what is problem solving in learning

Problem-Based Learning (PBL)

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

See also: Just-in-Time Teaching

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

By working with PBL, students will:

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

How to Begin PBL

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

Designing Classroom Instruction

See also: Inclusive Teaching Strategies

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

How to Orchestrate a PBL Activity

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

Teacher’s Role in PBL

See also: Flipped teaching

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

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

The Role of the Students

See also: ADDIE model

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

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

See also: Kirkpatrick Model: Four Levels of Learning Evaluation

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

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Why Teaching Problem-Solving Skills is Essential for Student Success

Teaching the art of problem-solving is crucial for preparing students to thrive in an increasingly complex and interconnected world. Beyond the ability to find solutions, problem-solving fosters critical thinking, creativity, and resilience: qualities essential for academic success and lifelong learning. 

This article explores the importance of problem-solving skills, critical strategies for nurturing them in students, and practical approaches educators and parents can employ. 

By equipping students with these skills, we empower them to tackle challenges confidently, innovate effectively, and contribute meaningfully to their communities and future careers .

Why Teaching Problem-Solving Skills is Important

Problem-solving is a crucial skill that empowers students to tackle challenges with confidence and creativity . In an educational context, problem-solving is not just about finding solutions; it involves critical thinking, analysis, and application of knowledge. Students who excel in problem-solving can understand complex problems, break them down into manageable parts, and develop effective strategies to solve them. This skill is applicable across all subjects, from math and science to language arts and social studies, fostering a more profound understanding and retention of material .

Beyond academics, problem-solving is a cornerstone of success in life. Successful people across various fields possess strong problem-solving abilities. They can navigate obstacles, innovate solutions, and adapt to changing circumstances. In engineering and business management careers, problem solvers are highly valued for their ability to find efficient and creative solutions to complex issues.

Educators prepare students for future challenges and opportunities by teaching problem-solving in schools. They learn to think critically , work collaboratively, and persist in facing difficulties, all essential lifelong learning and achievement skills. Thus, nurturing problem-solving skills in students enhances their academic performance and equips them for success in their future careers and personal lives.

Aspects of Problem Solving

Developing problem-solving skills is crucial for preparing students to navigate the complexities of the modern world. Critical thinking, project-based learning, and volunteering enhance academic learning and empower students to address real-world challenges effectively. By focusing on these aspects, students can develop the skills they need to innovate, collaborate, and positively impact their communities.

Critical Thinking

Critical thinking is a fundamental skill for problem-solving as it involves analysing and evaluating information to make reasoned judgments and decisions. It enables students to approach problems systematically, consider multiple perspectives, and identify underlying issues.

Critical thinking allows students to:

• Analyse information : Students can assess the relevance and reliability of information to determine its impact on problem-solving. For example, in a science project, critical thinking helps students evaluate experimental results to draw valid conclusions.
• Develop solutions : Students can choose the most effective solution by critically evaluating different approaches. In a group project, critical thinking enables students to compare and refine ideas to solve a problem creatively.

Project-Based Learning

Project-based learning (PBL) is an instructional approach where students learn by actively engaging in real-world and personally meaningful projects. It allows students to explore complex problems and develop essential skills such as collaboration and communication.

Here is how project-based learning helps students develop problem-solving skills.

• Apply knowledge : Students apply academic concepts to real-world problems by working on projects. For instance, in designing a community garden, students use math to plan the layout and science to understand plant growth.
• Develop skills : PBL fosters problem-solving by challenging students to address authentic problems. For example, in a history project, students might analyse primary sources to understand the causes of historical events and propose solutions to prevent similar conflicts.

Volunteering

Volunteering allows students to contribute to their communities while developing empathy, leadership , and problem-solving skills. It provides practical experiences that enhance learning and help students understand and address community needs.

Volunteering is important because it allows students to:

• Identify needs : Students can identify community needs and consider solutions by working in diverse settings. For example, volunteering at a food bank can inspire students to address food insecurity by organising donation drives.
• Collaborate : Volunteering encourages teamwork and collaboration to solve problems. Students learn to coordinate tasks and resources to achieve common goals when organising a charity event.

The Problem-Solving Process

Problem-solving involves a systematic approach to understanding, analysing, and solving problems. Here are the critical steps in the problem-solving process:

• Identify the problem : The first step is clearly defining and understanding the problem. This involves identifying the specific issue or challenge that needs to be addressed.
• Define goals : Once the problem is identified, it's essential to establish clear and measurable goals. This helps focus efforts and guide the problem-solving process.
• Explore possible solutions : The next step is brainstorming and exploring various solutions. This involves generating ideas and considering different approaches to solving the problem.
• Evaluate options : After generating potential solutions, evaluate each option based on its feasibility, effectiveness, and possible outcomes.
• Choose the best solution : Select the most appropriate solution that best meets the defined goals and addresses the root cause of the problem.
• Implement the solution : Once a solution is chosen, it must be implemented. This step involves planning the implementation process and taking necessary actions to execute the solution.
• Monitor progress : After implementing the solution, monitor its progress and evaluate its effectiveness. This step helps ensure that the problem is being resolved as expected.
• Reflect and adjust : Reflect on the problem-solving process, identify any lessons learned, and make adjustments if necessary. This continuous improvement cycle helps refine solutions and develop better problem-solving skills.

How to Become a General Problem Solver

Parents play a crucial role in nurturing their children's problem-solving skills. Here are some ways parents can help their children become effective problem solvers.

• Encourage critical thinking : Encourage children to ask questions, analyse information, and consider different perspectives. Engage them in discussions that challenge their thinking and promote reasoning.
• Support independence : Allow children to tackle challenges on their own. Offer guidance and encouragement without immediately providing solutions. This helps build confidence and resilience.
• Provide opportunities for problem-solving : Create opportunities for children to solve real-life problems, such as planning a family event, organising their room, or resolving conflicts with siblings or friends.
• Foster creativity : Encourage creative thinking and brainstorming. Provide materials and activities that stimulate imagination and innovation.
• Model problem-solving behaviours : Demonstrate problem-solving skills in your own life and involve children in decision-making processes. Show them how to approach challenges calmly and methodically.

How Online Schooling Encourages Problem-Solving

Online schooling encourages problem-solving skills by requiring students to navigate digital platforms, manage their time effectively , and troubleshoot technical issues independently. 

Students often engage in interactive assignments and projects that promote critical thinking and creativity. They learn to adapt to different learning environments and collaborate virtually, fostering innovative solutions. 

Online schooling also encourages self-directed learning , where students must identify and address their own learning gaps. This enhances problem-solving abilities and prepares them for the complexities of the digital age.

To find out more about online learning, click here . 

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What is Problem-Based Learning? A Complete Guide for Educators

Published on: 11/30/2023

By Scott Winstead

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As an educator, you’re always looking for the most effective ways to help your students master the material and develop the skills they need to succeed. With so many different instructional approaches to choose from, it can be tough to decide which one is right for your class. One approach that has shown promise in a variety of educational settings is problem-based learning (PBL) — a method that involves having students work through real-world, open-ended problems and scenarios as a means of learning new concepts.

In fact, studies have shown that problem based learning is often more effective than traditional lecturing.

How can you use problem-based learning it as a teacher, instructional designer ,  course creator , or trainer? In the guide below, I’ll talk more what problem-based learning is, how it can be used in the classroom, its pros and cons, and more.

What is Problem-Based Learning?

With problem-based learning, students work on a real-world, open-ended problem or issue and try to solve it.

By challenging students to come up with solutions to real problems, they learn to think critically and creatively. They also learn to work together and communicate effectively.

This form of experienced-based education can help students better master the material and develop the skills they need to succeed in college and their careers.

In my experience, when students are engaged in problem-based learning, they tend to be more motivated and enthusiastic about learning. And they retain information better too.

When using PBL, the instructor’s role switches from the more conventional paradigm. The teacher gives relevant content, tells the class what has to be done, and offers excellent knowledge for solving a particular problem.

The instructor serves as a facilitator in PBL. The learning is student-driven, intending to address the issue (note: the problem is established at the onset of learning instead of being presented last in the traditional model). Furthermore, the tasks range from a few weeks to a semester, with daily instructional time dedicated to group work.

If you’re looking for a way to help your students learn more effectively, problem-based learning may be the answer.

How to Use Problem-Based Learning in the Classroom

There are a few different ways you can incorporate problem-based learning into your classroom.

One option is to have students work on problems individually or in small groups.

Another option is to use problem-based learning as a whole-class activity.

This is a great way to get all of your students engaged and involved in the lesson.

Before you can implement problem-based learning, you should:

• Identify what it is exactly that you want the students to learn
• Determine what real-world problem or issue you want them to solve that ties into the learning objective.
• Come up with a plan and rules for how the students will work together on the problem.
• Define how the assignment will be evaluated.

Once you have a plan in place, you can start incorporating problem-based learning into your lessons.

The Pros and Cons of Problem-Based Learning

When it comes to teaching, there’s no one-size-fits-all approach.

What works for one teacher in one classroom might not work for another teacher in a different classroom.

The same goes for problem-based learning. While this instructional approach has its benefits, there are also some potential drawbacks to consider.

Pros of Problem-Based Learning:

• Helps students learn how to think critically and solve problems
• Encourages students to be creative
• Teaches students how to work together
• Helps students learn how to communicate effectively

Cons of Problem-Based Learning:

• May be challenging for some teachers to implement
• May be too much for some students who struggle with problem-solving
• If not done correctly, can lead to students feeling overwhelmed or frustrated

Before you decide to use problem-based learning in your classroom, weigh the pros and cons to see if it’s the right instructional approach for you and your students.

Final Thoughts on Problem-Based Learning

Problem-based learning (PBL) is a student-centered teaching method that encourages students to learn by actively solving real-world problems.

Unlike traditional instructional methods, PBL does not focus on delivering content but rather on facilitating student learning through problem-solving.

This type of learning has been shown to be particularly effective in promoting higher-order thinking skills such as critical thinking and creativity.

In addition, PBL can help to build students’ confidence and self-efficacy as they learn to tackle challenging problems.

For teachers, PBL can be a useful tool for differentiating instruction and meeting the needs of all learners.

When designed and implemented effectively, PBL can provide an engaging and rewarding learning experience for both teachers and students.

Other Useful Resources

• What is Adaptive Learning?
• What is Inquiry Based Learning?
• What is Just in Time Learning?
• What is Microlearning?
• What is Project Based Learning?
• What is Service Learning?

Do you have any experience using problem-based learning in your classroom? Share your thoughts by leaving a comment below.

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Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

Teaching Guides

Quick Links

• Services for Departments and Schools
• Examples of Online Instructional Modules

Why Every Educator Needs to Teach Problem-Solving Skills

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

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

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

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

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

Problem-Solving Skills Help Students…

   develop resilience.

