problem solving method of learning

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• Establishing Community Agreements and Classroom Norms
• Sample group work rubric
• Problem-Based Learning Clearinghouse of Activities, University of Delaware

Problem-Based Learning

Problem-based learning  (PBL) is a student-centered approach in which students learn about a subject by working in groups to solve an open-ended problem. This problem is what drives the motivation and the learning. 

Why Use Problem-Based Learning?

Nilson (2010) lists the following learning outcomes that are associated with PBL. A well-designed PBL project provides students with the opportunity to develop skills related to:

• Working in teams.
• Managing projects and holding leadership roles.
• Oral and written communication.
• Self-awareness and evaluation of group processes.
• Working independently.
• Critical thinking and analysis.
• Explaining concepts.
• Self-directed learning.
• Applying course content to real-world examples.
• Researching and information literacy.
• Problem solving across disciplines.

Considerations for Using Problem-Based Learning

Rather than teaching relevant material and subsequently having students apply the knowledge to solve problems, the problem is presented first. PBL assignments can be short, or they can be more involved and take a whole semester. PBL is often group-oriented, so it is beneficial to set aside classroom time to prepare students to   work in groups  and to allow them to engage in their PBL project.

Students generally must:

• Examine and define the problem.
• Explore what they already know about underlying issues related to it.
• Determine what they need to learn and where they can acquire the information and tools necessary to solve the problem.
• Evaluate possible ways to solve the problem.
• Solve the problem.
• Report on their findings.

Getting Started with Problem-Based Learning

• Articulate the learning outcomes of the project. What do you want students to know or be able to do as a result of participating in the assignment?
• Create the problem. Ideally, this will be a real-world situation that resembles something students may encounter in their future careers or lives. Cases are often the basis of PBL activities. Previously developed PBL activities can be found online through the University of Delaware’s PBL Clearinghouse of Activities .
• Establish ground rules at the beginning to prepare students to work effectively in groups.
• Introduce students to group processes and do some warm up exercises to allow them to practice assessing both their own work and that of their peers.
• Consider having students take on different roles or divide up the work up amongst themselves. Alternatively, the project might require students to assume various perspectives, such as those of government officials, local business owners, etc.
• Establish how you will evaluate and assess the assignment. Consider making the self and peer assessments a part of the assignment grade.

Nilson, L. B. (2010).  Teaching at its best: A research-based resource for college instructors  (2nd ed.).  San Francisco, CA: Jossey-Bass. 

Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Problem based learning: a teacher's guide

December 10, 2021

Find out how teachers use problem-based learning models to improve engagement and drive attainment.

Main, P (2021, December 10). Problem based learning: a teacher's guide. Retrieved from https://www.structural-learning.com/post/problem-based-learning-a-teachers-guide

What is problem-based learning?

Problem-based learning (PBL) is a style of teaching that encourages students to become the drivers of their learning process . Problem-based learning involves complex learning issues from real-world problems and makes them the classroom's topic of discussion ; encouraging students to understand concepts through problem-solving skills rather than simply learning facts. When schools find time in the curriculum for this style of teaching it offers students an authentic vehicle for the integration of knowledge .

Embracing this pedagogical approach enables schools to balance subject knowledge acquisition with a skills agenda . Often used in medical education, this approach has equal significance in mainstream education where pupils can apply their knowledge to real-life problems. 

PBL is not only helpful in learning course content , but it can also promote the development of problem-solving abilities , critical thinking skills , and communication skills while providing opportunities to work in groups , find and analyse research materials , and take part in life-long learning .

PBL is a student-centred teaching method in which students understand a topic by working in groups. They work out an open-ended problem , which drives the motivation to learn. These sorts of theories of teaching do require schools to invest time and resources into supporting self-directed learning. Not all curriculum knowledge is best acquired through this process, rote learning still has its place in certain situations. In this article, we will look at how we can equip our students to take more ownership of the learning process and utilise more sophisticated ways for the integration of knowledge .

Philosophical Underpinnings of PBL

Problem-Based Learning (PBL), with its roots in the philosophies of John Dewey, Maria Montessori, and Jerome Bruner, aligns closely with the social constructionist view of learning. This approach positions learners as active participants in the construction of knowledge, contrasting with traditional models of instruction where learners are seen as passive recipients of information.

Dewey, a seminal figure in progressive education, advocated for active learning and real-world problem-solving, asserting that learning is grounded in experience and interaction. In PBL, learners tackle complex, real-world problems, which mirrors Dewey's belief in the interconnectedness of education and practical life.

Montessori also endorsed learner-centric, self-directed learning, emphasizing the child's potential to construct their own learning experiences. This parallels with PBL’s emphasis on self-directed learning, where students take ownership of their learning process.

Jerome Bruner’s theories underscored the idea of learning as an active, social process. His concept of a 'spiral curriculum' – where learning is revisited in increasing complexity – can be seen reflected in the iterative problem-solving process in PBL.

Webb’s Depth of Knowledge (DOK) framework aligns with PBL as it encourages higher-order cognitive skills. The complex tasks in PBL often demand analytical and evaluative skills (Webb's DOK levels 3 and 4) as students engage with the problem, devise a solution, and reflect on their work.

The effectiveness of PBL is supported by psychological theories like the information processing theory, which highlights the role of active engagement in enhancing memory and recall. A study by Strobel and Van Barneveld (2009) found that PBL students show improved retention of knowledge, possibly due to the deep cognitive processing involved.

As cognitive scientist Daniel Willingham aptly puts it, "Memory is the residue of thought." PBL encourages learners to think critically and deeply, enhancing both learning and retention.

Here's a quick overview:

• John Dewey : Emphasized learning through experience and the importance of problem-solving.
• Maria Montessori : Advocated for child-centered, self-directed learning.
• Jerome Bruner : Underlined learning as a social process and proposed the spiral curriculum.
• Webb’s DOK : Supports PBL's encouragement of higher-order thinking skills.
• Information Processing Theory : Reinforces the notion that active engagement in PBL enhances memory and recall.

This deep-rooted philosophical and psychological framework strengthens the validity of the problem-based learning approach, confirming its beneficial role in promoting valuable cognitive skills and fostering positive student learning outcomes.

What are the characteristics of problem-based learning?

Adding a little creativity can change a topic into a problem-based learning activity. The following are some of the characteristics of a good PBL model:

• The problem encourages students to search for a deeper understanding of content knowledge;
• Students are responsible for their learning. PBL has a student-centred learning approach . Students' motivation increases when responsibility for the process and solution to the problem rests with the learner;
• The problem motivates pupils to gain desirable learning skills and to defend well-informed decisions ;
• The problem connects the content learning goals with the previous knowledge. PBL allows students to access, integrate and study information from multiple disciplines that might relate to understanding and resolving a specific problem—just as persons in the real world recollect and use the application of knowledge that they have gained from diverse sources in their life.
• In a multistage project, the first stage of the problem must be engaging and open-ended to make students interested in the problem. In the real world, problems are poorly-structured. Research suggests that well-structured problems make students less invested and less motivated in the development of the solution. The problem simulations used in problem-based contextual learning are less structured to enable students to make a free inquiry.

• In a group project, the problem must have some level of complexity that motivates students towards knowledge acquisition and to work together for finding the solution. PBL involves collaboration between learners. In professional life, most people will find themselves in employment where they would work productively and share information with others. PBL leads to the development of such essential skills . In a PBL session, the teacher would ask questions to make sure that knowledge has been shared between pupils;
• At the end of each problem or PBL, self and peer assessments are performed. The main purpose of assessments is to sharpen a variety of metacognitive processing skills and to reinforce self-reflective learning.
• Student assessments would evaluate student progress towards the objectives of problem-based learning. The learning goals of PBL are both process-based and knowledge-based. Students must be assessed on both these dimensions to ensure that they are prospering as intended from the PBL approach. Students must be able to identify and articulate what they understood and what they learned.

Why is Problem-based learning a significant skill?

Using Problem-Based Learning across a school promotes critical competence, inquiry , and knowledge application in social, behavioural and biological sciences. Practice-based learning holds a strong track record of successful learning outcomes in higher education settings such as graduates of Medical Schools.

Educational models using PBL can improve learning outcomes by teaching students how to implement theory into practice and build problem-solving skills. For example, within the field of health sciences education, PBL makes the learning process for nurses and medical students self-centred and promotes their teamwork and leadership skills. Within primary and secondary education settings, this model of teaching, with the right sort of collaborative tools , can advance the wider skills development valued in society.

At Structural Learning, we have been developing a self-assessment tool designed to monitor the progress of children. Utilising these types of teaching theories curriculum wide can help a school develop the learning behaviours our students will need in the workplace.

Curriculum wide collaborative tools include Writers Block and the Universal Thinking Framework . Along with graphic organisers, these tools enable children to collaborate and entertain different perspectives that they might not otherwise see. Putting learning in action by using the block building methodology enables children to reach their learning goals by experimenting and iterating. 

How is problem-based learning different from inquiry-based learning?

The major difference between inquiry-based learning and PBL relates to the role of the teacher . In the case of inquiry-based learning, the teacher is both a provider of classroom knowledge and a facilitator of student learning (expecting/encouraging higher-order thinking). On the other hand, PBL is a deep learning approach, in which the teacher is the supporter of the learning process and expects students to have clear thinking, but the teacher is not the provider of classroom knowledge about the problem—the responsibility of providing information belongs to the learners themselves.

As well as being used systematically in medical education, this approach has significant implications for integrating learning skills into mainstream classrooms .

Using a critical thinking disposition inventory, schools can monitor the wider progress of their students as they apply their learning skills across the traditional curriculum. Authentic problems call students to apply their critical thinking abilities in new and purposeful ways. As students explain their ideas to one another, they develop communication skills that might not otherwise be nurtured.

Depending on the curriculum being delivered by a school, there may well be an emphasis on building critical thinking abilities in the classroom. Within the International Baccalaureate programs, these life-long skills are often cited in the IB learner profile . Critical thinking dispositions are highly valued in the workplace and this pedagogical approach can be used to harness these essential 21st-century skills.

What are the Benefits of Problem-Based Learning?

Student-led Problem-Based Learning is one of the most useful ways to make students drivers of their learning experience. It makes students creative, innovative, logical and open-minded. The educational practice of Problem-Based Learning also provides opportunities for self-directed and collaborative learning with others in an active learning and hands-on process. Below are the most significant benefits of problem-based learning processes:

• Self-learning: As a self-directed learning method, problem-based learning encourages children to take responsibility and initiative for their learning processes . As children use creativity and research, they develop skills that will help them in their adulthood.
• Engaging : Students don't just listen to the teacher, sit back and take notes. Problem-based learning processes encourages students to take part in learning activities, use learning resources , stay active , think outside the box and apply critical thinking skills to solve problems.
• Teamwork : Most of the problem-based learning issues involve students collaborative learning to find a solution. The educational practice of PBL builds interpersonal skills, listening and communication skills and improves the skills of collaboration and compromise.
• Intrinsic Rewards: In most problem-based learning projects, the reward is much bigger than good grades. Students gain the pride and satisfaction of finding an innovative solution, solving a riddle, or creating a tangible product.
• Transferable Skills: The acquisition of knowledge through problem-based learning strategies don't just help learners in one class or a single subject area. Students can apply these skills to a plethora of subject matter as well as in real life.
• Multiple Learning Opportunities : A PBL model offers an open-ended problem-based acquisition of knowledge, which presents a real-world problem and asks learners to come up with well-constructed responses. Students can use multiple sources such as they can access online resources, using their prior knowledge, and asking momentous questions to brainstorm and come up with solid learning outcomes. Unlike traditional approaches , there might be more than a single right way to do something, but this process motivates learners to explore potential solutions whilst staying active.

Embracing problem-based learning

Problem-based learning can be seen as a deep learning approach and when implemented effectively as part of a broad and balanced curriculum , a successful teaching strategy in education. PBL has a solid epistemological and philosophical foundation and a strong track record of success in multiple areas of study. Learners must experience problem-based learning methods and engage in positive solution-finding activities. PBL models allow learners to gain knowledge through real-world problems, which offers more strength to their understanding and helps them find the connection between classroom learning and the real world at large.

As they solve problems, students can evolve as individuals and team-mates. One word of caution, not all classroom tasks will lend themselves to this learning theory. Take spellings , for example, this is usually delivered with low-stakes quizzing through a practice-based learning model. PBL allows students to apply their knowledge creatively but they need to have a certain level of background knowledge to do this, rote learning might still have its place after all.

Key Concepts and considerations for school leaders

1. Problem Based Learning (PBL)

Problem-based learning (PBL) is an educational method that involves active student participation in solving authentic problems. Students are given a task or question that they must answer using their prior knowledge and resources. They then collaborate with each other to come up with solutions to the problem. This collaborative effort leads to deeper learning than traditional lectures or classroom instruction .

Key question: Inside a traditional curriculum , what opportunities across subject areas do you immediately see?

2. Deep Learning

Deep learning is a term used to describe the ability to learn concepts deeply. For example, if you were asked to memorize a list of numbers, you would probably remember the first five numbers easily, but the last number would be difficult to recall. However, if you were taught to understand the concept behind the numbers, you would be able to remember the last number too.

Key question: How will you make sure that students use a full range of learning styles and learning skills ?

3. Epistemology

Epistemology is the branch of philosophy that deals with the nature of knowledge . It examines the conditions under which something counts as knowledge.

Key question:  As well as focusing on critical thinking dispositions, what subject knowledge should the students understand?

4. Philosophy

Philosophy is the study of general truths about human life. Philosophers examine questions such as “What makes us happy?”, “How should we live our lives?”, and “Why does anything exist?”

Key question: Are there any opportunities for embracing philosophical enquiry into the project to develop critical thinking abilities ?

5. Curriculum

A curriculum is a set of courses designed to teach specific subjects. These courses may include mathematics , science, social studies, language arts, etc.

Key question: How will subject leaders ensure that the integrity of the curriculum is maintained?

6. Broad and Balanced Curriculum

Broad and balanced curricula are those that cover a wide range of topics. Some examples of these types of curriculums include AP Biology, AP Chemistry, AP English Language, AP Physics 1, AP Psychology , AP Spanish Literature, AP Statistics, AP US History, AP World History, IB Diploma Programme, IB Primary Years Program, IB Middle Years Program, IB Diploma Programme .

Key question: Are the teachers who have identified opportunities for a problem-based curriculum?

7. Successful Teaching Strategy

Successful teaching strategies involve effective communication techniques, clear objectives, and appropriate assessments. Teachers must ensure that their lessons are well-planned and organized. They must also provide opportunities for students to interact with one another and share information.

Key question: What pedagogical approaches and teaching strategies will you use?

8. Positive Solution Finding

Positive solution finding is a type of problem-solving where students actively seek out answers rather than passively accept what others tell them.

Key question: How will you ensure your problem-based curriculum is met with a positive mindset from students and teachers?

9. Real World Application

Real-world application refers to applying what students have learned in class to situations that occur in everyday life.

Key question: Within your local school community , are there any opportunities to apply knowledge and skills to real-life problems?

10. Creativity

Creativity is the ability to think of ideas that no one else has thought of yet. Creative thinking requires divergent thinking, which means thinking in different directions.

Key question: What teaching techniques will you use to enable children to generate their own ideas ?

11. Teamwork

Teamwork is the act of working together towards a common goal. Teams often consist of two or more people who work together to achieve a shared objective.

Key question: What opportunities are there to engage students in dialogic teaching methods where they talk their way through the problem?

12. Knowledge Transfer

Knowledge transfer occurs when teachers use their expertise to help students develop skills and abilities .

Key question: Can teachers be able to track the success of the project using improvement scores?

13. Active Learning

Active learning is any form of instruction that engages students in the learning process. Examples of active learning include group discussions, role-playing, debates, presentations, and simulations .

Key question: Will there be an emphasis on learning to learn and developing independent learning skills ?

14. Student Engagement

Student engagement is the degree to which students feel motivated to participate in academic activities.

Key question: Are there any tools available to monitor student engagement during the problem-based curriculum ?

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Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and communication skills. It can also provide opportunities for working in groups, finding and evaluating research materials, and life-long learning (Duch et al, 2001).

PBL can be incorporated into any learning situation. In the strictest definition of PBL, the approach is used over the entire semester as the primary method of teaching. However, broader definitions and uses range from including PBL in lab and design classes, to using it simply to start a single discussion. PBL can also be used to create assessment items. The main thread connecting these various uses is the real-world problem.

Any subject area can be adapted to PBL with a little creativity. While the core problems will vary among disciplines, there are some characteristics of good PBL problems that transcend fields (Duch, Groh, and Allen, 2001):

• The problem must motivate students to seek out a deeper understanding of concepts.
• The problem should require students to make reasoned decisions and to defend them.
• The problem should incorporate the content objectives in such a way as to connect it to previous courses/knowledge.
• If used for a group project, the problem needs a level of complexity to ensure that the students must work together to solve it.
• If used for a multistage project, the initial steps of the problem should be open-ended and engaging to draw students into the problem.

The problems can come from a variety of sources: newspapers, magazines, journals, books, textbooks, and television/ movies. Some are in such form that they can be used with little editing; however, others need to be rewritten to be of use. The following guidelines from The Power of Problem-Based Learning (Duch et al, 2001) are written for creating PBL problems for a class centered around the method; however, the general ideas can be applied in simpler uses of PBL:

• Choose a central idea, concept, or principle that is always taught in a given course, and then think of a typical end-of-chapter problem, assignment, or homework that is usually assigned to students to help them learn that concept. List the learning objectives that students should meet when they work through the problem.
• Think of a real-world context for the concept under consideration. Develop a storytelling aspect to an end-of-chapter problem, or research an actual case that can be adapted, adding some motivation for students to solve the problem. More complex problems will challenge students to go beyond simple plug-and-chug to solve it. Look at magazines, newspapers, and articles for ideas on the story line. Some PBL practitioners talk to professionals in the field, searching for ideas of realistic applications of the concept being taught.
• What will the first page (or stage) look like? What open-ended questions can be asked? What learning issues will be identified?
• How will the problem be structured?
• How long will the problem be? How many class periods will it take to complete?
• Will students be given information in subsequent pages (or stages) as they work through the problem?
• What resources will the students need?
• What end product will the students produce at the completion of the problem?
• Write a teacher's guide detailing the instructional plans on using the problem in the course. If the course is a medium- to large-size class, a combination of mini-lectures, whole-class discussions, and small group work with regular reporting may be necessary. The teacher's guide can indicate plans or options for cycling through the pages of the problem interspersing the various modes of learning.
• The final step is to identify key resources for students. Students need to learn to identify and utilize learning resources on their own, but it can be helpful if the instructor indicates a few good sources to get them started. Many students will want to limit their research to the Internet, so it will be important to guide them toward the library as well.

The method for distributing a PBL problem falls under three closely related teaching techniques: case studies, role-plays, and simulations. Case studies are presented to students in written form. Role-plays have students improvise scenes based on character descriptions given. Today, simulations often involve computer-based programs. Regardless of which technique is used, the heart of the method remains the same: the real-world problem.

Where can I learn more?

• PBL through the Institute for Transforming Undergraduate Education at the University of Delaware
• Duch, B. J., Groh, S. E, & Allen, D. E. (Eds.). (2001). The power of problem-based learning . Sterling, VA: Stylus.
• Grasha, A. F. (1996). Teaching with style: A practical guide to enhancing learning by understanding teaching and learning styles. Pittsburgh: Alliance Publishers.

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Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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Don’t Just Tell Students to Solve Problems. Teach Them How.

The positive impact of an innovative uc san diego problem-solving educational curriculum continues to grow.

• Daniel Kane - [email protected]

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Problem solving is a critical skill for technical education and technical careers of all types. But what are best practices for teaching problem solving to high school and college students? 

The University of California San Diego Jacobs School of Engineering is on the forefront of efforts to improve how problem solving is taught. This UC San Diego approach puts hands-on problem-identification and problem-solving techniques front and center. Over 1,500 students across the San Diego region have already benefited over the last three years from this program. In the 2023-2024 academic year, approximately 1,000 upper-level high school students will be taking the problem solving course in four different school districts in the San Diego region. Based on the positive results with college students, as well as high school juniors and seniors in the San Diego region, the project is getting attention from educators across the state of California, and around the nation and the world.

