problem solving as a teaching and learning strategy

• Faculty & Staff

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.

Center for Teaching

Teaching problem solving.

Print Version

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

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.

Catalog search

Teaching tip categories.

• Assessment and feedback
• Blended Learning and Educational Technologies
• Career Development
• Course Design
• Course Implementation
• Inclusive Teaching and Learning
• Learning activities
• Support for Student Learning
• Support for TAs
• Learning activities ,

Problem-Solving Method in Teaching

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

Table of Contents

Definition of problem-solving method.

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

Meaning of Problem-Solving Method

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

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

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

Benefits of Problem-Solving Method

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

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

Steps in Problem-Solving Method

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

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

Verification of the concluded solution or Hypothesis

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

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

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

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. 

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 ?

Enhance Learner Outcomes Across Your School

Download an Overview of our Support and Resources

We'll send it over now.

Please fill in the details so we can send over the resources.

What type of school are you?

We'll get you the right resource

Is your school involved in any staff development projects?

Are your colleagues running any research projects or courses?

Do you have any immediate school priorities?

Please check the ones that apply.

Download your resource

Thanks for taking the time to complete this form, submit the form to get the tool.

Classroom Practice

• Accessible Document Design Fundamentals
• Word Accessibility Guide
• PowerPoint Accessibility Guide
• PDF Accessibility Guide
• Excel Accessibility Guide
• Basic HTML Accessibility Guide
• Accessible Course Design Guide
• Multimedia Accessibility Guides
• TA Resources
• Teaching Consultation
• Teaching Portfolio Program
• Grad Academy for College Teaching
• Faculty Events
• The Art of Teaching
• 2022 Illinois Summer Teaching Institute
• Large Classes
• Leading Discussions
• Laboratory Classes
• Lecture-Based Classes
• Planning a Class Session
• Questioning Strategies
• Classroom Assessment Techniques (CATs)
• Problem-Based Learning (PBL)
• The Case Method
• Community-Based Learning: Service Learning
• Group Learning
• Just-in-Time Teaching
• Creating a Syllabus
• Motivating Students
• Dealing With Cheating
• Discouraging & Detecting Plagiarism
• Diversity & Creating an Inclusive Classroom
• Harassment & Discrimination
• Professional Conduct
• Teaching Tips
• Graduate Teacher Certificate
• Certificate in Foundations of Teaching
• Teacher Scholar Certificate
• Certificate in Technology-Enhanced Teaching
• Master Course in Online Teaching (MCOT)
• 2022 Celebration of College Teaching
• 2023 Celebration of College Teaching
• Hybrid Teaching and Learning Certificate
• 2024 Celebration of College Teaching
• Classroom Observation Etiquette
• Teaching Philosophy Statement
• Pedagogical Literature Review
• Scholarship of Teaching and Learning
• Instructor Stories
• Podcast: Teach Talk Listen Learn
• Universal Design for Learning
• Teaching During an Election Year
• Foundations of Good Teaching
• Student Engagement
• Assessment Strategies
• Course Design
• Student Resources

Sign-Up to receive Teaching and Learning news and events

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.

Center for Innovation in Teaching & Learning

249 Armory Building 505 East Armory Avenue Champaign, IL 61820

217 333-1462

Email: [email protected]

Office of the Provost

Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

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

October 31, 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Related Content

Esther Care, Helyn Kim, Alvin Vista

October 17, 2017

David Owen, Alvin Vista

November 15, 2017

Loren Clarke, Esther Care

December 5, 2017

Global Education K-12 Education

Global Economy and Development

Center for Universal Education

Magdalena Rodríguez Romero

September 10, 2024

Tom Swiderski, Sarah Crittenden Fuller, Kevin C. Bastian

September 9, 2024

Julien Lafortune, Barbara Biasi, David Schönholzer

September 6, 2024

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 05 September 2024

The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: a mixed-method study

• Nawaf Awadh K. Alreshidi   ORCID: orcid.org/0000-0002-7934-4724 1 &
• Victor Lally 2  

Humanities and Social Sciences Communications volume  11 , Article number:  1137 ( 2024 ) Cite this article

