concepts and cement understanding can provide autonomy for learners as they begin to grapple with more complex content and explore individual learning processes.

## Example: Use This Strategy in the Classroom

Watch how this middle school educator facilitates cooperative problem solving with partners . Learners are encouraged to solve the problem individually, then discuss with their partners to compare their strategies. Collaboration in small groups helps to deepen understanding as learners discuss their ideas and explain their processes while strengthening their Communication Skills.

• Educators can assign challenging problems for students to work on independently then in small groups. Giving learners the opportunity to tackle the problems individually first allows them to evaluate their understanding prior to working with others. Then, as they work with others, they tackle the same problem with different strategies, developing their Core Academic Literacies and understanding what strategies work best for them. Cooperative problem solving can be used to practice skills during daily classroom learning, and can also be especially fruitful for larger tasks, including project-based learning. Educators should be mindful of grouping students flexibly for each task and to best support Collaboration across diverse strengths.

## Design It into Your Product

• Products can support cooperative problem solving by creating spaces where learners can work together to display and share their thinking with their peers. Including a chat and shared workspace features can support Collaboration and the development of Social Awareness & Relationship Skills. Products can include features that let learners copy or combine pieces of their individual work to create a shared answer that best represents their discussion and reasoning and outlines their thinking process.

Additional examples, research, and professional development. These resources are possible representations of this strategy, not endorsements.

Group Roles

Worksheet with different student roles for working in a group

Stick-It Together

Graphic organizer for supporting cooperative problem solving

Relationship Skills

A microcredential to support students' relationship skills

Developing Behaviors for Cooperative Learning

Module by Sanford Inspire

Collaboration Strategies

A teacher toolbox of strategies and graphic organizers to support collaboration in the classroom.

## Factors Supported by this Strategy

More cooperative learning strategies.

Collaborative writing activities allow peers to work together to plan, draft, edit, and revise during the composition process, supporting writing skills and engagement with content knowledge as students write to reflect upon and apply what they have learned.

Flexible grouping is a classroom practice that temporarily places students together in given groups to work together, with the purpose of achieving a given learning goal or activity.

Gallery walks are ways of showcasing content and materials as multiple “exhibitions” for students to view and interact with as part of larger learning goals.

An open classroom climate is an educational environment where students feel comfortable and confident expressing their opinions in class.

Respectful redirection, or error correction, outlines a clear and concise way that educators can provide feedback on behaviors that need immediate correction, in a positive manner.

Socratic seminar refers to a discussion technique that engages learners in the exploration of content through Critical Thinking and classroom dialogue in order to help learners make meaning from what they are learning.

Think-Pair-Share (TPS), also known as Turn & Talk (T&T), is when the teacher pauses instruction so students can discuss a topic or prompt in pairs or small groups, to enhance engagement and learning outcomes.

## We'll create a workspace for you

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## Stay Up to Date

This is our homepage. You can access many of the features of the Navigator here, and learn more about how learner variability intersects with topics in education and learning. To start, select a content area – we call them Learner Models – to visit a factor map.

## Factor Map pages show factor connections

Factor maps show research-based concepts, "factors," that likely impact learning. They are organized into four categories: Learner Background, Social and Emotional Learning, Cognition, and Content Area. The map is interactive. Move your cursor over a factor to see connected factors. Select any factor to visit its summary page. We'll look at factor summary pages next.

This is a factor summary page. It provides a brief definition and review of the factor, a factor connections diagram, additional resources, and strategies that support this factor. On the strategy card, the multi-colored boxes show all the factors that it supports. Select a strategy to visit its summary page.

## Strategy summary pages give more detail about ways to support learner variability

Strategy summary pages have an overview, information about using the strategy in different learning environments, resources of interest, the factors this strategy supports, and related strategies you can explore. To view all the strategies in a content area, use the strategies tab at the top of the page. We'll look at all the Strategies for this learner model next.

## Learner model strategy pages let you filter all strategies for that model

The strategy page shows ALL of the strategies for that learner model. You can select factors of interest for you or your learners, and it will narrow the strategies to only those that match all of the factors selected. This makes it easy to find key strategies to better design for learner variability. Again, select the strategy name to visit its summary page. Use the plus signs on each strategy card to add a strategy to a workspace. We'll explore those next.

## Find individual workspaces you've created on your Workspaces Landing Page

The “Tools & Workspaces” tab on the navigation bar or the “My Workspaces” button on the account menu takes you to a page that shows your workspaces. There are two tabs on the My Workspaces page: a Workspaces tab and a Reports tab. The Workspaces tab lists workspaces you can personalize and update. You can create new sections, move cards between sections, add annotations, share with collaborators, and write reflections. The second tab, "Reports", are a kind of workspace created through the Instructional Design Tool or the Product Assessment Tool and have fewer personalization options.

## The Learner Centered Design Tool is a guided experience to creates workspaces

There are three, step-by-step tools you can access on the Navigator to help make workspace or a workspace report. The Learner Centered Design Tool has four steps and helps you create a workspace. First, enter basic information and select a content area of interest. Second, select a few factors that you want to focus on. Third, review connected factors you may not have considered. Note – you don't have to select any extra factors on this step if you don’t want to. The fourth and final step, review and select strategies that you want to use, and save them to a workspace.

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## Rename Workspace

What is learner variability.

Learner variability is the recognition that each learner is a unique constellation of strengths and challenges that are interconnected across the whole child. Understanding these connections and how they vary according to context is essential for meeting the needs of each learner.

It disrupts the notion of a one-size-fits all education. Understanding learner variability helps educators embrace both students’ struggles and strengths as we connect practice to uplifting the whole learner.

Throughout the site, we talk about "factors" and "strategies." Factors are concepts research suggests have an impact on how people learn. Strategies are the approaches to teaching and learning that can be used to support people in how they learn best.

## Edit Workspace Notes

Use the Learner Centered Design Tool to build a workspace. Go to Learner Centered Design Tool.

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Use one of the guided tools to build a workspace.

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## Duplicate Workspace

Make a copy of this workspace.