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In Summer 2023, th e 27 community college students who took the unique problem-solving course developed at the UC San Diego Jacobs School of Engineering thrived, according to Alex Phan PhD, the Executive Director of Student Success at the UC San Diego Jacobs School of Engineering. Phan oversees the project. 

Over the course of three weeks, these students from Southwestern College and San Diego City College poured their enthusiasm into problem solving through hands-on team engineering challenges. The students brimmed with positive energy as they worked together. 

What was noticeably absent from this laboratory classroom: frustration.

“In school, we often tell students to brainstorm, but they don’t often know where to start. This curriculum gives students direct strategies for brainstorming, for identifying problems, for solving problems,” sai d Jennifer Ogo, a teacher from Kearny High School who taught the problem-solving course in summer 2023 at UC San Diego. Ogo was part of group of educators who took the course themselves last summer.

The curriculum has been created, refined and administered over the last three years through a collaboration between the UC San Diego Jacobs School of Engineering and the UC San Diego Division of Extended Studies. The project kicked off in 2020 with a generous gift from a local philanthropist.

Not getting stuck

One of the overarching goals of this project is to teach both problem-identification and problem-solving skills that help students avoid getting stuck during the learning process. Stuck feelings lead to frustration – and when it’s a Science, Technology, Engineering and Math (STEM) project, that frustration can lead students to feel they don’t belong in a STEM major or a STEM career. Instead, the UC San Diego curriculum is designed to give students the tools that lead to reactions like “this class is hard, but I know I can do this!” –  as Ogo, a celebrated high school biomedical sciences and technology teacher, put it. 

Three years into the curriculum development effort, the light-hearted energy of the students combined with their intense focus points to success. On the last day of the class, Mourad Mjahed PhD, Director of the MESA Program at Southwestern College’s School of Mathematics, Science and Engineering came to UC San Diego to see the final project presentations made by his 22 MESA students.

“Industry is looking for students who have learned from their failures and who have worked outside of their comfort zones,” said Mjahed. The UC San Diego problem-solving curriculum, Mjahed noted, is an opportunity for students to build the skills and the confidence to learn from their failures and to work outside their comfort zone. “And from there, they see pathways to real careers,” he said. 

What does it mean to explicitly teach problem solving? 

This approach to teaching problem solving includes a significant focus on learning to identify the problem that actually needs to be solved, in order to avoid solving the wrong problem. The curriculum is organized so that each day is a complete experience. It begins with the teacher introducing the problem-identification or problem-solving strategy of the day. The teacher then presents case studies of that particular strategy in action. Next, the students get introduced to the day’s challenge project. Working in teams, the students compete to win the challenge while integrating the day’s technique. Finally, the class reconvenes to reflect. They discuss what worked and didn't work with their designs as well as how they could have used the day’s problem-identification or problem-solving technique more effectively. 

The challenges are designed to be engaging – and over three years, they have been refined to be even more engaging. But the student engagement is about much more than being entertained. Many of the students recognize early on that the problem-identification and problem-solving skills they are learning can be applied not just in the classroom, but in other classes and in life in general. 

Gabriel from Southwestern College is one of the students who saw benefits outside the classroom almost immediately. In addition to taking the UC San Diego problem-solving course, Gabriel was concurrently enrolled in an online computer science programming class. He said he immediately started applying the UC San Diego problem-identification and troubleshooting strategies to his coding assignments. 

Gabriel noted that he was given a coding-specific troubleshooting strategy in the computer science course, but the more general problem-identification strategies from the UC San Diego class had been extremely helpful. It’s critical to “find the right problem so you can get the right solution. The strategies here,” he said, “they work everywhere.”

Phan echoed this sentiment. “We believe this curriculum can prepare students for the technical workforce. It can prepare students to be impactful for any career path.”

The goal is to be able to offer the course in community colleges for course credit that transfers to the UC, and to possibly offer a version of the course to incoming students at UC San Diego. 

As the team continues to work towards integrating the curriculum in both standardized high school courses such as physics, and incorporating the content as a part of the general education curriculum at UC San Diego, the project is expected to impact thousands more students across San Diego annually. 

Portrait of the Problem-Solving Curriculum

On a sunny Wednesday in July 2023, an experiential-learning classroom was full of San Diego community college students. They were about half-way through the three-week problem-solving course at UC San Diego, held in the campus’ EnVision Arts and Engineering Maker Studio. On this day, the students were challenged to build a contraption that would propel at least six ping pong balls along a kite string spanning the laboratory. The only propulsive force they could rely on was the air shooting out of a party balloon.

A team of three students from Southwestern College – Valeria, Melissa and Alondra – took an early lead in the classroom competition. They were the first to use a plastic bag instead of disposable cups to hold the ping pong balls. Using a bag, their design got more than half-way to the finish line – better than any other team at the time – but there was more work to do. 

As the trio considered what design changes to make next, they returned to the problem-solving theme of the day: unintended consequences. Earlier in the day, all the students had been challenged to consider unintended consequences and ask questions like: When you design to reduce friction, what happens? Do new problems emerge? Did other things improve that you hadn’t anticipated? 

Other groups soon followed Valeria, Melissa and Alondra’s lead and began iterating on their own plastic-bag solutions to the day’s challenge. New unintended consequences popped up everywhere. Switching from cups to a bag, for example, reduced friction but sometimes increased wind drag. 

Over the course of several iterations, Valeria, Melissa and Alondra made their bag smaller, blew their balloon up bigger, and switched to a different kind of tape to get a better connection with the plastic straw that slid along the kite string, carrying the ping pong balls. 

One of the groups on the other side of the room watched the emergence of the plastic-bag solution with great interest. 

“We tried everything, then we saw a team using a bag,” said Alexander, a student from City College. His team adopted the plastic-bag strategy as well, and iterated on it like everyone else. They also chose to blow up their balloon with a hand pump after the balloon was already attached to the bag filled with ping pong balls – which was unique. 

“I don’t want to be trying to put the balloon in place when it's about to explode,” Alexander explained. 

Asked about whether the structured problem solving approaches were useful, Alexander’s teammate Brianna, who is a Southwestern College student, talked about how the problem-solving tools have helped her get over mental blocks. “Sometimes we make the most ridiculous things work,” she said. “It’s a pretty fun class for sure.” 

Yoshadara, a City College student who is the third member of this team, described some of the problem solving techniques this way: “It’s about letting yourself be a little absurd.”

Alexander jumped back into the conversation. “The value is in the abstraction. As students, we learn to look at the problem solving that worked and then abstract out the problem solving strategy that can then be applied to other challenges. That’s what mathematicians do all the time,” he said, adding that he is already thinking about how he can apply the process of looking at unintended consequences to improve both how he plays chess and how he goes about solving math problems.

Looking ahead, the goal is to empower as many students as possible in the San Diego area and  beyond to learn to problem solve more enjoyably. It’s a concrete way to give students tools that could encourage them to thrive in the growing number of technical careers that require sharp problem-solving skills, whether or not they require a four-year degree. 

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Teaching problem solving

Strategies for teaching problem solving apply across disciplines and instructional contexts. First, introduce the problem and explain how people in your discipline generally make sense of the given information. Then, explain how to apply these approaches to solve the problem.

Introducing the problem

Explaining how people in your discipline understand and interpret these types of problems can help students develop the skills they need to understand the problem (and find a solution). After introducing how you would go about solving a problem, you could then ask students to:

• frame the problem in their own words
• define key terms and concepts
• determine statements that accurately represent the givens of a problem
• identify analogous problems
• determine what information is needed to solve the problem

Working on solutions

In the solution phase, one develops and then implements a coherent plan for solving the problem. As you help students with this phase, you might ask them to:

• identify the general model or procedure they have in mind for solving the problem
• set sub-goals for solving the problem
• identify necessary operations and steps
• draw conclusions
• carry out necessary operations

You can help students tackle a problem effectively by asking them to:

• systematically explain each step and its rationale
• explain how they would approach solving the problem
• help you solve the problem by posing questions at key points in the process
• work together in small groups (3 to 5 students) to solve the problem and then have the solution presented to the rest of the class (either by you or by a student in the group)

In all cases, the more you get the students to articulate their own understandings of the problem and potential solutions, the more you can help them develop their expertise in approaching problems in your discipline.

Problem-Solving Method in Teaching

The problem-solving method is a highly effective teaching strategy that is designed to help students develop critical thinking skills and problem-solving abilities . It involves providing students with real-world problems and challenges that require them to apply their knowledge, skills, and creativity to find solutions. This method encourages active learning, promotes collaboration, and allows students to take ownership of their learning.

Table of Contents

Definition of problem-solving method.

Problem-solving is a process of identifying, analyzing, and resolving problems. The problem-solving method in teaching involves providing students with real-world problems that they must solve through collaboration and critical thinking. This method encourages students to apply their knowledge and creativity to develop solutions that are effective and practical.

Meaning of Problem-Solving Method

The meaning and Definition of problem-solving are given by different Scholars. These are-

Woodworth and Marquis(1948) : Problem-solving behavior occurs in novel or difficult situations in which a solution is not obtainable by the habitual methods of applying concepts and principles derived from past experience in very similar situations.

Skinner (1968): Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal. It is the procedure of making adjustments in spite of interference

Benefits of Problem-Solving Method

The problem-solving method has several benefits for both students and teachers. These benefits include:

• Encourages active learning: The problem-solving method encourages students to actively participate in their own learning by engaging them in real-world problems that require critical thinking and collaboration
• Promotes collaboration: Problem-solving requires students to work together to find solutions. This promotes teamwork, communication, and cooperation.
• Builds critical thinking skills: The problem-solving method helps students develop critical thinking skills by providing them with opportunities to analyze and evaluate problems
• Increases motivation: When students are engaged in solving real-world problems, they are more motivated to learn and apply their knowledge.
• Enhances creativity: The problem-solving method encourages students to be creative in finding solutions to problems.

Steps in Problem-Solving Method

The problem-solving method involves several steps that teachers can use to guide their students. These steps include

• Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers can present students with a real-world problem or challenge that requires critical thinking and collaboration.
• Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying causes.
• Generating solutions: After analyzing the problem, students should generate possible solutions. This step requires creativity and critical thinking.
• Evaluating solutions: The next step is to evaluate each solution based on its effectiveness and practicality
• Selecting the best solution: The final step is to select the best solution and implement it.

Verification of the concluded solution or Hypothesis

The solution arrived at or the conclusion drawn must be further verified by utilizing it in solving various other likewise problems. In case, the derived solution helps in solving these problems, then and only then if one is free to agree with his finding regarding the solution. The verified solution may then become a useful product of his problem-solving behavior that can be utilized in solving further problems. The above steps can be utilized in solving various problems thereby fostering creative thinking ability in an individual.

The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to succeed in school and in life.

• Jonassen, D. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. Routledge.
• Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
• Mergendoller, J. R., Maxwell, N. L., & Bellisimo, Y. (2006). The effectiveness of problem-based instruction: A comparative study of instructional methods and student characteristics. Interdisciplinary Journal of Problem-based Learning, 1(2), 49-69.
• Richey, R. C., Klein, J. D., & Tracey, M. W. (2011). The instructional design knowledge base: Theory, research, and practice. Routledge.
• Savery, J. R., & Duffy, T. M. (2001). Problem-based learning: An instructional model and its constructivist framework. CRLT Technical Report No. 16-01, University of Michigan. Wojcikowski, J. (2013). Solving real-world problems through problem-based learning. College Teaching, 61(4), 153-156

ORIGINAL RESEARCH article

The problem-solving method: efficacy for learning and motivation in the field of physical education.

• 1 High Institute of Sport and Physical Education of Sfax, University of Sfax, Sfax, Tunisia
• 2 Research Unit of the National Sports Observatory (ONS), Tunis, Tunisia
• 3 Research Laboratory: Education, Motricity, Sport and Health, EM2S, LR19JS01, University of Sfax, Sfax, Tunisia
• 4 Department of Neuroscience, Rehabilitation, Ophthalmology, Genetics, Maternal and Child Health (DINOGMI), University of Genoa, Genoa, Italy
• 5 Centre for Intelligent Healthcare, Coventry University, Coventry, United Kingdom
• 6 Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, Canada
• 7 High Institute of Sport and Physical Education of Ksar Saîd, University Manouba, UMA, Manouba, Tunisia

Background: In pursuit of quality teaching and learning, teachers seek the best method to provide their students with a positive educational atmosphere and the most appropriate learning conditions.

Objectives: The purpose of this study is to compare the effects of the problem-solving method vs. the traditional method on motivation and learning during physical education courses.

Methods: Fifty-three students ( M age 15 ± 0.1 years), in their 1st year of the Tunisian secondary education system, voluntarily participated in this study, and randomly assigned to a control or experimental group. Participants in the control group were taught using the traditional methods, whereas participants in the experimental group were taught using the problem-solving method. Both groups took part in a 10-hour experiment over 5 weeks. To measure students' situational motivation, a questionnaire was used to evaluate intrinsic motivation, identified regulation, external regulation, and amotivation during the first (T0) and the last sessions (T2). Additionally, the degree of students' learning was determined via video analyses, recorded at T0, the fifth (T1), and T2.

Results: Motivational dimensions, including identified regulation and intrinsic motivation, were significantly greater (all p < 0.001) in the experimental vs. the control group. The students' motor engagement in learning situations, during which the learner, despite a degree of difficulty performs the motor activity with sufficient success, increased only in the experimental group ( p < 0.001). The waiting time in the experimental group decreased significantly at T1 and T2 vs. T0 (all p < 0.001), with lower values recorded in the experimental vs. the control group at the three-time points (all p < 0.001).

Conclusions: The problem-solving method is an efficient strategy for motor skills and performance enhancement, as well as motivation development during physical education courses.

1. Introduction

The education of children is a sensitive and poignant subject, where the wellbeing of the child in the school environment is a key issue ( Ergül and Kargin, 2014 ). For this, numerous research has sought to find solutions to the problems of the traditional method, which focuses on the teacher as an instructor, giver of knowledge, arbiter of truth, and ultimate evaluator of learning ( Ergül and Kargin, 2014 ; Cunningham and Sood, 2018 ). From this perspective, a teachers' job is to present students with a designated body of knowledge in a predetermined order ( Arvind and Kusum, 2017 ). For them, learners are seen as people with “knowledge gaps” that need to be filled with information. In this method, teaching is conceived as the act of transmitting knowledge from point A (responsible for the teacher) to point B (responsible for the students; Arvind and Kusum, 2017 ). According to Novak (2010) , in the traditional method, the teacher is the one who provokes the learning.

The traditional method focuses on lecture-based teaching as the center of instruction, emphasizing delivery of program and concept ( Johnson, 2010 ; Ilkiw et al., 2017 ; Dickinson et al., 2018 ). The student listens and takes notes, passively accepts and receives from the teacher undifferentiated and identical knowledge ( Bi et al., 2019 ). Course content and delivery are considered most important, and learners acquire knowledge through exercise and practice ( Johnson et al., 1998 ). In the traditional method, academic achievement is seen as the ability of students to demonstrate, replicate, or convey this designated body of knowledge to the teacher. It is based on a transmissive model, the teacher contenting themselves with exchanging and transmitting information to the learner. Here, only the “knowledge” and “teacher” poles of the pedagogical triangle are solicited. The teacher teaches the students, who play the role of the spectator. They receive information without participating in its creation ( Perrenoud, 2003 ). For this, researchers invented a new student-centered method with effects on improving students' graphic interpretation skills and conceptual understanding of kinematic motion represent an area of contemporary interest ( Tebabal and Kahssay, 2011 ). Indeed, in order to facilitate the process of knowledge transfer, teachers should use appropriate methods targeted to specific objectives of the school curricula.

For instance, it has been emphasized that the effectiveness of any educational process as a whole relies on the crucial role of using a well-designed pedagogical (teaching and/or learning) strategy ( Kolesnikova, 2016 ).

Alternate to a traditional method of teaching, Ergül and Kargin (2014 ), proposed the problem-solving method, which represents one of the most common student-centered learning strategies. Indeed, this method allows students to participate in the learning environment, giving them the responsibility for their own acquisition of knowledge, as well as the opportunity for the understanding and structuring of diverse information.

For Cunningham and Sood (2018) , the problem-solving method may be considered a fundamental tool for the acquisition of new knowledge, notably learning transfer. Moreover, the problem-solving method is purportedly efficient for the development of manual skills and experiential learning ( Ergül and Kargin, 2014 ), as well as the optimization of thinking ability. Additionally, the problem-solving method allows learners to participate in the learning environment, while giving them responsibility for their learning and making them understand and structure the information ( Pohan et al., 2020 ). In this context, Ali (2019) reported that, when faced with an obstacle, the student will have to invoke his/her knowledge and use his/her abilities to “break the deadlock.” He/she will therefore make the most of his/her potential, but also share and exchange with his/her colleagues ( Ali, 2019 ). Throughout the process, the student will learn new concepts and skills. The role of the teacher is paramount at the beginning of the activity, since activities will be created based on problematic situations according to the subject and the program. However, on the day of the activity, it does not have the main role, and the teacher will guide learners in difficulty and will allow them to manage themselves most of the time ( Ali, 2019 ).

The problem-solving method encourages group discussion and teamwork ( Fidan and Tuncel, 2019 ). Additionally, in this pedagogical approach, the role of the teacher is a facilitator of learning, and they take on a much more interactive and less rebarbative role ( Garrett, 2008 ).

For the teaching method to be effective, teaching should consist of an ongoing process of making desirable changes among learners using appropriate methods ( Ayeni, 2011 ; Norboev, 2021 ). To bring about positive changes in students, the methods used by teachers should be the best for the subject to be taught ( Adunola et al., 2012 ). Further, suggests that teaching methods work effectively, especially if they meet the needs of learners since each learner interprets and answers questions in a unique way. Improving problem-solving skills is a primary educational goal, as is the ability to use reasoning. To acquire this skill, students must solve problems to learn mathematics and problem-solving ( Hu, 2010 ); this encourages the students to actively participate and contribute to the activities suggested by the teacher. Without sufficient motivation, learning goals can no longer be optimally achieved, although learners may have exceptional abilities. The method of teaching employed by the teachers is decisive to achieve motivational consequences in physical education students ( Leo et al., 2022 ). Pérez-Jorge et al. (2021 ) posited that given we now live in a technological society in which children are used to receiving a large amount of stimuli, gaining and maintaining their attention and keeping them motivated at school becomes a challenge for teachers.

Fenouillet (2012) stated that academic motivation is linked to resources and methods that improve attention for school learning. Furthermore, Rolland (2009) and Bessa et al. (2021) reported a link between a learner's motivational dynamics and classroom activities. The models of learning situations, where the student is the main actor, directly refers to active teaching methods, and that there is a strong link between motivation and active teaching ( Rossa et al., 2021 ). In the same context, previous reports assert that the motivation of students in physical education is an important factor since the intra-individual motivation toward this discipline is recognized as a major determinant of physical activity for students ( Standage et al., 2012 ; Luo, 2019 ; Leo et al., 2022 ). Further, extensive research on the effectiveness of teaching methods shows that the quality of teaching often influences the performance of learners ( Norboev, 2021 ). Ayeni (2011) reported that education is a process that allows students to make changes desirable to achieve specific results. Thus, the consistency of teaching methods with student needs and learning influences student achievement. This has led several researchers to explore the impact of different teaching strategies, ranging from traditional methods to active learning techniques that can be used such as the problem-solving method ( Skinner, 1985 ; Darling-Hammond et al., 2020 ).