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

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

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

    Set and Achieve Goals

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

  Resolve Conflicts

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

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

    Achieve Success

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

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

Problem-Solving Skills Can Be Measured and Taught

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

What Are Performance-Based Assessments?

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

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

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

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

Preview a Performance-Based Assessment

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

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

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

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

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

Explore CAE’s Problem-Solving Assessments

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

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

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

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

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

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

Ready to Get Started?

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

Center for Teaching Innovation

Resource library.

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

Problem-Based Learning

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

Why Use Problem-Based Learning?

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

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

Considerations for Using Problem-Based Learning

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

Students generally must:

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

Getting Started with Problem-Based Learning

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

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

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.

What Is Problem-Based Learning?

By Maureen Leming

Take a little bit of creativity, add a dash of innovation, and sprinkle in some critical thinking. This recipe makes for a well-rounded and engaged student who's ready to tackle life beyond the classroom. It's called Problem-Based Learning (PBL), and it teaches concepts and inspires lifelong learning at the same time.

This open-ended problem-based learning style presents students with a real-world issue and asks them to come up with a well-constructed answer. They can tap into online resources, use their previously-taught knowledge, and ask critical questions to brainstorm and present a solid solution. Unlike traditional learning, there might not be just one right answer, but the process encourages young minds to stay active and think for themselves. 

We're all about the problem-based learning approach at The Hun School of Princeton . Through this article, you'll discover why — and what it looks like in real time.

An Overview of Problem-Based Learning

Problem-based learning (PBL) is a teaching style that pushes students to become the drivers of their learning education. 

Problem-based learning uses complex, real-world issues as the classroom's subject matter, encouraging students to develop problem-solving skills and learn concepts instead of just absorbing facts. 

This can take shape in a variety of different ways. For example, a problem-based learning project could involve students pitching ideas and creating their own business plans to solve a societal need. Students could work independently or in a group to conceptualize, design, and launch their innovative product in front of classmates and community leaders.

At the Hun School of Princeton, a problem-based learning mode is offered in conjunction with course content. This approach has been  shown to help students develop critical thinking and communication skills as well as problem-solving abilities.

Aspects of Problem-Based Learning

Problem-based learning can be applied to any school subject, from social studies and literature to mathematics and science. No matter the field, a  good problem-based learning approach should embody features like :

• Challenging students to understand classroom concepts on a deeper level.
• Pushing students to make decisions they're able to defend.
• Clearly connecting current course objectives to previous courses and knowledge.
• Encouraging students to work as a group to solve the complex issue at hand.
• Engaging students to solve an open-ended problem in multiple complex stages.

Benefits of Student-Led, Problem-Based Learning

Student-led learning is one of the most empowering ways to seat students at the forefront of their own educational experience. 

It pushes students to be innovative, creative, open-minded, and logical. It also offers opportunities to collaborate with others in a hands-on, active way. 

As part of our immersive educational model, we've discovered many benefits of problem-based learning:

• Promote self-learning : As a student-centered approach, problem-based learning pushes kids to take initiative and responsibility for their own learning. As they're pushed to use research and creativity, they develop skills that will benefit them into adulthood.
• Highly engaging : Instead of sitting back, listening and taking notes, problem-based learning puts students in the driver's seat. They have to stay sharp, apply critical thinking, and think outside the box to solve problems. 
• Develop transferable skills: The abilities students develop don't just translate to one classroom or subject matter. They can be applied to a plethora of school subjects as well as life beyond, from taking leadership to solving real-world dilemmas.
• Improve teamwork abilities : Many problem-based learning projects have students collaborate with classmates to come up with a solution. This teamwork approach challenges kids to build skills like collaboration, communication, compromise, and listening.
• Encourage intrinsic rewards : With problem-based learning projects, the reward is much greater than simply an A on an assignment. Students earn the self-respect and satisfaction of knowing they've solved a riddle, created an innovative solution, or manufactured a tangible product.

Five Examples of Problem-Based Learning in Action

With a little context in mind, it's time to take a look at problem-based learning in the real world. One of the best parts of this learning style is that it's very flexible. You can adapt it to your classroom, content, and students. The following five examples are success stories of problem-based learning in action:

• Maritime discovery: Students explore maritime culture and history through visits to a nearby maritime museum. They're tasked with choosing a specific voyage, researching it, and crafting their own museum display. Throughout their studies, they'll create a captain's log, including mapping out voyages and building their own working sextant.
• Urban planning : Perfect for humanities classes, this example challenges students to observe and interview members of their community and determine the biggest local issue. They formulate practical solutions that they will then pitch to a panel of professional urban planners.
• Zoo habitats : This scientific example starts with a visit to a local zoo. Students use their observations and classroom knowledge to form teams and create research-supported habitat plans, presented to professional zoologists. 
• Codebreakers : Instead of regular math lessons, let students lead with a code-breaking problem-based learning assignment. Students take on the role of a security agent tasked with decrypting a message, coding a new one in return, and presenting their findings to the classroom.
• Financial advisors : Challenge students to step into the role of a financial advisor and decide how to spend an allotted amount of money in a way that most benefits their community. Have them present their solution and explain their reasoning to the class.

The Hun School: Problem-Based Learning in Action

The Hun School of Princeton brings problem-based learning to life in our classrooms. Our collaborative school culture places a unique emphasis on hands-on, skilled-based education. NextTerm is just one example of problem-based learning in action here at The Hun School. 

NextTerm gives students the opportunity to apply classroom knowledge to solve real-world problems on a local, national, and global scale. Take our Migration and Identity class, for example. Students in this course travel to the U.S.-Mexican border to speak directly to border patrol agents, ranchers, and immigrants in order to learn about the complex issue of migration straight from the source. Of course, this location is one of many that our students can explore. Our mandatory three-week mini-course , NextTerm , brings students beyond the campus and into a new environment, from domestic locations in Arizona, Montana, and Memphis to international locales in France and Ghana. 

At our campus in Princeton, Hun students explore a relevant issue in collaboration with each other and field experts. They could be learning about the complexity of Ghanian economics or experiencing the modern-day impact of French history. This real-world immersion gives new power to their knowledge and helps them see the link between the classroom and the world at large. As they solve problems, Hun students can develop as individuals and teammates.

Ready to learn more about The Hun School approach and see problem-based learning strategies at work?

Inquire about Hun or schedule a tour to see problem-based learning in action!

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Problem based learning: a teacher's guide

December 10, 2021

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

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

What is problem-based learning?

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

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

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

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

Philosophical Underpinnings of PBL

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

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

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

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

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

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

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

Here's a quick overview:

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

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

What are the characteristics of problem-based learning?

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

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

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

Why is Problem-based learning a significant skill?

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

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

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

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

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

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

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

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

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

What are the Benefits of Problem-Based Learning?

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

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

Embracing problem-based learning

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

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

Key Concepts and considerations for school leaders

1. Problem Based Learning (PBL)

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

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

2. Deep Learning

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

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

3. Epistemology

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

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

4. Philosophy

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

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

5. Curriculum

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

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

6. Broad and Balanced Curriculum

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

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

7. Successful Teaching Strategy

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

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

8. Positive Solution Finding

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

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

9. Real World Application

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

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

10. Creativity

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

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

11. Teamwork

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

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

12. Knowledge Transfer

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

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

13. Active Learning

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

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

14. Student Engagement

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

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

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

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

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

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

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

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

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

Where can I learn more?

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

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Problem-Based Learning

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What is Problem-Based Learning

Problem-based learning & the classroom, the problem-based learning process, problem-based learning & the common core, project example: a better community, project example: preserving appalachia, project example: make an impact.

All Toolkits

A Learning is Open toolkit written by the New Learning Institute.

Problem-based learning (PBL) challenges students to identify and examine real problems, then work together to address and solve those problems through advocacy and by mobilizing resources. Importantly, every aspect of the problem solving process involves students in real work—work that is a reflection of the range of expertise required to solve issues in the world outside of school.

While problem-based learning can use any type of problem as its basis, the approach described here is deliberately focused on local ones. Local problems allow students to have a meaningful voice, and be instrumental in a process where real, recognizable change results. It also gives students opportunities to source and interact with a variety of local experts.

In many classrooms teachers give students information and then ask them to solve problems at the culmination of a unit. Problem-based learning turns this on its head by challenging students to define the problem before finding the resources necessary to address or solve it. In this approach, teachers are facilitators: they set the context for the problem, ask questions to propel students’ interests and learning forward, help students locate necessary resources and experts, and provide multiple opportunities to critique students’ process and progress. In some cases, the teacher may identify a problem that is connected to existing curriculum; in others the teacher may assign a larger topic and challenge the students to identify a specific problem they are interested in addressing.

This approach is interdisciplinary and provides natural opportunities for integrating a variety of required content areas. Because recognizing and making relationships between content areas is a necessary part of the problem-solving process—as it is in the real world—students are building skills to prepare them for life, work, and civic participation. Problem-based learning gives students a variety of ways to address and tackle a problem. It encourages everyone to contribute and rewards different kinds of success. This builds confidence in students who have not always been successful in school. With the changing needs of today’s world, there is a growing urgency for people who are competent in a range of areas including the ability to apply critical thinking to complex problems, collaborate, network and gather resources, and communicate and persuade others to actively take up a cause.

Problem-based learning builds agency & independence

Although students work collaboratively throughout the process, applying a wide range of skills to new tasks requires them to develop their own specialties that lead to greater confidence and competency. And because the process is student-driven, students are challenged to define the problem, conduct comprehensive research, sort through multiple solutions and present the one that allows them best move forward. This reinforces a sense of self-agency and independence.

Problem-based learning promotes adaptability & flexibility

Investigating and solving problems requires students to work with many different types of people and encounter many unknowns throughout the process. These experiences help students learn to be adaptable and flexible during periods of uncertainty. From an academic standpoint, this flexible mindset is an opportunity for students to develop a range of communication aptitudes and styles. For example, in the beginning research phases, students must gather multiple perspectives and gain a clear understanding of their various audiences. As they move into the later project phases they must develop more nuanced ways to communicate with each audience, from clearly presenting information to persuasion to defending the merits of a new idea.

Problem-based learning is persistent

Educators recognize that when students are working towards a real goal they care about, they show increased investment and willingness to persist through challenges. Problem-based learning requires students to navigate many variables including the diverse personalities on a project team, the decisions and perspectives of stakeholders, challenging and rigorous content, and real world deadlines. Students will experience frustration and failure, but they will learn that working though that by trying new things will be its own reward. And this is a critical lesson that will be carried on into life and work.

Problem-based learning is civically engaged

Because problem-based learning focuses on using local issues as jumping off points it gives students a meaningful context in which to voice their opinions and take the initiative to find solutions. Problems within schools and communities also provide opportunities for students to work directly with stakeholders (i.e. the school principal or a town council member) and experts (i.e. local residents, professionals, and business owners). These local connections make it more likely that students will successfully implement some aspect of their plan and gives students firsthand experience with civic processes.

