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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.

problem solving approach in teaching and learning

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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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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.

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

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

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

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

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

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

What was noticeably absent from this laboratory classroom: frustration.

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

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

Not getting stuck

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

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

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

What does it mean to explicitly teach problem solving? 

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

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

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

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

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

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

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

Portrait of the Problem-Solving Curriculum

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

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

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

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

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

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

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

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

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

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

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

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

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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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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

Problem-Based Learning (PBL)

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.

Pbl

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

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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.

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.

figure 1

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.

figure 2

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.

figure 3

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

Problem Solving

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.

Needlepoint of cats

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

Back of a needlepoint

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

Teacher teaching a math lesson

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?

problem solving approach in teaching and learning

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

Light bulb

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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  • Effective Teaching Strategies

Problem-Based Learning: Benefits and Risks

  • November 12, 2009
  • Maryellen Weimer, PhD

Problem-based learning, the instructional approach in which carefully constructed, open-ended problems are used by groups of students to work through content to a solution, has gained a foothold in many segments of higher education.

Originally PBL, as it’s usually called, was used in medical school and in some business curricula for majors. But now it is being used in a wide range of disciplines and with students at various educational levels. The article (reference below) from which material is about to be cited “makes a critical assessment” of how PBL is being used in the field of geography.

Much of the content is relevant to that discipline specifically, but the article does contain a useful table that summarizes the benefits and risks of PBL for students, instructors, and institutions. Material on the table is gleaned from an extensive review of the literature (all referenced in the article). Here’s some of the information contained in the table.

Benefits of Problem-Based Learning

For Students

  • It’s a student-centered approach.
  • Typically students find it more enjoyable and satisfying.
  • It encourages greater understanding.
  • Students with PBL experience rate their abilities higher.
  • PBL develops lifelong learning skills.

For Instructors

  • Class attendance increases.
  • The method affords more intrinsic reward.
  • It encourages students to spend more time studying.
  • It promotes interdisciplinarity.

For Institutions

  • It makes student learning a priority.
  • It may aid student retention.
  • It may be taken as evidence that an institution values teaching.

Risks of Problem-Based Learning

  • Prior learning experiences do not prepare students well for PBL.
  • PBL requires more time and takes away study time from other subjects.
  • It creates some anxiety because learning is messier.
  • Sometimes group dynamics issues compromise PBL effectiveness.
  • Less content knowledge may be learned.
  • Creating suitable problem scenarios is difficult.
  • It requires more prep time.
  • Students have queries about the process.
  • Group dynamics issues may require faculty intervention.
  • It raises new questions about what to assess and how.
  • It requires a change in educational philosophy for faculty who mostly lecture.
  • Faculty will need staff development and support.
  • It generally takes more instructors.
  • It works best with flexible classroom space.
  • It engenders resistance from faculty who question its efficacy.

Reference: Pawson, E., Fournier, E., Haight, M., Muniz, O., Trafford, J., and Vajoczki, S. 2006. Problem-based learning in geography: Towards a critical assessment of its purposes, benefits and risks. Journal of Geography in Higher Education 30 (1): 103–16.

Excerpted from The Teaching Professor , February 2007.

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

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Written by Marcus Guido

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  • Teaching Strategies

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

problem solving approach in teaching and learning

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

problem solving approach in teaching and learning

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

problem solving approach in teaching and learning

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

problem solving approach in teaching and learning

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 solving approach in teaching and learning

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

problem solving approach in teaching and learning

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

problem solving approach in teaching and learning

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

problem solving approach in teaching and learning

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

problem solving approach in teaching and learning

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.

Learning to Teach Mathematics Through Problem Solving

  • Open access
  • Published: 21 April 2022
  • Volume 57 , pages 407–423, ( 2022 )

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  • Judy Bailey   ORCID: orcid.org/0000-0001-9610-9083 1  

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While there has been much research focused on beginning teachers; and mathematical problem solving in the classroom, little is known about beginning primary teachers’ learning to teach mathematics through problem solving. This longitudinal study examined what supported beginning teachers to start and sustain teaching mathematics through problem solving in their first 2 years of teaching. Findings show ‘sustaining’ required a combination of three factors: (i) participation in professional development centred on problem solving (ii) attending subject-specific complementary professional development initiatives alongside colleagues from their school; and (iii) an in-school colleague who also teaches mathematics through problem solving. If only one factor is present, in this study attending the professional development focussed on problem solving, the result was little movement towards a problem solving based pedagogy. Recommendations for supporting beginning teachers to embed problem solving are included.

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problem solving approach in teaching and learning

Forging New Opportunities for Problem Solving in Australian Mathematics Classrooms through the First National Mathematics Curriculum

Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving.

Joanna O. Masingila, Dana Olanoff & Patrick M. Kimani

problem solving approach in teaching and learning

Part IV: Commentary – Characteristics of Mathematical Challenge in Problem-Based Approach to Teaching Mathematics

Avoid common mistakes on your manuscript.

Introduction

For many years curriculum documents worldwide have positioned mathematics as a problem solving endeavour (e.g., see Australian Curriculum, Assessment and Reporting Authority, 2018 ; Ministry of Education, 2007 ). There is evidence however that even with this prolonged emphasis, problem solving has not become a significant presence in many classrooms (Felmer et al., 2019 ). Research has reported on a multitude of potential barriers, even for experienced teachers (Clarke et al., 2007 ; Holton, 2009 ). At the same time it is widely recognised that beginning teachers encounter many challenges as they start their careers, and that these challenges are particularly compelling when seeking to implement ambitious methods of teaching, such as problem solving (Wood et al., 2012 ).