In the context of innovation, Blázquez (2016 ) emphasizes the importance of adopting active methods and implementing them as the main element promoting the development of skills, motivation and active participation. Pedagogical models are part of the active methods which, together with model-based practice, replace traditional teaching ( Hastie and Casey, 2014 ; Casey et al., 2021 ). Thus, many studies have identified pedagogical models as the most effective way to place students at the center of the teaching-learning process ( Metzler, 2017 ), making it possible to assess the impact of physical education on learning students ( Casey, 2014 ; Rivera-Pérez et al., 2020 ; Manninen and Campbell, 2021 ). Since each model is designed to focus on a specific program objective, each model has limitations when implemented in isolation ( Bunker and Thorpe, 1982 ; Rivera-Pérez et al., 2020 ). Therefore, focusing on developing students' social and emotional skills and capacities could help them avoid failure in physical education ( Ang and Penney, 2013 ). Thus, the current emergence of new pedagogical models goes with their hybridization with different methods, which is a wave of combinations proposed today as an innovative pedagogical strategy. The incorporation of this type of method in the current education system is becoming increasingly important because it gives students a greater role, participation, autonomy and self-regulation, and above all it improves their motivation ( Puigarnau et al., 2016 ). The teaching model of personal and social responsibility, for example, is closely related to the sports education model because both share certain approaches to responsibility ( Siedentop et al., 2011 ). One of the first studies to use these two models together was Rugby ( Gordon and Doyle, 2015 ), which found significant improvements in student behavior. Also, the recent study by Menendez and Fernandez-Rio (2017) on educational kickboxing.

Previous studies have indicated that hybridization can increase play, problem solving performance and motor skills ( Menendez and Fernandez-Rio, 2017 ; Ward et al., 2021 ) and generate positive psychosocial consequences, such as pleasure, intention to be physically active and responsibility ( Dyson and Grineski, 2001 ; Menendez and Fernandez-Rio, 2017 ).

But despite all these research results, the picture remains unclear, and it remains unknown which method is more effective in improving students' learning and motivation. Given the lack of published evidence on this topic, the aim of this study was to compare the effects of problem-solving vs. the traditional method on students' motivation and learning.

We hypothesized would that the problem-solving method would be more effective in improving students' motivation and learning better than the traditional method.

2. Materials and method

2.1. participants.

Fifty-three students, aged 15–16 ( M age 15 ± 0.1 years), in their 1st year of the Tunisian secondary education system, voluntarily participated in this study. All participants were randomly chosen. Repeating students, those who practice handball activity in civil/competitive/amateur clubs or in the high school sports association, and students who were absent, even for one session, were excluded. The first class consisted of 30 students (16 boys and 14 girls), who represented the experimental group and followed basic courses on a learning method by solving problems. The second class consisted of 23 students (10 boys and 13 girls), who represented the control group and followed the traditional teaching method. The total duration was spread over 5 weeks, or two sessions per week and each session lasted 50 min.

University research ethics board approval (CPPSUD: 0295/2021) was obtained before recruiting participants who were subsequently informed of the nature, objective, methodology, and constraints. Teacher, school director, parental/guardian, and child informed consent was obtained prior to participation in the study.

2.2. Procedure

Before the start of the experiment, the participants were familiarized with the equipment and the experimental protocol in order to ensure a good learning climate. For this and to mitigate the impact of the observer and the cameras on the students, the two researchers were involved prior to the data collection in a week of familiarization by making test recordings with the classes concerned.

An approach of a teaching cycle consisting of 10 sessions spread over 5 weeks, amounting to two sessions per week. Physical education classes were held in the morning from 8 a.m. to 9 a.m., with a single goal for each session that lasted 50 min. The cyclic programs were produced by the teacher responsible for carrying out the experiment with 18 years of service. To do this, the students had the same lessons with the same objectives, only pedagogy that differs: the experimental group worked using problem-solving pedagogy, while the control group was confronted with traditional pedagogy. The sessions took place in a handball field 40 m long and 20 m wide. Examples of training sessions using the problem-solving pedagogy and the traditional pedagogy are presented in Table 1 . In addition, a motivation questionnaire, the Situational Motivation Scale (SIMS; Guay et al., 2000 ), was administered to learners at the end of the session (i.e., in the beginning, and end of the cycle). Each student answered the questions alone and according to their own ideas. This questionnaire was taken in a classroom to prevent students from acting abnormally during the study. It lasted for a maximum of 10 min.

Table 1 . Example of activities for the different sessions.

Two diametrically opposed cameras were installed so to film all the movements and behaviors of each student and teacher during the three sessions [(i) test at the start of the cycle (T0), (ii) in the middle of the cycle (T1), and (iii) test at the end of the cycle (T2)]. These sessions had the same content and each consisted of four phases: the getting started, the warm-up, the work up (which consisted of three situations: first, the work was goes up the ball to two to score in the goal following a shot. Second, the same principle as the previous situation but in the presence of a defender. Finally, third, a match 7 ≠ 7), and the cooling down These recordings were analyzed using a Learning Time Analysis System grid (LTAS; Brunelle et al., 1988 ). This made it possible to measure individual learning by coding observable variables of the behavior of learners in a learning situation.

2.3. Data collection and analysis

2.3.1. the motivation questionnaire.

In this study, in order to measure the situational motivation of students, the situational motivation scale (SIMS; Guay et al., 2000 ), which used. This questionnaire assesses intrinsic motivation, identified regulation, external regulation and amotivation. SIMS has demonstrated good reliability and factor validity in the context of physical education in adolescents ( Lonsdale et al., 2011 ). The participants received exact instructions from the researchers in accordance with written instructions on how to conduct the data collection. Participants completed the SIMS anonymously at the start of a physical education class. All students had the opportunity to write down their answers without being observed and to ask questions if anything was unclear. To minimize the tendency to give socially desirable answers, they were asked to answer as honestly as possible, with the confidence that the teacher would not be able to read their answers and that their grades would not be affected by how they responded. The SIMS questionnaire was filled at T0 and T2. This scale is made up of 16 items divided into four dimensions: intrinsic motivation, identified regulation, external regulation and amotivation. Each item is rated on a 7-point Likert scale ranging from 1 (which is the weakest factor) “not at all” to 7 (which is the strongest factor) “exactly matches.”

In order to assess the internal consistency of the scales, a Cronbach alpha test was conducted ( Cronbach, 1951 ). The internal consistency of the scales was acceptable with reliability coefficients ranging from 0.719 to 0.87. The coefficient of reliability was 0.8.

In the present study, Cronbach's alphas were: intrinsic motivation = 0.790; regulation identified = 0.870; external regulation = 0.749; and amotivation = 0.719.

2.3.2. Camcorders

The audio-visual data collection was conducted using two Sony camcorders (Model; Handcam 4K) with a wireless microphone with a DJ transmitter-receiver (VHF 10HL F4 Micro HF) with a range of 80 m ( Maddeh et al., 2020 ). The collection took place over a period of 5 weeks, with three captures for each class (three sessions of 50 min for each at T0, T1, and T2). Two researchers were trained in the procedures and video capture techniques. The cameras were positioned diagonally, in order to film all the behavior of the students and teacher on the set.

2.3.3. The Learning Time Analysis System (LTAS)

To measure the degree of student learning, the analysis of videos recorded using the LTAS grid by Brunelle et al. (1988) was used, at T0, T1, and T2. This observation system with predetermined categories uses the technique of observation by small intervals (i.e., 6 s) and allows to measure individual learning by coding observable variables of their behaviors when they have been in a learning situation. This grid also permits the specification of the quantity and quality with which the participants engaged in the requested work and was graded, broadly, on two characteristics: the type of situation offered to the group by the teacher and the behavior of the target participant. The situation offered to the group was subdivided into three parts: preparatory situations; knowledge development situations, and motor development situations.

The observations and coding of behaviors are carried out “at intervals.” This technique is used extensively in research on behavior analysis. The coder observes the teaching situation and a particular student during each interval ( Brunelle et al., 1988 ). It then makes a decision concerning the characteristic of the observed behavior. The 6-s observation interval is followed by a coding interval of 6 s too. A cassette tape recorder is used to regulate the observation and recording intervals. It is recorded for this purpose with the indices “observe” and “code” at the start of each 6-s period. During each coding unit, the observer answered the following questions: What is the type of situation in which the class group finds itself? If the class group is in a learning situation proper, in what form of commitment does the observed student find himself? The abbreviations representing the various categories of behavior have been entered in the spaces which correspond to them. The coder was asked to enter a hyphen instead of the abbreviation when the same categories of behavior follow one another in consecutive intervals ( Brunelle et al., 1988 ).

During the preparatory period, the following behaviors were identified and analyzed:

- Deviant behavior: The student adopts a behavior incompatible with a listening attitude or with the smooth running of the preparatory situations.

- Waiting time: The student is waiting without listening or observing.

- Organized during: The student is involved in a complementary activity that does not represent a contribution to learning (e.g., regaining his place in a line, fetching a ball that has just left the field, replacing a piece of equipment).

During the motor development situations, the following behaviors were identified and analyzed:

- Motor engagement 1: The participant performs the motor activity with such easy that it can be inferred that their actions have little chance to engage in a learning process.

- Motor engagement 2: The participant-despite a certain degree of difficulty, performs the motor activity with sufficient success, which makes it possible to infer that they are in the process of learning.

- Motor engagement 3: The participant performs the motor activity with such difficulty that their efforts have very little chance of being part of a learning process.

2.4. Statistical analysis

Statistical tests were performed using statistical software 26.0 for windows (SPSS, Inc, Chicago, IL, USA). Data are presented in text and tables as means ± standard deviations and in figures as means and standard errors. Once the normal distribution of data was confirmed by the Shapiro-Wilk W -test, parametric tests were performed. Analysis of the results was performed using a mixed 2-way analysis of variance (ANOVA): Groups × Time with repeated measures.

For the learning parameters, the ANOVA took the following form: 2 Groups (Control Group vs. Experimental Group) × 3 Times (T0, T1, and T2).

For the dimensions of motivation, the ANOVA took the following form: 2 Groups (Control Group vs. Experimental Group) × 2 Time (T0 vs. T2).

In instances where the ANOVA showed a significant effect, a Bonferroni post-hoc test was applied in order to compare the experimental data in pairs, otherwise by an independent or paired Student's T -test. Effect sizes were calculated as partial eta-squared η p 2 to estimate the meaningfulness of significant findings, where η p 2 values of 0.01, 0.06, and 0.13 represent small, moderate, and large effect sizes, respectively ( Lakens, 2013 ). All observed differences were considered statistically significant for a probability threshold lower than p < 0.05.

Table 2 shows the results of learning variables during the preparatory and the development learning periods at T0, T1, and T2, in the control group and the experimental group.

Table 2 . Comparison of learning variables using two teaching methods in physical education.

The analysis of variance of two factors with repeated measures showed a significant effect of group, learning, and group learning interaction for the deviant behavior. The post-hoc test revealed significantly less frequent deviant behaviors in the experimental than in the control group at T0, T1, and T2 (all p < 0.001). Additionally, the deviant behavior decreased significantly at T1 and T2 compared to T0 for both groups (all p < 0.001).

For appropriate engagement, there were no significant group effect, a significant learning effect, and a significant group learning interaction effect. The post-hoc test revealed that compared to T0, Appropriate engagement recorded at T1 and T2 increased significantly ( p = 0.032; p = 0.031, respectively) in the experimental group, whilst it decreased significantly in the control group ( p < 0.001). Additionally, Appropriate engagement was higher in the experimental vs. control group at T1 and T2 (all p < 0.001).

For waiting time, a significant interaction in terms of group effect, learning, and group learning was found. The post-hoc test revealed that waiting time was higher at T1 and T2 vs. T0 (all p < 0.001) in the control group. In addition, waiting time in the experimental group decreased significantly at T1 and T2 vs. T0 (all p < 0.001), with higher values recorded at T2 vs. T1 ( p = 0.025). Additionally, lower values were recorded in the experimental group vs. the control group at the three-time points (all p < 0.001).

For Motor engagement 2, a significant group, learning, and group-learning interaction effect was noted. The post-hoc test revealed that Motor engagement 2 increased significantly in both groups at T1 ( p < 0.0001) and T2 ( p < 0.0001) vs. T0 ( p = 0.045), with significantly higher values recorded in the experimental group at T1 and T2.

Regarding Motor engagement 3, a non-significant group effect was reported. Contrariwise, a significant learning effect and group learning interaction was reported ( Table 1 ). The post-hoc test revealed a significant decrease in the control group and the experimental group at T1 ( p = 0.294) at T2 ( p = 0.294) vs. T0 ( p = 0.0543). In addition, a non-significant difference between the two groups was found.

A significant group and learning effect was noted for the organized during, and a non-significant group learning interaction. For organized during, the paired Student T -test showed a significant decrease in the control group and the experimental group (all p < 0.001). The independent Student T -test revealed a non-significant difference between groups at the three-time points.

Results of the motivational dimensions in the control group and the experimental group recorded at T0 and T2 are presented in Table 3 .

Table 3 . Comparison of the four motivational dimensions in two teaching methods in physical education.

For intrinsic motivation, a significant group effect and group learning interaction and also a non-significant learning effect was found. The post-hoc test indicated that the intrinsic motivation decreased significantly in the control group ( p = 0.029), whilst it increased in the experimental group ( p = 0.04). Additionally, the intrinsic motivation of the experimental group was higher at T0 ( p = 0.026) and T2 ( p < 0.001) compared to that of the control group.

For the identified regulation, a significant group effect, a non-significant learning effect and group learning interaction were reported. The paired Student's T -test revealed that from T0 to T1, the identified motivation increased significantly only in the experimental group ( p = 0.022), while it remained unchanged in the control group. The independent Student's T -test revealed that the identified regulation recorded in the experimental group at T0 ( p = 0.012) and T2 ( p < 0.001) was higher compared to that of the control group.

The external regulation presents a significant group effect. In addition, a non-significant learning effect and group learning interaction were reported. The paired Student's T -test showed that the external regulation decreased significantly in the experimental group ( p = 0.038), whereas it remained unchanged in the control group. Further, the independent Student's T -test revealed that the external regulation recorded at T2 was higher in the control group vs. the experimental group ( p < 0.001).

Relating to amotivation, results showed a significant group effect. Furthermore, a non-significant learning effect and group learning interaction were reported. The paired Student's T -test showed that, from T0 to T2, amotivation decreased significantly in the experimental group ( p = 0.011) and did not change in the control group. The independent Student T -test revealed that amotivation recorded at T2 was lower in the experimental compared to the control group ( p = 0.002).

4. Discussion

The main purpose of this study was to compare the effects of the problem-solving vs. traditional method on motivation and learning during physical education courses. The results revealed that the problem-solving method is more effective than the traditional method in increasing students' motivation and improving their learning. Moreover, the results showed that mean wait times and deviant behaviors decreased using the problem-solving method. Interestingly, the average time spent on appropriate engagement increased using the problem-solving method compared to the traditional method. When using the traditional method, the average wait times increased and, as a result, the time spent on appropriate engagement decreased. Then, following the decrease in deviant behaviors and waiting times, an increase in the time spent warming up was evident (i.e., appropriate engagement). Indeed, there was an improvement in engagement time using the problem-solving method and a decrease using the traditional method. On the other hand, there was a decrease in motor engagement 3 in favor of motor engagement 2. Indeed, it has been shown that the problem-solving method has been used in the learning process and allows for its improvement ( Docktor et al., 2015 ). In addition, it could also produce better quality solutions and has higher scores on conceptual and problem-solving measures. It is also a good method for the learning process to enhance students' academic performance ( Docktor et al., 2015 ; Ali, 2019 ). In contrast, the traditional method limits the ability of teachers to reach and engage all students ( Cook and Artino, 2016 ). Furthermore, it produces passive learning with an understanding of basic knowledge which is characterized by its weakness ( Goldstein, 2016 ). Taken together, it appears that the problem-solving method promotes and improves learning more than the traditional method.

It should be acknowledged that other factors, such as motivation, could influence learning. In this context, our results showed that the method of problem-solving could improve the motivation of the learners. This motivation includes several variables that change depending on the situation, namely the intrinsic motivation that pushes the learner to engage in an activity for the interest and pleasure linked to the practice of the latter ( Komarraju et al., 2009 ; Guiffrida et al., 2013 ; Chedru, 2015 ). The student, therefore, likes to learn through problem-solving and neglects that of the traditional method. These results are concordant with others ( Deci and Ryan, 1985 ; Chedru, 2015 ; Ryan and Deci, 2020 ). Regarding the three forms of extrinsic motivation: first, extrinsic motivation by an identified regulation which manifests itself in a high degree of self-determination where the learner engages in the activity because it is important for him ( Deci and Ryan, 1985 ; Chedru, 2015 ). This explains the significant difference between the two groups. Then, the motivation by external regulation which is characterized by a low degree of self-determination such as the behavior of the learner is manipulated by external circumstances such as obtaining rewards or the removal of sanctions ( Deci and Ryan, 1985 ; Chedru, 2015 ). For this, the means of this variable decreased for the experimental group which is intrinsically motivated. He does not need any reward to work and is not afraid of punishment because he is self-confident. Third, amotivation is at the opposite end of the self-determination continuum. Unmotivated students are the most likely to feel negative emotions ( Ratelle et al., 2007 ; David, 2010 ), to have low self-esteem ( Deci and Ryan, 1995 ), and who attempts to abandon their studies ( Vallerand et al., 1997 ; Blanchard et al., 2005 ). So, more students are motivated by external regulation or demotivated, less interest they show and less effort they make, and more likely they are to fail ( Grolnick et al., 1991 ; Miserandino, 1996 ; Guay et al., 2000 ; Blanchard et al., 2005 ).

It is worth noting that there is a close link between motivation and learning ( Bessa et al., 2021 ; Rossa et al., 2021 ). Indeed, when the learner's motivation is high, so will his learning. However, all this depends on the method used ( Norboev, 2021 ). For example, the method of problem-solving increase motivation more than the traditional method, as evidenced by several researchers ( Parish and Treasure, 2003 ; Artino and Stephens, 2009 ; Kim and Frick, 2011 ; Lemos and Veríssimo, 2014 ).

Given the effectiveness of the problem-solving method in improving students' learning and motivation, it should be used during physical education teaching. This could be achieved through the organization of comprehensive training programs, seminars, and workshops for teachers so to master and subsequently be able to use the problem-solving method during physical education lessons.

Despite its novelty, the present study suffers from a few limitations that should be acknowledged. First, a future study, consisting of a group taught using the mixed method would preferable so to better elucidate the true impact of this teaching and learning method. Second, no gender and/or age group comparisons were performed. This issue should be addressed in future investigations. Finally, the number of participants is limited. This may be due to working in a secondary school where the number of students in a class is limited to 30 students. Additionally, the number of participants fell to 53 after excluding certain students (exempted, absent for a session, exercising in civil clubs or member of the school association). Therefore, to account for classes of finite size, a cluster-based trial would be beneficial in the future. Moreover, future studies investigating the effect of the active method in reducing some behaviors (e.g., disruptive behaviors) and for the improvement of pupils' attention are warranted.

5. Conclusion

There was an improvement in student learning in favor of the problem-solving method. Additionally, we found that the motivation of learners who were taught using the problem-solving method was better than that of learners who were educated by the traditional method.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Ethics statement

University Research Ethics Board approval was obtained before recruiting participants who were subsequently informed of the nature, objective, methodology, and constraints. Teacher, school director, parental/guardian, and child informed consent was obtained prior to participation in the study. In addition, exclusion criteria included; the practice of handball activity in civil/competitive/amateur clubs or in the high school sports association. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Acknowledgments

Special thanks for all students and physical education teaching staff from the 15 November 1955 Secondary School, who generously shared their time, experience, and materials for the proposes of this study.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer MJ declared a shared affiliation, with no collaboration, with the authors GE, NS, LM, and KT to the handling editor at the time of review.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Tebabal, A., and Kahssay, G. (2011). The effects of student-centered approach in improving students' graphical interpretation skills and conceptual understanding of kinematical motion. Lat. Am. J. Phys. Educ. 5, 9.