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## Finding new features

On this page, using your heatmap, you will be asked to select factors to further explore, and then select new strategies you might incorporate into upcoming instruction. Once done, click “Show Summary" to view your Design Summary Report.

## Finding new strategies

On this page, using your heatmap, you will be asked to select factors to further explore, and then select new strategies you might incorporate into upcoming instruction. Once done, click “Show Report” to view your Design Summary Report.

By selecting "Show Report" you will be taken to the Assessment Summary Page. Once created, you will not be able to edit your report. If you select cancel below, you can continue to edit your factor and strategy selections.

## Announcement

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Learner variability is the recognition that each learner is a unique constellation of strengths and challenges that are interconnected across the whole child. Understanding these connections and how they vary according to context is essential for meeting the needs of each learner. It embraces both students’ struggles and strengths. It considers the whole child.

The Learner Variability Navigator is a free, online tool that translates the science of learner variability into factor maps and strategies that highlight connections across the whole learner. This puts the science of learning at teachers' fingertips,  empowering them to understand their own practice and support each learner.

• Collaborative Problem Solving® »
• What Is Collaborative Problem Solving? »

## What Is Collaborative Problem Solving?

Helping kids with challenging behavior requires understanding why they struggle in the first place. But what if everything we thought was true about challenging behavior was actually wrong? Our Collaborative Problem Solving ® approach recognizes what research has pointed to for years – that kids with challenging behavior are already trying hard. They don’t lack the  will  to behave well. They lack the  skills  to behave well.

Collaborative Problem Solving ® is different than most approaches to working with kids with behavioral challenges in that it has a guiding philosophy attached to it. And the philosophy is a simple one. Kids do well if they can. And what that means is if a kid could do well, they would do well. And if they're not doing well, let's figure out what's standing in their way so we can help. Unfortunately, most people tend to adhere more to the philosophy of kids do well if they want to, which means if a kid isn't doing well, it must be because they don't want to. Our job is to try to make them want to, to motivate them to do better. We use 50 years of research in the neurosciences to help us understand what's getting in a kid's way. Because what we've learned over the years is that kids who struggle with their behavior, they actually don't lack the will to behave well. What they lack are the skills to behave well. Skills like flexibility, and frustration tolerance, and problem solving.

In Collaborative Problem Solving, we think of it much in the way you might think of a learning disability, except instead of areas like reading and math and writing. This is in areas like flexibility, frustration, tolerance, problem-solving. These kids are delayed in the development of those skills. Now, a long time ago, we used to think kids with learning disabilities were simply "lazy" or "dumb." Thank goodness we've come to a very different place in understanding kids with learning disabilities. However, we haven't made as much progress when it comes to kids with behavioral challenges. We still assume that they aren't trying hard to behave well when the truth of the matter is they're trying harder than anybody else because it doesn't come naturally to them. We've yet to meet a child that prefers doing poorly to doing well.

We believe kids do well if they can. We teach adults a practical assessment process that helps identify the specific skills that these kids struggle with and the situations in which they happen. Then we provide adults with three basic options for handling any of those situations. We call those our three plans. We call it Plan A. When you try to impose your will to make the child do what you want them to do, we call it Plan B. When you do Collaborative Problem Solving, and we call it Plan C, when you decide strategically to drop your expectation for now or solve the problem the way the child wants it solved. So we teach adults that they really only have these three options when it comes to handling any problem with a kid. Which one they choose depends on what they're trying to accomplish. Not surprisingly, we spend most of our time teaching adults how to do Plan B, collaborate with kids to solve problems in mutually satisfactory ways, not just to solve the problem and reduce challenging behavior, but to actually practice and build the skills that these kids lack.

Plan B has three ingredients to it. It seems simple, but don't confuse simple with easy. Those three ingredients are first and foremost, trying to understand the kid's perspective. The kid's concern, the kid's point of view about the problem to be solved. And only once we understand the child's concern can we move to the second ingredient of Plan B, where we put the adult's concern on the table, not our adult solution, but the adult concern on the table. And only once we have two sets of concerns on the table, the child's concern and the adult's concern, do we move to the third and final ingredient of Plan B. And that's where you invite the child to brainstorm potential solutions to the problem, which the two of you are going to test out together, aiming for one that is mutually satisfactory, doable, and realistic. And we teach adults lots of guideposts along the way to help facilitate that process. And once again, the goal of Plan B, not just reducing challenging behavior and solving the problem, but also helping the child and the adult to practice a whole host of skills related to flexibility, frustration, tolerance, and problem-solving. So in summary, Collaborative Problem Solving provides a guiding philosophy and then a corresponding set of assessment tools, a planning process, and a robust intervention that builds relationship, reduces challenging behavior, and builds skill. But let's remember that it all starts with the underlying philosophy that kids do well if they can. And this is about skill, not will.

## Related Content

Managing challenging behavior during traumatic times, collaborative problem solving, a talk with dr. stuart ablon, rethinking challenging kids: where there’s a skill there’s a way, privacy overview.

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• Published: 11 January 2023

## The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

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Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

## A meta-analysis to gauge the impact of pedagogies employed in mixed-ability high school biology classrooms

Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

## Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

## Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

## Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

## Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

## Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

## Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

## The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

## The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

## The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

## The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

## Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

## Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

## Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

## Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

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## Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

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## Cooperative Group Problem Solving

 Students in introductory physics courses typically begin to solve a problem by plunging into the algebraic and numerical solution -- they search for and manipulate equations, plugging numbers into the equations until they find a combination that yields an answer (e.g. the plug-and-chug strategy). They seldom use their conceptual knowledge of physics to qualitatively analyze the problem situation, nor do they systematically plan a solution before they begin numerical and algebraic manipulations of equations. When they arrive at an answer, they are usually satisfied -- they rarely check to see if the answer makes sense. To help students integrate the conceptual and procedural aspects of problem solving so they could become better problem solvers, we introduced a structured, . However, we immediately encountered the following dilemma: If the problems are complex enough so the novice strategy clearly fails, then students are initially unsuccessful at using the structured problem-solving strategy, so they revert back to their novice stratege. To solve this dilemma, we (1) designed complex problems that discourage the use of plug-and-chug strategies, and (2) introduced cooperative group problem solving. Cooperative group problem solving has several advantages: Of course, there are several disadvantages of cooperative-group problem solving. Initially, many students do not like working in cooperative groups. They do not like exposing their "ignorance" to other students. Moreover, they have been trained to be competitive and work individually, so they lack collaborative skills.