Metrics details

The aim of this study was to understand the effect of training teachers in problem-based learning (PBL) implementation on students’ outcomes. Mixed methods were used to analyse the quasi-experimental study data. 127 students were divided into three groups: Group A ( N  = 52) was taught by a trained teacher using the PBL teaching strategy, group B ( N  = 39) was taught by an untrained teacher using traditional teaching methods, and group C ( N  = 36) was taught by an untrained teacher using the PBL teaching strategy. The results showed that students whose teachers received training in PBL implementation significantly improved in terms of applying knowledge compared with students whose teachers used traditional teaching methods. The findings also provide robust evidence to show that using PBL teaching methods significantly improves students’ attitudes towards mathematics compared with traditional teaching methods, regardless of the teacher training effect. The key element in training teachers in PBL to improve students’ application of mathematics is training teachers in using metacognitive strategies that facilitate students’ learning processes.

Similar content being viewed by others

Fostering twenty-first century skills among primary school students through math project-based learning

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

Secondary school students’ attitude towards mathematics word problems

Introduction.

Problem-based learning (PBL) is a teaching strategy in which a facilitator assists students to solve real-world problems as they work in small groups; the facilitator’s aim is to help the students to gain new knowledge and improve their problem-solving skills (see Barrows, 1986 ; Goodman, 2010 ). PBL aims to improve students’ knowledge application (Hmelo, 1998 ; Hmelo and Lin, 2000 ; Schmidt et al., 1996 ), and attitudes towards learning the subject (Hung, 2006 ; Westwood, 2011 ).

In mathematics, PBL is an instructional strategy that contextualises mathematics knowledge (i.e., real-life problems) in a way that helps students to understand where, when and how to apply knowledge. In PBL, when students encounter a real-life problem, they should identify what they have already learned about the problem (i.e., activating their prior knowledge) and establish what they need to know in order to solve the problem (i.e., missing information). They have to search for missing information and then combine it with what they already know (i.e., relevant prior knowledge), applying this to a new context (Bokonjic et al., 2007 ). Therefore, using a PBL teaching strategy in mathematics should reflect on students’ improvement in applying mathematics. Applying mathematics is the concept of using mathematics in real life (Mumcu, 2016 ).

Contextualising knowledge can be prepared by embedding learning opportunities in real-life contexts, which could it also be of interest for students, and it shows students the value of the function of the subject matter in the real world (Hung, 2006 ; Westwood, 2011 ). In the mathematics context, the content of PBL settings (real-life problems) shows the function of mathematics in reality and gives meaning to learning mathematics (Westwood, 2011 ). This should place value on learning mathematics for students, leading to an increase in positive attitudes towards learning mathematics. Attitudes towards mathematics is a negative or positive emotional disposition toward mathematics (Zan and Di Martino, 2007 ). In a systematic review and meta-analysis, Suparman et al. ( 2021 ) determined that PBL is one of the best teaching strategies for primary school mathematics teachers to enhance students’ mathematical abilities. However, students’ learning processes need to be facilitated by teachers in their approach to solving problems (Collins et al., 1989 ; Hmelo-Silver and Barrows, 2006 ; Hung, 2011 ). Thus, it is essential for teachers to be able to do this effectively to produce a noticeable improvement in students’ outcomes. This might require teachers to complete training in facilitation processes. To date, little is known about how the training of teachers in PBL implementation affects students’ outcomes. The results of the present study will help educational decision-makers to understand how training teachers in implementing PBL affects students’ mathematical applications and attitudes towards mathematics.

This article begins with a review of previous studies on PBL, followed by a discussion of teacher training in PBL implementation. The experiment conducted as part of this research examined the effects of training teachers on students’ knowledge application in mathematics and students’ attitudes towards mathematics.

Previous studies in problem-based learning

The overall review of empirical studies shows that PBL tends to significantly improve knowledge application (Abdalqader and Khalid, 2014 ; Primadoni et al., 2020 ; Tong et al., 2021 ; Wirkala and Kuhn, 2011 ; Wong and Day, 2009 ) and generate positive attitudes among students compared with traditional teaching methods (TTM; i.e., teacher-centred instruction) in kindergarten to 12th grade (K–12) settings (Goodnough and Cashion, 2006 ; Lou et al., 2011 ; Merritt et al., 2017 ; Nowak, 2001 ; Tong et al. 2021 ). For example, a quasi-experimental study including control groups conducted by Tong et al. ( 2021 ) examined the effectiveness of PBL on 10th-grade students’ mathematical application knowledge and their attitudes towards mathematics. The results showed that the students taught by the PBL group improved significantly in the application of knowledge and attitudes towards mathematics compared to the students taught by conventional methods. The real-life problems used with PBL are expected to drive students’ curiosity and capture their interest (Schmidt et al. 2009 ); therefore, PBL pedagogy and content could enhance students’ interest and promote their knowledge application.