A problem well put is half solved. – John Dewey

The problem-based learning process described in this toolkit has been refined and tested through the Model Classroom Program, a project of the New Learning Institute. Educators throughout the United States participated in this program by designing, implementing, and documenting projects. The resulting problem-based learning approach provides a clear process and diverse set of tools to support problem-based learning.

The problem-based learning process can help students define problems in new ways, explore multiple perspectives, challenge their thinking, and develop the real-world skills needed for planning and carrying out a project. Beyond this, because the approach emphasizes local and community-based issues, this process develops student drive and motivation as they work towards a tangible end result with the potential to impact their community.

Make it Real

The world is full of unsolved problems and opportunities just waiting to be addressed. The Make It Real phase is about identifying a real problem within the local community, then conducting further investigation to define the problem.

Identify what you do and don’t know about the problem Brainstorm what is known about the problem. What do you know about it at the local level? Is this problem globally relevant? How? What questions would you investigate further?

Discover the problem’s root causes and impacts on the community While it’s easy to find a problem, it’s much harder to understand it. Investigate how the problem impacts different people and places. As a result of these investigations, students will gain a clearer understanding of the problem.

Make it Relevant

Problems are everywhere, but it can often be difficult to convince people that a specific problem should matter to them. The word relevant is from the Latin root meaning “to raise” or “to lift up.” To Make It Relevant, elevate the problem so that people in the community and beyond will take interest and become invested in its resolution. Make important connections in order to begin a plan to address the problem.

Field Studies

Collect as much information as possible on the problem. Conduct the kind of research experts in the field—scientists and historians—conduct. While online and library research is a good starting point, it’s important that students get out into the real world to conduct their own original research! This includes using methods such as surveys, interviews, photo and video documentation, collection of evidence (such as science related activities), and working with a variety of experts and viewpoints.

Develop an action-plan Have students analyze their field studies data and create charts, graphs, and other visual representations to understand their findings. After analyzing, students will have the information needed to develop a plan of action. Importantly, they’ll need to consider how best to meet the needs of all stakeholders, which will include a diverse community such as local businesses, community members, experts, and even the natural world.

Make an Impact

Make An Impact with a creative implementation based on the best research-supported ideas. In many cases, making an impact is about solving the problem. Sometimes it’s about addressing it, making representations to stakeholders, or presenting a possible solution for future implementation. At the most rigorous level, students will implement a project that has lasting impact on their community.

Put your plan into action See the hard work of researching and analyzing the problem pay off as students begin implementing their plans. In so doing, they’ll act as part of a team creating a product to share. Depending on the problem, purpose, and audience, their products might be anything from a website to an art installation to the planning of a community-wide event.

Share your findings and make an impact Share results with important stakeholders and the larger community. Depending on the project, this effort may include awareness campaigns, a persuasive presentation to stakeholders, an action-oriented campaign, a community-wide event, or a re-designed program. In many cases this “final” act leads to the beginning of another project!

With the Common Core implementation, teachers have found different strategies and resources to help align their practice to the standards. Indeed, many schools and districts have discovered a variety of solutions. When considering Common Core alignment, the opportunity presented by methods like problem-based learning hinges on a belief in the art of teaching and the importance of developing students’ passion and love of learning. In short, with the ultimate goal of making students college-, career-, and life-ready, it’s essential that educators put students in the driver’s seat to collaboratively solve real problems.

The Common Core ELA standards draw a portrait of a college- and career-ready student. This portrait includes characteristics such as independence, the ability to adapt communication to different audiences and purposes, the ability to comprehend and critique, appreciation for the value of evidence (when reading and when creating their own work), and the capability to make strategic use of digital media. Developing creative solutions to complex problems provides students with multiple opportunities to develop all of these skills.

Independence

Students are challenged to define the problem and conduct comprehensive research, then present solutions. This student-driven process requires students to find multiple answers and think critically about the best way to act, ultimately building confidence and independence.

Adapting Communication to Different Audiences and Purposes

In the initial research phases, students must gather multiple perspectives and gain a clear understanding of who those audiences are. As they move into the later project phases, they must communicate in a variety of ways (including informative and persuasive methods) to reach diverse audiences.

Comprehending and Critiquing

In examining multiple perspectives, students must summarize various viewpoints, addressing their strengths and critiquing their weaknesses. Furthermore, as students develop solutions they must analyze each idea for its potential success, which compels them to critique their own work in addition to the work of others.

Valuing Evidence

Collecting evidence is essential to the process, whether through visual documentation of a problem, uncovering key facts, or collecting narratives from the community.

Strategic Use of Digital Media

The use of digital media is naturally integrated throughout the entire process. The problem-based learning approach not only builds the specific 21st century skills called for by the Common Core, it also embraces practices supported by hundreds of years of educational theory. This is not the next new thing – problem-based learning is one example of how vetted best educational practices will meet the needs of a future economy and society; and, more immediately, the new Common Core Standards.

Language Arts

The Key Design Considerations for the English Language Arts standards describe an integrated literacy model in which all communication processes are closely connected. Likewise, the problem-based learning approach expects students to read, write, and speak about the issue (whether through interviews or speeches) in a variety of ways (expository, persuasive). In addition, the Key Design Considerations describe how literacy is a shared responsibility across subject areas. Because problem-based learning is rooted in real issues, these naturally connect to science content areas (environmental sciences, engineering and design, innovation and invention), social studies (community history, geography/land forms), math (including operations such as graphing, statistics, economics, and mathematical modeling), and art. As part of this interdisciplinary model, problem-based learning follows a process that touches on key ELA skill areas including research, a variety of writing styles and formats (both reading and writing in these formats), publishing, and integration of digital media.

It’s also important to note that the Common Core calls for an increase in informational and nonfiction text. This objective is easily met through examining real problems. Quite simply, informational and nonfiction text is everywhere – in newspaper articles, public surveys, government documents, etc. Very often, when reading out of context, many students struggle to work through and comprehend these types of complex texts. Because problem-based learning authentically integrates a real purpose with reading informational text, students work harder to comprehend and apply their reading.

Note: Each project has the potential to meet many additional standards. The standards outlined here are only a sampling of those addressed by this approach.

Reading Standards

CCSS.ELA-Literacy.CCRA.R.6 Assess how point of view or purpose shapes the content and style of a text. In the early phases of problem-based learning, students investigate the topic by reading a range of informational and persuasive texts, and by talking to a variety of experts and community members. As an essential component to these investigations on multiple perspectives, students must be able to understand the purpose of the text, the intended audience, and the individual’s position on the issue (if applicable).

CCSS.ELA-Literacy.CCRA.R.7 Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words. As students consider multiple perspectives on their identified problem, they naturally will seek a wide range of print materials, media resources (videos, presentations), and formats (research studies, opinion pieces). Comparing and contrasting the viewpoints of these various texts will help students shape a more holistic view of the problem.

Writing Standards

CCSS.ELA-Literacy.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence. As students analyze the problem, multiple opportunities for persuasive writing emerge. In the early project phases, students might summarize their perspective on the problem using key evidence from a variety of research (online, community polling, and discussions with experts). In the later project phases, students might develop a proposal or presentation to persuade others to change personal habits or consider a larger change in the community.

Speaking & Listening Standards

CCSS.ELA-Literacy.CCRA.SL.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively. Multiple perspectives are an essential component to any problem-based project. As students investigate, they must seek a wide range of opinions and personal stories on the issues. Furthermore, this process is collaborative. Students must trust and work with each other, they must trust and work with key experts, and, in some cases, they must convince others to collaborate with them around a shared purpose or cause.

CCSS.ELA-Literacy.CCRA.SL.5 Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations. Because each problem-based project requires students to analyze information, share their findings with others, and collaborate on a variety of levels, digital media is naturally integrated into these tasks. Students might create charts, graphs, or other illustrative/photo/video displays to communicate their research results. Students might use a variety of digital formats including graphic posters, video public service announcements (PSAs), and digital presentations to mobilize the community to their cause. Inherent to these processes is special consideration of how images, videos, and other media support key ideas and key evidence and further the effectiveness of their presentation on the intended audience.

Mathematics

Simply put, math is problem solving. Problem-based learning provides multiple opportunities for students to apply and develop their understanding of various mathematical concepts within real contexts. Through the various stages of problem-based learning, students engage in the same dispositions encouraged by the Standards for Mathematical Practice

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. Problem-based learning is all about problem solving. An essential first step is understanding the problem as deeply as possible, rather than rushing to solve it. This is a process that takes time and perseverance, both individually and in collaborative student groups.

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. As students understand and deconstruct a problem, they must begin to form solutions. As part of this process, they must have evidence (including visual and mathematical evidence) to support their position. They must also understand other perspectives to solving the problem, and they must be prepared to critique those other perspectives based on verbal and mathematical reasoning.

CCSS.Math.Practice.MP4 Model with mathematics. Throughout the process, students must analyze information and data using a variety of mathematical models. These range from charts and graphs to 3-D modeling used in science or engineering projects.

CCSS.Math.Practice.MP5 Use appropriate tools strategically. According to the Common Core Math Practices standard, “Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.” In addition to providing opportunities to use these tools, problem-based learning asks students to make effective use of digital and mobile media as they collect information, document the issue, share their findings, and mobilize others to their cause.

School Name | Big Horn Elementary Location | Big Horn, Wyoming Total Time | 1 year Subjects | English Language Arts, Social Studies, Math, Science Grade Level | 3rd Grade Number of Participants | 40 students in two classrooms

Students informed the school about the importance of recycling, developed systems to improve recycling options and implemented a school-wide recycling program that involved all students, other teachers, school principals, school custodians, and the county recycling center.

While investigating their local county history, students were challenged to recognize their role in the community and ultimately realize the importance of stewardship for the county’s land, history and culture. Students began by researching their local history through many first hand experiences including museum visits, local resident interviews and visits to places representing the current culture.

Challenged to find ways to make “A Better Community”, students chose to investigate recycling.

They conducted hands-on research to determine the need for a recycling program through a school survey, town trash pickup and visit to the local Landfill and Recycling Center.

Students then developed a proposal for a school-wide recycling program, interviewed the principal to address their concerns and began to carry out their plan.

Students designed recycling bins for each classroom and worked with school janitors to develop a plan for collection.

Students visited each classroom to distribute the recycling bins and describe how to use them. Students developed a schedule for collecting bins and sorting materials. The program continues beyond the initial school-year; students continue to expand their efforts.

School Name | Bates Middle School Location | Danville, Kentucky Total Time | 8 weeks Subjects | English Language Arts Grade Level | 6th Grade Number of Participants |25 students

Students created Project Playhouse, a live production for the local community. Audience members included community members, parents, and other students. In addition, students designed a quilt sharing Appalachian history, and recorded their work on a community website.