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## Competitive Bargaining vs. Cooperative Problem-Solving

One of the biggest challenges of negotiation is that there are two different approaches that call for opposite strategies: competitive bargaining and cooperative problem-solving. This section gives an overview of both approaches and provides a rationale for why only one of them is appropriate for international conferences.

## Competitive Bargaining

Historically, the word negotiation means “business,” and negotiation has a major role in business transactions.

The crudest form of negotiation in an international conference resembles crude commercial negotiations, for example, when you are trying to buy or sell a second-hand car and the only point at issue is the price. In that case, the buyer wants to pay as little as possible, while the seller wants to receive as much as possible. A gain by one party means an equal loss by the other. This type of negotiation is sometimes referred to as “competitive bargaining.” It has been extensively studied over the centuries by traders everywhere and, more recently, in business schools.

You probably already understand this form of negotiation. The essential feature is that each party receives something that they accept as the outcome of the negotiation. At the simplest, they would receive equal shares; but the issues before international conferences are generally far too complex for that and the needs and capabilities of the nations concerned are too varied for any simple equilibrium. Instead, at the international level, the balance to be found is between trade-offs, in which not only the quantity but also the nature of what different parties receive is different.

Each party is concerned primarily to maximize its own gains and minimize the cost to themselves.

Then some important tactical principles come to the fore:

• Always ask for more than you expect to get. Think of some of the things asked for as “negotiating coin” that you can trade away in order to achieve your aim. You can also assume that the other party does not expect to get everything they ask for and that some of their requests are only negotiating coin.
• You might even start by demanding things you do not really hope to achieve, but which you know other parties strongly oppose. By doing so, you may hope that the other parties will make concessions to you just to refrain from pressing such demands.
• Always hide your “bottom line.” Because the other party’s aim is to concede to you as little as possible, you may get more if they are not aware of how little is acceptable to you.
• Take early and give late. Negotiators often undervalue whatever is decided in the early part of the negotiation and place excessive weight on whatever is agreed towards the end of the negotiation.
• As the negotiation progresses, carefully manage the “concession rate.” If you “concede” things to the other party too slowly, they many lose hope of achieving a satisfactory agreement; but if you “concede” too fast, they could end up with more than you needed to give them.
• The points at issue are seen as having the same worth for both sides—although they rarely do.

Precepts of this kind can readily generate a competitive or even combative spirit and encourage negotiators to consider a loss by their counterparts as a gain for themselves. It should be evident that such sentiments at the international level are harmful to relations and thus to the prospects of cooperation and mutual tolerance.

## Cooperative Problem-Solving

An entirely different style of negotiation is more common in international conferences than “competitive bargaining,” both because it is generally more productive and is widely seen as more appropriate in dealings between representatives of sovereign States. This style of negotiation starts from the premise that you both have an interest in reaching agreement and therefore an interest in making proposals that the other is likely to agree to. In other words, each has an interest in the other(s) also being satisfied.

Achieving your objective requires that you also work to achieve the objectives of the other party (or parties)—to the extent that such effort is compatible with your objectives. The same applies to your counterpart(s): it is in their interest to satisfy you to the maximum extent possible. This makes negotiation a cooperative effort to find an outcome that is attractive to all parties.

To succeed in this type of negotiation, principles apply which are quite contrary to those that apply in “competitive bargaining,” namely:

• It is important not to request concessions from the other side that you know are impossible for them. If you do so, they will find it difficult to believe that you are genuinely working for an agreement.
• It is in your interest that the other party should understand your position. Indeed, perhaps they should even know your “bottom line.” If they understand how close they are to that “bottom line” on one point, they will also understand the necessity to include other elements that you value to give you an incentive to agree.
• Sometimes it is in your interest to “give” a lot to the other side early in the negotiation process to give them a strong incentive to conclude the negotiation and therefore “give” you what you need to be able to reach agreement.
• The “concession rate” may not be important.
• There is a premium on understanding that the same points have different values for different negotiators and on finding additional points on which to satisfy them.
• The Chair's Activities in Guiding the Work of a Committee
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• Characteristics of Winning Proposals ›

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## Competitive Bargaining vs. Cooperative Problem Solving

… a core concept in  Leadership Skills and Atlas 109

## Concept description

The Model UN Guidebook (reference below) distinguishes are two different approaches to negotiation  – competitive bargaining and cooperative problem solving.

## Competitive bargaining

The Guidebook describes this approach to negotiation in the following way:

“The crudest form of negotiation in an international conference resembles crude commercial negotiations, for example, when you are trying to buy or sell a second-hand car and the only point at issue is the price. In that case the buyer wants to pay as little as possible, while the seller wants to receive as much as possible. A gain by one party means an equal loss by the other. This type of negotiation is sometimes referred to as ‘competitive bargaining’. It has been extensively studied over the centuries by traders everywhere and, more recently, in business schools.

“You probably already understand this form of negotiation. The essential feature is that each party receives something which they accept as the outcome of the negotiation. At the simplest they would receive equal shares; but the issues before international conferences are generally far too complex for that and the needs and capabilities of the nations concerned are too varied for any simple equilibrium. Instead, at the international level, the balance to be found is between trade-offs, in which not only the quantity but also the nature of what different parties receive is different.

“Each party is concerned primarily to maximize its own gains and minimize the cost to themselves.

“Then some important tactical principles come to the fore:

• Always ask for more than you expect to get. Think of some of the things asked for as ‘negotiating coin’ that you can trade away in order to achieve your aim. You can also assume that the other party does not expect to get everything they ask for and that some of their requests are only negotiating coin.
• You might even start off by demanding things you do not really hope to achieve, but which you know other parties strongly oppose. By such blackmail you may hope that the other parties will make concessions to you just to refrain from pressing such demands.
• Always hide your ‘bottom line’. Because the other party’s aim is to concede to you as little as possible, you may get more if they are not aware of how little is acceptable to you.
• Take early and give late. Negotiators often undervalue whatever is decided in the early part of the negotiation and place excessive weight on whatever is agreed towards the end of the negotiation.
• As the negotiation progresses, carefully manage the ‘concession rate’. If you ‘concede’ things to the other party too slowly, they many lose hope of achieving a satisfactory agreement; but if you ‘concede’ too fast, they could end up with more than you needed to give them.
• The points at issue are seen as having the same worth for both sides – although they rarely do.

