problem solving method of teaching is related to

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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 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. 

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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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: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part  blog series  on  teaching 21st century skills , including  problem solving ,  metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively  so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

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Why Every Educator Needs to Teach Problem-Solving Skills

Strong problem-solving skills will help students be more resilient and will increase their academic and career success .

Want to learn more about how to measure and teach students’ higher-order skills, including problem solving, critical thinking, and written communication?

Problem-solving skills are essential in school, careers, and life.

Problem-solving skills are important for every student to master. They help individuals navigate everyday life and find solutions to complex issues and challenges. These skills are especially valuable in the workplace, where employees are often required to solve problems and make decisions quickly and effectively.

Problem-solving skills are also needed for students’ personal growth and development because they help individuals overcome obstacles and achieve their goals. By developing strong problem-solving skills, students can improve their overall quality of life and become more successful in their personal and professional endeavors.

Problem-Solving Skills Help Students…

   develop resilience.

Problem-solving skills are an integral part of resilience and the ability to persevere through challenges and adversity. To effectively work through and solve a problem, students must be able to think critically and creatively. Critical and creative thinking help students approach a problem objectively, analyze its components, and determine different ways to go about finding a solution.  

This process in turn helps students build self-efficacy . When students are able to analyze and solve a problem, this increases their confidence, and they begin to realize the power they have to advocate for themselves and make meaningful change.

When students gain confidence in their ability to work through problems and attain their goals, they also begin to build a growth mindset . According to leading resilience researcher, Carol Dweck, “in a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

    Set and Achieve Goals

Students who possess strong problem-solving skills are better equipped to set and achieve their goals. By learning how to identify problems, think critically, and develop solutions, students can become more self-sufficient and confident in their ability to achieve their goals. Additionally, problem-solving skills are used in virtually all fields, disciplines, and career paths, which makes them important for everyone. Building strong problem-solving skills will help students enhance their academic and career performance and become more competitive as they begin to seek full-time employment after graduation or pursue additional education and training.

  Resolve Conflicts

In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes “thinking outside the box” and approaching a conflict by searching for different solutions. This is a very different (and more effective!) method than a more stagnant approach that focuses on placing blame or getting stuck on elements of a situation that can’t be changed.

While it’s natural to get frustrated or feel stuck when working through a conflict, students with strong problem-solving skills will be able to work through these obstacles, think more rationally, and address the situation with a more solution-oriented approach. These skills will be valuable for students in school, their careers, and throughout their lives.

    Achieve Success

We are all faced with problems every day. Problems arise in our personal lives, in school and in our jobs, and in our interactions with others. Employers especially are looking for candidates with strong problem-solving skills. In today’s job market, most jobs require the ability to analyze and effectively resolve complex issues. Students with strong problem-solving skills will stand out from other applicants and will have a more desirable skill set.

In a recent opinion piece published by The Hechinger Report , Virgel Hammonds, Chief Learning Officer at KnowledgeWorks, stated “Our world presents increasingly complex challenges. Education must adapt so that it nurtures problem solvers and critical thinkers.” Yet, the “traditional K–12 education system leaves little room for students to engage in real-world problem-solving scenarios.” This is the reason that a growing number of K–12 school districts and higher education institutions are transforming their instructional approach to personalized and competency-based learning, which encourage students to make decisions, problem solve and think critically as they take ownership of and direct their educational journey.

Problem-Solving Skills Can Be Measured and Taught

Research shows that problem-solving skills can be measured and taught. One effective method is through performance-based assessments which require students to demonstrate or apply their knowledge and higher-order skills to create a response or product or do a task.

What Are Performance-Based Assessments?

With the No Child Left Behind Act (2002), the use of standardized testing became the primary way to measure student learning in the U.S. The legislative requirements of this act shifted the emphasis to standardized testing, and this led to a  decline in nontraditional testing methods .

But   many educators, policy makers, and parents have concerns with standardized tests. Some of the top issues include that they don’t provide feedback on how students can perform better, they don’t value creativity, they are not representative of diverse populations, and they can be disadvantageous to lower-income students.

While standardized tests are still the norm, U.S. Secretary of Education Miguel Cardona is encouraging states and districts to move away from traditional multiple choice and short response tests and instead use performance-based assessment, competency-based assessments, and other more authentic methods of measuring students abilities and skills rather than rote learning. 

Performance-based assessments  measure whether students can apply the skills and knowledge learned from a unit of study. Typically, a performance task challenges students to use their higher-order skills to complete a project or process. Tasks can range from an essay to a complex proposal or design.

Preview a Performance-Based Assessment

Want a closer look at how performance-based assessments work?  Preview CAE’s K–12 and Higher Education assessments and see how CAE’s tools help students develop critical thinking, problem-solving, and written communication skills.

Performance-Based Assessments Help Students Build and Practice Problem-Solving Skills

In addition to effectively measuring students’ higher-order skills, including their problem-solving skills, performance-based assessments can help students practice and build these skills. Through the assessment process, students are given opportunities to practically apply their knowledge in real-world situations. By demonstrating their understanding of a topic, students are required to put what they’ve learned into practice through activities such as presentations, experiments, and simulations. 

This type of problem-solving assessment tool requires students to analyze information and choose how to approach the presented problems. This process enhances their critical thinking skills and creativity, as well as their problem-solving skills. Unlike traditional assessments based on memorization or reciting facts, performance-based assessments focus on the students’ decisions and solutions, and through these tasks students learn to bridge the gap between theory and practice.

Performance-based assessments like CAE’s College and Career Readiness Assessment (CRA+) and Collegiate Learning Assessment (CLA+) provide students with in-depth reports that show them which higher-order skills they are strongest in and which they should continue to develop. This feedback helps students and their teachers plan instruction and supports to deepen their learning and improve their mastery of critical skills.

Explore CAE’s Problem-Solving Assessments

CAE offers performance-based assessments that measure student proficiency in higher-order skills including problem solving, critical thinking, and written communication.

• College and Career Readiness Assessment (CCRA+) for secondary education and
• Collegiate Learning Assessment (CLA+) for higher education.

Our solution also includes instructional materials, practice models, and professional development.

We can help you create a program to build students’ problem-solving skills that includes:

• Measuring students’ problem-solving skills through a performance-based assessment    
• Using the problem-solving assessment data to inform instruction and tailor interventions
• Teaching students problem-solving skills and providing practice opportunities in real-life scenarios
• Supporting educators with quality professional development

Get started with our problem-solving assessment tools to measure and build students’ problem-solving skills today! These skills will be invaluable to students now and in the future.

Ready to Get Started?

Learn more about cae’s suite of products and let’s get started measuring and teaching students important higher-order skills like problem solving..

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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-Based Learning (PBL)

What is Problem-Based Learning (PBL)? PBL is a student-centered approach to learning that involves groups of students working to solve a real-world problem, quite different from the direct teaching method of a teacher presenting facts and concepts about a specific subject to a classroom of students. Through PBL, students not only strengthen their teamwork, communication, and research skills, but they also sharpen their critical thinking and problem-solving abilities essential for life-long learning.

See also: Just-in-Time Teaching

In implementing PBL, the teaching role shifts from that of the more traditional model that follows a linear, sequential pattern where the teacher presents relevant material, informs the class what needs to be done, and provides details and information for students to apply their knowledge to a given problem. With PBL, the teacher acts as a facilitator; the learning is student-driven with the aim of solving the given problem (note: the problem is established at the onset of learning opposed to being presented last in the traditional model). Also, the assignments vary in length from relatively short to an entire semester with daily instructional time structured for group work.

By working with PBL, students will:

• Become engaged with open-ended situations that assimilate the world of work
• Participate in groups to pinpoint what is known/ not known and the methods of finding information to help solve the given problem.
• Investigate a problem; through critical thinking and problem solving, brainstorm a list of unique solutions.
• Analyze the situation to see if the real problem is framed or if there are other problems that need to be solved.

How to Begin PBL

• Establish the learning outcomes (i.e., what is it that you want your students to really learn and to be able to do after completing the learning project).
• Find a real-world problem that is relevant to the students; often the problems are ones that students may encounter in their own life or future career.
• Discuss pertinent rules for working in groups to maximize learning success.
• Practice group processes: listening, involving others, assessing their work/peers.
• Explore different roles for students to accomplish the work that needs to be done and/or to see the problem from various perspectives depending on the problem (e.g., for a problem about pollution, different roles may be a mayor, business owner, parent, child, neighboring city government officials, etc.).
• Determine how the project will be evaluated and assessed. Most likely, both self-assessment and peer-assessment will factor into the assignment grade.