Most of the literature pertaining to PBL has been conducted in the field of medicine and its allied contexts at universities. A limited number of studies have been carried out in K–12 contexts, and very few studies have been conducted in primary schools see (Alshhrany and Mohammed ( 2010 ); Eviyanti et al., 2017 ). Additional empirical research is needed to investigate the effects of PBL on the outcomes of younger students.

Training in PBL implementation

Although training teachers to implement PBL is generally viewed as critical for improving students’ achievement (Arani et al., 2023 ; Barrows, 1996 ; Fernandes, 2021 ; Hmelo-Silver and Barrows, 2006 ; Leary et al., 2009 ; Wosinski et al., 2018 ) the effects of teacher training on students’ performance are still ambiguous. The agreement on the importance of training is supported by literature outside of PBL, where reports have shown that the most effective teachers are trained in how to use facilitation skills (Leary et al., 2009 ). A meta-analysis was conducted to investigate the relationship between teacher training and students’ learning outcomes, and 94 studies were selected for inclusion in the study. The results showed a significant relationship between teacher training and students’ achievement. The study suggested that untrained teachers have similar student outcomes to those of teachers who use TTM (Leary et al., 2013 ). The researchers concluded that the facilitator may be a key factor in students’ outcomes. In another study, Tawfik and Kolodner ( 2016 ) revisited PBL’s foundations from a case-based reasoning perspective suggested that novices must be trained to facilitate scaffolding students during PBL. Maxwell et al., ( 2005 ) suggested that PBL instruction can improve learning compared with conventional methods when teachers are trained well in PBL. El-Aziz El Naggar et al., ( 2013 ) found that training was necessary to improve facilitators’ skills in collaborative learning and self-directed environments. However, there is a lack of research studies that have experimentally examined the effects of teacher training on student learning. More primary research is required to measure the effects on students’ outcomes of training teachers in PBL.

The aim of training teachers in PBL is to develop teachers in their professional role (Friedman and Woodhead, 2008 ; Villegas-Reimers, 2003 ). Both teachers and students have a role in PBL. To delineate the role of teachers, first, we have to identify the role of students. In PBL, the role of students is to go through the PBL process. Students work in small groups to understand the problem, identify and learn what they need to know and generate hypotheses to solve the problem (Hmelo-Silver, 2004 ). The role of students also involves questioning, researching and using critical thinking in an active way to solve problems (Cerezo, 2004 ). Students are required to take responsibility for their learning and engage in meaning-making in terms of their knowledge (English and Kitsantas, 2013 ). For effective engagement in PBL, students must be responsible for their learning, and they must actively participate in constructing knowledge and making meaningful processes (English and Kitsantas, 2013 ). However, many students cannot easily shift into this role because they have developed ingrained habits from the typical traditional classroom experiences, and they rely on the passive receiving of knowledge (English and Kitsantas, 2013 ; Hung, 2011 ; Ronis, 2008 ). To shift effectively to the new role, students must develop self-regulated learning (SRL) skills (English and Kitsantas, 2013 ).

SRL refers to the extent to which the learner is motivationally, metacognitively and behaviourally active in their learning processes (Zimmerman, 1989 ). Self-regulated learners can set goals and plans, identify appropriate strategies, and self-monitor and self-evaluate their learning; they are intrinsically motivated to learn. Thus, for effective learning in PBL, SRL is an essential skill (English and Kitsantas, 2013 ). In PBL, teachers can consciously activate students’ behaviours, leading to SRL. When it comes to promoting students’ skills to be able to do this, the role of teachers is to structure activities to stimulate students’ motivation, encourage reflection and facilitate their learning processes through guidance, scaffolding feedback and prompting independent thinking (English and Kitsantas, 2013 ). The role of the teacher in PBL is to facilitate collaborative knowledge construction by students, monitor learning processes, model desired behaviours and concentrate students’ efforts on critical thinking (Hmelo-Silver and Barrows, 2006 , 2008 ); this can be done by raising awareness of students’ higher cognitive thinking (Barrows, 1998 ).