Appalachia has a rich culture full of unique traditions and an impressive heritage, yet many negative stereotypes persist. 6th grade students brainstormed existing stereotypes and their consequences on the community.

Students discussions led them to realize that, in their region, stereotypes were preventing people from overcoming adversity. They set about to conduct further research demonstrating the strengths of Appalachian heritage.

Students investigated Appalachian culture by working with local experts like Tammy Horn, professor at Eastern Kentucky University and specialist in Appalachian cultural traditions; taking a field trip to Logan Hubble Park to explore the natural region; talking with a “coon” hunter and other local Appalachians including quilters, cooks, artists, and writers.

Students developed a plan to curate an exhibition and live production for the local community. Finally, students connected virtually with museum expert Rebecca Kasemeyer, Associate Director of Education at the Smithsonian National Portrait Gallery to discuss exhibition design.

For their final projects students produced a series of works exhibiting Appalachian life, work, play and community structure including a quilt, a theatrical performance and a website.

Students invited the community to view their exhibit and theatrical performance.

School Name | Northwestern High School Location | Rock Hill, South Carolina Total Time | One Semester Subjects | Engineering Grade Level | High School Number of Participants | 20 students

Engineering teacher Bryan Coburn presented a scenario to his students inspired by the community’s very real drought, a drought so bad that cars could only be washed on specific days. Students identified and examined environmental issues related to water scarcity in their community.

Based on initial brainstorming, students divided into teams based on specific problems related to a water shortage. These included topics like watering gardens and lawns, watering cars, drinking water to name a few.

Based on their topic, students conducted online research on existing solutions to their specific problem.

Students analyzed their research to develop their own prototypes and plans for addressing the problem. Throughout the planning phase students received peer and teacher feedback on the viability of their prototypes, resulting in many edits before final designs were selected for creation.

Students created online portfolios showcasing their research, 3D designs, and multimedia presentations marketing their designs. Student portfolios included documentation of each stage of the design process, a design brief, decision matrix, a prototype using Autodesk Inventor 3D professional modeling tool, and a final presentation.

Students shared their presentations and portfolios in a public forum, pitching their proposed solution to a review committee consisting of local engineers from the community, the city water manager and the school principal.

Plan Your PBL Experience

Resources to help you plan.

Problem-based learning projects are inspired by students’ real world experiences and the pressing issues and concerns they want to address. Problem-based learning projects benefit teachers by increasing student motivation and engagement, while deepening knowledge and improving essential skills. In spite of the inherent value problem-based learning brings to any educational setting, planning a large project can be an overwhelming task.

Through the New Learning Institute’s Model Classroom, a range of problem-based learning planning tools have been developed and tested in a variety of educational settings. These tools make the planning process more manageable by supporting teachers in establishing the context and/or problem for a project, planning for and procuring the necessary resources for a real-world project (including community organizations, expert involvement, and tools needed for communicating, creating and sharing), and facilitating students through the project phases.

Here are some initial considerations when planning a problem-based learning project. (More detailed tips and planning tools follow.) These questions can help you determine where to begin your project planning. Once you have a clear idea, the problem-based learning planning tools will guide you through the process.

Are you starting from the curriculum? It’s probably tempting to jump in and define a problem for students based on the unit of study. And time constraints may make a teacher-defined problem necessary. If time permits, a problem-based learning project will be more successful if time is built-in for students to define a problem they’d like to address. Do this by building in topic exploration time, and then challenging students to define a problem based on their findings. Including this extra time will allow students to develop their own interests and questions about the topic, deepening engagement and ensuring that students are investigating a problem they’re invested in—all while covering curriculum requirements.

Are you starting from student interest? Perhaps your students want to solve a problem in the school, such as bullying or lack of recycling. Perhaps they’re concerned about a larger community problem, such as a contested piece of parkland that is up for development or a pollution problem in your local waterways. Starting with student interest can help ensure students’ investment and motivation. However, this starting point provides less direct navigation than existing projects or curriculum materials. When taking on a project of this nature, be sure to identify natural intersections with your curriculum. It also helps to enlist community or expert support.

Start Small – Focus on Practices as Entry Points

If you’re new to problem-based learning it makes sense to start small. Many teachers new to this approach report that starting with the smaller practices—such as integrating research methods or having students define a specific problem within a unit of study—ultimately sets the stage for larger projects and more easily leads them to implement a problem-based learning project.

Opportunities to address and solve problems are everywhere. Just look in your own backyard or schoolyard. Better yet, ask students to identify problems within the school community or based on a topic of interest within a unit of study. As you progress through the project, find natural opportunities for research and problem solving by working with the people who are affected by the issue and invested in solving it. Finally, make sure students share their work with an authentic audience who cares about the problem and its resolution.

Be Honest About Project Constraints

When you’re new to problem-based learning, the most important consideration is your project constraints. For example, perhaps you’re required to cover a designated set of standards and content. Or perhaps you have limited time for this project experience. Whatever the constraints, determine them in advance then plan backwards to determine the length and depth of your project.

Identify Intersections With Your Curriculum

Problem-based learning projects are interdisciplinary and have the ability to meet a range of standards. Identify where these intersections naturally occur with the topic students have selected, then design some activities or project requirements to ensure these content areas are covered.

Turn Limitations Into Opportunities

Many educators work in schools with pre-defined curriculum or schedule constraints that make implementing larger projects difficult. In these cases, it may help to find small windows of opportunity during the school day or after school to implement problem-based learning. For example, some teachers implement problem-based learning in special subject courses which have a more flexible curriculum. Others host afterschool “Genius Hour” programs that challenge students to explore and investigate their interests. Whatever opportunity you find, make the work highly visible to staff and parents. Make it an intention to get the school community exploring and designing possibilities of integrating these practices more holistically.

Take Risks and Model Perseverance

The problem-based learning process is messy and full of opportunities to fail, just like real life and real jobs. Many educators share that this is incredibly difficult for their students and themselves. Despite the initial letdown that comes with small failures, it’s important that students see the value in learning from failure and persevering through these challenges. Model risk taking for your students and when you make a mistake or face a challenge, welcome it with open arms by demonstrating what you’ve learned and what you’ll do differently next time around. Let students know that it’s okay to make mistakes; that mistakes are a welcome opportunity to learn and try something new.

Be Less Helpful

A key to building problem-solving and critical thinking capacities is to be less helpful. Let students figure things out on their own. In classroom implementation, teachers repeatedly share that handing over control to the students and “being less helpful” makes for a big mindshift. This shift is often described as becoming a facilitator, which means knowing when to stand back and knowing when to step-in and offer extra support.

Be Flexible

Recognize that there is no one-size-fits-all answer to any problem. Understanding this and being able to identify unique challenges will help students understand that an initial failure is just a bump in the road. Being flexible also helps students focus on the importance of process over product.

Experts are Everywhere

Experts are everywhere; their differing perspectives and expertise help bring learning to life. But think outside the box about who experts are and integrate multiple opportunities for their involvement. Parents and community members who are not often thought of as experts can speak to life, work, and lived historical experiences. Beyond that, the people usually thought of as experts—researchers, scientists, museum professionals, business professionals, university professors—are more available than many teachers think. It’s often just a matter of asking. And don’t take sole responsibility for finding experts! Seek your students’ help in identifying and securing expert or community support. And when trying to locate experts, don’t forget: students can also be experts.

Maintain a List of Your Support Networks

Some schools have brought the practice of working with the community and outside experts to scale by building databases of parent and community expertise and their interest in working with students. See if a school administrative assistant, student intern, or parent helper can take the lead in developing and maintaining this list for your school community.

Encourage Original Research

Online research is often a great starting point. It can be a way to identify a knowledge base, locate experts, and even find interest-based communities for the topic being approached. While online research is literally right at students’ fingertips, make sure your students spend time offline as well. Original research methods include student-conducted surveys, interviewing experts, and working alongside experts in the field.

This Learning is Open toolkit includes a number of tools and resources that may be helpful as you plan and reflect on your project.

Brainstorming Project Details (Google Presentation) This tool is designed to aid teachers as they brainstorm a project from a variety of starting-points. It’s a helpful tool for independent brainstorming, and would also make a useful workshop tool for teachers who are designing problem-based learning experiences.

Guide to Writing a Problem Statement (PDF) You’ve got to start somewhere. Finding—and defining—a problem is a great place to begin. This guide is a useful tool for teachers and students alike. It will walk you through the process of identifying a problem by providing inspiration on where to look. Then it will support you through the process of defining that problem clearly.

Project Planning Templates (PDF) Need a place to plan out each project phase? Use this project planner to record your ideas in one place. This template is great used alone or in tandem with the other problem-based learning tools.

Ladder of Real World Learning Experiences (PDF) Want to determine if your project is “real” enough? This ladder can be used to help teachers assess their project design based on the real world nature of the project’s learning context, type of activities, and the application of digital tools.

Digital Toolkit (Google Doc) This toolkit was developed in collaboration with teachers and continues to be a community-edited document. The toolkit provides extensive information on digital tools that can be used for planning, brainstorming, collaborating, creating, and sharing work.

Assessing student learning is a crucial part of any dynamic, nonlinear problem-based learning project. Problem-based projects have many parts to them. It’s important to understand each project as a whole as well as each individual component. This section of the toolkit will help you understand problem-based learning assessments and help you develop assessment tools for your problem-based learning experiences.

Because the subject of assessments is so complex, it may be helpful to define how it is approached here.

Portfolio-based Assessment

Each phase of problem-based learning has important tasks and outcomes associated with it. Assessing each phase of the process allows students to receive on-time feedback about their process and associated products and gives them the opportunity to refine and revise their work throughout the process.

Feedback-based Assessment

Problem-based learning emphasizes collaboration with classmates and a range of experts. Assessment should include multiple opportunities for peer feedback, teacher feedback, and expert feedback.

Assessment as a System of Interrelated Feedback Tools

These tools may include rubrics, checklists, observation, portfolios, or quizzes. Whatever the matrix of carefully selected tools, they should optimize the feedback that students receive about what and how they are learning and growing.

Assessment Tools

One way to approach developing assessment tools for your students’ specific problem-based learning project is to deconstruct the learning experience into various categories. Together, these categories make up a simple system through which students may receive feedback on their learning.

Assessing Process

Many students and teachers alike have been conditioned to emphasize and evaluate the end product. While problem-based learning projects often result in impressive end products, it’s important to emphasize each stage of the process with students.

Each phase of problem-based learning process emphasizes important skills, from research and data gathering in the early phases to problem solving, collaboration, and persuasion in the later phases. There are many opportunities to assess student understanding and skill throughout the process. The tools here provide many methods for students to self-assess their process, get feedback from peers, and get feedback from their teachers and other adults.

The Process Portfolio Tool (PDF) provides a place for students to collect their work, define their problem and goals, and reflect throughout the process. Use this as a self-assessment tool, as well as a place to organize the materials for student portfolios.