Designing Classroom Instruction

See also: Inclusive Teaching Strategies

• Take the curriculum and divide it into various units. Decide on the types of problems that your students will solve. These will be your objectives.
• Determine the specific problems that most likely have several answers; consider student interest.
• Arrange appropriate resources available to students; utilize other teaching personnel to support students where needed (e.g., media specialists to orientate students to electronic references).
• Decide on presentation formats to communicate learning (e.g., individual paper, group PowerPoint, an online blog, etc.) and appropriate grading mechanisms (e.g., rubric).
• Decide how to incorporate group participation (e.g., what percent, possible peer evaluation, etc.).

How to Orchestrate a PBL Activity

• Explain Problem-Based Learning to students: its rationale, daily instruction, class expectations, grading.
• Serve as a model and resource to the PBL process; work in-tandem through the first problem
• Help students secure various resources when needed.
• Supply ample class time for collaborative group work.
• Give feedback to each group after they share via the established format; critique the solution in quality and thoroughness. Reinforce to the students that the prior thinking and reasoning process in addition to the solution are important as well.

Teacher’s Role in PBL

See also: Flipped teaching

As previously mentioned, the teacher determines a problem that is interesting, relevant, and novel for the students. It also must be multi-faceted enough to engage students in doing research and finding several solutions. The problems stem from the unit curriculum and reflect possible use in future work situations.

• Determine a problem aligned with the course and your students. The problem needs to be demanding enough that the students most likely cannot solve it on their own. It also needs to teach them new skills. When sharing the problem with students, state it in a narrative complete with pertinent background information without excessive information. Allow the students to find out more details as they work on the problem.
• Place students in groups, well-mixed in diversity and skill levels, to strengthen the groups. Help students work successfully. One way is to have the students take on various roles in the group process after they self-assess their strengths and weaknesses.
• Support the students with understanding the content on a deeper level and in ways to best orchestrate the various stages of the problem-solving process.

The Role of the Students

See also: ADDIE model

The students work collaboratively on all facets of the problem to determine the best possible solution.

• Analyze the problem and the issues it presents. Break the problem down into various parts. Continue to read, discuss, and think about the problem.
• Construct a list of what is known about the problem. What do your fellow students know about the problem? Do they have any experiences related to the problem? Discuss the contributions expected from the team members. What are their strengths and weaknesses? Follow the rules of brainstorming (i.e., accept all answers without passing judgment) to generate possible solutions for the problem.
• Get agreement from the team members regarding the problem statement.
• Put the problem statement in written form.
• Solicit feedback from the teacher.
• Be open to changing the written statement based on any new learning that is found or feedback provided.
• Generate a list of possible solutions. Include relevant thoughts, ideas, and educated guesses as well as causes and possible ways to solve it. Then rank the solutions and select the solution that your group is most likely to perceive as the best in terms of meeting success.
• Include what needs to be known and done to solve the identified problems.
• Prioritize the various action steps.
• Consider how the steps impact the possible solutions.
• See if the group is in agreement with the timeline; if not, decide how to reach agreement.
• What resources are available to help (e.g., textbooks, primary/secondary sources, Internet).
• Determine research assignments per team members.
• Establish due dates.
• Determine how your group will present the problem solution and also identify the audience. Usually, in PBL, each group presents their solutions via a team presentation either to the class of other students or to those who are related to the problem.
• Both the process and the results of the learning activity need to be covered. Include the following: problem statement, questions, data gathered, data analysis, reasons for the solution(s) and/or any recommendations reflective of the data analysis.
• A well-stated problem and conclusion.
• The process undertaken by the group in solving the problem, the various options discussed, and the resources used.
• Your solution’s supporting documents, guests, interviews and their purpose to be convincing to your audience.
• In addition, be prepared for any audience comments and questions. Determine who will respond and if your team doesn’t know the answer, admit this and be open to looking into the question at a later date.
• Reflective thinking and transfer of knowledge are important components of PBL. This helps the students be more cognizant of their own learning and teaches them how to ask appropriate questions to address problems that need to be solved. It is important to look at both the individual student and the group effort/delivery throughout the entire process. From here, you can better determine what was learned and how to improve. The students should be asked how they can apply what was learned to a different situation, to their own lives, and to other course projects.

See also: Kirkpatrick Model: Four Levels of Learning Evaluation

I am a professor of Educational Technology. I have worked at several elite universities. I hold a PhD degree from the University of Illinois and a master's degree from Purdue University.

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• Published: 11 January 2023

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

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

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

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

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Introduction.

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

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

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

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

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

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

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

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

Data sources and search strategies

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

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

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

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

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

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

Eligibility criteria

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

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

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

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

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

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

Data coding design

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

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

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

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

Procedure for extracting and coding data

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

Publication bias test

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

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

Heterogeneity test

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

The analysis of the overall effect size

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

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

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

The analysis of moderator effect size

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Suggestions for critical thinking teaching

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

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

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

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

Implications and limitations

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

Conclusions

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

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

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

Data availability

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

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Acknowledgements

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

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Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

• The problem has important, useful mathematics embedded in it.
• The problem requires high-level thinking and problem solving.
• The problem contributes to the conceptual development of students.
• The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
• The problem can be approached by students in multiple ways using different solution strategies.
• The problem has various solutions or allows different decisions or positions to be taken and defended.
• The problem encourages student engagement and discourse.
• The problem connects to other important mathematical ideas.
• The problem promotes the skillful use of mathematics.
• The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

• It must begin where the students are mathematically.
• The feature of the problem must be the mathematics that students are to learn.
• It must require justifications and explanations for both answers and methods of solving.

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

• Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
• What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
• Can the activity accomplish your learning objective/goals?

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

• Allows students to show what they can do, not what they can’t.
• Provides differentiation to all students.
• Promotes a positive classroom environment.
• Advances a growth mindset in students
• Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

• YouCubed – under grades choose Low Floor High Ceiling
• NRICH Creating a Low Threshold High Ceiling Classroom
• Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

• Dan Meyer’s Three-Act Math Tasks
• Graham Fletcher3-Act Tasks ]
• Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

• The teacher presents a problem for students to solve mentally.
• Provide adequate “ wait time .”
• The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
• For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
• Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

• Inside Mathematics Number Talks
• Number Talks Build Numerical Reasoning

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

• “Everyone else understands and I don’t. I can’t do this!”
• Students may just give up and surrender the mathematics to their classmates.
• Students may shut down.

Instead, you and your students could say the following:

• “I think I can do this.”
• “I have an idea I want to try.”
• “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

• Provide your students a bridge between the concrete and abstract
• Serve as models that support students’ thinking
• Provide another representation
• Support student engagement
• Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Problem-Solving Method of Teaching: All You Need to Know

Ever wondered about the problem-solving method of teaching? We’ve got you covered, from its core principles to practical tips, benefits, and real-world examples.

The problem-solving method of teaching is a student-centered approach to learning that focuses on developing students’ problem-solving skills. In this method, students are presented with real-world problems to solve, and they are encouraged to use their own knowledge and skills to come up with solutions. The teacher acts as a facilitator, providing guidance and support as needed, but ultimately the students are responsible for finding their own solutions.

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5 Most Important Benefits of Problem-Solving Method of Teaching

The new way of teaching primarily helps students develop critical thinking skills and real-world application abilities. It also promotes independence and self-confidence in problem-solving.

The problem-solving method of teaching has a number of benefits. It helps students to:

1. Enhances critical thinking: By presenting students with real-world problems to solve, the problem-solving method of teaching forces them to think critically about the situation and to come up with their own solutions. This process helps students to develop their critical thinking skills, which are essential for success in school and in life.

2. Fosters creativity: The problem-solving method of teaching encourages students to be creative in their approach to solving problems. There is often no one right answer to a problem, so students are free to come up with their own unique solutions. This process helps students to develop their creativity, which is an important skill in all areas of life.

3. Encourages real-world application: The problem-solving method of teaching helps students learn how to apply their knowledge to real-world situations. By solving real-world problems, students are able to see how their knowledge is relevant to their lives and to the world around them. This helps students to become more motivated and engaged learners.

4. Builds student confidence: When students are able to successfully solve problems, they gain confidence in their abilities. This confidence is essential for success in all areas of life, both academic and personal.

5. Promotes collaborative learning: The problem-solving method of teaching often involves students working together to solve problems. This collaborative learning process helps students to develop their teamwork skills and to learn from each other.

Know 6 Steps in the Problem-Solving Method of Teaching

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The problem-solving method of teaching typically involves the following steps:

• Identifying the problem. The first step is to identify the problem that students will be working on. This can be done by presenting students with a real-world problem, or by asking them to come up with their own problems.
• Understanding the problem. Once students have identified the problem, they need to understand it fully. This may involve breaking the problem down into smaller parts or gathering more information about the problem.
• Generating solutions. Once students understand the problem, they need to generate possible solutions. This can be done by brainstorming, or by using problem-solving techniques such as root cause analysis or the decision matrix.
• Evaluating solutions. Students need to evaluate the pros and cons of each solution before choosing one to implement.
• Implementing the solution. Once students have chosen a solution, they need to implement it. This may involve taking action or developing a plan.
• Evaluating the results. Once students have implemented the solution, they need to evaluate the results to see if it was successful. If the solution is not successful, students may need to go back to step 3 and generate new solutions.