Effective teachers should know how to facilitate groups’ learning processes (Dolmans et al., 2002 ; El-Aziz El Naggar et al., 2013 ). To enhance cooperation and production within groups, teachers should use intervention strategies, such as making decisions on what, when and how to intervene (Bosse et al., 2010 ). Teachers may need to be trained to implement such strategies in such a way as to facilitate tutorial processes, since it is teachers’ responsibility to guide students’ learning (Yew et al., 2011 ). In this study, we attempt to understand the effect of training in implementing PBL on students’ outcomes. We address the following questions:

How do trained and untrained teachers in PBL techniques implement PBL?

What are the effects of teacher training in implementing PBL on students’ mathematical applications?

What are the effects of teacher training in implementing PBL on students’ attitudes towards mathematics?

Study design

A quasi-experimental design was adopted in this study as the main quantitative approach to minimise bias in estimating the difference between traditional instruction and PBL classes. In addition, a qualitative approach was used during the intervention using field observation notes and after the intervention using interviews, as a secondary approach (see Fig. 1 ).

The figure illustrates the study design; mathematical test and attitudes towards mathematics were applied before and after the intervention, while during the quasi-experimental implementation, field observation notes were taken, and at the end of the intervention semi-structured interviews were conducted with the teachers.

Figure 1 illustrates the study design; during the quasi-experimental implementation, field observation notes documenting the authors’ observations were taken with the aim of observing how teachers implemented PBL, while semi-structured interviews were conducted with both types of the teachers who only implemented PBL (trained and untrained teachers) after the implementation of PBL as a supplement, with the aim of being used as part of the triangulation method for the author’s observations in how teachers implemented PBL.

School and participating students

The school was located in an urban district in a major city, Hail, which is situated in the north of Saudi Arabia. The school was randomly selected from ten private schools. Then, seven of the third-grade classes out of nine in the selected school were randomly chosen. The third grade is an important level, as it is the final grade of lower primary school. The classes were instructed by three teachers; one taught three classes, and the others taught two classes each. These classes comprised the three following groups: group A (three classes taught by a trained teacher using a PBL teaching strategy), group B (two classes taught by an untrained teacher using TTM) and group C (two classes taught by an untrained teacher using a PBL teaching strategy; see the study design in Table 1 ).

Ethical approval was obtained, and all participants signed consent forms to participate. They were informed that they could withdraw any time with no need to justify their decision, nor would there be any consequences of withdrawal.

In total, 127 pupils participated in the study, and their ages ranged from eight to nine years old. They were in the last semester of the third grade. Most of the students at the school were Saudis; in each group, two to four students had Arab backgrounds, such as from Syria, Egypt and Sudan. All students had a middle-class socioeconomic status. Academic school records and pre-test’ scores were used to ensure that the groups were similar in terms of mathematical achievement. Within each group, students showed a wide range of academic achievements; the students spanned from very low to very high achievers. There were no special education pupils within the groups.

Three teachers were randomly selected from one large primary school to take part in this study. The first teacher was randomly selected to receive training courses in using the PBL teaching strategy. The second teacher did not receive any training, but he was provided with PBL materials—specifically, design problems and guidelines for implementing PBL; he was asked to conduct self-directed learning (SDL) to implement PBL in his classrooms. The aim of including a trained and an untrained teacher using PBL was to measure the effects of training teachers on students’ outcomes. The third teacher was not trained in PBL and was asked to teach students using TTM.

The teachers had similar characteristics in terms of qualifications, experience and expertise, as well as in their beliefs and perspectives on PBL and TTM. They are all male and they believed that the aim of teaching mathematics is to conduct real-life problem solving, and they considered active learning to be important for students. They had been teaching mathematics to third-grade school students for 10 years. They all had a first degree in mathematics. They were all Egyptians and aged in their late thirties. According to the teachers and the administration of the school, the teachers had all attended the same training courses in different aspects of education, such as active learning. However, none of them had ever been trained in using PBL teaching strategies.

The topic covered in the classes was ‘data display’. It covered representation through codes, interpretation of representation through codes, representation in columns and interpretation of representation in columns. The content was new to the students. The instruction took place during ten class sessions (45 min each) comprising four sessions per week over for two and a half weeks, with a total of 7.5 h for each group. To control for the time factor, all groups, whether PBL or traditional, were given the same amount of time.