Driving & Reflection Questioning Guidelines (PDF) is a simple tool for teachers who are integrating problem-based learning into the learning process. The tool highlights the two types of questions teachers/facilitators should consider with students: driving questions and reflection questions. Driving questions push students in their thinking, challenging them to build upon ideas and try new ways to solve problems. Reflection questions ask students to reflect on a process phase once it’s complete, challenging them to think about how they think.

The Peer Feedback Guidelines (PDF) will help students frame how they provide feedback to their peers. The guide includes tips on how and when to use these guidelines in different types of forums (i.e. whole group, gallery-style, and peer-to-peer).

The Buck Institute has also developed a series of rubrics that address various project phases. Their Collaboration Rubric (PDF) can help students be better teammates. (Being an effective teammate is critical to the problem-based learning process.) Their Presentation Rubric (PDF) can help students, adult mentors, and outside experts evaluate final presentations. Final presentations are often one of the most exciting parts of a project.

Assessing Subject Matter and Content

A common concern that emerges in any problem-based learning design is whether projects are able to meet all required subject matter content targets. Because many students are required to learn specific content, there is often tension around the student-directed nature of problem-based learning. While teachers acknowledge that students go deeper into specific content during problem-based learning experiences, teachers also want to ensure that their students are meeting all content goals.

Many teachers in the New Learning Institute’s Model Classroom Program addressed this issue directly by carefully examining their curriculum requirements throughout the planning and implementation phases. Begin by planning activities and real world explorations that address core content. As the project evolves, revisit content standards to mark off and record additional standards met and create a contingency plan for those that have not been addressed.

The Buck Institute’s Rubric for Rubrics (DOC) is an excellent source for designing a rubric to fit your needs. Developing a rubric can be the most simple and effective tool for planning a project around required content targets.

Blended learning is another emerging trend that educators are moving towards as a way to both address individualized skill needs and to create space for real world project strategies, like problem-based learning. In these learning environments, students address skill acquisition through blended experiences and then apply their skills through projects and other real world applications. To learn more about blended models, visit Blend My Learning .

Assessing Mindsets and Skills

In addition to assessing process and subject matter content, it may be helpful to consider the other important mindsets and skills that the problem-based learning project experience fosters. These include persistence, problem solving, collaboration, and adaptability. While problem-based learning supports the development of a large suite of 21st century mindsets and skills, it may be helpful to focus assessments on one or two issues that are most relevant. Some helpful tools may include:

The Buck Institute offers rubrics for Critical Thinking (PDF), Collaboration (PDF), and Creativity and Innovation (PDF) that are aligned to the Common Core State Standards. These can be used as is or tailored to your specific needs.

The Character Growth Card (PDF) from the CharacterLab at Kipp is designed for school assessments more than it is for project assessment, but the list of skills and character traits are relevant to design thinking. With the inclusion of a more relevant, effective scale, these can easily be turned into a rubric, especially when paired with the Buck Institute’s Rubric for Rubrics tool.

Host a Teacher Workshop

Teachers are instrumental in sharing and spreading best practices and innovative strategies to other teachers. Once you’re confident in your conceptual and practical grasp of problem-based learning, share your knowledge and expertise with others.

The downloadable presentation decks below (PowerPoint) are adaptable tools for helping you spread the word to other educators. The presentations vary in length and depth. A 90-minute presentation introduces problem-based learning and provides a hands-on opportunity to complete an activity. The half-day and full day presentations provide in-depth opportunities to explore projects and consider their classroom applications. While this series is structured in a way that each presentation builds on the previous one, each one can also be used individually as appropriate. Each is designed to be interactive and participatory.

Getting Started with Problem-based Learning (PPT) A presentation deck for introducing educators to the Learning is Open problem-based learning process during a 90-minute peer workshop.

Dig Deeper with Problem-based Learning – Half-day (PPT) A presentation deck for training educators on the Learning is Open problem-based learning process during a half-day peer workshop.

Dig Deeper with Problem-based Learning – Full day (PPT) A presentation deck for training educators on the Learning is Open problem-based learning process during a full day peer workshop.

Related Links

Problem-based learning: detailed case studies from the model classroom.

For three years, the New Learning Institute’s Model Classroom program worked with teachers to design and implement projects. This report details the work and provides extensive case studies.

Title: Model Classroom: 3-Year Report (PDF) Type: PDF Source: New Learning Institute

Setting up Learning Experiences Using Real Problems

This New York Times Learning Blog article explores how projects can be set-up with real problems, providing many examples and suggestions for this approach.

Title: “ Guest Lesson | For Authentic Learning Start with Real Problems ” Type: Article Source: Suzie Boss. New York Times Learning Blog

Guest Lesson: Recycling as a Focus for Project-based Learning

There are many ways to set-up a project with a real world problem. This article describes the problem of recycling, providing multiple examples of student projects addressing the issue.

Title: “ Guest Lesson | Recycling as a Focus for Project-Based Learning ” Type: Article Source: Suzie Boss. New York Times Learning Blog

Problem-based Learning: Professional Development Inspires Classroom Project

This video features how the Model Classroom professional development workshop model worked in practice, challenging teachers to collaboratively problem-solve using real world places and experts. It also shows how one workshop participant used her experience to design a yearlong problem-based learning project for first-graders called the “Streamkeepers Project.”

Title: Mission Possible: the Model Classroom Type: Video Source: New Learning Institute

Problem-based Learning in an Engineering Class: Solutions to a Water Shortage

Engineering teacher Bryan Coburn used the problem of a local water shortage to inspire his students to conduct research and design solutions.

Title: “ National Project Aims to Inspire the Model Classroom ” Type: Article Source: eSchool News

Making Project-based Learning More Meaningful

This article provides great tips on how to design projects to be relevant and purposeful for students. While it addresses the larger umbrella of project-based learning, the suggestions and tips provided apply to problem-based learning.

Title: “ How to Reinvent Project-Based Learning to Make it More Meaningful ” Type: Article Source: KQED Mindshift

PBL Downloads

Guide to Writing a Problem Statement (PDF)

A walk-through guide for identifying and defining a problem.

Project Planning Templates (PDF)

A planning template for standalone use or to be used along with other problem-based learning tools.

Process Portfolio Tool (PDF)

A self-assessment tool to support students as they collect their work, define their problem and goals, and make reflections throughout the process.

More PBL Downloads

Getting Started with Problem-based Learning (PPT)

A presentation deck for introducing educators to the Project MASH problem-based learning process during a 90-minute peer workshop.

Dig Deeper with Problem-based Learning – Half-day (PPT)

A presentation deck for training educators on the PBL process during a half-day peer workshop.

Dig Deeper with Problem-based Learning – Full day (PPT)

A presentation deck for training educators on the PBL process during a full day peer workshop.

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

Written by Marcus Guido

• 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

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

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

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

3. Continuous Engagement

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

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

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

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

4. Development of Transferable Skills

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

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

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

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

5. Improvement of Teamwork and Interpersonal Skills

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

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

1. Potentially Poorer Performance on Tests

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

2. Student Unpreparedness

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

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

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

3. Teacher Unpreparedness

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

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

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

4. Time-Consuming Assessment

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

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

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

5. Varying Degrees of Relevancy and Applicability

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

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

1. Identify an Applicable Real-Life Problem

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

• Students’ shared interests

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

2. Determine the Overarching Purpose of the Activity

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

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

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

3. Create and Distribute Helpful Material

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

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

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

4. Set Goals and Expectations for Your Students

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

5. Participate

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

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

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

6. Have Students Present Ideas and Findings

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

Wrapping Up

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

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

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Problem-Solving Strategies and Obstacles

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

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

JGI / Jamie Grill / Getty Images

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• Improvement

From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

• Perceptually recognizing the problem
• Representing the problem in memory
• Considering relevant information that applies to the problem
• Identifying different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality .  Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition .  Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

National Alliance on Mental Illness. Warning signs and symptoms .

Mayer RE. Thinking, problem solving, cognition, 2nd ed .

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

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“How My ADHD Brain Solved a Problem That Stumped Everyone Else”

Imaginative, resourceful, and fast-thinking adhd brains can often solve problems that stump everyone else. here, readers share their stories of seeing the solution everyone else missed..

When solving a particularly sticky problem, it helps if your brain is adept at divergent thinking — that is, generating original ideas by considering diverse and unprecedented possibilities.

Unsurprisingly, neurodivergent brains tend to be aces at divergent thinking. Folks with ADHD tend to think fast, dream big, and innovate solutions that are totally unexpected and brilliant, making them perfect people to turn to when there’s a problem that stumps everyone else.

From software snafus to construction conundrums, tough problems are no match for ADHD brains. Here, ADDitude readers share their problem-solving success stories .

“When I was buying a new mattress, the sales person told me I needed to rotate it top to bottom, once a month. I’m a single mum and having to handle a double mattress on my own didn’t sound fun. I thought for a second and said, ‘Can’t I just rotate my body instead of the mattress?’ The person looked at me for a second and said “Wow, actually yeah. No one has ever suggested that before .” —Emma, Scotland

“I came up with this crazy idea to design costumes for my colleagues and I to wear to a presentation for the higher-ups that really made this project idea hit home. It was fun and effective .” —Jen, Ontario

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Exploring the Effect of Mathematics Skills on Student Performance in Physics Problem-Solving: A Structural Equation Modeling Analysis

• Open access
• Published: 07 October 2024

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• Tong Tong 1 ,
• Feipeng Pi 1 ,
• Siyan Zheng 1 ,
• Yi Zhong 1 ,
• Xiaochun Lin 1 &
• Yajun Wei   ORCID: orcid.org/0000-0003-4871-9682 1  

Students’ success in physics problem-solving extends beyond conceptual knowledge of physics, relying significantly on their mathematics skills. Understanding the specific contributions of different mathematics skills to physics problem-solving can offer valuable insights for enhancing physics education. Yet such studies are rare, particularly at the high school level. This study addresses the underexplored area of this topic in secondary education by investigating the associations between physics problem-solving performance using a robust methodological framework. We applied exploratory factor analysis (EFA) to identify latent sub-mathmetics skills relevant to physics problem-solving and employed structural equation modeling (SEM) to examine the causal impact of these skills on students’ performance in physics. The study analyzed data from a municipal-wide assessment involving 1,878 grade 12 students in Southern China. The results demonstrate that mathematics skills impacting high school students’ physics problem-solving performance can be categorized into two sub skills, algebraic skills and geometric skills. It also indicates that algebraic skills have a stronger direct effect on physics problem-solving performance compared to geometric skills in high school setting. These findings suggest that integrating focused algebraic training within physics education can significantly improve student outcomes in STEM fields. We recommend that educators design curricula and instructional strategies that emphasize the development of algebraic skills necessary for solving complex physics problems. Additionally, these findings have important implications for policymakers, who should consider integrating targeted mathematics training within physics curricula to foster interdisciplinary learning and better prepare students for challenges in STEM education.