Problem solving has been central to mathematics knowledge construction from the beginning of human history (Felmer et al., 2019 ). Teaching and learning mathematics through problem solving supports learners’ development of deep and conceptual understandings (Inoue et al., 2019 ), and is regarded as an effective way of catering for diversity (Hunter et al., 2018 ). While the importance and challenge of mathematical problem solving in school classrooms is not questioned, the promotion and enabling of problem solving is a contentious endeavour (English & Gainsburg, 2016 ). One debate centres on whether to teach mathematics through problem solving or to teach problem solving in and of itself. Recent scholarship (and this research) leans towards teaching mathematics through problem solving as a means for students to learn mathematics and come to appreciate what it means to do mathematics (Schoenfeld, 2013 ).

Problem solving has been defined in a multitude of ways over the years. Of central importance to problem solving as it is explored in this research study is Schoenfeld’s ( 1985 ) proposition that, “if one has ready access to a solution schema for a mathematical task, that task is an exercise and not a problem” (p. 74). A more recent definition of what constitutes a mathematical problem from Mamona-Downs and Mamona ( 2013 ) also emphasises the centrality of the learner not knowing how to proceed, highlighting that problems cannot be solved by procedural effort alone. These are important distinctions because traditional school texts and programmes often position problems and problem solving as an ‘add-on’ providing a practice opportunity for a previously taught, specific procedure. Given the range of learners in any education setting an important point to also consider is that what constitutes a problem for some students may not be a problem for others (Schoenfeld, 2013 ).

A research focus exploring what supports beginning teachers’ learning about teaching mathematics through problem solving is particularly relevant at this time given calls for an increased curricular focus on mathematical practices such as problem solving (Grootenboer et al., 2021 ) and recent recommendations from an expert advisory panel on the English-medium Mathematics and Statistics curriculum in Aotearoa (Royal Society Te Apārangi, 2021 ). The ninth recommendation from this report advocates for the provision of sustained professional learning in mathematics and statistics for all teachers of Years 0–8. With regard to beginning primary teachers, the recommendation goes further suggesting that ‘mathematics and statistics professional learning’ (p. 36) be considered as compulsory in the first 2 years of teaching. This research explores what the nature of that professional learning might involve, with a focus on problem solving.

Scoping the Context for Learning and Sustaining Problem Solving

The literature reviewed for this study draws from two key fields: the nature of support and professional development effective for beginning teachers; and specialised supports helping teachers to employ problem solving pedagogies.

Beginning Teachers, Support and Professional Development

A teacher’s early years in the profession are regarded as critical in terms of constructing a professional practice (Feiman-Nemser, 2003 ) and avoiding high attrition (Karlberg & Bezzina, 2020 ). Research has established that beginning teachers need professional development opportunities geared specifically to their needs (Fantilli & McDougall, 2009 ) and their contexts (Gaikhorst, et al., 2017 ). Providing appropriate support is not an uncontentious matter with calls for institutions to come together and collaborate to provide adequate and ongoing support (Karlberg & Bezzina, 2020 ). The proposal is that support is needed from both within and beyond the beginning teacher’s school; and begins with effective pre-service teacher preparation (Keese et al., 2022 ).

Within schools where beginning teachers regard the support they receive positively, collaboration, encouragement and ‘involved colleagues’ are considered as vital; with the guidance of a 'buddy’ identified as some of the most valuable in-school support activities (Gaikhorst et al., 2014 ). Cameron et al.’s ( 2007 ) research in Aotearoa reports beginning teachers joining collaborative work cultures had greater opportunities to talk about teaching with their colleagues, share planning and resources, examine students’ work, and benefit from the collective expertise of team members.

Opportunities to participate in networks beyond the beginning teacher’s school have also been identified as being important for teacher induction (Akiri & Dori, 2021 ; Cameron et al., 2007 ). Fantilli & McDougall ( 2009 ) in their Canadian study found beginning teachers reported a need for many support and professional development opportunities including subject-specific (e.g., mathematics) workshops prior to and throughout the year. Akiri and Dori ( 2021 ) also refer to the need for specialised support from subject-specific mentors. This echoes the findings of Wood et al. ( 2012 ) who advocate that given the complexity of learning to teach mathematics, induction support specific to mathematics, and rich opportunities to learn are not only desirable but essential.

Akiri and Dori ( 2021 ) describe three levels of mentoring support for beginning teachers including individual mentoring, group mentoring and mentoring networks with all three facilitating substantive professional growth. Of relevance to this paper are individual and group mentoring. Individual mentoring involves pairing an experienced teacher with a beginning teacher, so that a beginning teacher’s learning is supported. Group mentoring involves a group of teachers working with one or more mentors, with participants receiving guidance from their mentor(s) (Akiri & Dori, 2021 ). Findings from Akiri and Dori suggest that of the varying forms of mentoring, individual mentoring contributes the most for beginning teachers’ professional learning.

Teachers Learning to Teach Mathematics Through Problem Solving

Learning to teach mathematics through problem solving begins in pre-service teacher education. It has been shown that providing pre-service teachers with opportunities to engage in problem solving as learners can be productive (Bailey, 2015 ). Opportunities to practise content-specific instructional strategies such as problem solving during student teaching has also been positively associated with first-year teachers’ enactment of problem solving (Youngs et al., 2022 ).