Vallerand, R. J., Fbrtier, M. S., and Guay, F. (1997). Self-determination and persistence in a real-life setting toward a motivational model of high school dropout. J. Pers. Soc. Psychol. 2, 1161–1176. doi: 10.1037/0022-3514.72.5.1161

Ward, P., Mitchell, M. F., van der Mars, H., and Lawson, H. A. (2021). Chapter 3: PK+12 School physical education: conditions, lessons learned, and future directions. J. Teach. Phys. Educ. 40, 363–371. doi: 10.1123/jtpe.2020-0241

Keywords: problem-solving method, traditional method, motivation, learning, students

Citation: Ezeddine G, Souissi N, Masmoudi L, Trabelsi K, Puce L, Clark CCT, Bragazzi NL and Mrayah M (2023) The problem-solving method: Efficacy for learning and motivation in the field of physical education. Front. Psychol. 13:1041252. doi: 10.3389/fpsyg.2022.1041252

Received: 10 September 2022; Accepted: 15 December 2022; Published: 25 January 2023.

Reviewed by:

Copyright © 2023 Ezeddine, Souissi, Masmoudi, Trabelsi, Puce, Clark, Bragazzi and Mrayah. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem solvers that we know they can become.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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Problem-Based and Inquiry-Based Learning: What’s the difference?

Sep 30th, 2019 by Kathryn Mulholland

“If your goal is to engage students in critical thinking… you need to present interesting challenges to solve, rather than simply explaining how other smart people have already solved those challenges.” – Therese Huston

Problem-Based Learning (PBL) and Inquiry-Based Learning (IBL) are both student-centered teaching pedagogies that encourage active learning and critical thinking through investigation. Both methods offer students interesting problems to consider. And research shows that both PBL and IBL are effective models of learning. 

So, what’s the difference between the two?

According to Banchi and Bell [4], there are four different levels of inquiry.

• Confirmation Inquiry: Students confirm a principle through an activity when the results are known in advance.
• Structured Inquiry: Students investigate a teacher-presented question through a prescribed procedure. 
• Guided Inquiry: Students investigate a teacher-presented question using student designed or selected procedures.
• Open Inquiry: Students investigate questions that are student formulated through student designed or selected procedures.

Most academics define Inquiry-Based-Learning as a pedagogy that is based on one of these levels. So IBL can be as methodical as guiding students through a procedure to discover a known result or as free-form as encouraging students to formulate original questions. For example, in a Physics laboratory, suppose the topic is Newton’s Second Law of Motion. The lab instructions could define a procedure to record the mass and impact force of various objects. Multiplying the mass by the acceleration due to gravity, the students should recover the force they recorded, thus confirming Newton’s Second Law.

Problem-Based-Learning can be classified as guided inquiry where the teacher-presented question is an unsolved, real-world problem. For example, in a Middle Eastern Studies course, the main problem posed by the instructor could be “Propose a solution to the Israeli–Palestinian conflict.” This question will motivate the study of the history of the region, the theological differences between Judaism and Islam, and current events. At the end of the semester, students would be expected to present and justify their solution. 

Therefore, using the definition above, PBL is a type of IBL .

PBL is great because it motivates course content and maximizes learning via investigation, explanation, and resolution of real and meaningful problems. At any level, inquiry can be an effective method of learning because it is student-centered and encourages the development of practical skills and higher-level thinking. 

As you plan for your next class, I invite you to reflect on your method of content delivery. Is it motivated? How? Would your students benefit from a day based on inquiry?

References.

• Inquiry Based Learning. University of Notre Dame Notes on Teaching and Learning. https://sites.nd.edu/kaneb/2014/11/10/inquiry-based-learning/ .
• Problem-Based Learning. Cornell University Center for Teaching Innovation . https://teaching.cornell.edu/teaching-resources/engaging-students/problem-based-learning .
• Hmelo-Silver, Cindy E.; Duncan, Ravit Golan; Chinn, Clark A. (2007). “Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006)”. Educational Psychologi st. 42 (2): 99–107. doi : 10.1080/00461520701263368 .
• Banchi, H., & Bell R. (2008). The many levels of inquiry. Science and Children.

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Introduction to Problem Solving Skills

What is problem solving and why is it important.

The ability to solve problems is a basic life skill and is essential to our day-to-day lives, at home, at school, and at work. We solve problems every day without really thinking about how we solve them. For example: it’s raining and you need to go to the store. What do you do? There are lots of possible solutions. Take your umbrella and walk. If you don't want to get wet, you can drive, or take the bus. You might decide to call a friend for a ride, or you might decide to go to the store another day. There is no right way to solve this problem and different people will solve it differently.

Problem solving is the process of identifying a problem, developing possible solution paths, and taking the appropriate course of action.

Why is problem solving important? Good problem solving skills empower you not only in your personal life but are critical in your professional life. In the current fast-changing global economy, employers often identify everyday problem solving as crucial to the success of their organizations. For employees, problem solving can be used to develop practical and creative solutions, and to show independence and initiative to employers.

Throughout this case study you will be asked to jot down your thoughts in idea logs. These idea logs are used for reflection on concepts and for answering short questions. When you click on the "Next" button, your responses will be saved for that page. If you happen to close the webpage, you will lose your work on the page you were on, but previous pages will be saved. At the end of the case study, click on the "Finish and Export to PDF" button to acknowledge completion of the case study and receive a PDF document of your idea logs.

What Does Problem Solving Look Like?

The ability to solve problems is a skill, and just like any other skill, the more you practice, the better you get. So how exactly do you practice problem solving? Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.

Algorithmic strategies are traditional step-by-step guides to solving problems. They are great for solving math problems (in algebra: multiply and divide, then add or subtract) or for helping us remember the correct order of things (a mnemonic such as “Spring Forward, Fall Back” to remember which way the clock changes for daylight saving time, or “Righty Tighty, Lefty Loosey” to remember what direction to turn bolts and screws). Algorithms are best when there is a single path to the correct solution.

But what do you do when there is no single solution for your problem? Heuristic methods are general guides used to identify possible solutions. A popular one that is easy to remember is IDEAL [ Bransford & Stein, 1993 ] :

• I dentify the problem
• D efine the context of the problem
• E xplore possible strategies
• A ct on best solution

IDEAL is just one problem solving strategy. Building a toolbox of problem solving strategies will improve your problem solving skills. With practice, you will be able to recognize and use multiple strategies to solve complex problems.

Watch the video

What is the best way to get a peanut out of a tube that cannot be moved? Watch a chimpanzee solve this problem in the video below [ Geert Stienissen, 2010 ].

[PDF transcript]

Describe the series of steps you think the chimpanzee used to solve this problem.

• [Page 2: What does Problem Solving Look Like?] Describe the series of steps you think the chimpanzee used to solve this problem.

Think of an everyday problem you've encountered recently and describe your steps for solving it.

• [Page 2: What does Problem Solving Look Like?] Think of an everyday problem you've encountered recently and describe your steps for solving it.

Developing Problem Solving Processes

Problem solving is a process that uses steps to solve problems. But what does that really mean? Let's break it down and start building our toolbox of problem solving strategies.

What is the first step of solving any problem? The first step is to recognize that there is a problem and identify the right cause of the problem. This may sound obvious, but similar problems can arise from different events, and the real issue may not always be apparent. To really solve the problem, it's important to find out what started it all. This is called identifying the root cause .

Example: You and your classmates have been working long hours on a project in the school's workshop. The next afternoon, you try to use your student ID card to access the workshop, but discover that your magnetic strip has been demagnetized. Since the card was a couple of years old, you chalk it up to wear and tear and get a new ID card. Later that same week you learn that several of your classmates had the same problem! After a little investigation, you discover that a strong magnet was stored underneath a workbench in the workshop. The magnet was the root cause of the demagnetized student ID cards.

The best way to identify the root cause of the problem is to ask questions and gather information. If you have a vague problem, investigating facts is more productive than guessing a solution. Ask yourself questions about the problem. What do you know about the problem? What do you not know? When was the last time it worked correctly? What has changed since then? Can you diagram the process into separate steps? Where in the process is the problem occurring? Be curious, ask questions, gather facts, and make logical deductions rather than assumptions.

Watch Adam Savage from Mythbusters, describe his problem solving process [ ForaTv, 2010 ]. As you watch this section of the video, try to identify the questions he asks and the different strategies he uses.

Adam Savage shared many of his problem solving processes. List the ones you think are the five most important. Your list may be different from other people in your class—that's ok!

• [Page 3: Developing Problem Solving Processes] Adam Savage shared many of his problem solving processes. List the ones you think are the five most important.

“The ability to ask the right question is more than half the battle of finding the answer.” — Thomas J. Watson , founder of IBM

Voices From the Field: Solving Problems

In manufacturing facilities and machine shops, everyone on the floor is expected to know how to identify problems and find solutions. Today's employers look for the following skills in new employees: to analyze a problem logically, formulate a solution, and effectively communicate with others.

In this video, industry professionals share their own problem solving processes, the problem solving expectations of their employees, and an example of how a problem was solved.

Meet the Partners:

• Taconic High School in Pittsfield, Massachusetts, is a comprehensive, fully accredited high school with special programs in Health Technology, Manufacturing Technology, and Work-Based Learning.
• Berkshire Community College in Pittsfield, Massachusetts, prepares its students with applied manufacturing technical skills, providing hands-on experience at industrial laboratories and manufacturing facilities, and instructing them in current technologies.
• H.C. Starck in Newton, Massachusetts, specializes in processing and manufacturing technology metals, such as tungsten, niobium, and tantalum. In almost 100 years of experience, they hold over 900 patents, and continue to innovate and develop new products.
• Nypro Healthcare in Devens, Massachusetts, specializes in precision injection-molded healthcare products. They are committed to good manufacturing processes including lean manufacturing and process validation.

Making Decisions

Now that you have a couple problem solving strategies in your toolbox, let's practice. In this exercise, you are given a scenario and you will be asked to decide what steps you would take to identify and solve the problem.

Scenario: You are a new employee and have just finished your training. As your first project, you have been assigned the milling of several additional components for a regular customer. Together, you and your trainer, Bill, set up for the first run. Checking your paperwork, you gather the tools and materials on the list. As you are mounting the materials on the table, you notice that you didn't grab everything and hurriedly grab a few more items from one of the bins. Once the material is secured on the CNC table, you load tools into the tool carousel in the order listed on the tool list and set the fixture offsets.

Bill tells you that since this is a rerun of a job several weeks ago, the CAD/CAM model has already been converted to CNC G-code. Bill helps you download the code to the CNC machine. He gives you the go-ahead and leaves to check on another employee. You decide to start your first run.

What problems did you observe in the video?

• [Page 5: Making Decisions] What problems did you observe in the video?
• What do you do next?
• Try to fix it yourself.
• Ask your trainer for help.

As you are cleaning up, you think about what happened and wonder why it happened. You try to create a mental picture of what happened. You are not exactly sure what the end mill hit, but it looked like it might have hit the dowel pin. You wonder if you grabbed the correct dowel pins from the bins earlier.

You can think of two possible next steps. You can recheck the dowel pin length to make sure it is the correct length, or do a dry run using the CNC single step or single block function with the spindle empty to determine what actually happened.

• Check the dowel pins.
• Use the single step/single block function to determine what happened.

You notice that your trainer, Bill, is still on the floor and decide to ask him for help. You describe the problem to him. Bill asks if you know what the end mill ran into. You explain that you are not sure but you think it was the dowel pin. Bill reminds you that it is important to understand what happened so you can fix the correct problem. He suggests that you start all over again and begin with a dry run using the single step/single block function, with the spindle empty, to determine what it hit. Or, since it happened at the end, he mentions that you can also check the G-code to make sure the Z-axis is raised before returning to the home position.

• Run the single step/single block function.
• Edit the G-code to raise the Z-axis.

You finish cleaning up and check the CNC for any damage. Luckily, everything looks good. You check your paperwork and gather the components and materials again. You look at the dowel pins you used earlier, and discover that they are not the right length. As you go to grab the correct dowel pins, you have to search though several bins. For the first time, you are aware of the mess - it looks like the dowel pins and other items have not been put into the correctly labeled bins. You spend 30 minutes straightening up the bins and looking for the correct dowel pins.

Finally finding them, you finish setting up. You load tools into the tool carousel in the order listed on the tool list and set the fixture offsets. Just to make sure, you use the CNC single step/single block function, to do a dry run of the part. Everything looks good! You are ready to create your first part. The first component is done, and, as you admire your success, you notice that the part feels hotter than it should.

You wonder why? You go over the steps of the process to mentally figure out what could be causing the residual heat. You wonder if there is a problem with the CNC's coolant system or if the problem is in the G-code.

• Look at the G-code.

After thinking about the problem, you decide that maybe there's something wrong with the setup. First, you clean up the damaged materials and remove the broken tool. You check the CNC machine carefully for any damage. Luckily, everything looks good. It is time to start over again from the beginning.

You again check your paperwork and gather the tools and materials on the setup sheet. After securing the new materials, you use the CNC single step/single block function with the spindle empty, to do a dry run of the part. You watch carefully to see if you can figure out what happened. It looks to you like the spindle barely misses hitting the dowel pin. You determine that the end mill was broken when it hit the dowel pin while returning to the start position.

After conducting a dry run using the single step/single block function, you determine that the end mill was damaged when it hit the dowel pin on its return to the home position. You discuss your options with Bill. Together, you decide the best thing to do would be to edit the G-code and raise the Z-axis before returning to home. You open the CNC control program and edit the G-code. Just to make sure, you use the CNC single step/single block function, to do another dry run of the part. You are ready to create your first part. It works. You first part is completed. Only four more to go.

As you are cleaning up, you notice that the components are hotter than you expect and the end mill looks more worn than it should be. It dawns on you that while you were milling the component, the coolant didn't turn on. You wonder if it is a software problem in the G-code or hardware problem with the CNC machine.

It's the end of the day and you decide to finish the rest of the components in the morning.

• You decide to look at the G-code in the morning.
• You leave a note on the machine, just in case.

You decide that the best thing to do would be to edit the G-code and raise the Z-axis of the spindle before it returns to home. You open the CNC control program and edit the G-code.

While editing the G-code to raise the Z-axis, you notice that the coolant is turned off at the beginning of the code and at the end of the code. The coolant command error caught your attention because your coworker, Mark, mentioned having a similar issue during lunch. You change the coolant command to turn the mist on.

• You decide to talk with your supervisor.
• You discuss what happened with a coworker over lunch.

As you reflect on the residual heat problem, you think about the machining process and the factors that could have caused the issue. You try to think of anything and everything that could be causing the issue. Are you using the correct tool for the specified material? Are you using the specified material? Is it running at the correct speed? Is there enough coolant? Are there chips getting in the way?

Wait, was the coolant turned on? As you replay what happened in your mind, you wonder why the coolant wasn't turned on. You decide to look at the G-code to find out what is going on.

From the milling machine computer, you open the CNC G-code. You notice that there are no coolant commands. You add them in and on the next run, the coolant mist turns on and the residual heat issues is gone. Now, its on to creating the rest of the parts.

Have you ever used brainstorming to solve a problem? Chances are, you've probably have, even if you didn't realize it.

You notice that your trainer, Bill, is on the floor and decide to ask him for help. You describe the problem with the end mill breaking, and how you discovered that items are not being returned to the correctly labeled bins. You think this caused you to grab the incorrect length dowel pins on your first run. You have sorted the bins and hope that the mess problem is fixed. You then go on to tell Bill about the residual heat issue with the completed part.

Together, you go to the milling machine. Bill shows you how to check the oil and coolant levels. Everything looks good at the machine level. Next, on the CNC computer, you open the CNC G-code. While looking at the code, Bill points out that there are no coolant commands. Bill adds them in and when you rerun the program, it works.

Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Talking with Bill, you discuss the best way to fix the problem. Bill suggests editing the G-code to raise the Z-axis of the spindle before it returns to its home position. You open the CNC control program and edit the G-code. Following the setup sheet, you re-setup the job and use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part. It works. Since you need four of each component, you move on to creating the rest of them before cleaning up and leaving for the day.

It's a new day and you have new components to create. As you are setting up, you go in search of some short dowel pins. You discover that the bins are a mess and components have not been put away in the correctly labeled bins. You wonder if this was the cause of yesterday's problem. As you reorganize the bins and straighten up the mess, you decide to mention the mess issue to Bill in your afternoon meeting.

You describe the bin mess and using the incorrect length dowels to Bill. He is glad you mentioned the problem to him. You are not the first person to mention similar issues with tools and parts not being put away correctly. Chances are there is a bigger safety issue here that needs to be addressed in the next staff meeting.

In any workplace, following proper safety and cleanup procedures is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money.

You now know that the end mill was damaged when it hit the dowel pin. It seems to you that the easiest thing to do would be to edit the G-code and raise the Z-axis position of the spindle before it returns to the home position. You open the CNC control program and edit the G-code, raising the Z-axis. Starting over, you follow the setup sheet and re-setup the job. This time, you use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part.

At the end of the day, you are reviewing your progress with your trainer, Bill. After you describe the day's events, he reminds you to always think about safety and the importance of following work procedures. He decides to bring the issue up in the next morning meeting as a reminder to everyone.

In any workplace, following proper procedures (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. One tool to improve communication is the morning meeting or huddle.

The next morning, you check the G-code to determine what is wrong with the coolant. You notice that the coolant is turned off at the beginning of the code and also at the end of the code. This is strange. You change the G-code to turn the coolant on at the beginning of the run and off at the end. This works and you create the rest of the parts.

Throughout the day, you keep wondering what caused the G-code error. At lunch, you mention the G-code error to your coworker, John. John is not surprised. He said that he encountered a similar problem earlier this week. You decide to talk with your supervisor the next time you see him.

You are in luck. You see your supervisor by the door getting ready to leave. You hurry over to talk with him. You start off by telling him about how you asked Bill for help. Then you tell him there was a problem and the end mill was damaged. You describe the coolant problem in the G-code. Oh, and by the way, John has seen a similar problem before.

Your supervisor doesn't seem overly concerned, errors happen. He tells you "Good job, I am glad you were able to fix the issue." You are not sure whether your supervisor understood your explanation of what happened or that it had happened before.

The challenge of communicating in the workplace is learning how to share your ideas and concerns. If you need to tell your supervisor that something is not going well, it is important to remember that timing, preparation, and attitude are extremely important.

It is the end of your shift, but you want to let the next shift know that the coolant didn't turn on. You do not see your trainer or supervisor around. You decide to leave a note for the next shift so they are aware of the possible coolant problem. You write a sticky note and leave it on the monitor of the CNC control system.

How effective do you think this solution was? Did it address the problem?

In this scenario, you discovered several problems with the G-code that need to be addressed. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring and avoid injury to personnel. The challenge of communicating in the workplace is learning how and when to share your ideas and concerns. If you need to tell your co-workers or supervisor that there is a problem, it is important to remember that timing and the method of communication are extremely important.

You are able to fix the coolant problem in the G-code. While you are glad that the problem is fixed, you are worried about why it happened in the first place. It is important to remember that if a problem keeps reappearing, you may not be fixing the right problem. You may only be addressing the symptoms.

You decide to talk to your trainer. Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Over lunch, you ask your coworkers about the G-code problem and what may be causing the error. Several people mention having similar problems but do not know the cause.

You have now talked to three coworkers who have all experienced similar coolant G-code problems. You make a list of who had the problem, when they had the problem, and what each person told you.

When you see your supervisor later that afternoon, you are ready to talk with him. You describe the problem you had with your component and the damaged bit. You then go on to tell him about talking with Bill and discovering the G-code issue. You show him your notes on your coworkers' coolant issues, and explain that you think there might be a bigger problem.

You supervisor thanks you for your initiative in identifying this problem. It sounds like there is a bigger problem and he will need to investigate the root cause. He decides to call a team huddle to discuss the issue, gather more information, and talk with the team about the importance of communication.

Root Cause Analysis

Root cause analysis ( RCA ) is a method of problem solving that identifies the underlying causes of an issue. Root cause analysis helps people answer the question of why the problem occurred in the first place. RCA uses clear cut steps in its associated tools, like the "5 Whys Analysis" and the "Cause and Effect Diagram," to identify the origin of the problem, so that you can:

• Determine what happened.
• Determine why it happened.
• Fix the problem so it won’t happen again.