Instruments

Six multiple-choice questions, short answer questions, fill-in table questions and drawing tests were applied at the beginning of the study (pre-test) and in the final experiment (post-test). Mathematics items were selected from Trends in International Mathematics and Science Study (TIMSS) 2003 , 2007 and 2011 (see Mullis et al., 2012 ). The TIMSS items that were selected matched the objectives of lessons for knowledge application exactly; they had already been examined for the purpose of the test. We chose TIMSS mathematics items because they were verified as appropriate for the students’ ages. The students had nearly finished the third grade, and the curriculum for that grade contained many TIMSS topics (see TIMSS, n.d. ). Each item on the test received a score of either one or zero. An example of the items is given in Appendix A . The measure ‘attitudes towards mathematics’ of TIMSS 2007 (Mullis et al., 2008 ) contains four items, as follows:

I would like to take more mathematics in school

I enjoy learning mathematics.

Mathematics is boring (reverse-coded).

I like mathematics.

This measure was adopted and assumed to meet the standard of a valid and reliable test (see, Mullis et al., 2008 ). Attitudes were assessed using four items applied twice as pre- and post-measures; four items with 4-point Likert scales (disagree a lot, disagree a little, agree a little, and agree a lot) were presented. Each item score ranged from 1 to 4. The total marks ranged from the number of items of the measure to multiply them by 4; the measure consisted of four items, so the total scores ranged from 4 to 16. Some items were reverse-coded; for example, for ‘mathematics is boring’, ‘disagree a lot’ would receive a score of 4, whereas ‘agree a lot’ would receive a score of 1.

The face validity method was used to assess the validity of the tests and attitude measures. Eight arbitrators checked and gave their opinions on the adequacy, clarity, and relevance of the items’ content. The opinions of the arbitrators were considered and included in the preparation of the final image of the tests and attitudes. However, no changes were reported, and face validity confirmed the tests’ validity. In addition, test-retest reliability was used to assess the reliability of the tests and attitude measures. The levels of reliability were acceptable, with a score of 0.86 for the mathematics test and 0.88 for the attitude measure. For further reliability, Cronbach’s alpha was used for each scale of the test and attitudes and for the whole test and attitudes. The results show that all items correlated with a good degree of total scales (no items scored less than 0.3), and the reliability for the test was 0.747, whereas that for attitude was 0.808. Therefore, the measures became high valid for the purposes of this study.

In qualitative methods, filed observation and semi-structured interview were used to assess teachers’ performance in PBL implementation. After filed observations completed, post- semi-structured interviews were conducted for the teachers to confirm the results of author observations of how teachers implemented PBL as a supplement for the methodological triangulation of the filed observations. Methodological triangulation involves a researcher using more than one method, such as interviews and observations, for collecting data to understand a phenomenon deeply (Flick et al., 2004 ; Neuman, 2000 ). The teachers’ responses to the questions in the semi-structured interviews were analysed and compared with the analysed observation data to enhance the validity of the study and to gain a deeper understanding of social events. As Neuman ( 2000 ) commented, “Looking at something from several different points gives a more accurate view of it” (p. 521).

The data obtained from qualitative methods were deductively analysed. Prior to conducting data collection from filed work. A structured categorisation matrix was developed by the authors based on a literature review (see Barrows, 1998 ; English and Kitsantas, 2013 ; Hmelo-Silver and Barrows, 2006 , 2008 ). It aimed to assess PBL implementation conducted by teachers and consisted of two main categories: understanding the problem and using metacognitive strategies (see Appendix B ). Field observation notes were used to describe how the teachers implemented PBL. In this study, field observation notes consisted of two parts: descriptive and reflective information (Patton, 1990 ). The descriptive part involved documenting the factual data obtained from inside the classroom. The main author moved between groups to make sure everything was proceeding well; the intention was to monitor the implementation of the study, and the authors had a diary that was used to document any observations, particularly the observations that took place during lessons and were made inside mathematics classrooms. The main focus was on teachers’ performance, particularly with respect to teacher intervention, individual and collective student practices, student responses, group interaction and PBL processes. In the reflective section, the authors reflected on the meaning of the observations outside of the classroom (see Appendix C ). At the end of the experiment, ten lessons by each teacher were observed.