Find Out Examples of the Problem-Solving Method of Teaching

Here are a few examples of how the problem-solving method of teaching can be used in different subjects:

• Math: Students could be presented with a real-world problem such as budgeting for a family or designing a new product. Students would then need to use their math skills to solve the problem.
• Science: Students could be presented with a science experiment, or asked to research a scientific topic and come up with a solution to a problem. Students would then need to use their science knowledge and skills to solve the problem.
• Social studies: Students could be presented with a historical event or current social issue, and asked to come up with a solution. Students would then need to use their social studies knowledge and skills to solve the problem.

5 How Tos For Using The Problem-Solving Method Of Teaching

Here are a few tips for using the problem-solving method of teaching effectively:

• Choose problems that are relevant to students’ lives and interests.
• Make sure that the problems are challenging but achievable.
• Provide students with the resources they need to solve the problems, such as books, websites, or experts.
• Encourage students to work collaboratively and to share their ideas.
• Be patient and supportive. Problem-solving can be a challenging process, but it is also a rewarding one.

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How to Choose: Let’s Draw a Comparison

The following table compares the different problem-solving methods:

Which Method is the Most Suitable?

The most suitable method of teaching will depend on a number of factors, such as the subject matter, the student’s age and ability level, and the teacher’s own preferences. However, the problem-solving method of teaching is a valuable approach that can be used in any subject area and with students of all ages.

Here are some additional tips for using the problem-solving method of teaching effectively:

• Differentiate instruction. Not all students learn at the same pace or in the same way. Teachers can differentiate instruction to meet the needs of all learners by providing different levels of support and scaffolding.
• Use formative assessment. Formative assessment can be used to monitor students’ progress and to identify areas where they need additional support. Teachers can then use this information to provide students with targeted instruction.
• Create a positive learning environment. Students need to feel safe and supported in order to learn effectively. Teachers can create a positive learning environment by providing students with opportunities for collaboration, celebrating their successes, and creating a classroom culture where mistakes are seen as learning opportunities.

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Some Unique Examples to Refer to Before We Conclude

Here are a few unique examples of how the problem-solving method of teaching can be used in different subjects:

• English: Students could be presented with a challenging text, such as a poem or a short story, and asked to analyze the text and come up with their own interpretation.
• Art: Students could be asked to design a new product or to create a piece of art that addresses a social issue.
• Music: Students could be asked to write a song about a current event or to create a new piece of music that reflects their cultural heritage.

The problem-solving method of teaching is a powerful tool that can be used to help students develop the skills they need to succeed in school and in life. By creating a learning environment where students are encouraged to think critically and solve problems, teachers can help students to become lifelong learners.

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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

Problem solving in mathematics education: tracing its foundations and current research-practice trends

• Original Paper
• Open access
• Published: 30 April 2024

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• Manuel Santos-Trigo   ORCID: orcid.org/0000-0002-7144-2098 1  

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In tracing recent research trends and directions in mathematical problem-solving, it is argued that advances in mathematics practices occur and take place around two intertwined activities, mathematics problem formulation and ways to approach and solve those problems. In this context, a problematizing principle emerges as central activity to organize mathematics curriculum proposals and ways to structure problem-solving learning environments. Subjects’ use of concrete, abstract, symbolic, or digital tools not only influences the ways to pose and pursue mathematical problems; but also shapes the type of representation, exploration, and reasoning they engage to work and solve problems. Problem-solving foundations that privilege learners’ development of habits of mathematical practices that involve an inquiry method to formulate conjectures, to look for different ways to represent and approach problems, and to support and communicate results shed light on directions of current research trends and the relevance of rethinking curriculum proposals and extending problem-solving environments in terms of teachers/students’ consistent use of digital tools and online developments.

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1 Introduction and rationale

Mathematical problem solving has been a prominent theme and research area in the mathematics education agenda during the last four decades. Problem-solving perspectives have influenced and shaped mathematics curriculum proposals and ways to support learning environments worldwide (Törner et al., 2007 ; Toh et al., 2023 ). Various disciplinary communities have identified and contributed to connect problem-solving approaches with the students’ learning, construction, and application of mathematical knowledge. The mathematics community recognizes that the formulation and resolution of problems are central activities in the development of the discipline (Halmos, 1980 , Polya, 1945 ). Indeed, the identification and presentation of lists of unsolved mathematical problems have been a tradition that has inspired the mathematics community to approach mathematical problems and to generate mathematical knowledge (Hilbert, 1902 ; Devlin, 2002 ). Thus, mathematical problems, results, and solution attempts provide information regarding what areas and contents were studied at different times during the development of the discipline (Santos-Trigo, 2020a , b ). Cai et al. ( 2023 ) stated that “ …[E]ngaging learners in the activity of problem posing reflects a potentially strong link to the discipline of mathematics” (p. 5). Thurston ( 1994 ) recognized that understanding and applying a mathematical concept implies analysing, coordinating, and integrating diverse meanings (geometric, visual, intuitive, and formal definition) associated with such concept and ways to carry out corresponding procedures and operations in problematic situations.

The centrality of problem-solving in mathematicians’ own work and in their teaching, is incontrovertible. Problem-solving is also a central topic for mathematics educators, who have developed conceptual frameworks to formulate general ideas about problem-solving (as opposed to the specific ideas needed for solving specific problems) (Fried, 2014 ; p.17).

That is, the mathematics education community is interested in analysing and documenting the students’ cognitive and social behaviours to understand and develop mathematical knowledge and problem-solving competencies. “…the idea of understanding how mathematicians treat and solve problems, and then implementing this understanding in instruction design, was pivotal in mathematics education research and practice” (Koichu, 2014 ). In addition, other disciplines such as psychology, cognitive science or artificial intelligence have provided tools and methods to delve into learners’ ways to understand mathematical concepts and to work on problem situations. Thus, members of various communities have often worked in collaboration to identify and relate relevant aspects of mathematical practices with the design and implementation of learning scenarios that foster and enhance students’ mathematical thinking and the development of problem-solving competencies.

2 Methods and procedures

Research focus, themes, and inquiry methods in the mathematical problem-solving agenda have varied and been influenced and shaped by theoretical and methodological developments of mathematics education as a discipline (English & Kirshner, 2016 ; Liljedahl & Cai, 2021 ). Further, research designs and methods used in cognitive, social, and computational fields have influenced the ways in which mathematical problem-solving research are framed. An overarching question to capture shifts and foundations in problem-solving developments was: How has mathematical problem-solving research agenda varied and evolved in terms of ways to frame, pose, and pursue research questions? In addressing this question, it was important to identify and contrast the structure and organization around some published problem-solving reviews (Lester, 1994 ; Törner et al., 2007 ; Rott et al., 2021 ; Liljedahl & Cai, 2021 ; Toh et al., 2023 ) to shed light on a possible route to connect seminal developments in the field with current research trends and perspectives in mathematical problem-solving developments. The goal was to identify common problem-solving principles that have provided a rational and foundations to support recent problem-solving approaches for learners to construct mathematical knowledge and to develop problem-solving competencies. The criteria to select the set of published peer-reviewed studies, to consider in this review, involved choosing articles published in indexed journals (ZDM-Mathematics Education, Educational Studies in Mathematics, Mathematical Thinking and Learning, Journal of Mathematical Behavior, and Journal for Research in Mathematics Education); contributions that appear in International Handbooks in Mathematics Education; and chapters published in recent mathematical problem-solving books. The initial search included 205 publications whose number was reduced to 55, all published in English, based on reviewing their abstracts and conclusions. Around 100 of the initial selection appeared in the references of an ongoing weekly mathematical problem-solving doctoral seminar that has been implemented during the last six years in our department. In addition, some well-known authors in the field were asked to identify their most representative publications to include in the review list. Here, some suggestions were received, but at the end the list of contributions, that appears in the references section, was chosen based on my vision and experience in the field. The goal was to identify main issues or dimensions to frame and analyse recent research trends and perspectives in mathematical problem-solving developments. Thus, seminal reviews in the field (Schoenfeld, 1992 ; Lester, 1994 ; Törner et al., 2007 ) provided directions on ways to structure and select the questions used to analyse the selected contributions. Table  1 shows chosen issues that resemble features of an adjusted framework that Lester ( 1994 ) proposed to organize, summarize, and analyse problem-solving developments in terms of research emphasis (themes and research questions), methodologies (research designs and methods), and achieved results that the problem-solving community addressed during the 1970–1994 period. Furthermore, relevant shifts in the mathematical problem-solving agenda could be identified and explained in terms of what the global mathematics education and other disciplines pursue at different periods.