The move from pre-service teacher education to the classroom can be fraught for beginning teachers (Feiman-Nemser, 2003 ), and all the more so for beginning teachers attempting to teach mathematics through problem solving (Wood et al., 2012 ). In a recent study (Darragh & Radovic, 2019 ) it has been shown that an individual willingness to change to a problem-based pedagogy may not be enough to sustain a change in practice in the long term, particularly if there is a contradiction with the context and ‘norms’ (e.g., school curriculum) within which a teacher is working. Cady et al. ( 2006 ) explored the beliefs and practices of two teachers from pre-service teacher education through to becoming experienced teachers. One teacher who initially adopted reform practices reverted to traditional beliefs about the learning and teaching of mathematics. In contrast, the other teacher implemented new practices only after understanding these and gaining teaching experience. Participation in mathematically focused professional development and involvement in resource development were thought to favourably influence the second teacher.

Lesson structures have been found to support teachers learning to teach mathematics through problem solving. Sullivan et al. ( 2016 ) explored the use of a structure comprising four phases: launching, exploring, summarising and consolidating. Teachers in Australia and Aotearoa have reported the structure as productive and feasible (Ingram et al., 2019 ; Sullivan et al., 2016 ). Teaching using challenging tasks (such as in problem solving) and a structure have been shown to accommodate student diversity, a pressing concern for many teachers. Student diversity has often been managed by grouping students according to perceived levels of capability (called ability grouping). Research identifies this practice as problematic, excluding and marginalising disadvantaged groups of students (e.g., see Anthony & Hunter, 2017 ). The lesson structure explored by Sullivan et al. ( 2016 ) caters for diversity by deliberately differentiating tasks, providing enabling and extending prompts. Extending prompts are offered to students who finish an original task quickly and ideally elicit abstraction and generalisation. Enabling prompts involve reducing the number of steps, simplifying the numbers, and/or varying forms of representation for students who cannot initially proceed, with the explicit intention that students then return to the original task.

Recognising the established challenges teachers encounter when learning about teaching mathematics through problem solving, and the paucity of recent research focussing on beginning teachers learning about teaching mathematics in this way, this paper draws on data from a 2 year longitudinal study. The study was guided by the research question:

What supports beginning teachers’ implementation of a problem solving pedagogy for the teaching and learning of mathematics?

Research Methodology and Methods

Data were gathered from three beginning primary teachers who had completed a 1 year graduate diploma programme in primary teacher education the previous year. The beginning teachers had undertaken a course in mathematics education (taught by the author for half of the course) as part of the graduate diploma. An invitation to be involved in the research was sent to the graduate diploma cohort at the end of the programme. Three beginning teachers indicated their interest and remained involved for the 2 year research period. The teachers had all secured their first teaching positions, and were teaching at different year levels at three different schools. Julia (pseudonyms have been used for all names) was teaching year 0–2 (5–6 years) at a small rural school; Charlotte, year 5–6 (9–10 years) at a large urban city school; and Reine, year 7–8 (11–12 years), at another small rural school. All three beginning teachers taught at their respective schools, teaching the same year levels in both years of the study. Ethical approval was sought and given by the author’s university ethics committee. Informed consent was gained from the teachers, school principals and involved parents and children.

Participatory action research was selected as the approach in the study because of its emphasis on the participation and collaboration of all those involved (Townsend, 2013 ). Congruent with the principles of action research, activities and procedures were negotiated throughout both years in a responsive and emergent way. The author acted as a co-participant with the teachers, aiming to improve practice, to challenge and reorient thinking, and transform contexts for children’s learning (Locke et al., 2013 ). The author’s role included facilitating the research-based problem solving workshops (see below), contributing her experience as a mathematics educator and researcher. The beginning teachers were involved in making sense of their own practice related to their particular sites and context.

The first step in the research process was a focus group discussion before the beginning teachers commenced their first year of teaching. This discussion included reflecting on their learning about problem solving during the mathematics education course; and envisaging what would be helpful to support implementation. It was agreed that a series of workshops would be useful. Two were subsequently held in the first year of the study, each for three hours, at the end of terms one and two. Four workshops were held during the second year, one during each term. At the end of the first year the author suggested a small number of experienced teachers who teach mathematics through problem solving join the workshops for the second year. The presence of these teachers was envisaged to support the beginning teachers’ learning. The beginning teachers agreed, and an invitation was extended to four teachers from other schools whom the author knew (e.g., through professional subject associations). The focus of the research remained the same, namely exploring what supported beginning teachers to implement a problem solving pedagogy.

Each workshop began with sharing and oral reflections about recent problem solving experiences, including successes and challenges. Key workshop tasks included developing a shared understanding of what constitutes problem solving, participating in solving mathematical problems (modelled using a lesson structure (Sullivan et al., 2016 ), and learning techniques such as asking questions. A time for reflective writing was provided at the end of each workshop to record what had been learned and an opportunity to set goals.

During the first focus group discussion it was also decided the author would visit and observe the beginning teachers teaching a problem solving lesson (or two) in term three or four of each year. A semi-structured interview between the author and each beginning teacher took place following each observed lesson. The beginning teachers also had an opportunity to ask questions as they reflected on the lesson, and feedback was given as requested. A second focus group discussion was held at the end of the first year (an approximate midpoint in the research), and a final focus group discussion was held at the end of the second year.