RCA works under the idea that systems and events are connected. An action in one area triggers an action in another, and another, and so on. By tracing back these actions, you can discover where the problem started and how it developed into the problem you're now facing. Root cause analysis can prevent problems from recurring, reduce injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money. There are many different RCA techniques available to determine the root cause of a problem. These are just a few:

• Root Cause Analysis Tools
• 5 Whys Analysis
• Fishbone or Cause and Effect Diagram
• Pareto Analysis

How Huddles Work

Communication is a vital part of any setting where people work together. Effective communication helps employees and managers form efficient teams. It builds trusts between employees and management, and reduces unnecessary competition because each employee knows how their part fits in the larger goal.

One tool that management can use to promote communication in the workplace is the huddle . Just like football players on the field, a huddle is a short meeting where everyone is standing in a circle. A daily team huddle ensures that team members are aware of changes to the schedule, reiterated problems and safety issues, and how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

The most important thing to remember about huddles is that they are short, lasting no more than 10 minutes, and their purpose is to communicate and identify. In essence, a huddle’s purpose is to identify priorities, communicate essential information, and discover roadblocks to productivity.

Who uses huddles? Many industries and companies use daily huddles. At first thought, most people probably think of hospitals and their daily patient update meetings, but lots of managers use daily meetings to engage their employees. Here are a few examples:

• Brian Scudamore, CEO of 1-800-Got-Junk? , uses the daily huddle as an operational tool to take the pulse of his employees and as a motivational tool. Watch a morning huddle meeting .
• Fusion OEM, an outsourced manufacturing and production company. What do employees take away from the daily huddle meeting .
• Biz-Group, a performance consulting group. Tips for a successful huddle .

Brainstorming

One tool that can be useful in problem solving is brainstorming . Brainstorming is a creativity technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination . The goal is to come up with as many ideas as you can in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually. Like most problem solving techniques, brainstorming is a process.

• Define a clear objective.
• Have an agreed a time limit.
• During the brainstorming session, write down everything that comes to mind, even if the idea sounds crazy.
• If one idea leads to another, write down that idea too.
• Combine and refine ideas into categories of solutions.
• Assess and analyze each idea as a potential solution.

When used during problem solving, brainstorming can offer companies new ways of encouraging staff to think creatively and improve production. Brainstorming relies on team members' diverse experiences, adding to the richness of ideas explored. This means that you often find better solutions to the problems. Team members often welcome the opportunity to contribute ideas and can provide buy-in for the solution chosen—after all, they are more likely to be committed to an approach if they were involved in its development. What's more, because brainstorming is fun, it helps team members bond.

• Watch Peggy Morgan Collins, a marketing executive at Power Curve Communications discuss How to Stimulate Effective Brainstorming .
• Watch Kim Obbink, CEO of Filter Digital, a digital content company, and her team share their top five rules for How to Effectively Generate Ideas .

Importance of Good Communication and Problem Description

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide when you talk to your supervisor.

Tips for clear communication of an issue:

• Provide a clear summary of your problem. Start at the beginning, give relevant facts, timelines, and examples.
• Avoid including your opinion or personal attacks in your explanation.
• Avoid using words like "always" or "never," which can give the impression that you are exaggerating the problem.
• If this is an ongoing problem and you have collected documentation, give it to your supervisor once you have finished describing the problem.
• Remember to listen to what's said in return; communication is a two-way process.

Not all communication is spoken. Body language is nonverbal communication that includes your posture, your hands and whether you make eye contact. These gestures can be subtle or overt, but most importantly they communicate meaning beyond what is said. When having a conversation, pay attention to how you stand. A stiff position with arms crossed over your chest may imply that you are being defensive even if your words state otherwise. Shoving your hands in your pockets when speaking could imply that you have something to hide. Be wary of using too many hand gestures because this could distract listeners from your message.

The challenge of communicating in the workplace is learning how and when to share your ideas or concerns. If you need to tell your supervisor or co-worker about something that is not going well, keep in mind that good timing and good attitude will go a long way toward helping your case.

Like all skills, effective communication needs to be practiced. Toastmasters International is perhaps the best known public speaking organization in the world. Toastmasters is open to anyone who wish to improve their speaking skills and is willing to put in the time and effort to do so. To learn more, visit Toastmasters International .

Methods of Communication

Communication of problems and issues in any workplace is important, particularly when safety is involved. It is therefore crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. As issues and problems arise, they need to be addressed in an efficient and timely manner. Effective communication is an important skill because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

There are many different ways to communicate: in person, by phone, via email, or written. There is no single method that fits all communication needs, each one has its time and place.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response through their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

Email: Email has become the communication standard for most businesses. It can be accessed from almost anywhere and is great for things that don’t require an immediate response. Email is a great way to communicate non-urgent items to large amounts of people or just your team members. One thing to remember is that most people's inboxes are flooded with emails every day and unless they are hyper vigilant about checking everything, important items could be missed. For issues that are urgent, especially those around safety, email is not always be the best solution.

Phone: Phone calls are more personal and direct than email. They allow us to communicate in real time with another person, no matter where they are. Not only can talking prevent miscommunication, it promotes a two-way dialogue. You don’t have to worry about your words being altered or the message arriving on time. However, mobile phone use and the workplace don't always mix. In particular, using mobile phones in a manufacturing setting can lead to a variety of problems, cause distractions, and lead to serious injury.

Written: Written communication is appropriate when detailed instructions are required, when something needs to be documented, or when the person is too far away to easily speak with over the phone or in person.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for your situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

Did you notice any other potential problems in the previous exercise?

• [Page 6:] Did you notice any other potential problems in the previous exercise?

Summary of Strategies

In this exercise, you were given a scenario in which there was a problem with a component you were creating on a CNC machine. You were then asked how you wanted to proceed. Depending on your path through this exercise, you might have found an easy solution and fixed it yourself, asked for help and worked with your trainer, or discovered an ongoing G-code problem that was bigger than you initially thought.

When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. Although, each path in this exercise ended with a description of a problem solving tool for your toolbox, the first step is always to identify the problem and define the context in which it happened.

There are several strategies that can be used to identify the root cause of a problem. Root cause analysis (RCA) is a method of problem solving that helps people answer the question of why the problem occurred. RCA uses a specific set of steps, with associated tools like the “5 Why Analysis" or the “Cause and Effect Diagram,” to identify the origin of the problem, so that you can:

Once the underlying cause is identified and the scope of the issue defined, the next step is to explore possible strategies to fix the problem.

If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don’t have the answer. When you collaborate to solve problems you improve workplace communication and accelerates finding solutions as similar problems arise.

One tool that can be useful for generating possible solutions is brainstorming . Brainstorming is a technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination. The goal is to come up with as many ideas as you can, in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually.

Depending on your path through the exercise, you may have discovered that a couple of your coworkers had experienced similar problems. This should have been an indicator that there was a larger problem that needed to be addressed.

In any workplace, communication of problems and issues (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they be addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

One strategy for improving communication is the huddle . Just like football players on the field, a huddle is a short meeting with everyone standing in a circle. A daily team huddle is a great way to ensure that team members are aware of changes to the schedule, any problems or safety issues are identified and that team members are aware of how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

To learn more about different problem solving strategies, choose an option below. These strategies accompany the outcomes of different decision paths in the problem solving exercise.

• View Problem Solving Strategies Select a strategy below... Root Cause Analysis How Huddles Work Brainstorming Importance of Good Problem Description Methods of Communication

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide during your meeting.

• Provide a clear summary of the problem. Start at the beginning, give relevant facts, timelines, and examples.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response in their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for the situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

"Never try to solve all the problems at once — make them line up for you one-by-one.” — Richard Sloma

Problem Solving: An Important Job Skill

Problem solving improves efficiency and communication on the shop floor. It increases a company's efficiency and profitability, so it's one of the top skills employers look for when hiring new employees. Recent industry surveys show that employers consider soft skills, such as problem solving, as critical to their business’s success.

The 2011 survey, "Boiling Point? The skills gap in U.S. manufacturing ," polled over a thousand manufacturing executives who reported that the number one skill deficiency among their current employees is problem solving, which makes it difficult for their companies to adapt to the changing needs of the industry.

In this video, industry professionals discuss their expectations and present tips for new employees joining the manufacturing workforce.

Quick Summary

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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The problem-solving method: Efficacy for learning and motivation in the field of physical education

Ghaith ezeddine.

1 High Institute of Sport and Physical Education of Sfax, University of Sfax, Sfax, Tunisia

Nafaa Souissi

2 Research Unit of the National Sports Observatory (ONS), Tunis, Tunisia

Liwa Masmoudi

3 Research Laboratory: Education, Motricity, Sport and Health, EM2S, LR19JS01, University of Sfax, Sfax, Tunisia

Khaled Trabelsi

4 Department of Neuroscience, Rehabilitation, Ophthalmology, Genetics, Maternal and Child Health (DINOGMI), University of Genoa, Genoa, Italy

Cain C. T. Clark

5 Centre for Intelligent Healthcare, Coventry University, Coventry, United Kingdom

Nicola Luigi Bragazzi

6 Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, Canada

Maher Mrayah

7 High Institute of Sport and Physical Education of Ksar Saîd, University Manouba, UMA, Manouba, Tunisia

Associated Data

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

In pursuit of quality teaching and learning, teachers seek the best method to provide their students with a positive educational atmosphere and the most appropriate learning conditions.

The purpose of this study is to compare the effects of the problem-solving method vs. the traditional method on motivation and learning during physical education courses.

Fifty-three students ( M age 15 ± 0.1 years), in their 1st year of the Tunisian secondary education system, voluntarily participated in this study, and randomly assigned to a control or experimental group. Participants in the control group were taught using the traditional methods, whereas participants in the experimental group were taught using the problem-solving method. Both groups took part in a 10-hour experiment over 5 weeks. To measure students' situational motivation, a questionnaire was used to evaluate intrinsic motivation, identified regulation, external regulation, and amotivation during the first (T0) and the last sessions (T2). Additionally, the degree of students' learning was determined via video analyses, recorded at T0, the fifth (T1), and T2.

Motivational dimensions, including identified regulation and intrinsic motivation, were significantly greater (all p < 0.001) in the experimental vs. the control group. The students' motor engagement in learning situations, during which the learner, despite a degree of difficulty performs the motor activity with sufficient success, increased only in the experimental group ( p < 0.001). The waiting time in the experimental group decreased significantly at T1 and T2 vs. T0 (all p < 0.001), with lower values recorded in the experimental vs. the control group at the three-time points (all p < 0.001).

Conclusions

The problem-solving method is an efficient strategy for motor skills and performance enhancement, as well as motivation development during physical education courses.

1. Introduction

The education of children is a sensitive and poignant subject, where the wellbeing of the child in the school environment is a key issue (Ergül and Kargin, 2014 ). For this, numerous research has sought to find solutions to the problems of the traditional method, which focuses on the teacher as an instructor, giver of knowledge, arbiter of truth, and ultimate evaluator of learning (Ergül and Kargin, 2014 ; Cunningham and Sood, 2018 ). From this perspective, a teachers' job is to present students with a designated body of knowledge in a predetermined order (Arvind and Kusum, 2017 ). For them, learners are seen as people with “knowledge gaps” that need to be filled with information. In this method, teaching is conceived as the act of transmitting knowledge from point A (responsible for the teacher) to point B (responsible for the students; Arvind and Kusum, 2017 ). According to Novak ( 2010 ), in the traditional method, the teacher is the one who provokes the learning.

The traditional method focuses on lecture-based teaching as the center of instruction, emphasizing delivery of program and concept (Johnson, 2010 ; Ilkiw et al., 2017 ; Dickinson et al., 2018 ). The student listens and takes notes, passively accepts and receives from the teacher undifferentiated and identical knowledge (Bi et al., 2019 ). Course content and delivery are considered most important, and learners acquire knowledge through exercise and practice (Johnson et al., 1998 ). In the traditional method, academic achievement is seen as the ability of students to demonstrate, replicate, or convey this designated body of knowledge to the teacher. It is based on a transmissive model, the teacher contenting themselves with exchanging and transmitting information to the learner. Here, only the “knowledge” and “teacher” poles of the pedagogical triangle are solicited. The teacher teaches the students, who play the role of the spectator. They receive information without participating in its creation (Perrenoud, 2003 ). For this, researchers invented a new student-centered method with effects on improving students' graphic interpretation skills and conceptual understanding of kinematic motion represent an area of contemporary interest (Tebabal and Kahssay, 2011 ). Indeed, in order to facilitate the process of knowledge transfer, teachers should use appropriate methods targeted to specific objectives of the school curricula.

For instance, it has been emphasized that the effectiveness of any educational process as a whole relies on the crucial role of using a well-designed pedagogical (teaching and/or learning) strategy (Kolesnikova, 2016 ).

Alternate to a traditional method of teaching, Ergül and Kargin ( 2014 ), proposed the problem-solving method, which represents one of the most common student-centered learning strategies. Indeed, this method allows students to participate in the learning environment, giving them the responsibility for their own acquisition of knowledge, as well as the opportunity for the understanding and structuring of diverse information.

For Cunningham and Sood ( 2018 ), the problem-solving method may be considered a fundamental tool for the acquisition of new knowledge, notably learning transfer. Moreover, the problem-solving method is purportedly efficient for the development of manual skills and experiential learning (Ergül and Kargin, 2014 ), as well as the optimization of thinking ability. Additionally, the problem-solving method allows learners to participate in the learning environment, while giving them responsibility for their learning and making them understand and structure the information (Pohan et al., 2020 ). In this context, Ali ( 2019 ) reported that, when faced with an obstacle, the student will have to invoke his/her knowledge and use his/her abilities to “break the deadlock.” He/she will therefore make the most of his/her potential, but also share and exchange with his/her colleagues (Ali, 2019 ). Throughout the process, the student will learn new concepts and skills. The role of the teacher is paramount at the beginning of the activity, since activities will be created based on problematic situations according to the subject and the program. However, on the day of the activity, it does not have the main role, and the teacher will guide learners in difficulty and will allow them to manage themselves most of the time (Ali, 2019 ).

The problem-solving method encourages group discussion and teamwork (Fidan and Tuncel, 2019 ). Additionally, in this pedagogical approach, the role of the teacher is a facilitator of learning, and they take on a much more interactive and less rebarbative role (Garrett, 2008 ).

For the teaching method to be effective, teaching should consist of an ongoing process of making desirable changes among learners using appropriate methods (Ayeni, 2011 ; Norboev, 2021 ). To bring about positive changes in students, the methods used by teachers should be the best for the subject to be taught (Adunola et al., 2012 ). Further, suggests that teaching methods work effectively, especially if they meet the needs of learners since each learner interprets and answers questions in a unique way. Improving problem-solving skills is a primary educational goal, as is the ability to use reasoning. To acquire this skill, students must solve problems to learn mathematics and problem-solving (Hu, 2010 ); this encourages the students to actively participate and contribute to the activities suggested by the teacher. Without sufficient motivation, learning goals can no longer be optimally achieved, although learners may have exceptional abilities. The method of teaching employed by the teachers is decisive to achieve motivational consequences in physical education students (Leo et al., 2022 ). Pérez-Jorge et al. ( 2021 ) posited that given we now live in a technological society in which children are used to receiving a large amount of stimuli, gaining and maintaining their attention and keeping them motivated at school becomes a challenge for teachers.

Fenouillet ( 2012 ) stated that academic motivation is linked to resources and methods that improve attention for school learning. Furthermore, Rolland ( 2009 ) and Bessa et al. ( 2021 ) reported a link between a learner's motivational dynamics and classroom activities. The models of learning situations, where the student is the main actor, directly refers to active teaching methods, and that there is a strong link between motivation and active teaching (Rossa et al., 2021 ). In the same context, previous reports assert that the motivation of students in physical education is an important factor since the intra-individual motivation toward this discipline is recognized as a major determinant of physical activity for students (Standage et al., 2012 ; Luo, 2019 ; Leo et al., 2022 ). Further, extensive research on the effectiveness of teaching methods shows that the quality of teaching often influences the performance of learners (Norboev, 2021 ). Ayeni ( 2011 ) reported that education is a process that allows students to make changes desirable to achieve specific results. Thus, the consistency of teaching methods with student needs and learning influences student achievement. This has led several researchers to explore the impact of different teaching strategies, ranging from traditional methods to active learning techniques that can be used such as the problem-solving method (Skinner, 1985 ; Darling-Hammond et al., 2020 ).

In the context of innovation, Blázquez ( 2016 ) emphasizes the importance of adopting active methods and implementing them as the main element promoting the development of skills, motivation and active participation. Pedagogical models are part of the active methods which, together with model-based practice, replace traditional teaching (Hastie and Casey, 2014 ; Casey et al., 2021 ). Thus, many studies have identified pedagogical models as the most effective way to place students at the center of the teaching-learning process (Metzler, 2017 ), making it possible to assess the impact of physical education on learning students (Casey, 2014 ; Rivera-Pérez et al., 2020 ; Manninen and Campbell, 2021 ). Since each model is designed to focus on a specific program objective, each model has limitations when implemented in isolation (Bunker and Thorpe, 1982 ; Rivera-Pérez et al., 2020 ). Therefore, focusing on developing students' social and emotional skills and capacities could help them avoid failure in physical education (Ang and Penney, 2013 ). Thus, the current emergence of new pedagogical models goes with their hybridization with different methods, which is a wave of combinations proposed today as an innovative pedagogical strategy. The incorporation of this type of method in the current education system is becoming increasingly important because it gives students a greater role, participation, autonomy and self-regulation, and above all it improves their motivation (Puigarnau et al., 2016 ). The teaching model of personal and social responsibility, for example, is closely related to the sports education model because both share certain approaches to responsibility (Siedentop et al., 2011 ). One of the first studies to use these two models together was Rugby (Gordon and Doyle, 2015 ), which found significant improvements in student behavior. Also, the recent study by Menendez and Fernandez-Rio ( 2017 ) on educational kickboxing.

Previous studies have indicated that hybridization can increase play, problem solving performance and motor skills (Menendez and Fernandez-Rio, 2017 ; Ward et al., 2021 ) and generate positive psychosocial consequences, such as pleasure, intention to be physically active and responsibility (Dyson and Grineski, 2001 ; Menendez and Fernandez-Rio, 2017 ).

But despite all these research results, the picture remains unclear, and it remains unknown which method is more effective in improving students' learning and motivation. Given the lack of published evidence on this topic, the aim of this study was to compare the effects of problem-solving vs. the traditional method on students' motivation and learning.

We hypothesized would that the problem-solving method would be more effective in improving students' motivation and learning better than the traditional method.

2. Materials and method

2.1. participants.

Fifty-three students, aged 15–16 ( M age 15 ± 0.1 years), in their 1st year of the Tunisian secondary education system, voluntarily participated in this study. All participants were randomly chosen. Repeating students, those who practice handball activity in civil/competitive/amateur clubs or in the high school sports association, and students who were absent, even for one session, were excluded. The first class consisted of 30 students (16 boys and 14 girls), who represented the experimental group and followed basic courses on a learning method by solving problems. The second class consisted of 23 students (10 boys and 13 girls), who represented the control group and followed the traditional teaching method. The total duration was spread over 5 weeks, or two sessions per week and each session lasted 50 min.

University research ethics board approval (CPPSUD: 0295/2021) was obtained before recruiting participants who were subsequently informed of the nature, objective, methodology, and constraints. Teacher, school director, parental/guardian, and child informed consent was obtained prior to participation in the study.

2.2. Procedure

Before the start of the experiment, the participants were familiarized with the equipment and the experimental protocol in order to ensure a good learning climate. For this and to mitigate the impact of the observer and the cameras on the students, the two researchers were involved prior to the data collection in a week of familiarization by making test recordings with the classes concerned.