It is important to mention that the content and structure of this paper involve a narrative synthesis of selected articles that includes contributions related to mathematical problem-solving foundations and those that address recent developments published in the last 9 years that involve the use of digital technologies. Table  1 shows themes, issues, and overarching questions that were used to delve into problem-solving developments.

To contextualize the current state of art in the field, it is important to revisit problem-solving principles and tenets that provide foundations and a rationale to centre and support the design and implementation of learning environments around problem-solving activities (Santos-Trigo, 2020a , b ). The identification of mathematical problem-solving foundations also implies acknowledging what terms, concepts, and language or discourse that the problem-solving community has used to refer to and frame problem-solving approaches. For example, routine and nonroutine tasks, heuristic and metacognitive strategies, students’ beliefs, mathematical thinking and practices, resources, orientations, etc. are common terms used to explain, foster, and characterize students’ problem-solving behaviours and performances. Recently, the consistent use of digital technologies in educational tasks has extended the problem-solving language to include terms such as subjects’ tool appropriation, dynamic models, dragging or moving orderly objects, tracing loci, visual or empirical solution, ChatGPT prompts, etc.

3 On mathematical problem-solving foundations and the problematizing principle

There might be different ways to interpret and implement a problem-solving approach for students to understand concepts and to solve problems (Törner, Schoenfeld, & Reiss, 2007 ; Toh et al., 2023 ); nevertheless, there are common principles or tenets that distinguish and support a problem-solving teaching/learning environment. A salient feature in any problem-solving approach to learn mathematics is a conceptualization of the discipline that privileges and enhance the students’ development of mathematical practices or reasoning habits of mathematical thinking (Cuoco, et, al., 1996 ; Dick & Hollebrands, 2011 ; Schoenfeld, 2022 ). In this context, students need to conceptualize and think of their own learning as a set of dilemmas that are represented, explored, and solved in terms of mathematical resources and strategies (Santos-Trigo, 2023 ; Hiebert et al., 1996 ).

Furthermore, students’ problem-solving experiences and behaviours reflect and become a way of thinking that is consistent with mathematics practices and is manifested in terms of the activities they engage throughout all problem-solving phases. Thus, they privilege the development of mathematics habits such as to always look for different ways to model and explore mathematical problems, to formulate conjectures, and to search for arguments to support them, share problem solutions, defend their ideas, and to develop a proper language to communicate results. In terms of connecting ways of developing mathematical knowledge and the design of learning environments to develop mathematical thinking and problem-solving competencies, Polya ( 1945 ) identifies an inquiry approach for students to understand, make sense, and apply mathematical concepts. He illustrated the importance for students to pose and pursue different questions around four intertwined problem-solving phases: Understanding and making sense of the problem statement (what is the problem about? What data are provided? What is asked to find? etc.), the design of a solution plan (how the problem can be approached? ), the implementation of such plan (how the plan can be achieved? ), and the looking-back phase that involves reviewing the solution process (data used, checking the involved operations, consistency of units, and partial and global solution), generalizing the solution methods and posing new problems. Indeed, the looking-back phase involves the formulation of new or related problems (Toh et al., 2023 ). “For Pólya, mathematics was about inquiry; it was about sense making; it was about understanding how and why mathematical ideas fit together the ways they do” (cited in Schoenfeld, 2020 , p. 1167).

Likewise, the Nobel laureate I. I. Rabi mentioned that, when he came home from school, “while other mothers asked their kids ‘ Did you learn anything today ?’ [my mother] would say, ‘ Izzy, did you ask a good question today ?’” (Berger, 2014 , p.67).

Thus, the problematizing principle is key for students to engage in mathematical problem-solving activities, and it gets activated by an inquiry or inquisitive method that is expressed in terms of questions that students pose and pursue to delve into concepts meaning, representations, explorations, operations, and to work on mathematical tasks (Santos-Trigo, 2020a , b ).

4 The importance of mathematical tasks and the role of tools in problem-solving perspectives

In a problem-solving approach, learners develop a way of thinking to work on different types of tasks that involve a variety of context and aims (Cai & Hwang, 2023 ). A task might require students to formulate a problem from given information, to estimate how much water a family spend in one year, to prove a geometry theorem, to model genetic sequences or to understand the interplay between climate and geography. In this process, students identify mathematical resources, concepts, and strategies to model and explore partial and global solutions, and ways to extend solution methods and results. Furthermore, mathematical tasks or problems are essential for students to engage in mathematical practice and to develop problem-solving competencies. Task statements should be situated in different contexts including realistic, authentic, or mathematical domains, and prompts or questions to solve or respond or even provide information or data for students to formulate and solve their own problems (problem posing). Current events or problematic situations such as climate change, immigration, or pandemics not only are part of individuals concerns; but also, a challenge for teachers and students to model and analyze those complex problems through mathematics and others disciplines knowledge (English, 2023 ). Santos-Trigo ( 2019 ) proposed a framework to transform exercises or routine textbook problems into a series of nonroutine tasks in which students have an opportunity to dynamically model, explore, and extend, the initial problem. Here, the use of technology becomes important to explore the behavior of some elements within the model to find objects’ mathematical relationships. That is, students work on tasks in such a way that even routine problems become a starting point for them to engage in mathematical reflection to extend the initial nature of the task (Santos-Trigo & Reyes-Martínez, 2019 ). Recently, the emergence of tools such as the ChatGPT has confirmed the importance for learners to problematize situations, including complex problems, in terms of providing prompts or inputs that the tool processes and answers. Here, students analyze the tool’ responses and assess its pertinence to work and solve the task. Indeed, a way to use ChatGPT involves that students understand or make sense of the problem statement and pose questions (inputs or prompts) to ask the tool for concept information or ways to approach or solve the task. Then, students analyze the relevance, viability, and consistency of the tool’s answer and introduce new inputs to continue with the solution process or to look for another way to approach the task. Based on the ChatGPT output or task solution, students could always ask whether the tool can provide other ways to solve the task.

5 Main problem-solving research themes and results

In this section the focus will be on identifying certain problem-solving developments that have permeated recent directions of the field. One relates to the importance of extending research designs to analyse and characterize learners’ problem-solving process to work on different types of tasks. Another development involves ways in which theoretical advances in mathematics education have shaped the mathematical problem-solving research agenda and the extent to which regional or national educational systems or traditions influence the developments of conceptual frameworks in the field and ways to implement problem-solving activities within the corresponding system. Finally, research results in the field have provided directions to design and implement curriculum proposals around the world and these proposals have evolved in terms of both content structure and classroom dynamics including the use of digital technologies. Santos-Trigo ( 2023 ) stated that the teachers and students’ systematic use of digital technologies not only expands their ways of reasoning and solving mathematical problems; but also opens new research areas that aim to analyse the integration of several digital tools in curriculum proposals and learning scenarios. The focus of this review will be on presenting problem-solving directions and results in the last 9 years; however, it became relevant to identify and review what principles and tenets provided bases or foundations to support and define current research trends and directions in the field. That is, accumulated research that has contributed to advance and expand the problem-solving research agenda included shifts in the tools used to delve into learners’ problem approaches, the development of conceptual frameworks to explain and characterize students’ mathematical thinking, the tools used to work on mathematical tasks (from paper and pencil, ruler and compass or semiotic tools to digital apps), and in the design of curriculum proposals and the implementation of problem-solving learning scenarios.

5.1 Relevant shifts in problem-solving developments and results

Questions used to analyse important developments in the field include: What research designs and tools are used to foster and analyse learners’ problem-solving performances? How have conceptual frameworks evolved to pose and frame research questions in the field? How have accumulated research results in the field been used to support curriculum proposals and their implementation?

5.1.1 Methodological and research paradigms

Research designs in problem-solving studies have gradually moved from quantitative or statistical paradigms to qualitative perspectives that involve data collection from different sources such as task-based interviews, fieldnotes from observations, students’ written reports, etc. to analyse students’ problem-solving approaches and performances. Trustworthiness of results included triangulating and interpreting data sources from students’ videotapes transcriptions, outside observer notes, class observations, etc. (Stake, 2000 ). Hence, the work of Krutestkii ( 1976 ) was seminal in providing tools to delve into the students’ thinking while solving mathematical tasks. His research program aimed to study the nature and structure of children’ mathematical abilities. His methodological approach involved the use of student’s task-based interviews, teachers, and mathematicians’ questionaries to explore the nature of mathematical abilities, the analysis of eminent mathematicians and physicists regarding their nature and emergence of their talents and case studies of gifted children in mathematics. A major contribution of his research was the variety of mathematical tasks used to explore and analyse the mathematical abilities of school children. Recently, the mathematical problem-posing agenda has been revisited to advance conceptual frameworks to enhance the students’ formulation of problems to learn concepts and to develop problem-solving competencies (Cai et al., 2023 ). In general, the initial qualitative research tendency privileged case studies where individual students were asked to work on mathematical tasks to document their problem-solving performances. Later, research designs include the students’ participation in small groups and the analysis of students’ collaboration with the entire group (Brady et al., 2023 ). Bricolage frameworks that share tenets and information from different fields have become a powerful tool for researchers to understand complex people’ problem-solving proficiency (Lester, 2005 ; English, 2023 ).