All focus group discussions, problem solving workshops, observations and interviews were audio-recorded and transcribed. Field notes of workshops (recorded by the author), reflections from the beginning teachers (written at the end of each workshop), and lesson observation notes (recorded by the author) were also gathered. The final data collected included occasional emails between each beginning teacher and the author.

Data Analysis

The analysis reported in this paper drew on all data sets, primarily using inductive thematic analysis (Braun & Clarke, 2006 ). The research question guided the key question for analysis, namely: What supports beginning teachers’ implementation of a problem solving pedagogy for the teaching and learning of mathematics? Alongside this question, consideration was also given to the challenges beginning teachers encountered as they implemented a problem solving pedagogy. Data familiarisation was developed through reading and re-reading the whole body of data. This process informed data analysis and the content for each subsequent workshop and focus group discussions. Colour-coding and naming of themes included comparing and contrasting data from each beginning teacher and throughout the 2-year period. As a theme was constructed (Braun & Clarke, 2006 ) subsequent data was checked to ascertain whether the theme remained valid and/or whether it changed during the 2 years. Three key themes emerged revealing what supported the beginning teachers’ developing problem solving pedagogy, and these constitute the focus for this paper.

Mindful of the time pressures beginning teachers experience in their early years, the author undertook responsibility for data analysis. The author’s understanding of the unfolding ‘story’ of each beginning teacher’s experiences and the emerging themes were shared with the beginning teachers, usually at the beginning of a workshop, focus group discussion or observation. Through this process the author’s understandings were checked and clarified. This iterative process of member checking (Lincoln & Guba, 1985 ) began at a mid-point during the first year, once a significant body of data had been gathered. At a later point in the analysis and writing, the beginning teachers also had an opportunity to read, check and/or amend quotes chosen to exemplify their thinking and experiences.

Findings and Discussion

In this section the three beginning teachers’ experiences at the start of the 2 year research timeframe is briefly described, followed by the first theme centred on the use of a lesson structure including prompts for differentiation. The second and third themes are presented together, starting with a brief outline of each beginning teacher’s ‘story’ providing the context within which the themes emerged. Sharing the ‘story’ of each beginning teacher and including their ‘voice’ through quotes acknowledges them and their experiences as central to this research.

The beginning teachers’ pre-service teacher education set the scene for learning about teaching mathematics through problem solving. A detailed list brainstormed during the first focus group discussion suggested a developing understanding from their shared pre-service mathematics education course. In their first few weeks of teaching, all three beginning teachers implemented a few problems. It transpired however this inclusion of problem solving occurred only while children were being assessed and grouped. Following this, all three followed a traditional format of skill-based (with a focus on number) mathematics, taught using ability groups. The beginning teachers’ trajectories then varied with Julia and Reine both eventually adopting a pedagogy primarily based on problem solving, while Charlotte employed a traditional skill-based mathematics using a combination of whole class and small group teaching.

A Lesson Structure that Caters for Diversity Supports Early Efforts

Data show that developing familiarity with a lesson structure including prompts for differentiation supported the beginning teachers’ early efforts with a problem solving pedagogy. This addressed a key issue that emerged during the first workshop. During the workshop while a ‘list’ of ideas for teaching a problem solving lesson was co-constructed, considerable concern was expressed about catering for a range of learners when introducing and working with a problem. For example, Charlotte queried, “ Well, what happens when you are trying to do something more complicated, and we’re (referring to children) sitting here going, ‘I’ve no idea what you're talking about” ? Reine suggested keeping some children with the teacher, thinking he would say, “ If you’re unsure of any part stay behind” . He was unsure however about how he would then maintain the integrity of the problem.

It was in light of this discussion that a lesson structure with differentiated prompts (Sullivan et al., 2016 ) was introduced, experienced and reflected on during the second workshop. While the co-constructed list developed during the first workshop had included many components of Sullivan’s lesson structure, (e.g., a consideration of ‘extensions’) there had been no mention of ‘enabling prompts’. Now, with the inclusion of both enabling and extending prompts, the beginning teachers’ discussion revealed them starting to more fully envisage the possibilities of using a problem solving approach, and being able to cater for all children. Reine commented that, “… you can give the entire class a problem, you've just got to have a plan, [and] your enabling and extension prompts” . Charlotte was also now considering and valuing the possibility of having a whole class work on the same problem. She said, “I think … it’s important and it’s useful for your whole class to be working on the same thing. And … have enablers and extenders to make sure that everyone feels successful” . Julia also referred to the planning prompts. She thought it would be key to “plan it well so that we’ve got enabling and extending prompts” .

Successful Problem Solving Lessons

Following the second workshop all three beginning teachers were observed teaching a lesson using the structure. These lessons delighted the beginning teachers, with them noting prolonged engagement of children, the children’s learning and being able to cater for all learners. Reine commented on how excited and engaged the children were, saying they were, “ just so enthusiastic about it ”. In Charlotte’s words, “ it really worked ”, and Julia enthusiastically pondered this could be “ the only way you teach maths !”.

During the focus group discussion at the end of the first year, all three reflected on the value of the lesson structure. Reine called it a ‘framework’ commenting,

I like the framework. So from start to finish, how you go through that whole lesson. So how you set it up and then you go through the phases… I like the prompts that we went through…. knowing where you could go, if they’re like, ‘What do I do?’ And then if they get it too easy then ‘Where can you go?’ So you've got all these little avenues.