“Precepts of this kind can readily generate a competitive or even combative spirit and encourage negotiators to consider a loss by their counterparts as a gain for themselves. It should be evident that such sentiments at the international level are harmful to relations and thus to the prospects of cooperation and mutual tolerance.”

## Cooperative problem-solving

The Guidebook describes this approach to negotiation as follows:

“An entirely different style of negotiation is more common in international conferences than ‘competitive bargaining’, both because it is generally more productive and is widely seen as more appropriate in dealings between representatives of sovereign states. This style of negotiation starts from the premise that you both have an interest in reaching agreement and therefore an interest in making proposals that the other is likely to agree to. In other words, each has an interest in the other(s) also being satisfied.

“Achieving your objective requires that you also work to achieve the objectives of the other party (or parties) – to the extent that such effort is compatible with your objectives. The same applies to your counterpart(s): it is in their interest to satisfy you to the maximum extent possible. This makes negotiation a cooperative effort to find an outcome that is attractive to all parties.

“To succeed in this type of negotiation, principles apply which are quite contrary to those that apply in ‘competitive bargaining’, namely:

• It is important not to request concessions from the other side that you know are impossible for them. If you do so, they will find it difficult to believe that you are genuinely working for an agreement.
• It is in your interest that the other party should understand your position. Indeed, perhaps they should even know your ‘bottom line’. If they understand how close they are to that ‘bottom line’ on one point, they will also understand the necessity to include other elements that you value so as to give you an incentive to agree.
• Sometimes it is in your interest to ‘give’ a lot to the other side early in the negotiation process so as to give them a strong incentive to conclude the negotiation and therefore ‘give’ you what you need to be able to reach agreement.
• The ‘concession rate’ may not be important.
• There is a premium on understanding that the same points have different values for different negotiators and also on finding additional points on which to satisfy them.

## Win-win negotiation skills

The MindTools Editorial Team (reference below) applies a similar perspective in its advice on negotiations in most workplace situations. It notes that:

“Where you do not expect to deal with people ever again and you do not need their goodwill, then it may be appropriate to “play hardball”, seeking to win a negotiation while the other person loses out. Many people go through this when they buy or sell a house – this is why house-buying can be such a confrontational and unpleasant experience.

“Similarly, where there is a great deal at stake in a negotiation, then it may be appropriate to prepare in detail and legitimate “gamesmanship” to gain advantage. Anyone who has been involved with large sales negotiations will be familiar with this.

“Neither of these approaches is usually much good for resolving disputes with people with whom you have an ongoing relationship: If one person plays hardball, then this disadvantages the other person – this may, quite fairly, lead to reprisal later. Similarly, using tricks and manipulation during a negotiation can undermine trust and damage teamwork. While a manipulative person may not get caught out if negotiation is infrequent, this is not the case when people work together routinely. Here, honesty and openness are almost always the best policies.”

MindTools counsels that excessive preparation for negotiation to resolve a workplace disagreement can be counter-productive because it can be seen as manipulative because, just as it strengthens your position, it can weaken the other person’s. However, it advises that if one needs to resolve a major disagreement then it is important to prepare thoroughly by thinking through:

• Goals: what do you want to get out of the negotiation? What do you think the other person wants?
• Trades: What do you and the other person have that you can trade? What do you each have that the other wants? What are you each comfortable giving away?
• Alternatives: if you don’t reach agreement with the other person, what alternatives do you have? Are these good or bad? How much does it matter if you do not reach agreement? Does failure to reach an agreement cut you out of future opportunities? And what alternatives might the other person have?
• Relationships: what is the history of the relationship? Could or should this history impact the negotiation? Will there be any hidden issues that may influence the negotiation? How will you handle these?
• Expected outcomes: what outcome will people be expecting from this negotiation? What has the outcome been in the past, and what precedents have been set?
• The consequences: what are the consequences for you of winning or losing this negotiation? What are the consequences for the other person?
• Power: who has what power in the relationship? Who controls resources? Who stands to lose the most if agreement isn’t reached? What power does the other person have to deliver what you hope for?
• Possible solutions: based on all of the considerations, what possible compromises might there be?

## Dealing with emotions

MindTools says that style is critical and that:

“For a negotiation to be ‘win-win’, both parties should feel positive about the negotiation once it’s over. This helps people keep good working relationships afterwards. This governs the style of the negotiation – histrionics and displays of emotion are clearly inappropriate because they undermine the rational basis of the negotiation and because they bring a manipulative aspect to them.

“Despite this, emotion can be an important subject of discussion because people’s emotional needs must fairly be met. If emotion is not discussed where it needs to be, then the agreement reached can be unsatisfactory and temporary. Be as detached as possible when discussing your own emotions – perhaps discuss them as if they belong to someone else.”

UN4 MUN, Competitive Bargaining vs. Cooperative problem solving, at http://outreach.un.org/mun/guidebook/skills/negotiation/strategies/ , accessed 25 March 2016.

MindTools Editorial Team, Win-Win Negotiation – Finding a Fair Compromise, at https://www.mindtools.com/CommSkll/NegotiationSkills.htm? , accessed 25 March 2016.

Atlas topic and subject

Negotiating  (core topic) in  Leadership Skills .

Image: UN4 MUN, A view of the Conference on Disarmament, Competitive Bargaining vs. Cooperative problem solving, at http://outreach.un.org/mun/guidebook/skills/negotiation/strategies/ , accessed 25 March 2016.

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## PISA 2015 Results (Volume V)

What is collaborative problem solving, collaborative problem solving.