5.1.2 Theoretical developments in mathematics education

In mathematics education, the constructivism perspective became relevant to orient and support research programs. Specifically, the recognition that students construct mathematical concepts and ideas through active participation as a part of a learning community that fosters and values what they bring into the classroom (eliciting students’ understanding) and sharing and discussing with peers their ways to work on mathematical activities. Further, it was recognized that students’ learning of mathematics takes place within a sociocultural environment (situated learning) that promotes the students’ interaction in small groups, pairs, and whole group discussions. Thus, problem-solving environments transited from teachers being a main figure to organize learning activities and to model problem-solving behaviours to being centred on students’ active participation to work on a variety of mathematical tasks as a part of a learning community (Lester & Cai, 2016 ). English ( 2023 ) proposed A STEM-based problem-solving framework that addresses the importance of a multidisciplinary approach and experiences to work on complex problems. Here, students develop a system of inquiry that integrates critical thinking, mathematical modelling, and a creative and innovative approach to deal with problematic situations situated in contexts beyond school problems. The STEM-based problem-solving framework enhances and favours the students’ development of multidisciplinary thinking to formulate and approach challenging problematic situations. To this end, they need to problematize information to characterize local and global problems and to collaboratively work on feasible approaches and solutions. It integrates 21st century skills that include an inquiry problem-solving approach to develop and exhibit critical thinking, creativity, and innovative solutions.

5.1.3 Countries or regional education traditions and their influence on the problem-solving agenda

The emergence of problem-solving frameworks takes place within an educational and socio-cultural context that provides conditions for their development and dissemination, but also limitations in their applications inside the mathematics education community. Brady et al. ( 2023 ) pointed out that:

…shifts in the theoretical frameworks of mathematics education researchers favored a widening of the view on problem solving from information-processing theories toward sociocultural theories that encouraged a conception of problem-solving as situated cognition unfolding within a community of practice (p. 34).

In addition, regional or national educational systems and research traditions also shape the problem-solving research and practice agenda. For example, in France, problem-solving approaches and research are framed in terms of two relevant theoretical and practical frameworks: Theory of Didactic Situation and the Anthropological Theory of Didactics (Artigue & Houdement, 2007 ). While, in the Netherlands, problem-solving approaches are situated within the theory of Realistic Mathematics that encourages and supports the students’ construction of meaning of concepts and methods in terms of modelling real-life and mathematical situations (Doorman et al., 2007 ). Ding et al. ( 2022 ) stated that the Chinese educational system refers to problem solving as an instructional goal and an approach to learn mathematics. Here, students deal with different types of problem-solving activities that include finding multiple solutions to one problem, one solution to multiple problems, and one problem multiple changes. Thus, ‘teaching with variation’ is emphasized in Chinese instruction in terms of “variations in solutions, presentations, and conditions/conclusions” (p. 482). Cai and Rott ( 2023 ) proposed a general problem-posing process model that distinguishes four problem-posing phases: Orientation (understanding the situation and what is required or is asked to pose); Connection that involves finding out or generating ideas and strategies to pose problems in different ways such as varying the given situation, or posing new problems; Generation refers to making the posed problem visible for others to understand it; and Reflection involves reflecting on her/his own process to pose the problem including ways to improve problem statements. The challenge in this model is to make explicit how the use of digital technologies can contribute to providing conditions for students to engage in all phases around problem- posing process.

5.1.4 Curriculum proposals and problem-solving teaching/learning scenarios

In the USA, the Common Core State Mathematics Standards curriculum proposal (CCSMS) identifies problem solving as a process standard that supports core mathematical practices that involve reasoning and proof, communication, representation, and connections. Thus, making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, constructing viable arguments and critiquing the reasoning of others, modelling with mathematics, etc. are essential activities for students to develop mathematics proficiency and problem-solving approaches (Schoenfeld, 2023 ). In Singapore, the curriculum proposal identifies problem solving as the centre of its curriculum framework that relates its development with the study of concepts, skills, processes, attitudes, and metacognition (Lee et al., 2019 ). Recently, educational systems have begun to reform curriculum proposals to relate what the use of digital technologies demands in terms of selecting and structuring mathematical contents and ways to extend instructional settings (Engelbrecht & Borba, 2023 ). Indeed, Engelbrecht et al. ( 2023 ) identify what they call a classroom in movement or a distributed classroom - that transforms traditional cubic spaces to study the discipline into a movable setting that might combine remote and face-to-face students work.

It is argued that previous results in mathematical problem-solving research not only have contributed to recognize what is relevant and what common tenets distinguish and support problem-solving approaches; but also have provided bases to identify and pursue current problem-solving developments and directions. Hence, the consistent and coordinated use of several digital technologies and online developments (teaching and learning platforms) has opened new routes for learners to represent, explore, and work on mathematical problems; and to engage them in mathematical discussions beyond formal class settings. How does the students’ use of digital technologies expand the ways they reason and solve mathematical problems? What changes in classroom environments and physical settings are needed to recognize and include students’ face-to-face and remote work? (Engelbrecht et al., 2023 ).

In the next sections, the goal is to characterize the extent to which the consistent use of digital technologies and online developments provides affordances to restructure mathematical curriculum proposals and classrooms or learning settings and to enhance and expand students’ mathematical reasoning.

6 Current mathematical problem-solving trends and developments: the use of digital technologies

Although the use of technologies has been a recurrent theme in research studies, curriculum proposals, and teaching practices in mathematics education; during the COVID-pandemic lockdown, all teachers and students relied on digital technologies to work on mathematical tasks. At different phases, they developed and implemented not only novel paths to present, discuss, and approach teaching/learning activities; but also, ways to monitor and assess students’ problem-solving performances. When schools returned to teachers and students’ face-to-face activities, some questions emerged: What adjustments or changes in school practices are needed to consider and integrate those learning experiences that students developed during the social confinement? What digital tools should teachers and students use to work on mathematical tasks? How should teaching/learning practices reconcile students remote and face-to-face work? To address these questions, recent studies that involve ways to integrate technology in educational practices were reviewed, and their main themes and findings are organized and problematized to shed light on what the use of digital technologies contributes to frame and support learning environments.

6.1 The use of technology to reconceptualize students mathematical learning

There are different studies that document the importance and ways in which the students’ use of tools such as CAS or Excel offers an opportunity for them to think of concepts and problems in terms of different representations to transit from intuitive, visual, or graphic to formal or analytical reasoning (Arcavi et al., 2017 ). Others digital technologies, such as a Dynamic Geometry System Footnote 1 DGS, provide affordances for students to dynamically represent and explore mathematical problems. In students’ use of digital technologies, the problematizing principle becomes relevant to transform the tool into an instrument to work on mathematical tasks. Santos-Trigo ( 2019 ) provides examples where students rely on GeoGebra affordances to reconstruct figures that are given in problem statements; to transform routine problem into an investigation task; to model and explore tasks that involve variational reasoning; and to construct dynamic configurations to formulate and support mathematical relations. In this process, students not only exhibit diverse problem-solving strategies; but also, identify and integrate and use different concepts and resources that are studied in algebra, geometry, and calculus. That is, the use of technology provides an opportunity for students to integrate and connect knowledge from diverse areas or domains. For instance, Sinclair and Ferrara ( 2023 ) used the multi-touch application (TouchCounts) for children to work on mathematical challenging tasks.

6.2 The use of digital technologies to design a didactic route

There is indication, that the use of digital technologies offers different paths for students to learn mathematics (Leung & Bolite-Frant, 2015 ; Leung & Baccaglini-Frank, 2017 ). For instance, in the construction of a dynamic model of a problem, they are required to think of concepts and information embedded in the problem in terms of geometric representation or meaning. Thus, focusing on ways for students to represent and explore concepts geometrically could be the departure point to understand concepts and to solve mathematical problems. In addition, students can explore problems’ dynamic models (dragging schemes) in terms of visual, empirical, and graphic representations to initially identify relations that become relevant to approach and solve the problems. Thus, tool affordances become relevant for students to detect patterns, to formulate conjectures and to transit from empirical to formal argumentation to support problem solutions (Pittalis & Drijvers, 2023 ). Engelbrecht and Borba ( 2023 ) recognized that the prominent use of digital technologies in school mathematics has produced pedagogical shifts in teaching and learning practices to “encourage more active students learning, foster greater engagement, and provide more flexible access to learning’ (p. 1). Multiple use technologies such as internet, communication apps (ZOOM, Teams, Google Meet, etc.) become essential tools for teachers and students to present, communicate, and share information or to collaborate with peers. While tools used to represent, explore, and delve into concepts and to work and solve mathematical problems (Dynamic Geometry Systems, Wolframalpha, etc.) expand the students’ ways of reasoning and solving problems. Both types of technologies are not only important for teachers and students to continue working on school tasks beyond formal settings, but they also provide students with an opportunity to consult online resources such as Wikipedia or KhanAcademy to review or extend their concepts understanding, to analyse solved problems, and to contrast their teachers’ explanation of themes or concepts with those provided in learning platforms.