Charlotte also valued the lesson structure for the breadth of learning that could occur, explaining,

… it really helped, and really worked. So I found that useful for me and my class ‘cause they really understood. And I think also making sure that you know all the ins and outs of a problem. So where could they go? What do you need to know? What do they need to know?

While the beginning teachers’ pre-service teacher education and the subsequent research process, including the use of the lesson structure, supported the beginning teachers’ early efforts teaching mathematics through problem solving, two key factors further enabled two of the beginning teachers (Julia and Reine) to sustain a problem solving pedagogy. These were:

Being involved in complementary mathematics professional development alongside members of their respective school staff (a form of group mentoring); and

Having a colleague in the same school teaching mathematics through problem solving (a form of individual mentoring).

Charlotte did not have these opportunities and she indicated this limited her implementation. Data for these findings for each teacher are presented below.

Complementary Professional Development and Problem Solving Colleague in Same School

Julia began to significantly implement problem solving from the second term in the first year. This coincided with her attending a 2-day workshop (with staff from her school) that focused on the use of problem solving to support children who are not achieving at expected levels (see ALiM: Accelerated Learning in Maths—Ministry of Education, 2022 ). She explained, “ … I did the PD with (colleague’s name), which was really helpful. And we did lots of talking about rich learning tasks and problem solving tasks…. And what it means ”. Following this, Julia reported using rich tasks and problem solving in her mathematics teaching in a regular (at least weekly) and ongoing way.

During the observation in term three of the first year Julia again referred to the impact of having a colleague also teaching mathematics through problem solving. When asked what she believed had supported her to become a teacher who teaches mathematics in this way she firstly identified her involvement in the research project, and then spoke about her colleague. She said, “ I’m really lucky one of our other teachers is doing the ALiM project… So we’re kind of bouncing off each other a little bit with resources and activities, and things like that. So that’s been really good ”.

At the beginning of the second year, Julia reiterated this point again. On this occasion she said having a colleague teaching mathematics through problem solving, “ made a huge difference for me last year ”, explaining the value included having someone to talk with on a daily basis. Mid-way through the second year Julia repeated her opinion about the value of frequent contact with a practising problem solving colleague. Whereas her initial comments spoke of the impact in terms of being “ a little bit ”, later references recount these as ‘ huge ’ and ‘ enabling ’. She described:

a huge effect… it enabled me. Cause I mean these workshops are really helpful. But when it’s only once a term, having [colleague] there just enabled me to kind of bounce ideas off. And if I did a lesson that didn’t work very well, we could talk about why that was, and actually talk about what the learning was instead…. . It was being able to reflect together, but also share ideas. It was amazing.

Julia’s comments raise two points. It is likely that participating in the ALiM professional development (which could be conceived as a form of group mentoring) consolidated the learning she first encountered during pre-service teacher education and later extended through her involvement in the research. Having a colleague (in essence, an individual mentor) within the same school teaching mathematics through problem solving appears to be another factor that supported Julia to implement problem solving in a more sustained way. Julia’s comments allude to a number of reasons for this, including: (i) the more frequent discussion opportunities with a colleague who understands what it means for children to learn mathematics through problem solving; (ii) being able to share and plan suitable activities and resources; and (iii) as a means for reflection, particularly when challenges were encountered.

Reine’s mathematics programme throughout the first year was based on ability groups and could be described as traditional. He occasionally used some mathematical problems as ‘extension activities’ for ‘higher level’ children, or as ‘fillers’. In the second year, Reine moved to working with mixed ability groups (where students work together in small groups with varying levels of perceived capability) and initially implemented problem solving approximately once a fortnight. In thinking back to these lessons he commented, “ We weren’t really unpacking one problem properly, it was just lots of busy stuff ”. A significant shift occurred in Reine’s practice to teaching mathematics primarily by problem solving towards the last half of the second year. He explained, “ I really ramped up towards terms three and four, where it’s more picking one problem across the whole maths class but being really, really conscious of that problem. Low entry, high ceiling, and doing more of it too ”.

Reine attributed this change to a number of factors. In response to a question about what he considered led to the change he explained,

… having this, talking about this stuff, trialling it and then with our PD at school with the research into ability grouping... We’ve got a lot of PD saying why it can be harmful to group on ability, and that’s been that last little kick I needed, I think. And with other teachers trialling this as well. Our senior teacher has flipped her whole maths program and just does problem solving.

Like Julia, Reine firstly referred to his involvement in the research project including having opportunities to try problems in his class and discuss his experiences within the research group. He then told of a colleague teaching at his school leading school-wide professional development focussed on the pitfalls of ability grouping in mathematics (e.g., see Clarke, 2021 ) and instead using problem solving tasks. He also referred to having another teacher also teaching mathematics through problem solving. It is interesting to consider that having positive experiences in pre-service teacher education, the positive and encouraging support of colleagues (Reine’s principal and co-teacher in both years), regular participation in ongoing professional development (the problem solving workshops), and having a highly successful one-off problem solving teaching experience (the first year observation) were not enough for Reine to meaningfully sustain problem solving in his first year of teaching.