The OECD Programme for International Student Assessment (PISA) examines not just what students know in science, reading and mathematics, but what they can do with what they know. Results from PISA show educators and policy makers the quality and equity of learning outcomes achieved elsewhere, and allow them to learn from the policies and practices applied in other countries. PISA 2015 Results (Volume V): Collaborative Problem Solving , is one of five volumes that present the results of the PISA 2015 survey, the sixth round of the triennial assessment. It examines students’ ability to work with two or more people to try to solve a problem. The volume provides the rationale for assessing this particular skill and describes performance within and across countries. In addition, it highlights the relative strengths and weaknesses of each school system and examines how they are related to individual student characteristics, such as gender, immigrant background and socio-economic status. The volume also explores the role of education in building young people’s skills in solving problems collaboratively.

English Also available in: French

• https://doi.org/10.1787/9789264285521-en
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This chapter introduces the PISA 2015 assessment of collaborative problem solving. It provides the rationale for assessing collaborative problemsolving competence in PISA and introduces the innovative features of the 2015 assessment, particularly in contrast to the individual problem-solving assessment of PISA 2012. The framework for the assessment is discussed and sample items are presented.

## Cite this content as:

Author(s) OECD

21 Nov 2017

Pages: 45 - 64

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## The cooperative problem-solving process

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M Wooldridge, NR Jennings, The cooperative problem-solving process, Journal of Logic and Computation , Volume 9, Issue 4, August 1999, Pages 563–592, https://doi.org/10.1093/logcom/9.4.563

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We present a model of cooperative problem solving that describes the process from its beginning, with some agent recognizing the potential for cooperation with respect to one of its goals, through to team action. Our approach is to characterize the mental states of the agents that lead them to solicit, and take part in, cooperative action. The model is formalized by expressing it as a theory in a quantified multi-modal logic.

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## Explain what is Piaget and What is Cooperative problem solving.

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## 2 Cooperation

From the noba project by  jake p. moskowitz  and  paul k. piff university of california, irvine.

Introduction

People cooperate with others throughout their life. Whether on the playground with friends, at home with family, or at work with colleagues, cooperation is a natural instinct (Keltner et al. 2014). Children as young as 14 months cooperate with others on joint tasks (Warneken et al. 2007). Humans’ closest evolutionary relatives, chimpanzees and bonobos, maintain long-term cooperative relationships as well, sharing resources and caring for each other’s young (de Waal & Lanting, 1997; Langergraber et al. 2007). Ancient animal remains found near early human settlements suggest that our ancestors hunted in cooperative groups (Mithen, 1996). Cooperation, it seems, is embedded in our evolutionary heritage.

Yet, cooperation can also be difficult to achieve; there are often breakdowns in people’s ability to work effectively in teams, or in their willingness to collaborate with others. Even with issues that can only be solved through large-scale cooperation, such as climate change and world hunger, people can have difficulties joining forces with others to take collective action. Psychologists have identified numerous individual and situational factors that influence the effectiveness of cooperation across many areas of life. From the trust that people place in others to the lines they draw between “us” and “them,” many different processes shape cooperation. This chapter will explore these individual, situational, and cultural influences on cooperation.

## The Prisoner’s Dilemma

This scenario, in which two people independently choose between cooperation and defection, is known as the  prisoner’s dilemma . It gets its name from the situation in which two prisoners who have committed a crime are given the opportunity to either (A) both confess their crime (and get a moderate sentence), (B) rat out their accomplice (and get a lesser sentence), or (C) both remain silent (and avoid punishment altogether). Psychologists use various forms of the prisoner’s dilemma scenario to study self-interest and cooperation. Whether framed as a monetary game or a prison game, the prisoner’s dilemma illuminates a conflict at the core of many decisions to cooperate: it pits the motivation to maximize  personal reward  against the motivation to maximize  gains for the group  (you and your partner combined).

For someone trying to maximize his or her own personal reward, the most “rational” choice is to defect (not cooperate), because defecting always results in a larger personal reward, regardless of the partner’s choice. However, when the two participants view their partnership as a joint effort (such as a friendly relationship), cooperating is the best strategy of all, since it provides the largest combined sum of money (\$10—which they share), as opposed to partial cooperation (\$8), or mutual defection (\$4). In other words, although defecting represents the “best” choice from an individual perspective, it is also the worst choice to make for the group as a whole.

This divide between personal and collective interests is a key obstacle that prevents people from cooperating. Think back to our earlier definition of cooperation is when multiple partners work together toward a common goal that will benefit everyone. As is frequent in these types of scenarios, even though cooperation may benefit the whole group, individuals are often able to earn even larger, personal rewards by defecting—as demonstrated in the prisoner’s dilemma example above.

You can see a small, real-world example of the prisoner’s dilemma phenomenon at live music concerts. At venues with seating, many audience members will choose to stand, hoping to get a better view of the musicians onstage. As a result, the people sitting directly behind those now-standing people are also forced to stand to see the action onstage. This creates a chain reaction in which the entire audience now has to stand, just to see over the heads of the crowd in front of them. While choosing to stand may improve one’s own concert experience, it creates a literal barrier for the rest of the audience, hurting the overall experience of the group.

Simple models of  rational self-interest predict 100% defection in cooperative tasks. That is, if people were only interested in benefiting themselves, we would always expect to see selfish behavior. Instead, there is a surprising tendency to cooperate in the prisoner’s dilemma and similar tasks (Batson & Moran, 1999; Oosterbeek et al., 2004). Given the clear benefits to defect, why then do some people choose to cooperate, whereas others choose to defect?

## Individual Differences in Cooperation

Social value orientation.

One key factor related to individual differences in cooperation is the extent to which people value not only their own outcomes, but also the outcomes of others.  Social value orientation (SVO) describes people’s preferences when dividing important resources between themselves and others (Messick & McClintock, 1968). A person might, for example, generally be competitive with others, or cooperative, or self-sacrificing. People with different social values differ in the importance they place on their own positive outcomes relative to the outcomes of others. For example, you might give your friend gas money because she drives you to school, even though that means you will have less spending money for the weekend. In this example, you are demonstrating a cooperative orientation.