6.3 Students’ access to mathematics learning

Nowadays, cell phones are essential tools for people or students to interact or to approach diverse tasks and an educational challenge is how teachers/students can use them to work on mathematical tasks. During the COVID-19 social confinement, students relied on communication apps not only to interact with their teachers during class lectures; but also, to keep discussing tasks with peers beyond formal class meetings. That is, students realized that with the use of technology they could expand their learning space to include sharing and discussing ideas and problem solutions with peers beyond class sessions, consulting online learning platforms or material to review or extend their concepts understanding, and to watch videos to contrast experts’ concepts explanations and those provided by their teachers. In this perspective, the use of digital technologies increases the students’ access to different resources and the ways to work on mathematical tasks. Thus, available digital developments seem to extend the students collaborative work in addition to class activities. Furthermore, the flipped classroom model seems to offer certain advantages for students to learn the discipline and this model needs to be analysed in terms of what curriculum changes and ways to assess or monitor students learning are needed in its design and implementation (Cevikbas & Kaiser, 2022 ).

6.4 Changes in curriculum and mathematical assessment

It is recognized that the continuous development and availability of digital technologies is not only altering the ways in which individuals interact and face daily activities; but is also transforming educational practices and settings. Likewise, people’s concerns about multiple events or global problems such climate change, immigration, educational access, renewable resources, or racial conflicts or wars are themes that permeate the educational arena. Thus, curriculum reforms should address ways to connect students’ education with the analysis of these complex problems. English ( 2023 ) stated that:

The ill-defined problems of today, coupled with unexpected disruptions across all walks of life, demand advanced problem-solving by all citizens. The need to update outmoded forms of problem solving, which fail to take into account increasing global challenges, has never been greater (p.5).

In this perspective, mathematics curriculum needs to be structured around essential contents and habits of mathematical thinking for students to understand and make sense of real-world events that lead them to formulate, represent, and deal with a variety of problem situations. “Educators now increasingly seek to emphasise the practical applications of mathematics, such as modelling real-life scenarios and understanding statistical data (Engelbrecht & Borba, 2023 , p. 7). For instance, during the pandemic it was important to problematize the available data to follow, analyze and predict its spread behavior and to propose health measures to reduce people contagion. Thus, exponential functions, graphics, and their interpretations, data analysis, etc. were important mathematics content to understand the pandemic phenomena. Drijvers and Sinclair ( 2023 ) recognized that features of computational thinking share common grounds with mathematical thinking in terms of problem-solving activities that privilege model construction, the use of algorithms, abstraction processes and generalization of results. Thus, “a further integration of computational thinking in the mathematics curriculum is desirable”. In terms of ways to assess and monitor students’ learning, the idea is that with the use of a digital tool (digital wall or log), students could organize, structure, register, and monitor their individual and group work and learning experiences. That is, they could periodically report and share what difficulties they face to understand concepts or to work on a task, what questions they posed, what sources consult, etc. The information that appears in the digital wall is shared within the group and the teacher and students can provide feedback or propose new ideas or solutions (Santos-Trigo et al., 2022 ).

6.5 The integration of technologies and the emergence of conceptual frameworks

Institutions worldwide, in general, are integrating the use of different technologies in their educational practices, and they face the challenge to reconcile previous pandemic models and post confinement learning scenarios. “A pedagogical reason for using technology is to empower learners with extended or amplified abilities to acquire knowledge…technology can empower their cognitive abilities to reason in novice ways (Leung, 2011 , p. 327). Drijvers and Sinclair ( 2023 ) proposed a five-dimensional framework to delve into the rationale and purposes for the mathematics education community to integrate the use of digital technologies in mathematical teaching environments and students learning. The five interrelated categories address issues regarding how teachers and students’ use of digital technology contributes to reconceptualize and improve mathematics learning; to understand and explain how students’ mathematics learning develops; to design environments for mathematics learning; to foster and provide equitable access to mathematics learning; and to change mathematics curricula and teaching and assessment practices (Drijvers & Sinclair, 2023 ). Schoenfeld ( 2022 ) stated that “The challenge is to create robust learning environments that support every student in developing not only the knowledge and practices that underlie effective mathematical thinking, but that help them develop the sense of agency to engage in sense making” (p. 764). Højsted et al. ( 2022 ) argue about the importance of adjusting theoretical frameworks to explicitly integrate the use of digital technologies such as DGS and Computer Algebra Systems (CAS) in teaching practices. They referred to the Danish “Competencies and Mathematical Learning framework” (KOM) that gets articulated through tenets associated with the Theory of Instrumental Orchestration (TIO) and the notion of Justification Mediation (JM). In general terms, the idea is that learners get explicitly involved in a tool’ appropriation process that transforms the artifact into an instrument to understand concepts and to solve mathematical problems. That is, learners’ tool appropriation involves the development of cognitive schemata to rely on technology affordances to work on mathematical tasks. Koichu et al. ( 2022 ) pointed out that the incorporation of problem-solving approaches in instruction should be seen as a specific case of implementing innovation. To this end, they proposed a framework of problem-solving implementation chain that involves “a sequence of actions and interactions beginning with the development of a PS resource by researchers, which teachers then engage with in professional development (PD), and finally, teachers and students make use of in classrooms” (p. 4). In this case, problem-solving resources include the design of problematic situations (tasks) to engage students in mathematical discussions to make sense of problem statements or to ask them to pose a task.

7 Reflections and concluding remarks

Throughout different periods, the research and practice mathematical problem-solving agenda has contributed significantly to understand not only essentials in mathematical practices; but also, the development of conceptual frameworks to explain and document subjects’ cognitive, social, and affective behaviours to understand mathematical concepts and to develop problem-solving competencies. Leikin and Guberman ( 2023 ) pointed out that “…problem-solving is an effective didactical tool that allows pupils to mobilize their existing knowledge, construct new mathematical connections between known concepts and properties, and construct new knowledge in the process of overcoming challenges embedded in the problems” (p. 325). The study of people cognitive functioning to develop multidisciplinary knowledge and to solve problems involves documenting ways in which individuals make decisions regarding ways to organize their subject or disciplinary learning (how to interact with teachers or experts and peers; what material to consult, what tools to use, how to monitor their own learning, etc.) and to engage in disciplinary practices to achieve their learning goals. Both strategic and tactic decisions shape teachers and students’ ways to work on mathematical tasks. Kahneman ( 2011 ) shed light on how human beings make decisions to deal with questions and problematic situations. He argues that individuals rely on two systems to make decisions and engage in thinking processes; system one (fast thinking) that involves automatic, emotional, instinctive reasoning and system two (slow thinking) that includes logical, deliberative, effortful, or conscious reasoning. In educational tasks, the idea is that teachers and students develop experiences based on the construction and activation of system two. Thus, how teachers/students decide what tools or digital developments to use to work on mathematical problems becomes a relevant issue to address in the mathematics education agenda. Recent and consistent developments and the availability of digital technologies open novel paths for teachers and students to represent, explore, and approach mathematical tasks and, provide different tools to extend students and teachers’ mathematical discussions beyond classroom settings. In this perspective, it becomes important to discuss what changes the systematic use of digital technologies bring to the mathematics contents and to the ways to frame mathematical instruction. For example, the use of a Dynamic Geometry System to model and explore calculus, geometry or algebra classic problems dynamically not only offer students an opportunity to connect foundational concepts such as rate of change or the perpendicular bisector concept to geometrically study variational phenomena or conic sections; but also, to engage them in problem-posing activities (Santos-Trigo et al., 2021 ). Thus, teachers need to experience themselves different ways to use digital technologies to work on mathematical tasks and to identify instructional paths for students to internalize the use of digital apps as an instrument to understand concepts and to pose and formulate mathematical problems. Specifically, curriculum proposal should be structured around the development of foundational concepts and problem-solving strategies to formulate and pursue complex problems such as those involving climate changes, wealth distribution, immigration, pollution, mobility, connectivity, etc. To formulate and approach these problems, students need to develop a multidisciplinary thinking and rely on different tools to represent, explore, and share and continuously report partial solutions. To this end, they are encouraged to work with peers and groups as a part of learning community that fosters and values collective problem solutions. Finding multiple paths to solve problems becomes important for students to develop creative and innovative problem solutions (Leikin & Guberman, 2023 ). In this perspective, learning environments should provide conditions for students to transform digital applications in problem-solving tools to work on problematic situations. Online students’ assignments become an important component to structure and organize students and teachers’ face-to-face interactions. Likewise, the use of technology can also provide a tool for students to register and monitor their work and learning experiences. A digital wall or a problem-solving digital notebook (Santos-Trigo et al., 2022 ) could be introduced for students to register and monitor their learning experiences. Here, Students are asked to record on a weekly basis their work, questions, comments, and ideas that include: Questions they pose to understand concepts and problem statements; online resources and platforms they consult to contextualize problems and review and extend their understanding of involved concepts; concepts and strategies used to solve problems through different approaches; the Identification of other problems that can be solved with the methods that were used to solve the problem; digital technologies and online resources used to work on and solve the problem; dynamic models used to solve the problem and strategies used to identify and explore mathematical relations (dragging objects, measuring object attributes, tracing loci, using sliders, etc.; the formulation of new related problems including possible extensions for the initial problem; discussion of solutions of some new problems; and short recorded video presentation of their work and problem solutions. That is, the digital wall becomes an space for learners to share their work and to contrast and reflect on their peers work including extending their problem-solving approaches based on their teachers feedback and peers’ ideas or solutions.