As for Julia, pivotal factors leading to a sustaining of problem solving teaching practice in the second year included complementary mathematics professional development (a form of group mentoring) and at least one other teacher (acting as an individual mentor) in the same school teaching mathematics through problem solving. It could be argued that pre-service teacher education and the problem solving workshops ‘paved the way’ for Julia and Reine to make a change. However, for both, the complementary professional development and presence of a colleague also teaching through problem solving were pivotal. It is also interesting to note that three of the four experienced teachers in the larger research group taught at the same level as Reine (see Table 1 below) yet he did not relate this to the significant change in his practice observed towards the end of the second year.

Charlotte’s mathematics programme during the first year was also traditional, teaching skill-based mathematics using ability groups. At the beginning of the second year Charlotte moved to teaching her class as a whole group, using flexible grouping as needed (children are grouped together in response to learning needs with regard to a specific idea at a point in time, rather than perceived notions of ability). She reported that she occasionally taught a lesson using problem solving in the first year, and approximately once or twice a term in the second year. Charlotte did not have opportunities for professional development in mathematics nor did she have a colleague in the same school teaching mathematics through problem solving. Pondering this, Charlotte said,

It would have been helpful if I had someone else in my school doing the same thing. I just thought about when you were saying the other lady was doing it [referring to Julia’s colleague]. You know, someone that you can just kind of back-and-forth like. I find with Science, I usually plan with this other lady, and we share ideas and plan together. We come up with some really cool stuff whereas I don’t really have the same thing for this.

Based on her experiences with teaching science it is clear Charlotte recognised the value of working alongside a colleague. In this, her view aligns with what Julia and Reine experienced.

Table 1 provides a summary of the variables for each beginning teacher, and whether a sustained implementation of teaching mathematics through problem solving occurred.

The table shows two variables common to Julia and Reine, the beginning teachers who began and sustained problem solving. They both participated in complementary professional development with colleagues from their school, and the presence of a colleague, also at their school, teaching mathematics through problem solving. Given that Julia was able to implement problem solving in the absence of a ‘research workshop colleague’ teaching at the same year level, and Reine’s lack of comment about the potential impact of this, suggests that this was not a key factor enabling a sustained implementation of problem solving.

Attributing the changes in Julia and Reine’s teaching practice primarily to their involvement in complementary professional development attended by members of their school staff, and the presence of at least one other teacher teaching mathematics through problem solving in their school, is further supported by a consideration of the timing of the changes. The data shows that while Julia could be considered an ‘early adopter’, Reine changed his practice reasonably late in the 2 year period. Julia’s early adoption of teaching mathematics through problem solving coincided with her involvement, early in the 2 years, in the professional development and opportunity to work alongside a problem solving practising colleague. Reine encountered these similar conditions towards the end of the 2 years and it is notable that this was the point at which he changed his practice. That problem solving did not become embedded or frequent within Charlotte’s mathematics programme tends to support the argument.

Understanding what supports primary teachers to teach mathematics through problem solving at the beginning of their careers is important because all students, including those taught by beginning teachers, need opportunities to develop high-level thinking, reasoning, and problem solving skills. It is also important in light of recent calls for mathematics curricula to include more emphasis on mathematical practices (such as problem solving) (e.g., see Grootenboer et al., 2021 ); and the Royal Society Te Apārangi report ( 2021 ). Findings from this research suggest that learning about problem solving during pre-service teacher education is enough for beginning teachers to trial teaching mathematics in this way. Early efforts were supported by gaining experience with a lesson structure that specifically attends to diversity. The lesson structure prompted the beginning teachers to anticipate different children’s responses, and consider how they would respond to these. An increased confidence and sense of security to trial teaching mathematics through problem solving was enabled, based on their more in-depth preparation. Beginning teachers finding the lesson structure useful extends the findings of Sullivan et al. ( 2016 ) in Australia and Ingram et al. ( 2019 ) in Aotearoa to include less experienced teachers.

In order for teaching mathematics through problem solving to be sustained however, a combination of three factors, subsequent to pre-service teacher education, was needed: (i) active participation in problem solving workshops (in this context provided by the research-based problem solving workshops); (ii) attending complementary professional development initiatives alongside colleagues from their school (a form of group mentoring); and (iii) the presence of an in-school colleague who also teaches mathematics through problem solving (a form of individual mentoring). It seems possible these three factors acted synergistically resulting in Julia and Reine being able to sustain implementation. If only one factor is present, in this study attending the problem solving workshops, and despite a genuine interest in using a problem based pedagogy, the result was limited movement towards this way of teaching.

Akiri and Dori ( 2021 ) have reported that individual mentoring contributes the most to beginning teachers’ professional growth. In a manner consistent with these findings, an in-school colleague (who in essence was acting as an individual mentor) played a critical role in supporting Reine and Julia. However, while Akiri and Dori, amongst others (e.g., Cameron et al., 2007 ; Karlberg & Bezzina, 2020 ), have identified the value of supportive, approachable colleagues, for both Julia and Reine it was important that their colleague was supportive and approachable, and actively engaged in teaching mathematics through problem solving. Having supportive and approachable colleagues, as Reine experienced in his first year, on their own were not enough to support a sustained problem solving pedagogy.

Implications for Productive Professional Learning and Development

This study sought to explore the conditions that supported problem solving for beginning teachers, each in their unique context and from their perspective. The research did not examine how the teaching of mathematics through problem solving affected children’s learning. However, multiple sets of data were collected and analysed over a 2-year period. While it is neither possible nor appropriate to make claims as to generalisability some suggestions for productive beginning teacher professional learning and development are offered.