Avoid common mistakes on your manuscript.

Introduction

In the landscape of STEM education, mathematics is often recognized as the foundational pillar that supports scientific learning (Dierdorp et al., 2014 ; Nakakoji & Wilson, 2018 ; Turşucu et al., 2020 ). For example, physics problem-solving is not merely a function of conceptual understanding; it critically depends on students’ ability to apply mathematical principles to analyze and interpret physical phenomena. As such, mathematics serves as a crucial tool in navigating the quantitative aspects of problem-solving in physics (Dierdorp et al., 2014 ). Despite the well-established interdependence of these disciplines, there remains a gap in our understanding of how specific mathematics skills—particularly geometric and algebraic skills—contribute to physics problem-solving performance, particularly at the secondary school level.

Many studies have explored the impact of mathematics learning in science education, particularly in physics education. These studies often highlight a strong correlation between students’ mathematics skills and their performance in physics (Arbabifar, 2021 ; Dehipawala et al., 2014 ; Matthews et al., 2009 ). Yet, further study on this topic is necessary for two major reasons. Firstly, much of this previous research has focused on university education settings but research findings at the university level might not automatically apply to a high school setting. (Jackson & Johnson, 2013 ; Meltzer, 2002 ; Rylands & Coady, 2009 ). The first research question in this study is to check if such a strong correlation, well documented at the college level, is evident among high school students, who are known to differ from adults in terms of factors influencing academic outcomes (Breitwieser & Brod, 2020 ; Dunlosky et al., 2013 ; Schneider & Preckel, 2017 ). Secondly, while previous research has documented correlations between general mathematics ability and science problem-solving, the specific roles of distinct mathematics skills—such as geometric and algebraic skills—remain underexplored, particularly in the context of secondary education. In other words, the second research question seeks to determine which skill, algebraic or geometric, has a higher impact, or if their impact levels are the same.

Using data from a municipal-wide assessment in Southern China with 1,878 grade 12 students, we employ exploratory factor analysis (EFA) and structural equation modeling (SEM) to evaluate the contributions of these skills. Our findings indicate that algebraic skills have a more significant impact on physics problem-solving than geometric skills, highlighting the importance of incorporating targeted mathematics instruction within physics curricula. This approach can better equip students with the tools necessary to tackle complex scientific problems, ultimately enhancing STEM education outcomes.

Literature Review

The relationship between mathematics and physics problem-solving in secondary education.

Physics, being an elemental science, inherently involves problem-solving, which plays a crucial role in evaluating students’ knowledge and skills in physics education (Reddy & Panacharoensawad, 2017 ; Ince, 2018 ). Successful problem-solving in physics is not solely dependent on students’ understanding of physics concepts but also significantly relies on their ability to apply mathematics principles (Redish & Kuo, 2015 ). Mathematics provides the language and tools necessary for the precise expression and application of physics laws and relationships, effectively bridging the gap between physics cognition and practical application (Bing & Redish, 2009 ; Franestian, 2020 ). In this way, mathematics plays a vital role in enabling students to navigate the quantitative aspects of physics problem-solving, making it indispensable for achieving success in this field.

Prior studies have established that students’ mathematics skills are closely associated with their performance in physics problem-solving. For example, Ogunleye ( 2011 ) identified poor mathematics proficiency as a major obstacle to students’ ability to solve physics problems, while Panorkou and Germia ( 2021 ) demonstrated that strong mathematics skills support a deeper understanding of physical phenomena, such as gravity, and enhance problem-solving abilities in this domain. These studies underscore the importance of integrating mathematics instruction with physics education to improve students’ problem-solving skills and overall academic performance.

However, most research exploring the relationship between mathematics and physics has been conducted at the post-secondary level, focusing primarily on college students (Jackson & Johnson, 2013 ; Meltzer, 2002 ; Rylands & Coady, 2009 ). These studies have often highlighted correlations between general mathematics ability and success in physics courses (Arbabifar, 2021 ; Dehipawala et al., 2014 ; Matthews et al., 2009 ). While valuable, the findings from these studies may not be directly applicable to high school students, who differ from college students in significant ways (Talsma et al., 2018a ; Schneider & Preckel, 2017 ).

Teenagers are distinct from adult learners in several respects, including their cognitive processes, learning habits, emotional development, and self-efficacy (Richardson et al., 2012 ; Talsma et al., 2018a ). Also, teenager’s approach to learning and problem-solving is often less mature and more variable compared to that of college students, who have generally developed more advanced reasoning skills and learning habits (Schneider & Preckel, 2017 ). Consequently, the strategies and educational interventions that are effective for college students may not necessarily be effective for teenagers. This underscores the importance of studying the relationship between mathematics skills and physics problem-solving specifically within the high school context. By focusing on high school students, this study aims to provide insights that are directly relevant to secondary education, helping to bridge the gap between theory and practice in STEM education at this crucial stage of development.

Latent Mathematics Skills Needed for Physics Problem-Solving

When studying problem-solving tasks in physics, researchers and practitioners have identified several latent mathematics skills necessary for successfully solving these tasks (Awodun et al., 2013 ; Panorkou & Germia, 2021 ; Redish, 2023 ; Rebello et al., 2007 ). Awodun et al. ( 2013 ) explored the mathematics skills required to tackle physics questions among upper secondary school students, identifying six key skills: computation skills, geometry skills, graph and table interpretation skills, probability and statistics skills, algebraic skills, and measurement skills. Similarly, Daniel et al. ( 2020 ) concluded that deficiencies in analytical skills, algebraic processing skills, geometric skills, computational skills, as well as table and graph interpretation skills, were the primary reasons behind students’ poor performance in physics. Despite the recognition of these various sub-mathematics skills, little effort has been made to determine the relative importance of these skills. This gap in the literature calls for a deeper investigation into which sub-mathematics skill plays a more critical role in improving students’ physics problem-solving abilities.

Algebraic Skills and Physics Problem-Solving

Algebra is a fundamental component of mathematics and serves as a powerful tool in physics (Monk, 1994 ). Algebraic skills in mathematics education include the ability to manipulate variables, solve equations, create formulas, work with functions, and apply these concepts to solve problems (Drijvers, 2011 ). Physics problem-solving benefits from the correct understanding and proper use of algebraic skills (Erdoğan et al., 2014 ). Research has shown that students with strong algebraic skills are more likely to succeed in physics problem-solving compared to those who struggle with algebra (Kanderakis, 2016 ; Rebello et al., 2007 ). Awodun et al. ( 2013 ) also found a positive impact of algebraic skills on problem-solving performance in secondary school physics.

Geometric Skills and Physics Problem-Solving

Geometric skills involve the ability to recognize and work with geometric shapes, visualize spatial relationships, sketch images, and apply geometric concepts to solve problems (Astuti et al., 2018 ). According to Hoffer ( 1981 ), geometric skills in mathematics encompass five types: visual skills, language skills, drawing skills, logical skills, and applied skills. These skills are essential in various physics problem-solving scenarios, such as analyzing forces, understanding light reflection and refraction, and evaluating projectile motion. The application of geometric skills is common in many areas of physics, and mastering these skills is vital for solving problems in this subject. Studies have consistently shown that geometric skills positively impact students’ performance in physics problem-solving at the secondary school level (Basson, 2002 ; Daniel et al., 2020 ).

Other Skills and Physics Problem-Solving

In addition to algebraic and geometric skills, graph and table interpretation skills, as well as probability and statistics skills, have been found to be closely related to students’ performance in physics (Awodun et al., 2013 ; Daniel et al., 2020 ). For instance, when analyzing a velocity-time graph, a student who cannot interpret the graph will struggle to determine whether an object is accelerating, decelerating, or moving at a constant speed. Research has consistently shown that graph and table interpretation plays a significant role in physics performance (McKenzie & Padilla, 1986 ; Redish, 2023 ). Moreover, probability and statistics skills are closely tied to logical thinking in mathematics and encompass five key competencies: understanding probability concepts, applying these concepts, calculating probability values, interpreting these values accurately, and visualizing and communicating probabilities and their implications (Puspitasari et al., 2019 ; Tiro et al., 2021 ). These skills are particularly relevant in the thermodynamics of physics; for example, students use them to grasp concepts like entropy and the second law from a microscopic perspective (Malgieri et al., 2016 ).

Research Questions

In summary, previous research has identified various sub-mathematics skills required for high performance in physics problem-solving, but little effort has been made to explore which specific sub-mathemtaics skill plays a more significant role in enhancing physics learning. Furthermore, most studies examining the relationship between mathematics and physics problem-solving have focused on college students, leaving a gap in understanding how these skills function among high school students, who differ significantly from adult learners.

This study aims to investigate the causal relationship between mathematics and physics problem-solving in upper secondary school physics education. Based on the data of a large scale assessment, we use exploratory factor analysis (EFA) to identify the latent mathematics skills involved in solving physics problems. Additionally, we employ structural equation modeling (SEM) to evaluate the relative strength of specific sub-mathematics skills’ impact on physics problem-solving for high school students. The specific research questions are as follows:

Q1: Does the association between students’ mathematics skills and physics problem-solving performance also hold in a high school setting?

Q2: What sub-mathematics skill plays a more important role in enhancing high school students’ physics problem-solving performance?

Methodology

The methodology of this study involved analyzing data from a municipal-wide assessment of 1,878 grade 12 students in Southern China, who were in the final year of a non-calculus-based physics course. The assessment included physics and mathematics tests, with the physics test comprising multiple-choice, blank-filling, and open-ended items, and the mathematics test featuring similar formats. Data analysis proceeded through three stages: assessing internal consistency and data collinearity, conducting exploratory factor analysis (EFA) to identify latent mathematics skills, and applying structural equation modeling (SEM) to explore the causal relationships between these skills and students’ performance in physics problem-solving.

The data were obtained from a well-developed municipal-wide assessment for evaluating upper secondary school students’ knowledge and problem-solving skills in physics. At the time of the test, the students were in the last year (grade 12) of a three-year-long physics course at upper secondary schools in a city in Southern China. The course, which is non-calculus-based, covers classical mechanics, electromagnetism, optics, and thermal physics, thereby preparing students for further studies in STEM subjects at university. These topics of physics are all covered in the first two years of the course, and the third year is solely dedicated to revision and training in physics problem-solving.

1,900 students were in grade 12 of the school, but 22 (1.16%) didn’t participate in either the physics or mathematics test of the assessment. Excluding these non-participants resulted in a valid sample size of 1,878. The data obtained from the school administration was anonymized, containing only a temporary test taker’s identification number (not real ID number) and performance scores on each item. The data did not contain students’ detailed demographic information, but the participants were nearly all aged 17 or 18 years, in accordance with the country’s strict age requirement for enrollment in K-12 education.