Semi-structured interview questions were developed according to analysed data of class observations which includes: The three main questions:

How was PBL implemented in your teaching strategies?

How did you assess your students in relation to understanding the problem?

How did you support your students to solve the problem?

In semi-structured interview, tape recordings were used for the interviews with each teacher, which ranged from 13 to 23 min in length. The interviews were conducted in Arabic, transcribed and subsequently translated into English by the authors.

The data were deductively coded (i.e., both the interview and observation) by the main author, and according to the identified categories mentioned above. When a deductive content analysis is used, a categorisation matrix is developed; following this, the data are coded according to the categories (Polit and Beck, 2004 ). In addition, if a structured matrix is chosen, only aspects that fit the matrix are selected from the data (Patton, 1990 ).

Professional development

The PBL programme used in this study aimed to train teachers by focusing on how to implement PBL in mathematics classrooms. The programme continued to provide feedback during the implementation after each session, taking advantage of the literature recommendations. Therefore, the trained teacher learned how to facilitate groups’ learning processes and guide students’ learning by adopting strategies such as posing meta-cognitive questions and focusing on the process of learning to model students’ learning strategies. The teacher was trained in intervention strategies, such as making decisions based on what, when and how intervention should occur to enhance cooperation. The programme included examples of PBL implementations. Teacher training lasted for one week (8–10 h), and daily meetings took place during the course of the training to provide an opportunity to present feedback and resolve unexpected problems. The programme for training the teacher to implement PBL in his class was developed by the author. It was expected that, following the teacher’s completion of the programme, the teacher would be able to do the following:

provide scaffolding and feedback as needed

prompt independent thinking

facilitate collaborative knowledge construction for students

monitor learning processes

model desired behaviours

concentrate students’ efforts on critical thinking.

use intervention strategies, such as making decisions on what, when and how to intervene

The programme included three real-life sessions, each lasting 45 min. The teacher was asked to implement the PBL strategy using an ill-structured problem, which was taken from a mathematics textbook and related to the topics that the students had been studying. A group of students from outside the study sample was selected to assess the teacher’s performance and establish whether he was able to implement PBL effectively. This was followed by providing the teacher with extensive feedback, which lasted more than an hour for each session.

The students were trained in two sessions in how to deal with the PBL teaching strategy.

Problem-based learning implementation

Problems were presented to the students. Students worked in small groups of four to six members. They discussed their understanding of the problems, and then the teacher discussed the understanding of the problem with the whole class. This was followed by students solving the problems. Finally, the teacher discussed the solution with all the students.

In this study, the six core characteristics of PBL mentioned by Barrows ( 1996 ) were adopted. These are as follows:

The student is the centre of the learning.

Learning occurs in small groups of students.

At the beginning of the learning, the students are presented with authentic problems.

The problems are used as a means of developing problem-solving skills.

New knowledge is gained through SDL. (Barrows, 1996 )

From the literature review (see Barrows, 1986 ; Gallagher and Stepien, 1996 ; Hung et al., 2008 ), six characteristics were adopted in the problems after reviewing the literature related to the problem of PBL. These were as follows:

the role of students as stakeholders

ill-structured problems

real-life problems

age-appropriate problems

clear and short problems

not too difficult problems

Statistical analysis (quantitative analysis)

The study used mixed-factor analysis of variance (ANOVA) models (Field, 2013 ; Howell, 2012 ) within one factor (time: pre- and post-tests and between). Tukey’s post hoc test (Field, 2013 ; Howell, 2012 ) was applied when appropriate and where significant results were observed—that is, an effect size (partial eta squared [η p 2 ]). The effect size, classified as Cohen suggested, could be small 0.01; medium, 0.06; or large, 0.14. All analyses were performed on IBM SPSS v22 and at a 5% (0.05) level of significance.

A quasi-experimental design was adopted in this study as the main quantitative approach, while a qualitative approach was used during the intervention using class observation notes and interviews, as a secondary approach. In total, 127 pupils participated in the study. They were in the last semester of the third grade. Ethical approval was obtained, and all participants signed consent forms to participate. Three teachers were randomly selected from one large primary school to take part in this study. The first teacher was randomly selected to receive training courses in using the PBL teaching strategy. The second teacher was not trained and asked to conduct SDL to implement PBL in his classrooms. The third teacher was not trained in PBL and was asked to teach students using TTM. The topic covered in the classes was ‘data display’. The content was new to the students. The instruction took place during 10 class sessions. Instruments of the study include mathematics test and attitudes towards mathematics were prepared and verified. Applying a pre-test (a measure of attitudes towards mathematics and an exam to measure mathematics application). Conducting the study took about 2 and a half weeks. Applying for a post-test (a measure of attitudes towards mathematics and an exam to measure mathematics application). During the intervention, class observations were carried out for each lesson.