An approach of a teaching cycle consisting of 10 sessions spread over 5 weeks, amounting to two sessions per week. Physical education classes were held in the morning from 8 a.m. to 9 a.m., with a single goal for each session that lasted 50 min. The cyclic programs were produced by the teacher responsible for carrying out the experiment with 18 years of service. To do this, the students had the same lessons with the same objectives, only pedagogy that differs: the experimental group worked using problem-solving pedagogy, while the control group was confronted with traditional pedagogy. The sessions took place in a handball field 40 m long and 20 m wide. Examples of training sessions using the problem-solving pedagogy and the traditional pedagogy are presented in Table 1 . In addition, a motivation questionnaire, the Situational Motivation Scale (SIMS; Guay et al., 2000 ), was administered to learners at the end of the session (i.e., in the beginning, and end of the cycle). Each student answered the questions alone and according to their own ideas. This questionnaire was taken in a classroom to prevent students from acting abnormally during the study. It lasted for a maximum of 10 min.

Example of activities for the different sessions.

Two diametrically opposed cameras were installed so to film all the movements and behaviors of each student and teacher during the three sessions [(i) test at the start of the cycle (T0), (ii) in the middle of the cycle (T1), and (iii) test at the end of the cycle (T2)]. These sessions had the same content and each consisted of four phases: the getting started, the warm-up, the work up (which consisted of three situations: first, the work was goes up the ball to two to score in the goal following a shot. Second, the same principle as the previous situation but in the presence of a defender. Finally, third, a match 7 ≠ 7), and the cooling down These recordings were analyzed using a Learning Time Analysis System grid (LTAS; Brunelle et al., 1988 ). This made it possible to measure individual learning by coding observable variables of the behavior of learners in a learning situation.

2.3. Data collection and analysis

2.3.1. the motivation questionnaire.

In this study, in order to measure the situational motivation of students, the situational motivation scale (SIMS; Guay et al., 2000 ), which used. This questionnaire assesses intrinsic motivation, identified regulation, external regulation and amotivation. SIMS has demonstrated good reliability and factor validity in the context of physical education in adolescents (Lonsdale et al., 2011 ). The participants received exact instructions from the researchers in accordance with written instructions on how to conduct the data collection. Participants completed the SIMS anonymously at the start of a physical education class. All students had the opportunity to write down their answers without being observed and to ask questions if anything was unclear. To minimize the tendency to give socially desirable answers, they were asked to answer as honestly as possible, with the confidence that the teacher would not be able to read their answers and that their grades would not be affected by how they responded. The SIMS questionnaire was filled at T0 and T2. This scale is made up of 16 items divided into four dimensions: intrinsic motivation, identified regulation, external regulation and amotivation. Each item is rated on a 7-point Likert scale ranging from 1 (which is the weakest factor) “not at all” to 7 (which is the strongest factor) “exactly matches.”

• In order to assess the internal consistency of the scales, a Cronbach alpha test was conducted (Cronbach, 1951 ). The internal consistency of the scales was acceptable with reliability coefficients ranging from 0.719 to 0.87. The coefficient of reliability was 0.8.
• In the present study, Cronbach's alphas were: intrinsic motivation = 0.790; regulation identified = 0.870; external regulation = 0.749; and amotivation = 0.719.

2.3.2. Camcorders

The audio-visual data collection was conducted using two Sony camcorders (Model; Handcam 4K) with a wireless microphone with a DJ transmitter-receiver (VHF 10HL F4 Micro HF) with a range of 80 m (Maddeh et al., 2020 ). The collection took place over a period of 5 weeks, with three captures for each class (three sessions of 50 min for each at T0, T1, and T2). Two researchers were trained in the procedures and video capture techniques. The cameras were positioned diagonally, in order to film all the behavior of the students and teacher on the set.

2.3.3. The Learning Time Analysis System (LTAS)

To measure the degree of student learning, the analysis of videos recorded using the LTAS grid by Brunelle et al. ( 1988 ) was used, at T0, T1, and T2. This observation system with predetermined categories uses the technique of observation by small intervals (i.e., 6 s) and allows to measure individual learning by coding observable variables of their behaviors when they have been in a learning situation. This grid also permits the specification of the quantity and quality with which the participants engaged in the requested work and was graded, broadly, on two characteristics: the type of situation offered to the group by the teacher and the behavior of the target participant. The situation offered to the group was subdivided into three parts: preparatory situations; knowledge development situations, and motor development situations.

The observations and coding of behaviors are carried out “at intervals.” This technique is used extensively in research on behavior analysis. The coder observes the teaching situation and a particular student during each interval (Brunelle et al., 1988 ). It then makes a decision concerning the characteristic of the observed behavior. The 6-s observation interval is followed by a coding interval of 6 s too. A cassette tape recorder is used to regulate the observation and recording intervals. It is recorded for this purpose with the indices “observe” and “code” at the start of each 6-s period. During each coding unit, the observer answered the following questions: What is the type of situation in which the class group finds itself? If the class group is in a learning situation proper, in what form of commitment does the observed student find himself? The abbreviations representing the various categories of behavior have been entered in the spaces which correspond to them. The coder was asked to enter a hyphen instead of the abbreviation when the same categories of behavior follow one another in consecutive intervals (Brunelle et al., 1988 ).

During the preparatory period, the following behaviors were identified and analyzed:

• - Deviant behavior: The student adopts a behavior incompatible with a listening attitude or with the smooth running of the preparatory situations.
• - Waiting time: The student is waiting without listening or observing.
• - Organized during: The student is involved in a complementary activity that does not represent a contribution to learning (e.g., regaining his place in a line, fetching a ball that has just left the field, replacing a piece of equipment).

During the motor development situations, the following behaviors were identified and analyzed:

• - Motor engagement 1: The participant performs the motor activity with such easy that it can be inferred that their actions have little chance to engage in a learning process.
• - Motor engagement 2: The participant-despite a certain degree of difficulty, performs the motor activity with sufficient success, which makes it possible to infer that they are in the process of learning.
• - Motor engagement 3: The participant performs the motor activity with such difficulty that their efforts have very little chance of being part of a learning process.

2.4. Statistical analysis

Statistical tests were performed using statistical software 26.0 for windows (SPSS, Inc, Chicago, IL, USA). Data are presented in text and tables as means ± standard deviations and in figures as means and standard errors. Once the normal distribution of data was confirmed by the Shapiro-Wilk W -test, parametric tests were performed. Analysis of the results was performed using a mixed 2-way analysis of variance (ANOVA): Groups × Time with repeated measures.

• For the learning parameters, the ANOVA took the following form: 2 Groups (Control Group vs. Experimental Group) × 3 Times (T0, T1, and T2).
• For the dimensions of motivation, the ANOVA took the following form: 2 Groups (Control Group vs. Experimental Group) × 2 Time (T0 vs. T2).

In instances where the ANOVA showed a significant effect, a Bonferroni post-hoc test was applied in order to compare the experimental data in pairs, otherwise by an independent or paired Student's T -test. Effect sizes were calculated as partial eta-squared η p 2 to estimate the meaningfulness of significant findings, where η p 2 values of 0.01, 0.06, and 0.13 represent small, moderate, and large effect sizes, respectively (Lakens, 2013 ). All observed differences were considered statistically significant for a probability threshold lower than p < 0.05.

Table 2 shows the results of learning variables during the preparatory and the development learning periods at T0, T1, and T2, in the control group and the experimental group.

Comparison of learning variables using two teaching methods in physical education.

* Significantly different from control group at p <0.05.

# Significantly different from T0 at p <0.05.

$ Significantly different from T1 at p <0.05.

For motor engagement 1 (ME1), the time devoted to this variable is equal zero for the three measurement times (T0, T1, and T2).

The analysis of variance of two factors with repeated measures showed a significant effect of group, learning, and group learning interaction for the deviant behavior. The post-hoc test revealed significantly less frequent deviant behaviors in the experimental than in the control group at T0, T1, and T2 (all p < 0.001). Additionally, the deviant behavior decreased significantly at T1 and T2 compared to T0 for both groups (all p < 0.001).

For appropriate engagement, there were no significant group effect, a significant learning effect, and a significant group learning interaction effect. The post-hoc test revealed that compared to T0, Appropriate engagement recorded at T1 and T2 increased significantly ( p = 0.032; p = 0.031, respectively) in the experimental group, whilst it decreased significantly in the control group ( p < 0.001). Additionally, Appropriate engagement was higher in the experimental vs. control group at T1 and T2 (all p < 0.001).

For waiting time, a significant interaction in terms of group effect, learning, and group learning was found. The post-hoc test revealed that waiting time was higher at T1 and T2 vs. T0 (all p < 0.001) in the control group. In addition, waiting time in the experimental group decreased significantly at T1 and T2 vs. T0 (all p < 0.001), with higher values recorded at T2 vs. T1 ( p = 0.025). Additionally, lower values were recorded in the experimental group vs. the control group at the three-time points (all p < 0.001).

For Motor engagement 2, a significant group, learning, and group-learning interaction effect was noted. The post-hoc test revealed that Motor engagement 2 increased significantly in both groups at T1 ( p < 0.0001) and T2 ( p < 0.0001) vs. T0 ( p = 0.045), with significantly higher values recorded in the experimental group at T1 and T2.

Regarding Motor engagement 3, a non-significant group effect was reported. Contrariwise, a significant learning effect and group learning interaction was reported ( Table 1 ). The post-hoc test revealed a significant decrease in the control group and the experimental group at T1 ( p = 0.294) at T2 ( p = 0.294) vs. T0 ( p = 0.0543). In addition, a non-significant difference between the two groups was found.

A significant group and learning effect was noted for the organized during, and a non-significant group learning interaction. For organized during, the paired Student T -test showed a significant decrease in the control group and the experimental group (all p < 0.001). The independent Student T -test revealed a non-significant difference between groups at the three-time points.

Results of the motivational dimensions in the control group and the experimental group recorded at T0 and T2 are presented in Table 3 .

Comparison of the four motivational dimensions in two teaching methods in physical education.

For intrinsic motivation, a significant group effect and group learning interaction and also a non-significant learning effect was found. The post-hoc test indicated that the intrinsic motivation decreased significantly in the control group ( p = 0.029), whilst it increased in the experimental group ( p = 0.04). Additionally, the intrinsic motivation of the experimental group was higher at T0 ( p = 0.026) and T2 ( p < 0.001) compared to that of the control group.

For the identified regulation, a significant group effect, a non-significant learning effect and group learning interaction were reported. The paired Student's T -test revealed that from T0 to T1, the identified motivation increased significantly only in the experimental group ( p = 0.022), while it remained unchanged in the control group. The independent Student's T -test revealed that the identified regulation recorded in the experimental group at T0 ( p = 0.012) and T2 ( p < 0.001) was higher compared to that of the control group.

The external regulation presents a significant group effect. In addition, a non-significant learning effect and group learning interaction were reported. The paired Student's T -test showed that the external regulation decreased significantly in the experimental group ( p = 0.038), whereas it remained unchanged in the control group. Further, the independent Student's T -test revealed that the external regulation recorded at T2 was higher in the control group vs. the experimental group ( p < 0.001).

Relating to amotivation, results showed a significant group effect. Furthermore, a non-significant learning effect and group learning interaction were reported. The paired Student's T -test showed that, from T0 to T2, amotivation decreased significantly in the experimental group ( p = 0.011) and did not change in the control group. The independent Student T -test revealed that amotivation recorded at T2 was lower in the experimental compared to the control group ( p = 0.002).

4. Discussion

The main purpose of this study was to compare the effects of the problem-solving vs. traditional method on motivation and learning during physical education courses. The results revealed that the problem-solving method is more effective than the traditional method in increasing students' motivation and improving their learning. Moreover, the results showed that mean wait times and deviant behaviors decreased using the problem-solving method. Interestingly, the average time spent on appropriate engagement increased using the problem-solving method compared to the traditional method. When using the traditional method, the average wait times increased and, as a result, the time spent on appropriate engagement decreased. Then, following the decrease in deviant behaviors and waiting times, an increase in the time spent warming up was evident (i.e., appropriate engagement). Indeed, there was an improvement in engagement time using the problem-solving method and a decrease using the traditional method. On the other hand, there was a decrease in motor engagement 3 in favor of motor engagement 2. Indeed, it has been shown that the problem-solving method has been used in the learning process and allows for its improvement (Docktor et al., 2015 ). In addition, it could also produce better quality solutions and has higher scores on conceptual and problem-solving measures. It is also a good method for the learning process to enhance students' academic performance (Docktor et al., 2015 ; Ali, 2019 ). In contrast, the traditional method limits the ability of teachers to reach and engage all students (Cook and Artino, 2016 ). Furthermore, it produces passive learning with an understanding of basic knowledge which is characterized by its weakness (Goldstein, 2016 ). Taken together, it appears that the problem-solving method promotes and improves learning more than the traditional method.

It should be acknowledged that other factors, such as motivation, could influence learning. In this context, our results showed that the method of problem-solving could improve the motivation of the learners. This motivation includes several variables that change depending on the situation, namely the intrinsic motivation that pushes the learner to engage in an activity for the interest and pleasure linked to the practice of the latter (Komarraju et al., 2009 ; Guiffrida et al., 2013 ; Chedru, 2015 ). The student, therefore, likes to learn through problem-solving and neglects that of the traditional method. These results are concordant with others (Deci and Ryan, 1985 ; Chedru, 2015 ; Ryan and Deci, 2020 ). Regarding the three forms of extrinsic motivation: first, extrinsic motivation by an identified regulation which manifests itself in a high degree of self-determination where the learner engages in the activity because it is important for him (Deci and Ryan, 1985 ; Chedru, 2015 ). This explains the significant difference between the two groups. Then, the motivation by external regulation which is characterized by a low degree of self-determination such as the behavior of the learner is manipulated by external circumstances such as obtaining rewards or the removal of sanctions (Deci and Ryan, 1985 ; Chedru, 2015 ). For this, the means of this variable decreased for the experimental group which is intrinsically motivated. He does not need any reward to work and is not afraid of punishment because he is self-confident. Third, amotivation is at the opposite end of the self-determination continuum. Unmotivated students are the most likely to feel negative emotions (Ratelle et al., 2007 ; David, 2010 ), to have low self-esteem (Deci and Ryan, 1995 ), and who attempts to abandon their studies (Vallerand et al., 1997 ; Blanchard et al., 2005 ). So, more students are motivated by external regulation or demotivated, less interest they show and less effort they make, and more likely they are to fail (Grolnick et al., 1991 ; Miserandino, 1996 ; Guay et al., 2000 ; Blanchard et al., 2005 ).

It is worth noting that there is a close link between motivation and learning (Bessa et al., 2021 ; Rossa et al., 2021 ). Indeed, when the learner's motivation is high, so will his learning. However, all this depends on the method used (Norboev, 2021 ). For example, the method of problem-solving increase motivation more than the traditional method, as evidenced by several researchers (Parish and Treasure, 2003 ; Artino and Stephens, 2009 ; Kim and Frick, 2011 ; Lemos and Veríssimo, 2014 ).

Given the effectiveness of the problem-solving method in improving students' learning and motivation, it should be used during physical education teaching. This could be achieved through the organization of comprehensive training programs, seminars, and workshops for teachers so to master and subsequently be able to use the problem-solving method during physical education lessons.

Despite its novelty, the present study suffers from a few limitations that should be acknowledged. First, a future study, consisting of a group taught using the mixed method would preferable so to better elucidate the true impact of this teaching and learning method. Second, no gender and/or age group comparisons were performed. This issue should be addressed in future investigations. Finally, the number of participants is limited. This may be due to working in a secondary school where the number of students in a class is limited to 30 students. Additionally, the number of participants fell to 53 after excluding certain students (exempted, absent for a session, exercising in civil clubs or member of the school association). Therefore, to account for classes of finite size, a cluster-based trial would be beneficial in the future. Moreover, future studies investigating the effect of the active method in reducing some behaviors (e.g., disruptive behaviors) and for the improvement of pupils' attention are warranted.

5. Conclusion

There was an improvement in student learning in favor of the problem-solving method. Additionally, we found that the motivation of learners who were taught using the problem-solving method was better than that of learners who were educated by the traditional method.

Data availability statement

Ethics statement.

University Research Ethics Board approval was obtained before recruiting participants who were subsequently informed of the nature, objective, methodology, and constraints. Teacher, school director, parental/guardian, and child informed consent was obtained prior to participation in the study. In addition, exclusion criteria included; the practice of handball activity in civil/competitive/amateur clubs or in the high school sports association. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Acknowledgments

Special thanks for all students and physical education teaching staff from the 15 November 1955 Secondary School, who generously shared their time, experience, and materials for the proposes of this study.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer MJ declared a shared affiliation, with no collaboration, with the authors GE, NS, LM, and KT to the handling editor at the time of review.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Pave the Way for Self-regulation and Problem-solving With Social-emotional Learning

Posted: April 3, 2024

Problem-solving is a social-emotional learning (SEL) skill children need for lifelong success. Effective problem-solving skills support children's ability to self-regulate, focus on tasks, think flexibly and creatively, work with others, and generate multiple ways to solve problems. When young children develop and build these skills, it positively impacts their interactions with others, grows their capacity to manage challenges, and boosts a sense of competence.

A group of school-age children are stacking plastic blocks with an educator.

The foundation for effective social problem-solving is grounded in self-regulation, or the ability to regulate emotions when interacting with others. It is easier to focus on one's feelings and the feelings and perspectives of others and to work cooperatively toward solutions when a child can self-regulate and calm down. Children develop self-regulation skills over time, with practice and with adult guidance. Equally important is how an adult models emotion regulation and co-regulation. 

"Caregivers play a key role in cultivating the development of emotion regulation through co-regulation, or the processes by which they provide external support or scaffolding as children navigate their emotional experiences" (Paley & Hajal, 2022, p. 1).

When adults model calm and self-regulated approaches to problem-solving, it shows children how to approach problems constructively. For example, an educator says, "I'm going to take a breath and calm down so I can think better." This model helps children see and hear a strategy to support self-regulation.

Problem-solving skills help children resolve conflicts and interact with others as partners and collaborators. Developing problem-solving skills helps children learn and grow empathy for others, stand up for themselves, and build resilience and competence to work through challenges in their world. 

Eight strategies to support problem-solving 

• Teach about emotions and use feeling words throughout the day. When children have more words to express themselves and their feelings, it is easier to address and talk about challenges when they arise. 
• Recognize and acknowledge children's feelings throughout the day. For example, when children enter the classroom during circle time, mealtime, and outside time, ask them how they feel. Always acknowledge children's feelings, both comfortable and uncomfortable, to support an understanding that all feelings are OK to experience.  
• Differentiate between feelings and behaviors. By differentiating feelings from behaviors, educators contribute to children’s understanding that all feelings are OK, but not all behaviors are OK. For example, an educator says, "It looks like you may be feeling mad because you want the red blocks, and Nila is playing with them. It's OK to feel mad but not OK to knock over your friend’s blocks."
• Support children's efforts to calm down. When children are self-regulated, they can think more clearly. For example, practice taking a breath with children as a self-regulation technique during calm moments. Then, when challenges arise, children have a strategy they have practiced many times and can use to calm down before problem-solving begins.  
• Encourage children's efforts to voice the problem and their feelings after they are calm. For example, when a challenge arises, encourage children to use the phrase, "The problem is_______, and I feel______." This process sets the stage to begin problem-solving.
• Acknowledge children's efforts to think about varied ways to solve problems. For example, an educator says, "It looks like you and Nila are trying to work out how to share the blocks. What do you think might work so you can both play with them? Do you have some other ideas about how you could share?"
• Champion children's efforts as they problem-solve. For example, "You and Nila thought about two ways you could share. One way is to divide the red blocks so you can each build, and the other is to build a tower together. Great thinking, friends!"
• Create opportunities for activities and play that offer problem-solving practice. For example, when children play together in the block area, it provides opportunities to negotiate plans for play and role-play, build perspective, talk about feelings, and share. The skills children learn during play, along with adult support, enhance children’s ability to solve more complex and challenging social problems and conflicts when they occur in and out of the early learning setting.