Instruments

The municipal-wide high school students’ knowledge and problem-solving skills physics assessment was structured with 10 multiple-choice items (7 single-correct-choice items, 3 multiple-correct-choice items), 2 blank-filling items, and 3 open-ended items. The assessment was a mock exam of the college entrance examination, with its content constructed by a panel of physics education experts and reviewed and validated by another team of experts independently. Table  1 lists the measurement indicators of students’ physics knowledge for each item in this test.

We scored the items dichotomously or polytomously based on the item formats. For the single-correct-choice items, which are multiple-choice problems with only one correct solution out of four options, students received a score of 1 if they answered the item correctly and a score of 0 otherwise. For the multiple-correct-choice items, which are multiple-choice problems with one to four possible correct solutions out of the list of four, students received a score of 2 if they picked all the correct options, a score of 1 if they picked some of the correct options, and a score of 0 if they picked any incorrect options. For the blank-filling items and open-ended items, we assigned a score of 1 to students whose item scores were higher than the average item score and a score of 0 to the rest, due to the discrete distribution. The Cronbach’s alpha of the 15 items ranged from 0.80 to 0.85 (Table  1 ). The overall Cronbach’s alpha was 0.83, indicating the high reliability of the physics assessment.

The municipal-wide upper secondary school students’ mathematics skills assessment was structured with 11 multiple-choice items (8 single-correct-choice items, 3 multiple-correct-choice items), 3 blank-filling items, and 5 open-ended items. They were scored in the same way as the physics test. We scaled the scores of the students’ mathematics skills assessment to make the average assessment scores equal to 0 due to the discrete distribution. The overall Cronbach’s alpha of the assessment was 0.74, indicating the acceptable reliability of the physics assessment.

Both the physics and mathematics assessments were part of a municipal-wide mock exam for the national college entrance examination, which is taken very seriously. All problem items were composed by a panel of six science and mathematics education experts, including university professors and experienced secondary school teachers, and were independently reviewed by another panel of such experts. The students took the 120-minute mathematics assessment on April 22, 2024, and the 75-minute physics assessment one day later.

Data Analysis

Almost all grade 12 students in the megalopolis municipal, with a population of 15 million, attend this municipal-wide mock exam in April 2024. Our data is extracted from one district of the municipality. This district has 1.5 million residents, with 1,900 grade 12 students who take science in high school. Among those 1,900 students, 1,878 successfully took both the mathematics and physics assessments. All of the 1,878 data points are included in this study.

To answer the research questions, we implemented three stages to analyze the data. Firstly, we computed the covariances across items to evaluate the items’ internal consistency and data collinearity issues. Then, exploratory factor analysis (EFA) with eigenvalues and model fit was conducted to explore the latent factors of the mathematics skills in solving physics assessment items. The third stage was to conduct structural equation modeling (SEM) to estimate the causal relationships between students’ mathematics skills and their performance in physics problem-solving, given the latent mathematics skills Figure  1 .

Procedure of data analysis

Exploring and Extracting Latent Factors

Before implementing the EFA, we initially assessed the assumption of sphericity through Bartlett’s test (Bartlett, 1954 ) to ensure that the correlation matrix was not random and evaluated sampling adequacy by the Kaiser-Meyer-Olkin (KMO test; Kaiser, 1974 ) measure. According to widely accepted evaluation criteria (Khine et al., 2018 ; Tabachnick & Fidell, 2007 ), EFA can proceed without violating assumptions or inflating estimated bias when the p-value of Bartlett’s test is less than 0.05, and the KMO test is greater than 0.5.

Following the assumption evaluation, we structured EFA using the weighted least squares estimation and the promax oblique rotation (Hendrickson & White, 1964 ), as we assumed the latent factors were correlated, and implemented three criteria to determine the number of latent factors. One criterion was based on the mathematical rules, as recommended by Cliff ( 1988 ), indicating that the eigenvalues should be larger than 1. This criterion was conducted using the ‘psych’ package (Revelle, 2023 ) in R version 4.3.1.

The second criterion was based on the EFA model fit information, which included the chi-square test, Tucker-Lewis Index (TLI; Tucker & Lewis, 1973 ), Bentler Comparative Fit Index (CFI; Bentler, 1990 ), Root Mean Square Error of Approximation (RMSEA; Steiger, 1990 ), and standardized root mean square residual (SRMR). We extracted the number of latent factors when the chi-square p-value was smaller than 0.05, the CFI and TLI exceeded 0.95 (Hu & Bentler, 1999 ), and the RMSEA and SRMR were lower than 0.05 (Browne & Cudeck, 1993 ). These model fit indexes indicate a close fit of a model to data (Kline, 2016 ). This analysis was conducted using the ‘lavaan’ package (Rosseel, 2012 ) in R version 4.3.1.

After extracting the number of factors, we named the latent factors based on the EFA factor loading outcomes. Additionally, items with factor loadings no less than 0.40 were selected as having a moderate or even strong association between the item and the latent factor (Stevens, 1992 ).

Estimating Causal Relationships via SEM

The SEM was structured in two parts. The first part involved the confirmatory factor analysis (CFA), which included a minimum of three items per factor to ensure the identification of model performance (Kline, 2016 ). The second part involved the structural part, including the path analysis for the direct effects in light of our hypothesis in the current study.

The CFA was conducted using the ‘lavaan’ package (Rosseel, 2012 ) with the method of maximum likelihood estimation. The model fit was evaluated by the chi-square test, Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Standardized Root Mean Square Residual (SRMR), and Root Mean Square Error of Approximation (RMSEA). The CFI and TLI exceeded 0.95 (Hu & Bentler, 1999 ), while the SRMR was below 0.05 (Hu & Bentler, 1999 ). Additionally, RMSEA was lower than 0.05 (Browne & Cudeck, 1993 ), indicating a perfect fit (Kline, 2016 ).

For the path analysis, we estimated the direct effect of students’ mathematics skills on each extracted latent factor. The number of paths in the structural part was the same as the number of extracted factors.

Covariances across Items

Table  2 shows the correlation between physics items and the mathematics assessment, none of which is smaller than 0.01. Therefore, we did not rule out any physics items in the following exploratory factor analysis.

Exploratory Factor Analysis

The result of Bartlett’s test of sphericity was significant, with a p -value smaller than 0.001 ( \(\:{\chi\:}^{2}\) (105) = 5419.5514, p  < .001) and the KMO test was 0.93. Both Bartlett’s test and the Kaiser-Meyer-Olkin measure indicated that the data were appropriate to proceed with the EFA.

Figure  2 is the scree plot visualizing the eigenvalues outcomes. The eigenvalues-greater-than-1 criterion suggested extracting two latent factors. The EFA model fit information with two factors, as shown in Table  3 , indicated that its TLI and CFI were larger than 0.950, and the RMSEA and SRMR were smaller than 0.050, all of which were acceptable values, indicating the extraction of two latent factors Figure  3 .

Scree plot of eigenvalues

Structural model with standardized estimates Note MS: Mathematics Skill; Gmt: Geometric Skills; Alg: Algebraic Skills

Given the most salient manifest variables that latent factors have in common (Watkins, 2018 ), the two factors were named as follows: Factor 1: Geometric Skills with three items and Factor 2: Algebraic Skills with seven items.

Structural Equation Modeling Results

The final fitted structural model had a perfect fit ( \(\:{\chi\:}^{2}\) (52) = 71.969, p  < .05, CFI = 0.992, TLI = 0.991 SRMR = 0.039, and RMSEA = 0.014), as shown in Fig.  2 .

Table  5 lists the standardized factor loadings in the CFA part. The factor loadings of the 11 items ranged between 0.62 and 0.88, all of which were above 0.50. Each item had a statistically significant p -value smaller than 0.001.

In the structural part, there were two paths: students’ mathematics skills to algebraic skills in physics problem-solving and students’ mathematics skills to geometric skills in physics problem-solving. The standardized coefficient of the path from mathematics skills to the item responses involving algebraic skills was 0.797, indicating that students’ achievement increases by 0.797 scores in this category of physics problem-solving items as their mathematics skills increase by one unit. Likewise, the standardized coefficient of the path from mathematics skills to the item responses involving geometric skills was 0.737, indicating that students’ achievement increases by 0.737 scores in this category of physics problem-solving items as their mathematics skills increase by one unit.

Interpretation of the Results

This study aimed to investigate the causal effects of students’ mathematics skills on their physics problem-solving performance at the upper secondary school level. To achieve this, we employed Exploratory Factor Analysis (EFA) to identify the latent mathematics skills underlying physics problem-solving tasks. Subsequently, Structural Equation Modeling (SEM) was utilized to assess how these identified skills impacted students’ performance across different types of problem-solving tasks.

This study reaffirms the strong relationship between mathematics skills and physics problem-solving performance observed in prior research. Our observation of the strong association between mathematics scores and physics scores in 1,878 students is consistent with many previous studies. For example, Arbabifar ( 2021 ), Dehipawala et al. ( 2014 ), and Matthews et al. ( 2009 ) highlighted correlations between general mathematics ability and success in physics courses among college students. Similarly, Ogunleye ( 2011 ) identified poor mathematics proficiency as a major obstacle in students’ ability to solve physics problems, while Panorkou and Germia ( 2021 ) demonstrated that strong mathematics skills support a deeper understanding of physical phenomena, such as gravity, and enhance problem-solving abilities in this domain. Our research confirms that mathematics skills significantly influence students’ ability to solve physics problems.

Compared to college and university, physics education is sparsely researched at high school level (Kanim & Cid, 2020 ). Yet previous studies suggest that teaching methods and educational research findings that are effective for college students might not automatically apply to teenagers, highlighting the need for more empirical studies to understand their learning (Breitwieser & Brod, 2020 ; Dunlosky et al., 2013 ; Schneider & Preckel, 2017 ). Our results from this group effectively bridge this critical gap in this topic of exploring the association between mathematics skills and physics problem solving, delivering insights essential for developing age-appropriate teaching strategies. Along with few studies targeted at teenage learners (Roorda, 2015 ; Turşucu, 2020), we extend this association from college students to high school teenage learners.

Awodun et al. ( 2013 ) explored the underlying mathematics skills required to tackle physics questions among upper secondary school students, identifying six key skills: computation skills, geometry skills, graph and table interpretation skills, probability and statistics skills, algebraic skills, and measurement skills. Similarly, Daniel et al. ( 2020 ) concluded that deficiencies in analytical skills, algebraic processing skills, geometric skills, computational skills, as well as table and graph interpretation skills, were the primary reasons behind students’ poor performance in physics. Unlike these studies, our result indicates that mathematics skills influencing high school physics problem solving fall into only two categories, algebraic and geometric skills. We suggest this is because some other skills considered in those previous studies might potentially be included in either algebraic skills or geometric skills. For instance, computational skills may mainly be included in algebraic skills and graph interpretation skills may mainly fall into geometric skills. Also, some skills, such as analytical skill, are not subject-specific skill, as it doesn’t need mathematics conceptual knowledge and it is also an essential skill for other subjects (Powers & Enright, 1987 ; Bravo et al., 2016 ; Wei, 2024 ).