The term Dynamic Geometry System is used, instead of Dynamic Geometry Environment or Dynamic Geometry Software, to emphasize that the app or tool interface encompasses a system of affordances that combines the construction of dynamic models, the use of Computer Algebra Systems and the use spreadsheet programs.

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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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Top 10 Challenges to Teaching Math and Science Using Real Problems

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Nine in ten educators believe that using a problem-solving approach to teaching math and science can be motivating for students, according to an EdWeek Research Center survey.

But that doesn’t mean it’s easy.

Teachers perceive lack of time as a big hurdle. In fact, a third of educators—35 percent—worry that teaching math or science through real-world problems—rather than focusing on procedures—eats up too many precious instructional minutes.

Other challenges: About another third of educators said they weren’t given sufficient professional development in how to teach using a real-world problem-solving approach. Nearly a third say reading and writing take priority over STEM, leaving little bandwidth for this kind of instruction. About a quarter say that it’s tough to find instructional materials that embrace a problem-solving perspective.

Nearly one in five cited teachers’ lack of confidence in their own problem solving, the belief that this approach isn’t compatible with standardized tests, low parent support, and the belief that student behavior is so poor that this approach would not be feasible.

The nationally representative survey included 1,183 district leaders, school leaders, and teachers, and was conducted from March 27 to April 14. (Note: The chart below lists 11 challenges because the last two on the list—dealing with teacher preparation and student behavior—received the exact percentage of responses.)

Trying to incorporate a problem-solving approach to tackling math can require rethinking long-held beliefs about how students learn, said Elham Kazemi, a professor in the teacher education program at the University of Washington.

Most teachers were taught math using a procedural perspective when they were in school. While Kazemi believes that approach has merit, she advocates for exposing students to both types of instruction.

Many educators have “grown up around a particular model of thinking of teaching and learning as the teacher in the front of the room, imparting knowledge, showing kids how to do things,” Kazemi said.

To be sure, some teachers have figured out how to incorporate some real-world problem solving alongside more traditional methods. But it can be tough for their colleagues to learn from them because “teachers don’t have a lot of time to collaborate with one another and see each other teach,” Kazemi said.

What’s more, there are limited instructional materials emphasizing problem solving, Kazemi said.

Though that’s changing, many of the resources available have “reinforced the idea that the teacher demonstrates solutions for kids,” Kazemi said.

Molly Daley, a regional math coordinator for Education Service District 112, which serves about 30 districts near Vancouver, Wash., has heard teachers raise concerns that teaching math from a problem-solving perspective takes too long—particularly given the pressure to get through all the material students will need to perform well on state tests.

Daley believes, however, that being taught to think about math in a deeper way will help students tackle math questions on state assessments that may look different from what they’ve seen before.

“It’s myth that it’s possible to cover everything that will be on the test,” as it will appear, she said. “There’s actually no way to make sure that kids have seen every single possible thing the way it will show up. That’s kind of a losing proposition.”

But rushing through the material in a purely procedural way may actually be counterproductive, she said.

Teachers don’t want kids to “sit down at the test and say, ‘I haven’t seen this and therefore I can’t do it,’” Daley said. “I think a lot of times teachers can unintentionally foster that because they’re so urgently trying to cover everything. That’s where the kind of mindless [teaching] approaches come in.”

Teachers may think to themselves: “’OK, I’m gonna make this as simple as possible, make sure everyone knows how to follow the steps and then when they see it, they can follow it,” Daley said.

But that strategy might “take away their students’ confidence that they can figure out what to do when they don’t know what to do, which is really what you want them to be thinking when they go to approach a test,” Daley said.

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5 Advantages and Disadvantages of Problem-Based Learning [+ Activity Design Steps]

Written by Marcus Guido

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Advantages of Problem-Based Learning

Disadvantages of problem-based learning, steps to designing problem-based learning activities.

Used since the 1960s, many teachers express concerns about the effectiveness of problem-based learning (PBL) in certain classroom settings.

Whether you introduce the student-centred pedagogy as a one-time activity or mainstay exercise, grouping students together to solve open-ended problems can present pros and cons.

Below are five advantages and disadvantages of problem-based learning to help you determine if it can work in your classroom.

If you decide to introduce an activity, there are also design creation steps and a downloadable guide to keep at your desk for easy reference.

1. Development of Long-Term Knowledge Retention

Students who participate in problem-based learning activities can improve their abilities to retain and recall information, according to a literature review of studies about the pedagogy .

The literature review states “elaboration of knowledge at the time of learning” -- by sharing facts and ideas through discussion and answering questions -- “enhances subsequent retrieval.” This form of elaborating reinforces understanding of subject matter , making it easier to remember.

Small-group discussion can be especially beneficial -- ideally, each student will get chances to participate.

But regardless of group size, problem-based learning promotes long-term knowledge retention by encouraging students to discuss -- and answer questions about -- new concepts as they’re learning them.

2. Use of Diverse Instruction Types

You can use problem-based learning activities to the meet the diverse learning needs and styles of your students, effectively engaging a diverse classroom in the process. In general, grouping students together for problem-based learning will allow them to:

• Address real-life issues that require real-life solutions, appealing to students who struggle to grasp abstract concepts
• Participate in small-group and large-group learning, helping students who don’t excel during solo work grasp new material
• Talk about their ideas and challenge each other in a constructive manner, giving participatory learners an avenue to excel
• Tackle a problem using a range of content you provide -- such as videos, audio recordings, news articles and other applicable material -- allowing the lesson to appeal to distinct learning styles

Since running a problem-based learning scenario will give you a way to use these differentiated instruction approaches , it can be especially worthwhile if your students don’t have similar learning preferences.

3. Continuous Engagement

Providing a problem-based learning challenge can engage students by acting as a break from normal lessons and common exercises.

It’s not hard to see the potential for engagement, as kids collaborate to solve real-world problems that directly affect or heavily interest them.

Although conducted with post-secondary students, a study published by the Association for the Study of Medical Education reported increased student attendance to -- and better attitudes towards -- courses that feature problem-based learning.

These activities may lose some inherent engagement if you repeat them too often, but can certainly inject excitement into class.

4. Development of Transferable Skills

Problem-based learning can help students develop skills they can transfer to real-world scenarios, according to a 2015 book that outlines theories and characteristics of the pedagogy .

The tangible contexts and consequences presented in a problem-based learning activity “allow learning to become more profound and durable.” As you present lessons through these real-life scenarios, students should be able to apply learnings if they eventually face similar issues.

For example, if they work together to address a dispute within the school, they may develop lifelong skills related to negotiation and communicating their thoughts with others.

As long as the problem’s context applies to out-of-class scenarios, students should be able to build skills they can use again.

5. Improvement of Teamwork and Interpersonal Skills

Successful completion of a problem-based learning challenge hinges on interaction and communication, meaning students should also build transferable skills based on teamwork and collaboration . Instead of memorizing facts, they get chances to present their ideas to a group, defending and revising them when needed.

What’s more, this should help them understand a group dynamic. Depending on a given student, this can involve developing listening skills and a sense of responsibility when completing one’s tasks. Such skills and knowledge should serve your students well when they enter higher education levels and, eventually, the working world.

1. Potentially Poorer Performance on Tests

Devoting too much time to problem-based learning can cause issues when students take standardized tests, as they may not have the breadth of knowledge needed to achieve high scores. Whereas problem-based learners develop skills related to collaboration and justifying their reasoning, many tests reward fact-based learning with multiple choice and short answer questions. Despite offering many advantages, you could spot this problem develop if you run problem-based learning activities too regularly.