Given the first years of teaching constitute a particular and critical phase of teacher learning (Karlberg & Bezzina, 2020 ) and the findings from this research, it is imperative that well-funded, subject-focussed support occurs throughout a beginning teacher’s first 2 years of teaching. This is consistent with the ninth recommendation in the Royal Society Te Apārangi report ( 2021 ) suggesting compulsory professional learning during the induction period (2 years in Aotearoa New Zealand). Participation in subject-specific professional development has been recognised to favourably influence new teachers’ efforts to adopt reform practices such as problem solving (Cady et al., 2006 ).

Findings from this study suggest professional development opportunities that complement each other support beginning teacher learning. In the first instance complementarity needs to be with what beginning teachers have learned during their pre-service teacher education. In this study, the research-based problem solving workshops served this role. Complementarity between varying forms of professional development also appears to be important. Furthermore, as indicated by Julia and Reine’s experiences, subsequent professional development need not be on exactly the same topic. Rather, it can be complementary in the sense that there is an underlying congruence in philosophy and/or focus on a particular issue. For example, it emerged in the problem solving workshops, that being able to cater for diversity was a central concern for the beginning teachers. Attending to this issue within the problem solving workshops via the introduction of a lesson structure that enabled differentiation, was congruent with the nature of the professional development in the two schools: ALiM in Julia’s school, and mixed ability grouping and teaching mathematics through problem solving in Reine’s school. All three of these settings were focussed on positively responding to diversity in learning needs.

The presence of a colleague within the same school teaching mathematics through problem solving also appears to be pivotal. This is consistent with Darragh and Radovic ( 2019 ) who have shown the significant impact a teacher’s school context has on their potential to sustain problem based pedagogies in mathematics. Given that problem solving is not prevalent in many primary classrooms, it would seem clear that colleagues who have yet to learn about teaching mathematics through problem solving, particularly those that have a role supporting beginning teachers, will also require access to professional development opportunities. It seems possible that beginning and experienced teachers learning together is a potential pathway forward. Finding such pathways will be critical if mathematical problem solving is to be consistently implemented in primary classrooms.

Finally, these implications together with calls for institutions to collaborate to provide adequate and ongoing support for new teachers (Karlberg & Bezzina, 2020 ) suggest there is a need for pre-service teacher educators, professional development providers and the Teaching Council of Aotearoa New Zealand to work together to support beginning teachers’ starting and sustaining teaching mathematics through problem solving pedagogies.

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Bailey, J. Learning to Teach Mathematics Through Problem Solving. NZ J Educ Stud 57 , 407–423 (2022). https://doi.org/10.1007/s40841-022-00249-0

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Teaching and Learning

Elevating math education through problem-based learning, by lisa matthews     feb 14, 2024.

Elevating Math Education Through Problem-Based Learning

Image Credit: rudall30 / Shutterstock

Imagine you are a mountaineer. Nothing excites you more than testing your skill, strength and resilience against some of the most extreme environments on the planet, and now you've decided to take on the greatest challenge of all: Everest, the tallest mountain in the world. You’ll be training for at least a year, slowly building up your endurance. Climbing Everest involves hiking for many hours per day, every day, for several weeks. How do you prepare for that?

The answer, as in many situations, lies in math. Climbers maximize their training by measuring their heart rate. When they train, they aim for a heart rate between 60 and 80 percent of their maximum. More than that, and they risk burning out. A heart rate below 60 percent means the training is too easy — they’ve got to push themselves harder. By combining this strategy with other types of training, overall fitness will increase over time, and eventually, climbers will be ready, in theory, for Everest.

problem solving approach in teaching and learning

Knowledge Through Experience

The influence of constructivist theories has been instrumental in shaping PBL, from Jean Piaget's theory of cognitive development, which argues that knowledge is constructed through experiences and interactions , to Leslie P. Steffe’s work on the importance of students constructing their own mathematical understanding rather than passively receiving information .

You don't become a skilled mountain climber by just reading or watching others climb. You become proficient by hitting the mountains, climbing, facing challenges and getting right back up when you stumble. And that's how people learn math.

problem solving approach in teaching and learning

So what makes PBL different? The key to making it work is introducing the right level of problem. Remember Vygotsky’s Zone of Proximal Development? It is essentially the space where learning and development occur most effectively – where the task is not so easy that it is boring but not so hard that it is discouraging. As with a mountaineer in training, that zone where the level of challenge is just right is where engagement really happens.

I’ve seen PBL build the confidence of students who thought they weren’t math people. It makes them feel capable and that their insights are valuable. They develop the most creative strategies; kids have said things that just blow my mind. All of a sudden, they are math people.

problem solving approach in teaching and learning

Skills and Understanding

Despite the challenges, the trend toward PBL in math education has been growing , driven by evidence of its benefits in developing critical thinking, problem-solving skills and a deeper understanding of mathematical concepts, as well as building more positive math identities. The incorporation of PBL aligns well with the contemporary broader shift toward more student-centered, interactive and meaningful learning experiences. It has become an increasingly important component of effective math education, equipping students with the skills and understanding necessary for success in the 21st century.

At the heart of Imagine IM lies a commitment to providing students with opportunities for deep, active mathematics practice through problem-based learning. Imagine IM builds upon the problem-based pedagogy and instructional design of the renowned Illustrative Mathematics curriculum, adding a number of exclusive videos, digital interactives, design-enhanced print and hands-on tools.