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The effect of a STEM integrated curriculum on design thinking dispositions in middle school students

• Published: 13 April 2024

Cite this article

• Dina Thomason   ORCID: orcid.org/0000-0002-4275-7912 1 &
• Pei-Ling Hsu   ORCID: orcid.org/0000-0002-1870-5717 1  

STEM, the integration of science, technology, engineering, and mathematics subjects is a popular topic as schools grapple with how to best prepare students for an ever-evolving society. As societal and technological challenges emerge, design thinking has been lauded as a method to enable people to help tackle those challenges. The steps of the design thinking process, empathize, define, ideate, prototype and test align with engineering design and can be used as a problem-solving method in classrooms to help promote creativity, critical thinking, and collaboration. The purpose of this explanatory sequential mixed methods study was to better understand if a STEM integrated curriculum helps promote design thinking in middle schoolers. The study compared two middle school groups, one that uses an integrated STEM curriculum and one that does not. Quantitative data was collected using the design thinking disposition survey through pre and post testing. Qualitative data was collected through free response questions and student and teacher interviews. There was no difference found in the change of design thinking dispositions between students at the two schools, however both groups scored lowest on the design thinking disposition of prototype. Free response questions showed that students at the STEM integrated school perceived an increased ability to design solutions to problems. Student and teacher interviews highlighted benefits of using a STEM integrated curriculum including providing collaborative opportunities to solve hands-on, open-ended problems. How a STEM integrated curriculum can develop design thinking should continue to be examined.

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Thomason, D., Hsu, PL. The effect of a STEM integrated curriculum on design thinking dispositions in middle school students. Int J Technol Des Educ (2024). https://doi.org/10.1007/s10798-024-09894-6

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Do You Understand the Problem You’re Trying to Solve?

To solve tough problems at work, first ask these questions.

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

In this episode, you’ll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

Key episode topics include: leadership, decision making and problem solving, power and influence, business management.

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HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Problem solving skills are invaluable in any job. But even the most experienced among us can fall into the trap of solving the wrong problem.

Thomas Wedell-Wedellsborg says that all too often, we jump to find solutions to a problem – without taking time to really understand what we’re facing.

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

  In this episode, you’ll learn how to reframe tough problems, by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

This episode originally aired on HBR IdeaCast in December 2016. Here it is.

SARAH GREEN CARMICHAEL: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Sarah Green Carmichael.

Problem solving is popular. People put it on their resumes. Managers believe they excel at it. Companies count it as a key proficiency. We solve customers’ problems.

The problem is we often solve the wrong problems. Albert Einstein and Peter Drucker alike have discussed the difficulty of effective diagnosis. There are great frameworks for getting teams to attack true problems, but they’re often hard to do daily and on the fly. That’s where our guest comes in.

Thomas Wedell-Wedellsborg is a consultant who helps companies and managers reframe their problems so they can come up with an effective solution faster. He asks the question “Are You Solving The Right Problems?” in the January-February 2017 issue of Harvard Business Review. Thomas, thank you so much for coming on the HBR IdeaCast .

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

SARAH GREEN CARMICHAEL: So, I thought maybe we could start by talking about the problem of talking about problem reframing. What is that exactly?

THOMAS WEDELL-WEDELLSBORG: Basically, when people face a problem, they tend to jump into solution mode to rapidly, and very often that means that they don’t really understand, necessarily, the problem they’re trying to solve. And so, reframing is really a– at heart, it’s a method that helps you avoid that by taking a second to go in and ask two questions, basically saying, first of all, wait. What is the problem we’re trying to solve? And then crucially asking, is there a different way to think about what the problem actually is?

SARAH GREEN CARMICHAEL: So, I feel like so often when this comes up in meetings, you know, someone says that, and maybe they throw out the Einstein quote about you spend an hour of problem solving, you spend 55 minutes to find the problem. And then everyone else in the room kind of gets irritated. So, maybe just give us an example of maybe how this would work in practice in a way that would not, sort of, set people’s teeth on edge, like oh, here Sarah goes again, reframing the whole problem instead of just solving it.

THOMAS WEDELL-WEDELLSBORG: I mean, you’re bringing up something that’s, I think is crucial, which is to create legitimacy for the method. So, one of the reasons why I put out the article is to give people a tool to say actually, this thing is still important, and we need to do it. But I think the really critical thing in order to make this work in a meeting is actually to learn how to do it fast, because if you have the idea that you need to spend 30 minutes in a meeting delving deeply into the problem, I mean, that’s going to be uphill for most problems. So, the critical thing here is really to try to make it a practice you can implement very, very rapidly.

There’s an example that I would suggest memorizing. This is the example that I use to explain very rapidly what it is. And it’s basically, I call it the slow elevator problem. You imagine that you are the owner of an office building, and that your tenants are complaining that the elevator’s slow.

Now, if you take that problem framing for granted, you’re going to start thinking creatively around how do we make the elevator faster. Do we install a new motor? Do we have to buy a new lift somewhere?

The thing is, though, if you ask people who actually work with facilities management, well, they’re going to have a different solution for you, which is put up a mirror next to the elevator. That’s what happens is, of course, that people go oh, I’m busy. I’m busy. I’m– oh, a mirror. Oh, that’s beautiful.

And then they forget time. What’s interesting about that example is that the idea with a mirror is actually a solution to a different problem than the one you first proposed. And so, the whole idea here is once you get good at using reframing, you can quickly identify other aspects of the problem that might be much better to try to solve than the original one you found. It’s not necessarily that the first one is wrong. It’s just that there might be better problems out there to attack that we can, means we can do things much faster, cheaper, or better.

SARAH GREEN CARMICHAEL: So, in that example, I can understand how A, it’s probably expensive to make the elevator faster, so it’s much cheaper just to put up a mirror. And B, maybe the real problem people are actually feeling, even though they’re not articulating it right, is like, I hate waiting for the elevator. But if you let them sort of fix their hair or check their teeth, they’re suddenly distracted and don’t notice.

But if you have, this is sort of a pedestrian example, but say you have a roommate or a spouse who doesn’t clean up the kitchen. Facing that problem and not having your elegant solution already there to highlight the contrast between the perceived problem and the real problem, how would you take a problem like that and attack it using this method so that you can see what some of the other options might be?

THOMAS WEDELL-WEDELLSBORG: Right. So, I mean, let’s say it’s you who have that problem. I would go in and say, first of all, what would you say the problem is? Like, if you were to describe your view of the problem, what would that be?

SARAH GREEN CARMICHAEL: I hate cleaning the kitchen, and I want someone else to clean it up.

THOMAS WEDELL-WEDELLSBORG: OK. So, my first observation, you know, that somebody else might not necessarily be your spouse. So, already there, there’s an inbuilt assumption in your question around oh, it has to be my husband who does the cleaning. So, it might actually be worth, already there to say, is that really the only problem you have? That you hate cleaning the kitchen, and you want to avoid it? Or might there be something around, as well, getting a better relationship in terms of how you solve problems in general or establishing a better way to handle small problems when dealing with your spouse?

SARAH GREEN CARMICHAEL: Or maybe, now that I’m thinking that, maybe the problem is that you just can’t find the stuff in the kitchen when you need to find it.

THOMAS WEDELL-WEDELLSBORG: Right, and so that’s an example of a reframing, that actually why is it a problem that the kitchen is not clean? Is it only because you hate the act of cleaning, or does it actually mean that it just takes you a lot longer and gets a lot messier to actually use the kitchen, which is a different problem. The way you describe this problem now, is there anything that’s missing from that description?

SARAH GREEN CARMICHAEL: That is a really good question.

THOMAS WEDELL-WEDELLSBORG: Other, basically asking other factors that we are not talking about right now, and I say those because people tend to, when given a problem, they tend to delve deeper into the detail. What often is missing is actually an element outside of the initial description of the problem that might be really relevant to what’s going on. Like, why does the kitchen get messy in the first place? Is it something about the way you use it or your cooking habits? Is it because the neighbor’s kids, kind of, use it all the time?

There might, very often, there might be issues that you’re not really thinking about when you first describe the problem that actually has a big effect on it.

SARAH GREEN CARMICHAEL: I think at this point it would be helpful to maybe get another business example, and I’m wondering if you could tell us the story of the dog adoption problem.

THOMAS WEDELL-WEDELLSBORG: Yeah. This is a big problem in the US. If you work in the shelter industry, basically because dogs are so popular, more than 3 million dogs every year enter a shelter, and currently only about half of those actually find a new home and get adopted. And so, this is a problem that has persisted. It’s been, like, a structural problem for decades in this space. In the last three years, where people found new ways to address it.

So a woman called Lori Weise who runs a rescue organization in South LA, and she actually went in and challenged the very idea of what we were trying to do. She said, no, no. The problem we’re trying to solve is not about how to get more people to adopt dogs. It is about keeping the dogs with their first family so they never enter the shelter system in the first place.

In 2013, she started what’s called a Shelter Intervention Program that basically works like this. If a family comes and wants to hand over their dog, these are called owner surrenders. It’s about 30% of all dogs that come into a shelter. All they would do is go up and ask, if you could, would you like to keep your animal? And if they said yes, they would try to fix whatever helped them fix the problem, but that made them turn over this.

And sometimes that might be that they moved into a new building. The landlord required a deposit, and they simply didn’t have the money to put down a deposit. Or the dog might need a $10 rabies shot, but they didn’t know how to get access to a vet.

And so, by instigating that program, just in the first year, she took her, basically the amount of dollars they spent per animal they helped went from something like $85 down to around $60. Just an immediate impact, and her program now is being rolled out, is being supported by the ASPCA, which is one of the big animal welfare stations, and it’s being rolled out to various other places.

And I think what really struck me with that example was this was not dependent on having the internet. This was not, oh, we needed to have everybody mobile before we could come up with this. This, conceivably, we could have done 20 years ago. Only, it only happened when somebody, like in this case Lori, went in and actually rethought what the problem they were trying to solve was in the first place.

SARAH GREEN CARMICHAEL: So, what I also think is so interesting about that example is that when you talk about it, it doesn’t sound like the kind of thing that would have been thought of through other kinds of problem solving methods. There wasn’t necessarily an After Action Review or a 5 Whys exercise or a Six Sigma type intervention. I don’t want to throw those other methods under the bus, but how can you get such powerful results with such a very simple way of thinking about something?

THOMAS WEDELL-WEDELLSBORG: That was something that struck me as well. This, in a way, reframing and the idea of the problem diagnosis is important is something we’ve known for a long, long time. And we’ve actually have built some tools to help out. If you worked with us professionally, you are familiar with, like, Six Sigma, TRIZ, and so on. You mentioned 5 Whys. A root cause analysis is another one that a lot of people are familiar with.

Those are our good tools, and they’re definitely better than nothing. But what I notice when I work with the companies applying those was those tools tend to make you dig deeper into the first understanding of the problem we have. If it’s the elevator example, people start asking, well, is that the cable strength, or is the capacity of the elevator? That they kind of get caught by the details.

That, in a way, is a bad way to work on problems because it really assumes that there’s like a, you can almost hear it, a root cause. That you have to dig down and find the one true problem, and everything else was just symptoms. That’s a bad way to think about problems because problems tend to be multicausal.

There tend to be lots of causes or levers you can potentially press to address a problem. And if you think there’s only one, if that’s the right problem, that’s actually a dangerous way. And so I think that’s why, that this is a method I’ve worked with over the last five years, trying to basically refine how to make people better at this, and the key tends to be this thing about shifting out and saying, is there a totally different way of thinking about the problem versus getting too caught up in the mechanistic details of what happens.

SARAH GREEN CARMICHAEL: What about experimentation? Because that’s another method that’s become really popular with the rise of Lean Startup and lots of other innovation methodologies. Why wouldn’t it have worked to, say, experiment with many different types of fixing the dog adoption problem, and then just pick the one that works the best?

THOMAS WEDELL-WEDELLSBORG: You could say in the dog space, that’s what’s been going on. I mean, there is, in this industry and a lot of, it’s largely volunteer driven. People have experimented, and they found different ways of trying to cope. And that has definitely made the problem better. So, I wouldn’t say that experimentation is bad, quite the contrary. Rapid prototyping, quickly putting something out into the world and learning from it, that’s a fantastic way to learn more and to move forward.

My point is, though, that I feel we’ve come to rely too much on that. There’s like, if you look at the start up space, the wisdom is now just to put something quickly into the market, and then if it doesn’t work, pivot and just do more stuff. What reframing really is, I think of it as the cognitive counterpoint to prototyping. So, this is really a way of seeing very quickly, like not just working on the solution, but also working on our understanding of the problem and trying to see is there a different way to think about that.

If you only stick with experimentation, again, you tend to sometimes stay too much in the same space trying minute variations of something instead of taking a step back and saying, wait a minute. What is this telling us about what the real issue is?

SARAH GREEN CARMICHAEL: So, to go back to something that we touched on earlier, when we were talking about the completely hypothetical example of a spouse who does not clean the kitchen–

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

SARAH GREEN CARMICHAEL: Yes. For the record, my husband is a great kitchen cleaner.

You started asking me some questions that I could see immediately were helping me rethink that problem. Is that kind of the key, just having a checklist of questions to ask yourself? How do you really start to put this into practice?

THOMAS WEDELL-WEDELLSBORG: I think there are two steps in that. The first one is just to make yourself better at the method. Yes, you should kind of work with a checklist. In the article, I kind of outlined seven practices that you can use to do this.

But importantly, I would say you have to consider that as, basically, a set of training wheels. I think there’s a big, big danger in getting caught in a checklist. This is something I work with.

My co-author Paddy Miller, it’s one of his insights. That if you start giving people a checklist for things like this, they start following it. And that’s actually a problem, because what you really want them to do is start challenging their thinking.

So the way to handle this is to get some practice using it. Do use the checklist initially, but then try to step away from it and try to see if you can organically make– it’s almost a habit of mind. When you run into a colleague in the hallway and she has a problem and you have five minutes, like, delving in and just starting asking some of those questions and using your intuition to say, wait, how is she talking about this problem? And is there a question or two I can ask her about the problem that can help her rethink it?

SARAH GREEN CARMICHAEL: Well, that is also just a very different approach, because I think in that situation, most of us can’t go 30 seconds without jumping in and offering solutions.

THOMAS WEDELL-WEDELLSBORG: Very true. The drive toward solutions is very strong. And to be clear, I mean, there’s nothing wrong with that if the solutions work. So, many problems are just solved by oh, you know, oh, here’s the way to do that. Great.

But this is really a powerful method for those problems where either it’s something we’ve been banging our heads against tons of times without making progress, or when you need to come up with a really creative solution. When you’re facing a competitor with a much bigger budget, and you know, if you solve the same problem later, you’re not going to win. So, that basic idea of taking that approach to problems can often help you move forward in a different way than just like, oh, I have a solution.

I would say there’s also, there’s some interesting psychological stuff going on, right? Where you may have tried this, but if somebody tries to serve up a solution to a problem I have, I’m often resistant towards them. Kind if like, no, no, no, no, no, no. That solution is not going to work in my world. Whereas if you get them to discuss and analyze what the problem really is, you might actually dig something up.

Let’s go back to the kitchen example. One powerful question is just to say, what’s your own part in creating this problem? It’s very often, like, people, they describe problems as if it’s something that’s inflicted upon them from the external world, and they are innocent bystanders in that.

SARAH GREEN CARMICHAEL: Right, or crazy customers with unreasonable demands.

THOMAS WEDELL-WEDELLSBORG: Exactly, right. I don’t think I’ve ever met an agency or consultancy that didn’t, like, gossip about their customers. Oh, my god, they’re horrible. That, you know, classic thing, why don’t they want to take more risk? Well, risk is bad.

It’s their business that’s on the line, not the consultancy’s, right? So, absolutely, that’s one of the things when you step into a different mindset and kind of, wait. Oh yeah, maybe I actually am part of creating this problem in a sense, as well. That tends to open some new doors for you to move forward, in a way, with stuff that you may have been struggling with for years.

SARAH GREEN CARMICHAEL: So, we’ve surfaced a couple of questions that are useful. I’m curious to know, what are some of the other questions that you find yourself asking in these situations, given that you have made this sort of mental habit that you do? What are the questions that people seem to find really useful?

THOMAS WEDELL-WEDELLSBORG: One easy one is just to ask if there are any positive exceptions to the problem. So, was there day where your kitchen was actually spotlessly clean? And then asking, what was different about that day? Like, what happened there that didn’t happen the other days? That can very often point people towards a factor that they hadn’t considered previously.

SARAH GREEN CARMICHAEL: We got take-out.

THOMAS WEDELL-WEDELLSBORG: S,o that is your solution. Take-out from [INAUDIBLE]. That might have other problems.

Another good question, and this is a little bit more high level. It’s actually more making an observation about labeling how that person thinks about the problem. And what I mean with that is, we have problem categories in our head. So, if I say, let’s say that you describe a problem to me and say, well, we have a really great product and are, it’s much better than our previous product, but people aren’t buying it. I think we need to put more marketing dollars into this.

Now you can go in and say, that’s interesting. This sounds like you’re thinking of this as a communications problem. Is there a different way of thinking about that? Because you can almost tell how, when the second you say communications, there are some ideas about how do you solve a communications problem. Typically with more communication.

And what you might do is go in and suggest, well, have you considered that it might be, say, an incentive problem? Are there incentives on behalf of the purchasing manager at your clients that are obstructing you? Might there be incentive issues with your own sales force that makes them want to sell the old product instead of the new one?

So literally, just identifying what type of problem does this person think about, and is there different potential way of thinking about it? Might it be an emotional problem, a timing problem, an expectations management problem? Thinking about what label of what type of problem that person is kind of thinking as it of.

SARAH GREEN CARMICHAEL: That’s really interesting, too, because I think so many of us get requests for advice that we’re really not qualified to give. So, maybe the next time that happens, instead of muddying my way through, I will just ask some of those questions that we talked about instead.

THOMAS WEDELL-WEDELLSBORG: That sounds like a good idea.

SARAH GREEN CARMICHAEL: So, Thomas, this has really helped me reframe the way I think about a couple of problems in my own life, and I’m just wondering. I know you do this professionally, but is there a problem in your life that thinking this way has helped you solve?

THOMAS WEDELL-WEDELLSBORG: I’ve, of course, I’ve been swallowing my own medicine on this, too, and I think I have, well, maybe two different examples, and in one case somebody else did the reframing for me. But in one case, when I was younger, I often kind of struggled a little bit. I mean, this is my teenage years, kind of hanging out with my parents. I thought they were pretty annoying people. That’s not really fair, because they’re quite wonderful, but that’s what life is when you’re a teenager.

And one of the things that struck me, suddenly, and this was kind of the positive exception was, there was actually an evening where we really had a good time, and there wasn’t a conflict. And the core thing was, I wasn’t just seeing them in their old house where I grew up. It was, actually, we were at a restaurant. And it suddenly struck me that so much of the sometimes, kind of, a little bit, you love them but they’re annoying kind of dynamic, is tied to the place, is tied to the setting you are in.

And of course, if– you know, I live abroad now, if I visit my parents and I stay in my old bedroom, you know, my mother comes in and wants to wake me up in the morning. Stuff like that, right? And it just struck me so, so clearly that it’s– when I change this setting, if I go out and have dinner with them at a different place, that the dynamic, just that dynamic disappears.

SARAH GREEN CARMICHAEL: Well, Thomas, this has been really, really helpful. Thank you for talking with me today.

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

HANNAH BATES: That was Thomas Wedell-Wedellsborg in conversation with Sarah Green Carmichael on the HBR IdeaCast. He’s an expert in problem solving and innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

We’ll be back next Wednesday with another hand-picked conversation about leadership from the Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

We’re a production of Harvard Business Review. If you want more podcasts, articles, case studies, books, and videos like this, find it all at HBR dot org.

This episode was produced by Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Music by Coma Media. Special thanks to Maureen Hoch, Adi Ignatius, Karen Player, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener.