2. Student Unpreparedness

Problem-based learning exercises can engage many of your kids, but others may feel disengaged as a result of not being ready to handle this type of exercise for a number of reasons. On a class-by-class and activity-by-activity basis, participation may be hindered due to:

• Immaturity  -- Some students may not display enough maturity to effectively work in a group, not fulfilling expectations and distracting other students.
• Unfamiliarity  -- Some kids may struggle to grasp the concept of an open problem, since they can’t rely on you for answers.
• Lack of Prerequisite Knowledge  -- Although the activity should address a relevant and tangible problem, students may require new or abstract information to create an effective solution.

You can partially mitigate these issues by actively monitoring the classroom and distributing helpful resources, such as guiding questions and articles to read. This should keep students focused and help them overcome knowledge gaps. But if you foresee facing these challenges too frequently, you may decide to avoid or seldom introduce problem-based learning exercises.

3. Teacher Unpreparedness

If supervising a problem-based learning activity is a new experience, you may have to prepare to adjust some teaching habits . For example, overtly correcting students who make flawed assumptions or statements can prevent them from thinking through difficult concepts and questions. Similarly, you shouldn’t teach to promote the fast recall of facts. Instead, you should concentrate on:

• Giving hints to help fix improper reasoning
• Questioning student logic and ideas in a constructive manner
• Distributing content for research and to reinforce new concepts
• Asking targeted questions to a group or the class, focusing their attention on a specific aspect of the problem

Depending on your teaching style, it may take time to prepare yourself to successfully run a problem-based learning lesson.

4. Time-Consuming Assessment

If you choose to give marks, assessing a student’s performance throughout a problem-based learning exercise demands constant monitoring and note-taking. You must take factors into account such as:

• Completed tasks
• The quality of those tasks
• The group’s overall work and solution
• Communication among team members
• Anything you outlined on the activity’s rubric

Monitoring these criteria is required for each student, making it time-consuming to give and justify a mark for everyone.

5. Varying Degrees of Relevancy and Applicability

It can be difficult to identify a tangible problem that students can solve with content they’re studying and skills they’re mastering. This introduces two clear issues. First, if it is easy for students to divert from the challenge’s objectives, they may miss pertinent information. Second, you could veer off the problem’s focus and purpose as students run into unanticipated obstacles. Overcoming obstacles has benefits, but may compromise the planning you did. It can also make it hard to get back on track once the activity is complete. Because of the difficulty associated with keeping activities relevant and applicable, you may see problem-based learning as too taxing.

If the advantages outweigh the disadvantages -- or you just want to give problem-based learning a shot -- follow these steps:

1. Identify an Applicable Real-Life Problem

Find a tangible problem that’s relevant to your students, allowing them to easily contextualize it and hopefully apply it to future challenges. To identify an appropriate real-world problem, look at issues related to your:

• Students’ shared interests

You must also ensure that students understand the problem and the information around it. So, not all problems are appropriate for all grade levels.

2. Determine the Overarching Purpose of the Activity

Depending on the problem you choose, determine what you want to accomplish by running the challenge. For example, you may intend to help your students improve skills related to:

• Collaboration
• Problem-solving
• Curriculum-aligned topics
• Processing diverse content

A more precise example, you may prioritize collaboration skills by assigning specific tasks to pairs of students within each team. In doing so, students will continuously develop communication and collaboration abilities by working as a couple and part of a small group. By defining a clear purpose, you’ll also have an easier time following the next step.

3. Create and Distribute Helpful Material

Handouts and other content not only act as a set of resources, but help students stay focused on the activity and its purpose. For example, if you want them to improve a certain math skill , you should make material that highlights the mathematical aspects of the problem. You may decide to provide items such as:

• Data that helps quantify and add context to the problem
• Videos, presentations and other audio-visual material
• A list of preliminary questions to investigate

Providing a range of resources can be especially important for elementary students and struggling students in higher grades, who may not have self-direction skills to work without them.

4. Set Goals and Expectations for Your Students

Along with the aforementioned materials, give students a guide or rubric that details goals and expectations. It will allow you to further highlight the purpose of the problem-based learning exercise, as you can explain what you’re looking for in terms of collaboration, the final product and anything else. It should also help students stay on track by acting as a reference throughout the activity.

5. Participate

Although explicitly correcting students may be discouraged, you can still help them and ask questions to dig into their thought processes. When you see an opportunity, consider if it’s worthwhile to:

• Fill gaps in knowledge
• Provide hints, not answers
• Question a student’s conclusion or logic regarding a certain point, helping them think through tough spots

By participating in these ways, you can provide insight when students need it most, encouraging them to effectively analyze the problem.

6. Have Students Present Ideas and Findings

If you divided them into small groups, requiring students to present their thoughts and results in front the class adds a large-group learning component to the lesson. Encourage other students to ask questions, allowing the presenting group to elaborate and provide evidence for their thoughts. This wraps up the activity and gives your class a final chance to find solutions to the problem.

Wrapping Up

The effectiveness of problem-based learning may differ between classrooms and individual students, depending on how significant specific advantages and disadvantages are to you. Evaluative research consistently shows value in giving students a question and letting them take control of their learning. But the extent of this value can depend on the difficulties you face.It may be wise to try a problem-based learning activity, and go forward based on results.

Create or log into your teacher account on Prodigy -- an adaptive math game that adjusts content to accommodate player trouble spots and learning speeds. Aligned to US and Canadian curricula, it’s used by more than 350,000 teachers and 10 million students. It may be wise to try a problem-based learning activity, and go forward based on results.

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Marines say no more ‘death by PowerPoint’ as Corps overhauls education

WASHINGTON, D.C. ― Marines and those who teach them will see more direct, problem-solving approaches to how they learn and far less “death by PowerPoint” as the Corps overhauls its education methods .

Decades of lecturers “foot stomping” material for Marines to learn, recall and regurgitate on a test before forgetting most of what they heard is being replaced by “outcomes-based” learning, a method that’s been in use in other fields but only recently brought into military training.

“Instead of teaching them what to think, we’re teaching them how to think,” said Col. Karl Arbogast, director of the policy and standards division at training and education command .

Here’s what’s in the Corps’ new training and education plan

New ranges, tougher swimming. inside the corps' new training blueprint..

Arbogast laid out some of the new methods that the command is using at the center for learning and faculty development while speaking at the Modern Day Marine Expo.

“No more death by PowerPoint,” Arbogast said. “No more ‘sage on the stage’ anymore, it’s the ‘guide on the side.’”

To do that, Lt. Col. Chris Devries, director of the learning and faculty center, is a multiyear process in which the Marines have developed two new military occupational specialties, 0951 and 0952.

The exceptional MOS is in addition to their primary MOS but allows the Marines to quickly identify who among their ranks is qualified to teach using the new methods.

Training for those jobs gives instructors, now called facilitators, an entry-level understanding of how to teach in an outcomes-based learning model.

Devries said the long-term goal is to create two more levels of instructor/facilitator that a Marine could return to in their career, a journeyman level and a master level. Those curricula are still under development.

The new method helps facilitators first learn the technology they’ll need to share material with and guide students. It also teaches them more formal assessment tools so they can gauge how well students are performing.

For the students, they can learn at their own pace. If they grasp the material the group is covering, they’re encouraged to advance in their study, rather than wait for the entire group to master the introductory material.

More responsibility is placed on the students. For example, in a land navigation class, a facilitator might share materials for students to review before class on their own and then immediately jump into working with maps, compasses and protractors on land navigation projects in the next class period, said John deForest, learning and development officer at the center.

That creates more time in the field for those Marines to practice the skills in a realistic setting.

Marines with Marine Medium Tiltrotor Squadron (VMM) 268, Marine Aircraft Group 24, 1st Marine Aircraft Wing, fire M240-B machine guns at the Marine Corps Air Station Kaneohe Bay range, Hawaii, March 5. (Lance Cpl. Tania Guerrero/Marine Corps)

For the infantry Marine course, the school split up the large classroom into squad-sized groups led by a sergeant or staff sergeant, allowing for more individual focus and participation among the students, Arbogast said.

“They have to now prepare activities for the learner to be directly involved in their own learning and then they have to steer and guide the learners correct outcome,” said Timothy Heck, director of the center’s West Coast detachment.

The students are creating products and portfolios of activities in their training instead of simply taking a written test, said Justina Kirkland, a facilitator at the West Coast detachment.

Students are also pushed to discuss problems among themselves and troubleshoot scenarios. The role of the facilitator then is to monitor the conversation and ask probing questions to redirect the group if they get off course, Heck said.

That involves more decision games, decision forcing cases and even wargaming, deForest said.

We “put the student in an active learning experience where they have to grapple with uncertainty, where they have to grapple with the technical skills and the knowledge they need,” deForest said.

That makes the learning more about application than recall, he said.

Todd South has written about crime, courts, government and the military for multiple publications since 2004 and was named a 2014 Pulitzer finalist for a co-written project on witness intimidation. Todd is a Marine veteran of the Iraq War.

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