Furthermore, despite previous research has identified various sub-mathematics skills required for high performance in physics (Panorkou & Germia, 2021 ; Redish, 2023 ; Rebello et al., 2007 ), little effort has been made to explore which specific sub-mathematics skill plays a more significant role in enhancing physics learning. Our findings clearly suggest the more critical role of algebraic skills in enhancing physics problem-solving abilities among high school students. This aspect of the research provides actionable insights that can guide curriculum developers and educators in refining their teaching strategies and educational content.

Contribution to the Literature

The contributions of this research to the current body of literature in this field are twofold. Firstly, by extending the exploration to high school students, this study enriches the sparse body of high school-level research (Kanim & Cid, 2020 ), providing robust, data-driven evidence. Secondly, the study introduces an empirical comparison of sub-mathematics skills, marking the first time such a data-driven analysis of algebraic versus geometric skills has been conducted, to the best of our knowledge.

In response to our research questions, the evidence clearly shows that an association between students’ mathematics skills and physics problem-solving performance does indeed hold in a high school setting. Furthermore, the evidence decisively indicates that algebraic skills are more critical than geometric skills for solving physics problems, underscoring the need for a curricular focus on enhancing algebraic training. These insights should compel policymakers to advocate for educational reforms that prioritize these skills. Educators and practitioners can leverage our findings to develop targeted instructional strategies, thereby better equipping students to tackle complex physics problems effectively.

Teaching Strategies

These results are particularly relevant when considering the implications for educational practices. Given the pronounced impact of algebraic skills on physics problem-solving, it is imperative that physics curricula include targeted algebra training. By systematically integrating algebraic problem-solving techniques into physics instruction, educators can better prepare students to navigate complex analytical tasks, thereby enhancing their overall performance. We suggest that educators adopt targeted strategies to enhance students’ problem-solving proficiency. Initially, educators should identify the specific mathematics skills required for each physics problem-solving task. They can then focus on strengthening these skills, helping students translate physics problems into mathematical terms and apply these concepts to various physical scenarios. Such preparation allows students to better understand and tackle problem-solving tasks by effectively using their knowledge of both mathematics and science.

Furthermore, our findings indicate that mathematics skills significantly influence students’ success in physics problem-solving, particularly when tasks demand strong algebraic skills. For instance, when addressing Newton’s second law of motion, students who possess a strong foundation in algebraic manipulation—such as solving equations involving multiple variables—are significantly more likely to succeed. This illustrates the practical necessity of embedding algebraic training within the physics curriculum.

To foster a practical integration of physics and mathematics, we propose that educators and policymakers implement a coordinated teaching approach, similar to the “Mathematical Methods in Physics” format (Arbabifar, 2021 ). Such an approach would involve collaboration between mathematics and physics teachers to cover problem-solving tasks. For instance, in a scenario involving vehicle pursuits, mathematics teachers would focus on algebra, geometry, and data interpretation, while physics teachers would concentrate on the relevant physical principles, such as Newton’s laws. This collaborative teaching ensures that students receive a unified and coherent learning experience, enhancing their understanding and ability to apply mathematics skills in physics contexts.

Additionally, we recommend enhancing communication and collaboration between mathematics and physics teachers to develop integrated teaching strategies. By forming instructional groups, educators can share insights and strategies for translating physics problems into mathematical language and vice versa. This approach not only helps teachers address their instructional challenges but also enriches the student learning experience by linking theoretical concepts with practical applications.

Policy Making

A review of education policies across various countries reveals a universal emphasis on the role of mathematics in science education (Department for Education, 2015 ; NGSS Lead States, 2013 ; MOE of PRC, 2020 ). For example, the Principles and Standards for School Mathematics highlight the necessity of mathematics education in preparing students for careers as engineers, scientists, and other related professions (NCTM, 2000 ). Similarly, the Next Generation Science Standards advocate for integrating rigorous scientific content with the mathematics skills commonly used by scientists and engineers (NGSS Lead States, 2013 ). This interdisciplinary approach is crucial for students’ overall development and equips them for future academic and professional challenges.

In light of these insights and the findings of this research, we present specific recommendations for policymakers. Firstly, to better equip students for interdisciplinary challenges, we recommend the establishment of integrated mathematics and physics curricula. This approach ensures that students can apply mathematics skills in physics contexts with greater efficacy, reflecting the interconnected nature of these disciplines in both academic and professional environments.

Secondly, teacher training programs for physics educators should focus on enhancing mathematics skills, especially algebraic skills. This aligns with Turşucu et al. ( 2020 ), who suggest that the ability to explain fundamental mathematics should be a required competency for physics teachers. Accordingly, our study recommends a concentrated effort on developing algebraic skills in pre-service physics teachers to better prepare them for teaching complex physics problems.

Implementing these strategies promises significant improvements in secondary school students’ abilities to solve physics problems, ultimately leading to enhanced outcomes in physics education and laying a robust foundation for their future endeavors.

Limitations and Future Research

While this study provides valuable insight into secondary school students’ mathematics skills and physics problem-solving performance, with practical implications for both practitioners and policymakers, it is important to acknowledge several limitations.

Firstly, the physics problem-solving tasks in our empirical data encompassed multiple fields of physics knowledge, such as mechanics, thermodynamics, kinematics, and electromagnetism, rather than focusing on a single field. Each field may have varying degrees of association with mathematics skills, given the different latent mathematics skills involved in problem-solving tasks. In this study, we treated all physics knowledge as a whole to investigate the relationship between students’ problem-solving achievement and their mathematics skills, due to the limited number of items in our empirical data. Therefore, we suggest further refining the categorization of physics knowledge to gain a more comprehensive understanding of the specific impact of mathematics skills in different fields of physics, providing more targeted guidance for teaching practice.

Secondly, the sample of the present study was limited to one city in southern China with a similar ethnic background. This limits our ability to generalize the findings to a broader population with different ethnic backgrounds or in other settings, such as rural schools. However, the problem-solving items in the empirical research are commonly included in the national physics assessment for upper secondary school students. Given that our sample was large enough to meet the requirements of a normal distribution, the identified sub-mathematics skills for physics problem-solving tasks are still informative. The conclusions of the current study, to some extent, provide valuable insights into teaching problem-solving in physics education in upper secondary schools. In future research, we recommend that researchers collect samples across multiple regions to draw more comprehensive and generalizable conclusions. Collecting samples from different countries for comparison, and combining the education policies of different countries for discussion, may help to draw more in-depth conclusions and promote the development of science education.

Thirdly, the reliance on quantitative data may overlook the nuanced interplay between students’ cognitive, motivational, and contextual factors that can affect their performance in physics problem-solving. Qualitative data could enrich our understanding of how students apply their mathematics skills in physics contexts and the challenges they face in real-time problem-solving scenarios.

Lastly, the study’s focus on the causal relationships between mathematics skills and physics problem-solving may not fully capture the dynamic and iterative processes that students undergo when learning and applying these skills. Future studies could benefit from longitudinal designs that track changes in students’ problem-solving capabilities and mathematics skills development over time, offering deeper insights into the learning trajectories and educational interventions that are most effective.

Although the current study delved into the relationship between upper secondary school students’ mathematics skills and their performance in solving physics problems, the conclusions have the potential to be applied more broadly to science education. Other subjects within science, such as chemistry and biology, are also closely linked with mathematics. For example, in chemistry, mathematics is used to describe the relationship between conductivity and concentration (Shang, 2021 ). Secondary school chemistry courses covering stoichiometry problems, Avogadro’s number, balancing equations, and other areas require a robust understanding of mathematics (Weisman, 1981 ). In biology, mathematical methods are employed to understand the diversity and complexity of living systems (Kauffman, 1993 ). As biology and biotechnology continue to evolve, there is an increasing demand for quantitative skills (Gross, 2004 ; Karsai & Kampis, 2010 ).

This study’s methodological lens, focusing on the causal relationships facilitated by quantitative analysis through EFA and SEM, could serve as a model for similar research in other disciplines. By applying this proven approach, researchers and practitioners in fields like chemistry and biology could further investigate the pivotal role that mathematics plays in understanding and solving complex scientific problems. Therefore, we recommend that researchers and practitioners in other fields of science who share our research goal explore in-depth the causal relationship between mathematics ability and student achievement in problem-solving, considering various mathematics skills.

Conclusions and Implications

While prior studies exploring the relationship between mathematics skills and physics problem-solving at the high school level exist, they are rarer compared to those conducted at the college level. This study enriches this modest corpus by providing robust, data-driven evidence that highlights the distinct roles of algebraic and geometric skills in secondary physics education. Our analysis of the mathematics and physics assessment of 1878 grade 12 students using EFA and SEM demonstrates that mathematics skills needed for physics problem-solving in high school settings can be categorized into two sub-skills, with algebraic skills having a much more pronounced impact on physics problem-solving capabilities than geometric skills. These findings not only corroborate but also deepen our understanding of science education at this crucial academic stage.

Implications for Educational Practice

The significant influence of algebraic skills on physics problem-solving uncovered in this study suggests a need for strategic educational approaches. Physics educators are encouraged to integrate focused algebra training within their curricula, which could include the development of specific modules or interactive workshops that emphasize the application of algebraic concepts to physical problems. Such targeted training can equip students with the necessary tools to tackle complex scientific problems, thereby enhancing their overall academic success in STEM fields.

Policy Recommendations

This research underscores the importance of supportive educational policies that advocate for the integration of mathematics and physics education at the high school level. Policymakers should consider initiatives that fund and develop resources facilitating such integrated curricula. These policies could significantly contribute to creating a cohesive learning environment that effectively prepares students for advanced studies and careers in STEM disciplines.

Conclusions

This study significantly contributes to the limited but growing body of literature on high school students’ mathematics skills and their effect on physics problem-solving. By offering concrete, data-backed insights into the specific mathematics skills that most influence physics problem-solving success, our research provides a valuable foundation for further studies and informs both current educational practices and policy-making in STEM education. As STEM fields continue to evolve, the need for robust educational frameworks that prepare students through an interdisciplinary approach becomes increasingly crucial. The insights gained from this study not only contribute to academic discourse but also have practical implications for shaping future educational practices and policies.

Data availability

The raw data supporting the conclusions of this article will be made available by the authors on reasonable request.

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Tong, T., Pi, F., Zheng, S. et al. Exploring the Effect of Mathematics Skills on Student Performance in Physics Problem-Solving: A Structural Equation Modeling Analysis. Res Sci Educ (2024). https://doi.org/10.1007/s11165-024-10201-5

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