The value of imagine im's enhancements is evident in the beautifully produced inspire math videos, from which the mountaineer scenario stems. inspire math videos showcase the math for each imagine im unit in a relevant and often unexpected real-world context to help spark curiosity. the videos use contexts from all around the world to make cross-curricular connections and increase engagement..

This article was sponsored by Imagine Learning and produced by the Solutions Studio team.

Imagine Learning

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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

Micro Teaching Skills

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  2. Developing Problem-Solving Skills for Kids

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  3. Teaching The IDEAL Problem-Solving Method To Diverse Learners

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  4. Applying Problem Based Learning (PBL)

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  5. Problem Solving Method Of Teaching || Methods of Teaching || tsin-eng

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  6. 4 Tips on Teaching Problem Solving (From a Student)

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COMMENTS

  1. Teaching Problem Solving

    Teaching Problem Solving Print Version Tips and Techniques Expert vs. Novice Problem Solvers Tips and Techniques Communicate Have students identify specific problems, difficulties, or confusions. Don't waste time working through problems that students already understand.

  2. Teaching Problem Solving

    Problem solving is a "goal-oriented" process that includes creating and manipulating problems as mental models (Jonassen, 2000). Brown faculty from a variety of disciplines were interviewed by Sheridan staff and asked, "What skills do students need to problem solve effectively?" They responded that students need to be able to do the following:

  3. 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.

  4. Teaching Problem-Solving Skills

    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).

  5. Teaching problem solving

    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

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

    This approach to teaching problem solving includes a significant focus on learning to identify the problem that actually needs to be solved, in order to avoid solving the wrong problem. The curriculum is organized so that each day is a complete experience. It begins with the teacher introducing the problem-identification or problem-solving ...

  7. Problem-Based Learning (PBL)

    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 ...

  8. 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 ...

  9. Full article: Understanding and explaining pedagogical problem solving

    In this approach problem solving involves diagnosing the issue and identifying alternative potential solutions, whereas decision making is concerned with evaluating and choosing among these options then committing and implementing this choice. ... Secondly, pedagogy analysis must explore the processes of teaching and learning, but also the ...

  10. The process of implementing problem-based learning in a teacher

    Problem-based learning (PBL) is a student-centred instructional approach in which complex real-world problems are used as the vehicle to promote students' learning of concepts and principles.

  11. The effectiveness of collaborative problem solving in promoting

    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...

  12. PDF Problem Based Learning: A Student-Centered Approach

    Problem-based learning is a teaching method in which students' learn through the complex and open ended problems. These problems are real world problems and are used to encourage students' learning through principles and concept. PBL is both a teaching method and approach to the curriculum.

  13. Teaching Mathematics Through Problem Solving

    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 ...

  14. Elementary teachers' experience of engaging with Teaching Through

    For many decades, problem solving has been a focus of elementary mathematics education reforms. Despite this, in many education systems, the prevalent approach to mathematics problem solving treats it as an isolated activity instead of an integral part of teaching and learning. In this study, two mathematics teacher educators introduced 19 Irish elementary teachers to an alternative problem ...

  15. Problem-Based Learning: Benefits and Risks

    Problem-based learning, the instructional approach in which carefully constructed, open-ended problems are used by groups of students to work through content to a solution, has gained a foothold in many segments of higher education. Originally PBL, as it's usually called, was used in medical school and in some business curricula for majors.

  16. 5 Advantages and Disadvantages of Problem-Based Learning [+ Activity

    Advantages of Problem-Based Learning 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.

  17. Problem Solving in Mathematics Education

    A salient feature of a problem solving approach to learn mathematics is that teachers and students develop and apply an enquiry or inquisitive method to delve into mathematical concepts and tasks. ... On understanding, learning and teaching problem solving (Vol. 2). New York, NY: Wiley. Google Scholar Resnick, L., & Glaser, R. (1976). Problem ...

  18. Enhancing students' problem-solving skills through context-based learning

    Problem solving is often challenging for students because they do not understand the problem-solving process (PSP). This study presents a three-stage, contextbased, problem-solving, learning ...

  19. Analyzing the effects of the problem solving approach to the

    The problem solving approach emphasizes that important mathematics concepts and procedures can be best taught through problem solving tasks or activities which engage students in thinking about the important mathematical concepts and skills they need to learn.

  20. Learning to Teach Mathematics Through Problem Solving

    Teaching and learning mathematics through problem solving supports learners' development of deep and conceptual understandings (Inoue et al., 2019 ), and is regarded as an effective way of catering for diversity (Hunter et al., 2018 ).

  21. Teaching and learning problem solving in science. Part I: A general

    A systematic approach to solving problems and on designing instruction where students learn this approach. Teaching and learning problem solving in science. Part I: A general strategy | Journal of Chemical Education

  22. Elevating Math Education Through Problem-Based Learning

    The Traditional Approach. Problem-based learning has a rich history in American education, with John Dewey laying the theoretical groundwork in 1916 and McMaster University pioneering the PBL program for medical education in 1969. More recently, the National Council of Teachers of Mathematics published Principles and Standards for School Mathematics in 2000, setting forth a vision that ...

  23. The problem-solving method: Efficacy for learning and motivation in the

    Methods. Fifty-three students (M age 15 ± 0.1 years), in their 1st year of the Tunisian secondary education system, voluntarily participated in this study, and randomly assigned to a control or experimental group.Participants in the control group were taught using the traditional methods, whereas participants in the experimental group were taught using the problem-solving method.

  24. 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.