People generally fall into one of three categories of SVO: cooperative, individualistic, or competitive . While most people want to bring about positive outcomes for all (cooperative orientation), certain types of people are less concerned about the outcomes of others (individualistic), or even seek to undermine others in order to get ahead (competitive orientation).

Are you curious about your own orientation? One technique psychologists use to sort people into one of these categories is to have them play a series of  decomposed games —short laboratory exercises that involve making a choice from various distributions of resources between oneself and an “other.” Consider the example shown in Figure 2, which offers three different ways to distribute a valuable resource (such as money). People with  competitive  SVOs, who try to maximize their relative advantage over others, are most likely to pick option A. People with  cooperative  SVOs, who try to maximize joint gain for both themselves and others, are more likely to split the resource evenly, picking option B. People with  individualistic  SVOs, who always maximize gains to the self, regardless of how it affects others, will most likely pick option C.

Researchers have found that a person’s SVO predicts how cooperative he or she is in both laboratory experiments and the outside world. For example, in one laboratory experiment, groups of participants were asked to play a  commons dilemma game. In this game, participants each took turns drawing from a central collection of points to be exchanged for real money at the end of the experiment. These points represented a  common-pool resource  for the group, like valuable goods or services in society (such as farm land, ground water, and air quality) that are freely accessible to everyone but prone to overuse and degradation. Participants were told that, while the common-pool resource would gradually replenish after the end of every turn, taking too much of the resource too quickly would eventually deplete it. The researchers found that participants with cooperative SVOs withdrew fewer resources from the common-pool than those with competitive and individualistic SVOs, indicating a greater willingness to cooperate with others and act in a way that is sustainable for the group (Kramer et al., 1986; Roch & Samuelson, 1997).

Research has also shown that people with cooperative SVOs are more likely to commute to work using public transportation—an act of cooperation that can help reduce carbon emissions—rather than drive themselves, compared to people with competitive and individualistic SVOs (Van Vugt, Meertens, & Van Lange, 1995; Van Vugt et al., 1996). People with cooperative SVOs also more frequently engage in behavior intended to help others, such as volunteering and giving money to charity (McClintock & Allison, 1989; Van Lange et al., 2007). Taken together, these findings show that people with cooperative SVOs act with greater consideration for the overall well-being of others and the group as a whole, using resources in moderation and taking more effortful measures (like using public transportation to protect the environment) to benefit the group.

## Empathic Ability

Empathy   is the ability to feel and understand another’s emotional experience. When we empathize with someone else, we take on that person’s perspective, imagining the world from his or her point of view and vicariously experiencing his or her emotions (Davis, 1994; Goetz et al., 2010). Research has shown that when people empathize with their partner, they act with greater cooperation and overall  altruism —the desire to help the partner, even at a potential cost to the self. People that can experience and understand the emotions of others are better able to work with others in groups, earning higher job performance ratings on average from their supervisors, even after adjusting for different types of work and other aspects of personality (Côté & Miners, 2006).

When empathizing with a person in distress, the natural desire to help is often expressed as a desire to cooperate. In one study, just before playing an economic game with a partner in another room, participants were given a note revealing that their partner had just gone through a rough breakup and needed some cheering up. While half of the subjects were urged by the experimenters to “remain objective and detached,” the other half were told to “try and imagine how the other person feels.” Though both groups received the same information about their partner, those who were encouraged to engage in empathy—by actively experiencing their partner’s emotions—acted with greater cooperation in the economic game (Batson & Moran, 1999). The researchers also found that people who empathized with their partners were more likely to act cooperatively, even after being told that their partner had already made a choice to  not  cooperate (Batson & Ahmad, 2001)! Evidence of the link between empathy and cooperation has even been found in studies of preschool children (Marcus et al., 1979). From a very early age, emotional understanding can foster cooperation.

Although empathizing with a partner can lead to more cooperation between two people, it can also undercut cooperation within larger groups. In groups, empathizing with a single person can lead people to abandon broader cooperation in favor of helping only the target individual. In one study, participants were asked to play a cooperative game with three partners. In the game, participants were asked to (A) donate resources to a central pool, (B) donate resources to a specific group member, or (C) keep the resources for themselves. According to the rules, all donations to the central pool would be increased by 50% then distributed evenly, resulting in a net gain to the entire group. Objectively, this might seem to be the best option. However, when participants were encouraged to imagine the feelings of one of their partners said to be in distress, they were more likely to donate their tickets to that partner and not engage in cooperation with the group—rather than remaining detached and objective (Batson et al., 1995). Though empathy can create strong cooperative bonds between individuals, it can sometimes lead to actions that, despite being well-intentioned, end up undermining the group’s best interests.

## Situational Influences of Cooperation

Communication and commitment.

Open communication between people is one of the best ways to promote cooperation (Dawes et al., 1977; Dawes, 1988). This is because communication provides an opportunity to size up the trustworthiness of others. It also affords us a chance to prove our own trustworthiness, by verbally committing to cooperate with others. Since cooperation requires people to enter a   state of vulnerability  and trust with partners, we are very sensitive to the social cues and interactions of potential partners before deciding to cooperate with them.

In one line of research, groups of participants were allowed to chat for five minutes before playing a multi-round “public goods” game. During the chats, the players were allowed to discuss game strategies and make verbal commitments about their in-game actions. While some groups were able to reach a consensus on a strategy (e.g., “always cooperate”), other groups failed to reach a consensus within their allotted five minutes or even picked strategies that ensured  non cooperation (e.g., “every person for themselves”). The researchers found that when group members made explicit commitments to each other to cooperate, they ended up honoring those commitments and acting with greater cooperation. Interestingly, the effect of face-to-face verbal commitments persisted even when the cooperation game itself was completely anonymous (Kerr & Kaufman-Gilliland, 1994; Kerr et al., 1997). This suggests that those who explicitly commit to cooperate are driven not by the fear of external punishment by group members, but by their own personal desire to honor such commitments. In other words, once people make a specific promise to cooperate, they are driven by “that still, small voice”—the voice of their own inner conscience—to fulfill that commitment (Kerr et al., 1997).