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A novel and effective method for solving the router nodes placement in wireless mesh networks using reinforcement learning

Contributed equally to this work with: Le Huu Binh, Thuy-Van T. Duong

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Affiliation Faculty of Information Technology, University of Sciences, Hue University, Hue City, Vietnam

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Affiliation Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Viet Nam

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• Published: April 10, 2024
• https://doi.org/10.1371/journal.pone.0301073
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Router nodes placement (RNP) is an important issue in the design and implementation of wireless mesh networks (WMN). This is known as an P-hard problem, which cannot be solved using conventional algorithms. Consequently, approximate optimization strategies are commonly used to solve this problem. With heavy node density and wide-area WMNs, solving the RNP problem using approximation algorithms often faces many difficulties, therefore, a more effective solution is necessary. This motivated us to conduct this work. We propose a new method for solving the RNP problem using reinforcement learning (RL). The RNP problem is modeled as an RL model with environment, agent, action, and reward are equivalent to the network system, routers, coordinate adjustment, and connectivity of the RNP problem, respectively. To the best of our knowledge, this is the first study that applies RL to solve the RNP problem. The experimental results showed that the proposed method increased the network connectivity by up to 22.73% compared to the most recent methods.

Citation: Binh LH, Duong T-VT (2024) A novel and effective method for solving the router nodes placement in wireless mesh networks using reinforcement learning. PLoS ONE 19(4): e0301073. https://doi.org/10.1371/journal.pone.0301073

Editor: Mohammed Balfaqih, University of Jeddah, SAUDI ARABIA

Received: August 9, 2023; Accepted: March 9, 2024; Published: April 10, 2024

Copyright: © 2024 Binh, Duong. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting information files.

Funding: The authors received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Wireless communication is growing and being widely applied in many fields. In the local area network of agencies, businesses, schools, and so on, wireless mesh networks (WMN) [ 1 , 2 ] are the best choice today because of their significant advantages compared to wireless networks using traditional access points. The most notable benefit of the WMN is that it reduces congestion owing to its ability to balance the loads. In addition, the installation of a WMN is very convenient because there is no need to construct wired connections from the gateway to all routers. Fig 1 illustrates an example of a WMN consisting of six mesh routers (represented by r 1 to r 6 ) and eleven mesh clients (represented by c 1 to c 11 ). In addition, at least one the router of the Internet service provider serves as a gateway for clients to access the Internet. If two mesh routers are within range of each other, a wireless link is established between them. A mesh topology consists of of all the mesh routers and wireless links. For a WMN to deliver Internet services, several mesh routers must be connected to the gateway router via wireless or cable links. As shown in Fig 1 , the mesh routers r 1 and r 2 are connected to the gateway router (GPON or FTTh router) via wireless links. Mesh clients are terminal devices that are users of network services. When a mesh client enters the network region, it can be covered by one or more mesh routers; the mesh client connects to the nearest mesh router to access network services.

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https://doi.org/10.1371/journal.pone.0301073.g001

With the rapid development of wireless and mobile communication technologies, network services are becoming more diverse and rich, especially those on fifth-generation (5G) and sixth-generation (6G) wireless network platforms. To effectively provide these services, WMNs must be designed and installed in the most efficient manner possible, allowing network resources to be fully utilized. This is the motivation for researchers to focus on WMN. Some of the most prevalent subjects that have been implemented include network topology control [ 3 – 7 ], router node placement (RNP) [ 8 – 24 ], optimum routing protocols [ 25 – 29 ], and access point allocation [ 30 – 33 ], with the RNP challenge being the most fascinating. Because the RNP problem is known to be NP-hard, it cannot be solved using conventional algorithms. Recently, approximate optimization methods have become useful for solving this problem [ 8 – 12 ]. The authors of [ 8 ] have used the coyote optimization algorithm (COA) to solve the RNP problem. Their proposed method optimizes both network connectivity and user coverage, which are two critical performance criteria. Using MATLAB simulations, the authors demonstrated that the COA algorithm outperformed other well-known optimization algorithms. In [ 10 ], the authors suggested an optimal method called the Chemical Reaction Optimization (CRO) algorithm to solve this problem. The CRO algorithm was inspired by how molecules interact to achieve a low, stable energy state in chemical reactions. In terms of client coverage and network connection, the simulation findings reveal that their suggested approach outperforms the Genetic approach (GA) and Simulated Annealing (SA). Another study employed a genetic algorithm and simulated annealing to discover a low-cost WMN configuration while satisfying restrictions and identifying the number of gateways needed [ 34 ]. Experiments showed that the evolutionary algorithm and simulated annealing were successful in lowering WMN network expenses while maintaining QoS. The new models significantly outperformed the conventional solutions. QoS was also considered in the RNP problem in [ 23 ]. The authors described a unique particle swarm optimization method for improving network connectivity and client coverage. The QoS restrictions for this study are the delay, relay load, and Internet gateway capacity. In [ 35 ], the authors suggested an improved version of the Moth Flame Optimization (MFO) algorithm, namely, Enhanced Chaotic Lévy Opposition-based MFO (ECLO-MFO), for solving the RNP problem. To improve the optimization performance of MFO, the proposed method integrates three strategies: the chaotic map concept, Lévy flying strategy, and Opposition-Based Learning (OBL) technique. The simulation results showed that the proposed algorithm was more efficient than the method of applying popular optimization algorithms.

Based on the results of published works, we find that the method of using approximate optimal algorithms provide good solutions. However, because randomness is used in several steps of the algorithm, the results often differ for different executions. For accurate results, each script must be executed multiple times, and then the average of all executions is obtained. For example, the authors of [ 8 , 11 ] executed each simulation scenario 50 times. Furthermore, with heavy node density and wide-area WMNs, solving the RNP problem with approximation algorithms often presents many difficulties, necessitating a more effective solution. In this paper, we propose a new and effective algorithm to solve this problem. The main contributions of this study are summarized as follows:

• (i) We proposed a novel and effective method for solving the RNP problem using RL. The RNP problem is modeled as an RL model, with the environment, agent, action, and reward representing the network system, routers, coordinate adjustment, and connectivity respectively, of the RNP problem. To the best of our knowledge, this is the first study to apply reinforcement learning to the RNP problem.
• (ii) We compared and evaluated the performance of the RNP problem solving method using the heuristic algorithms and the RL method.

The remainder of this paper is organized as follows. The next section describes the formulation of the RNP problem in the WMN. The following sections present our proposed solution and experimental results. Finally, concluding remarks and promising future studies are presented in the last section.

RNP problem

In this section, we formulate the RNP problem in a WMN. First, graph theory was used to describe the WMN. We then define some metrics to use for the objective function of the RNP problem, similar to [ 11 ]. Finally, the RNP problem was formulated as a nonlinear programming problem. For convenience, we define the mathematical symbols shown in Table 1 .

https://doi.org/10.1371/journal.pone.0301073.t001

Mathematical model of a WMN using graph theory

Consider a WMN comprising m mesh routers, n mesh clients, and k gateway routers. Mathematically, this WMN can be represented as an undirected graph, denoted by G = ( V , E ), where V and E are the vertex and edge sets, respectively. V is equivalent to the set of all nodes in the WMN and is determined by V = R ∪ C ∪ W , where R , C and W are the sets of mesh routers, mesh clients, and gateway routers, respectively. E is equivalent to the set of all wireless links in the WMN and consists of three types: links between mesh routers, links between mesh client and mesh router, and links between gateway and mesh router.

RNP problem formulation

In this section, we formulate the RNP problem using some concepts and metrics from [ 11 ], including the connected router, connected client, connected router ratio, and connected client ratio.

Connected router.

The mesh router r i is a connected router if and only if at least one path exists between it and the gateway router. If we return to the WMN example in Fig 1 , we can see that mesh routers r 1 , r 2 , r 3 , r 4 and r 6 are the connected routers but r 5 is not because no path exists from this mesh router to the gateway router.

Connected router ratio (CRR).

Connected client.

Connected client ratio (CCR).

Formulate the RNP into a nonlinear programming problem.

The RNP problem in the WMN is stated as follows: Consider a case where it is necessary to design and install a WMN with the following assumptions:

• The network system is located in an area of W × H meters.

• The number of mesh routers was m , and the coverage radius of each mesh router was d r .

RL-based mesh router nodes placement

Fundamentals of rl.

https://doi.org/10.1371/journal.pone.0301073.g002

RL has been successfully applied to control protocols in wireless networks, typically routing in WMN [ 25 , 27 , 29 ], topology control in wireless sensor networks [ 37 ], improving the performance of energy-harvesting wireless body area networks [ 38 , 39 ]. In this paper, we apply RL to solve the RNP in WMN. Details of this new proposal are presented in the following sections.

Solving the RNP in WMN using RL

The RL has recently been successfully employed to solve technical challenges in wireless communication such as routing [ 27 , 36 ], topology management [ 37 ], and resource allocation. In this study, we use RL to solve the RNP problem. To the best of our knowledge, this is the first study to use RL to address the RNP problem. To do this, the RNP problem must be modeled as a reinforcement learning model with five characteristic factors: agent, environment, state, action, and reward.

An agent is a mesh router that regularly adjusts its coordinates to obtain an optimal topology.

Environment.

In a RL model, the environment is everything that exists around the agent, and it is where the agent acts and interacts. The environment for the RNP problem using RL is the network system, which includes a set of mesh routers, clients, gateway routers, and network area.

Each state is determined by a triple { P c , P r , P w }, where P c , P r and P w are the sets of coordinates for the mesh clients, mesh router, and gateway routers, respectively. The sets are listed in Table 1 .

Action is the way in which the agent interacts with the environment to change its state. For the RNP problem using reinforcement learning, the agents are the mesh routers. Each action was defined by a mesh router that adjusted its coordinates. The set of actions at a specific state s t for each mesh router r i is defined as A t = { mn1s, me1s, ms1s, mw1s, mn2s, me2s, ms2s, mw2s }, where the actions are described in Table 2 , step is a given distance.

https://doi.org/10.1371/journal.pone.0301073.t002

RL algorithm for solving RNP problem.

Algorithm 1 The pseudo-code of the reinforcement learning algorithm for solving RNP problem

• Network area ( W × H );

• The set of mesh routers ( R = { r i | i = 1.. m }), and the coverage radius of each mesh router ( d r );

2: while ( learn ≤ numLearn ) do

3:  Randomly choose mesh router r i ∈ R ;

4:   for ( each action a j ∈ A ) do

5:   Update Q ( r i , s t , a t , j ) using ( 11 );

6:   end for

7:  Choose the action a t , k ∈ A t using policy derived from Q-values (e.g., ε -greedy ) according to ( 12 );

8:  Take action a t , k , observe reward R ( r i , s t , a t , k ) and next state s t +1 ;

9:  Update next state ( s t +1 ) to current state ( s t );

10:   learn ← learn + 1;

11: end while

12: P r ← P r in state s t ;

Analyze the computational complexity.

The computational complexity of Algorithm 1 depends mainly on the iteration in Step (2), the number of possible actions in Step (4), and the algorithm for updating the Q value in Step (5). Q ( r i , s t , a t , j ) is updated using Eq. ( 11 ), where the greatest complexity is the calculation of RW ( r i , s t , a t ) according to ( 10 ). RW ( r i , s t , a t ) contains two metrics, CRR and CCR , which are defined by ( 1 ) and ( 5 ), respectively. To determine CRR , we employed a breadth-first search algorithm on a network of m vertices, which is the number of mesh routers. Therefore, the computational complexity was O ( m 2 ). The CCR is calculated using two nested loops of sizes m and n , where n is the number of mesh clients. Therefore, the complexity was O ( m × n ). Because n is always greater than m in a WMN, the computational complexity of RW ( r i , s t , a t ) is O ( m × n ). Consequently, the computational complexity of Algorithm 1 is O ( I × | A | × m × n ), where I is the number of iterations and | A | is the number of possible actions.

The computational complexity of Algorithm 1 is greater than that of the algorithms solving the RNP problem using GA [ 40 ], PSO [ 24 ], and WOA [ 41 ], which we compare in the following section. However, because its computing complexity is a polynomial function, it can be implemented in practice. Furthermore, because the algorithms for solving the RNP problem are run offline, the polynomial complexity is acceptable.

Simulation results and discussion

Simulation scenarios.

The performance of the proposed method was evaluated through a simulation using Python. Our proposed method is compared with the most recent methods that use approximate optimization algorithms to address the RNP problem, including GA [ 40 ], PSO [ 24 ], WOA [ 41 ], and MVO [ 11 ]. All experiments were run on a 3.6 GHz Core i7 CPU computer. The surveyed network instances (NI) are presented in Table 3 . NI-1 and NI-2 were used to investigate the effect of the number of mesh routers on the network performance, with the number of mesh routers ranging from 20 to 45 covering 150 mesh clients (NI-1) and 350 mesh clients (NI-2). NI-3 and NI-4 ware used to study the effect of client density, varying from 100 to 400. In NI-5 and N-6, the effect of the coverage radius of each mesh router was thoroughly examined. The final two NIs were used to investigate the influence of the network area. The parameters of the simulation scenarios and algorithms are presented in Table 4 , where th parameters of the GA, PSO, WOA, and MVO are set as in [ 11 ].

https://doi.org/10.1371/journal.pone.0301073.t003

https://doi.org/10.1371/journal.pone.0301073.t004

Simulation results

Topology evaluation..

First, we evaluate the topology obtained when solving the RNP problem using the GA, PSO, WOA, MVO, and our proposed method, which employs reinforcement learning. The results obtained in Fig 3 clearly show topological differences between the methods. These findings were obtained using NI-2 with 30 mesh routers covering 350 mesh clients in an area of 2000 × 2000 [ m 2 ] and a coverage radius of 200 [ m ] for each mesh router. We can observe that the method using RL provides the most optimal topology compared with the methods using approximate optimization algorithms, GA, WOA, PSO, and MVO. Specifically, for the method using reinforcement learning, there are 334 mesh clients covered by at least one mesh router, corresponding to a rate of 95.43%. These values were 292 (83.43%), 309 (88.29%), 313 (89.43%), and 313 (88.86%) for the WOA, GA, PSO, and MVO algorithms, respectively. In addition, the topology of the reinforcement learning method has a wider coverage area than the other methods, which can increase the percentage of clients covered in the case of denser clients.

(a) WOA, (b) GA, (c) PSO, (d) MVO, and (e) reinforcement learning.

https://doi.org/10.1371/journal.pone.0301073.g003

Impact of mesh router density.

The results obtained in Fig 4 clearly show the difference in network connectivity between the proposed method and the method using approximate optimization algorithms. These findings were obtained using NI-1, in which the number of mesh routers varieed from 20 to 45, covering 150 mesh clients in an area of 2000 × 2000 [ m 2 ] and a coverage radius of 200 [ m ] for each mesh router. We can observe that the NC increases proportionally with the number of mesh routers for all methods. This is evident because as the number of mesh routers increases, the coverage area expands, increasing the probability of mesh clients being covered. Comparing the methods of solving RNP problems, the method using RL (legend namely RL-based RNP) gives the highest NC. For example, considering the case of 35 mesh routers, The NC values of the methods using the WOA, PSO, GA, MVO, and RL are 85.64, 87.42, 90.67, 93.42, and 95.68%, respectively. Thus, compared with the method using algorithms WOA, PSO, GA, and MVO, the proposed method improved NC by 10.03, 8.25, 5.01%, and 2.25%, respectively. This is a significant result in improving WMN performance.

https://doi.org/10.1371/journal.pone.0301073.g004

The results obtained were quite similar for the implementation on NI-2, as shown in Fig 5 . The assumptions of this simulation scenario are the same as those in NI-1, except that the number of mesh clients increases to 350. We can see that the proposed method is highly effective in terms of NC. We can observe that the proposed solution provides high efficiency in terms of NC for most values of the number of mesh routers. The NC of the method using RL increases by an average of 4 to 20% compared with the cases where approximate optimization algorithms are used. As is the case with 35 mesh routers, the NC of the RL is 98.71%. These values of the WOA, PSO, GA, and MVO algorithms were 81.66%, 86.89%, 88.59%, and 94.44% respectively. Thus, the method using RL improved the NC from 4.26% to 17.04%.

https://doi.org/10.1371/journal.pone.0301073.g005

Based on the findings in Figs 4 and 5 , we can conclude that changing the number of mesh routers affects on network performance in terms of NC. The larger the number of routers, the higher the NC for all investigated RNP problem solving methods. In particular, the method based on RL is the most efficient.

Impact of mesh client density.

In this section, we investigate the effect of client density on network performance. In a WMN, the denser the clients, the greater is the number of connection requests to the routers. As a result, network performance was affected. This is more evident in Fig 6 , where we plot NC as a function of the number of mesh clients. These results are obtained by executing NI-3, where the number of mesh routers is 30, covering 150 to 300 mesh clients. We can easily observe that the method using RL always yields the highest NC regardless of whether the client density is sparse or dense. The NC value of this method from 90.43% to 95.79%. Meanwhile, the NC values for the cases of algorithm WOA, PSO, GA, and MVO are fom 74.59% to 84.08%, from 77.00% to 85.63%, from 82.32% to 91.46%, and from 88.27% to 90.83%, respectively. When 45 mesh routers were used (NI-4), the NC value increased for all methods. This is clearly shown in Fig 7 , where we represent NC versus the number of mesh clients. Comparing the methods, we find that the method using RL outperforms the method using approximate optimal algorithms in terms of NC.

https://doi.org/10.1371/journal.pone.0301073.g006

https://doi.org/10.1371/journal.pone.0301073.g007

Impart of the coverage radius of mesh routers.

The coverage radius of the mesh routers is another technological parameter that has a considerable impact on the WMN performance. In this section, we investigate the effect of this technological parameter on the NC metric. The results obtained in Fig 8 clearly show the change in NC with respect to the coverage radius of the mesh routers. These results were implemented using NI-5, which has 30 mesh routers and 150 mesh clients. The coverage radius of each router ranged from 150 to 300 [ m ]. The plots in Fig 8 indicate that the NC increases proportionally to the coverage radius of the mesh routers. This is because expanding the coverage radius increases the likelihood that clients will be covered. As a result, NC increases. In particular, the method using RL yielded the highest NC, reaching close to 100% when the coverage radius was 250 [m] or more. The results are also similar for NI-6, as shown in Fig 9 . The NC value of this NI is greater than that of the NI-5 because this uses more mesh routers. As in the previous scenarios, the method using RL always yields the highest NC.

https://doi.org/10.1371/journal.pone.0301073.g008

https://doi.org/10.1371/journal.pone.0301073.g009

Impact of network area.

In the last section, we investigate the effect of network area on the efficiency of RNP problem solving methods. Figs 10 and 11 show the results obtained by executing NI-7 and NI-8, respectively. In these NIs, the network area varies from 2000 × 2000 [ m 2 ] to 3000 × 3000 [ m 2 ]. The NC value decreased according to the network area for all the algorithms. This is because, for a given number of mesh routers, the larger the network area, the lower the percentage of area covered, leading to a decrease in the NC value. However, the NC value of the method using RL is always the largest.

https://doi.org/10.1371/journal.pone.0301073.g010

https://doi.org/10.1371/journal.pone.0301073.g011

Based on the above findings, we can conclude that the proposed method, which uses reinforcement learning to solve the RNP problem, is more efficient than a method that uses approximate optimal algorithms. This is a crucial result in the design and implementation of a WMN, which helps find an optimal network topology to exploit network resources more efficiently.

The placement of router nodes in wireless mesh networks is a significant problem that has recently attracted the interest of several research groups. This problem is recognized as NP-hard, and cannot be resolved using conventional algorithms. In this study, we proposed a new and effective method for solving this problem using RL. The process of finding the optimal coordinates for placing mesh routers is modeled as an RL with the main components being environment, agent, action, and reward, which are equivalent to the network system, routers, coordinate adjustment, and network connectivity of the RNP problem, respectively. Simulation results show that our proposed method outperforms the most recent methods in terms of coverage and network connectivity.

In future work, we will continue to develop this method by considering additional constraints on the quality of transmission and load balancing to improve network performance. In addition, the deep reinforcement learning method can also be applied to static and dynamic RNP problems to further improve the performance of the WMN.

Supporting information

S1 dataset..

https://doi.org/10.1371/journal.pone.0301073.s001

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