When it comes to cooperation, trust is key (Chaudhuri et al., 2002; Parks et al., 1996). Working with others toward a common goal requires a level of faith that our partners will repay our hard work and generosity, and not take advantage of us for their own selfish gains. Social trust, or the belief that another person’s actions will be beneficial to one’s own interests (Kramer, 1999), enables people to work together as a single unit, pooling their resources to accomplish more than they could individually. Trusting others, however, depends on their actions and reputation.

One common example of the difficulties in trusting others that you might recognize from being a student occurs when you are assigned a group project. Many students dislike group projects because they worry about social loafing —the way that one person expends less effort but still benefits from the efforts of the group. Imagine, for example, that you and five other students are assigned to work together on a difficult class project. At first, you and your group members split the work up evenly. As the project continues, however, you notice that one member of your team isn’t doing his “fair share.” He fails to show up to meetings, his work is sloppy, and he seems generally uninterested in contributing to the project. After a while, you might begin to suspect that this student is trying to get by with minimal effort, perhaps assuming others will pick up the slack. Your group now faces a difficult choice: either join the slacker and abandon all work on the project, causing it to collapse, or keep cooperating and allow for the possibility that the uncooperative student may receive a decent grade for others’ work.

If this scenario sounds familiar to you, you’re not alone. Economists call this situation the  free rider problem -when individuals benefit from the cooperation of others without contributing anything in return (Grossman & Hart, 1980). Although these sorts of actions may benefit the free rider in the short-term, free riding can have a negative impact on a person’s social reputation over time. In the above example, for instance, the “free riding” student may develop a reputation as lazy or untrustworthy, leading others to be less willing to work with him or her in the future.

Indeed, research has shown that a poor reputation for cooperation can serve as a warning sign for others  not  to cooperate with the person in disrepute. For example, in one experiment involving a group economic game, participants seen as being uncooperative were punished harshly by their fellow participants. According to the rules of the game, individuals took turns being either a “donor” or a “receiver” over the course of multiple rounds. If donors chose to give up a small sum of actual money, receivers would receive a slightly larger sum, resulting in an overall net gain. However, unbeknownst to the group, one participant was secretly instructed  never  to donate. After just a few rounds of play, this individual was effectively shunned by the rest of the group, receiving almost zero donations from the other members (Milinski et al., 2001). When someone is seen being consistently uncooperative, other people have no incentive to trust him/her, resulting in a collapse of cooperation.

On the other hand, people are more likely to cooperate with others who have a good reputation for cooperation and are therefore deemed trustworthy. In one study, people played a group economic game similar to the one described above: over multiple rounds, they took turns choosing whether to donate to other group members. Over the course of the game, donations were more frequently given to individuals who had been generous in earlier rounds of the game (Wedekind & Milinski, 2000). In other words, individuals seen cooperating with others were afforded a reputational advantage, earning them more partners willing to cooperate and a larger overall monetary reward.

## Group Identification

Another factor that can impact cooperation is a person’s  social identity , or the extent to which he or she identifies as a member of a particular social group (Tajfel & Turner, 1979/1986). People can identify with groups of all shapes and sizes: a group might be relatively small, such as a local high school class, or very large, such as a national citizenship or a political party. While these groups are often bound together by shared goals and values, they can also form according to seemingly arbitrary qualities, such as musical taste, hometown, or even completely randomized assignment, such as a coin toss (Tajfel et al., 1971; Bigler et al., 2001; Locksley et al. 1980). When members of a group place a high value on their group membership, their identity (the way they view themselves) can be shaped in part by the goals and values of that group.

Research shows that when people’s group identity is emphasized (for example, when laboratory participants are referred to as “group members” rather than “individuals”), they are less likely to act selfishly in a commons dilemma game. In such experiments, so-called “group members” withdraw fewer resources, with the outcome of promoting the sustainability of the group (Brewer & Kramer, 1986). In one study, students who strongly identified with their university were less likely to leave a cooperative group of fellow students when given an attractive option to exit (Van Vugt & Hart, 2004). In addition, the strength of a person’s identification with a group or organization is a key driver behind participation in large-scale cooperative efforts, such as collective action in political and workers’ groups (Klandersman, 2002), and engaging in organizational citizenship behaviors (Cropanzano & Byrne, 2000).

Emphasizing group identity is not without its costs: although it can increase cooperation within  groups, it can also undermine cooperation  between  groups. Researchers have found that groups interacting with other groups are more competitive and less cooperative than individuals interacting with other individuals, a phenomenon known as  interindividual-intergroup discontinuity  (Schopler &; Insko, 1999; Wildschut et al. 2003). For example, groups interacting with other groups displayed greater self-interest and reduced cooperation in a prisoner’s dilemma game than did individuals completing the same tasks with other individuals (Insko et al., 1987). Such problems with trust and cooperation are largely due to people’s general reluctance to cooperate with members of an outgroup, or those outside the boundaries of one’s own social group (Allport, 1954; Van Vugt et al., 2000).  Outgroups  do not have to be explicit rivals for this effect to take place. Indeed, in one study, simply telling groups of participants that other groups preferred a different style of painting led them to behave less cooperatively than pairs of individuals completing the same task (Insko et al., 2005). Though a strong group identity can bind individuals within the group together, it can also drive divisions between different groups, reducing overall trust and cooperation on a larger scope.

Under the right circumstances, however, even rival groups can be turned into cooperative partners in the presence of superordinate goals. In a classic demonstration of this phenomenon, Muzafer Sherif and colleagues observed the cooperative and competing behaviors of two groups of twelve-year-old boys at a summer camp in Robber’s Cave State Park, in Oklahoma (Sherif et al. 1961). The twenty-two boys in the study were all carefully interviewed to determine that none of them knew each other beforehand. Importantly, Sherif and colleagues kept both groups unaware of each other’s existence, arranging for them to arrive at separate times and occupy different areas of the camp. Within each group, the participants quickly bonded and established their own group identity—“The Eagles” and “The Rattlers”—identifying leaders and creating flags decorated with their own group’s name and symbols.

For the next phase of the experiment, the researchers revealed the existence of each group to the other, leading to reactions of anger, territorialism, and verbal abuse between the two. This behavior was further compounded by a series of competitive group activities, such as baseball and tug-of-war, leading the two groups to engage in even more spiteful behavior: The Eagles set fire to The Rattlers’ flag, and The Rattlers retaliated by ransacking The Eagles’ cabin, overturning beds and stealing their belongings. Eventually, the two groups refused to eat together in the same dining hall, and they had to be physically separated to avoid further conflict.

However, in the final phase of the experiment, Sherif and colleagues introduced a dilemma to both groups that could only be solved through mutual cooperation. The researchers told both groups that there was a shortage of drinking water in the camp, supposedly due to “vandals” damaging the water supply. As both groups gathered around the water supply, attempting to find a solution, members from each group offered suggestions and worked together to fix the problem. Since the lack of drinking water affected both groups equally, both were highly motivated to try and resolve the issue. Finally, after 45 minutes, the two groups managed to clear a stuck pipe, allowing fresh water to flow. The researchers concluded that when conflicting groups share a superordinate goal, they are capable of shifting their attitudes and bridging group differences to become cooperative partners. The insights from this study have important implications for group-level cooperation. Since many problems facing the world today, such as climate change and nuclear proliferation, affect individuals of all nations, and are best dealt with through the coordinated efforts of different groups and countries, emphasizing the shared nature of these dilemmas may enable otherwise competing groups to engage in cooperative and collective action.

Culture can have a powerful effect on people’s beliefs about and ways they interact with others. Might culture also affect a person’s tendency toward cooperation? To answer this question, Joseph Henrich and his colleagues surveyed people from 15 small-scale societies around the world, located in places such as Zimbabwe, Bolivia, and Indonesia. These groups varied widely in the ways they traditionally interacted with their environments: some practiced small-scale agriculture, others foraged for food, and still others were nomadic herders of animals (Henrich et al., 2001).

To measure their tendency toward cooperation, individuals of each society were asked to play the ultimatum game, a task similar in nature to the prisoner’s dilemma. The game has two players: Player A (the “allocator”) is given a sum of money (equal to two days’ wages) and allowed to donate any amount of it to Player B (the “responder”). Player B can then either accept or reject Player A’s offer. If Player B accepts the offer, both players keep their agreed-upon amounts. However, if Player B rejects the offer, then neither player receives anything. In this scenario, the responder can use his/her authority to punish unfair offers, even though it requires giving up his or her own reward. In turn, Player A must be careful to propose an acceptable offer to Player B, while still trying to maximize his/her own outcome in the game.

According to a model of rational economics, a self-interested Player B should always choose to accept any offer, no matter how small or unfair. As a result, Player A should always try to offer the minimum possible amount to Player B, in order to maximize his/her own reward. Instead, the researchers found that people in these 15 societies donated on average 39% of the sum to their partner (Henrich et al., 2001). This number is almost identical to the amount that people of Western cultures donate when playing the ultimatum game (Oosterbeek et al., 2004). These findings suggest that allocators in the game, instead of offering the least possible amount, try to maintain a sense of fairness and “shared rewards” in the game, in part so that their offers will not be rejected by the responder.

Henrich and colleagues (2001) also observed significant variation between cultures in terms of their level of cooperation. Specifically, the researchers found that the extent to which individuals in a culture needed to collaborate with each other to gather resources to survive predicted how likely they were to be cooperative. For example, among the people of the Lamelara in Indonesia, who survive by hunting whales in groups of a dozen or more individuals, donations in the ultimatum game were extremely high—approximately 58% of the total sum. In contrast, the Machiguenga people of Peru, who are generally economically independent at the family level, donated much less on average—about 26% of the total sum. The interdependence of people for survival, therefore, seems to be a key component of why people decide to cooperate with others.

Though the various survival strategies of small-scale societies might seem quite remote from your own experiences, take a moment to think about how your life is dependent on collaboration with others. Very few of us in industrialized societies live in houses we build ourselves, wear clothes we make ourselves, or eat food we grow ourselves. Instead, we depend on others to provide specialized resources and products, such as food, clothing, and shelter that are essential to our survival. Studies show that Americans give about 40% of their sum in the ultimatum game—less than the Lamelara give, but on par with most of the small-scale societies sampled by Henrich and colleagues (Oosterbeek et al., 2004). While living in an industrialized society might not require us to hunt in groups like the Lamelara do, we still depend on others to supply the resources we need to survive.

## Take a Quiz

An optional quiz is available to accompany this chapter here: https://nobaproject.com/modules/cooperation

## Discussion Questions

• Which groups do you identify with? Consider sports teams, home towns, and universities. How does your identification with these groups make you feel about other members of these groups? What about members of competing groups?
• Thinking of all the accomplishments of humanity throughout history which do you believe required the greatest amounts of cooperation? Why?
• In your experience working on group projects—such as group projects for a class—what have you noticed regarding the themes presented in this module (eg. Competition, free riding, cooperation, trust)? How could you use the material you have just learned to make group projects more effective?
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A classic paradox in which two individuals must independently choose between defection (maximizing reward to the self) and cooperation (maximizing reward to the group).

cooperation is when multiple partners work together toward a common goal that will benefit everyone.

The often challenged principle that people will make logical decisions based on maximizing their own gains and benefits.

An assessment of how an individual prefers to allocate resources between their self and another person.

A task in which an individual chooses from multiple allocations of resources to distribute between him- or herself and another person.

A game in which members of a group must balance their desire for personal gain against the deterioration and possible collapse of a resource.

A collective product or service that is freely available to all individuals of a society, but is vulnerable to overuse and degradation.

The ability to understand another person's emotional experience

A desire to improve the welfare of another person, at a potential cost to the self and without any expectation of reward.

When a person places their self in a position in which they might be exploited or harmed. This is often done out of trust that others will not exploit the vulnerability.

The belief that another person’s actions will be beneficial to one’s own interests

The reduction of individual effort exerted when people work in groups compared with when they work alone.

when individuals benefit from the cooperation of others without contributing anything in return

A person’s sense of who they are, based on their group membership(s).

The tendency for relations between groups to be less cooperative than relations between individuals.

A social category or group with which an individual does not identify.

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