Problem-based learning implementation of trained and untrained teachers

Unlike the untrained teacher, the trained teacher properly implemented PBL. The differences between their performances lay in differences in ‘giving students sufficient time to understand the problem’ and ‘using more metacognitive strategies to coach students in relation to their thinking skills’.

Table 2 and Fig. 2 summarise the difference between trained and untrained teachers after analysing both the teachers’ interviews and the author’s observations. The two following themes were extracted from the data analyses: ‘understanding the problem’ and ‘using meta-cognitive teaching skills’. These themes are detailed below.

This figure illustrates the difference between trained and untrained teachers' performances in PBL implementation.

Understanding the problem

The trained teacher did not allow students to solve the problem until they demonstrated their understanding of it. The author frequently noted that the trained teacher prevented the students from solving the problem until they demonstrated their understanding of it. When the trained teacher was asked how he knew that the students understood the problem, he replied, ‘I frequently asked random students… : ‘could you please explain to us the problem in your own words?’ If they did not do very well, I asked them how they could understand the problem more deeply? I waited longer … for them to solve the problem and gave them more time to reflect on their understanding and discuss with their group to deeply understand the problem’. The author observed that the teacher frequently and asked ransom students the following question: ‘Could [you] explain the problem [to us in] your own words’. Some students could, while others could not. Then, he encouraged them to understand the problem by asking them the following questions: ‘How can you understand the problem deeply? and Could you identify the obstacles and discuss [them] with your [respective] groups?’ Later, he again asked them whether they could explain the problem. However, the untrained teacher’s students had been given a shorter amount of time to understand the problem than those who were with the trained teacher (author’s observation).

In all lessons, the untrained teacher asked students whether they understood the problem; he often proceeded after hearing anyone shout ‘yes’ (author’s observation). The untrained teacher confirmed this when he was asked how he knew that his students had understood the problem before carrying on: ‘I always ask my students, if they do not understand the problem, to stop me any time and feel free to ask’. He did not ask his students to explain the problem in their own words (author’s observation). It was noted that the trained teacher gave more time for understanding the problem and questioned his students’ understanding more than the untrained teacher did.

Using meta-cognitive teaching skills

The trained teacher used more metacognitive strategies than the untrained teacher. Throughout all the lessons, the author observed that the trained teacher facilitated his students’ learning processes via PBL by using meta-cognitive strategies. He confirmed this in stating:

They [the students] work within groups to solve the problem, and I monitor them and coach their thinking with meta-cognitive questions …. For example, I ask students: what they did so far, and what next, did they consider this or that … and so on…. Sometimes, I think aloud and model right behaviours to let them engage in learning processes.

It was observed that students gradually began to depend on their own selves to solve the problems when they found their teacher pushed them to be independent. The trained teacher confirmed the following:

I did not want my students to depend on me. I never give them the solution, but encouraged them to depend on their own effort … And I found coaching their thinking improved their independence.

In contrast, the untrained teacher showed less ability to use meta-cognitive strategies through implementing PBL (author’s observation). The untrained teacher said: ‘They [the students] worked with their groups to solve the problem, and I helped them to solve the problem by indirectly explaining any difficulties, for example, by giving them some examples’. He explained the difficulties and led his students to solve the problem. He did not explain the solution directly, but he gave similar examples, which led them to the correct answer (author’s observation). In some ways, this strategy may be considered a metacognitive activation strategy.

The author observed that students frequently asked their teachers to give them more examples to understand how to solve the problems. The untrained teacher confirmed this: ‘My students are allowed to ask me to give examples to solve the problems, and I always meet their needs’.

Knowledge application in mathematics

From Table 3 , it can be seen that the improvement in the ‘applying achievement’ mean scores increased in all groups. From the mixed-measures ANOVA, as shown in Table 4 , it was found that a statistically significant improvement occurred for the average of students’ scores in knowledge application, F (2, 121) = 76.795, p  = 0.000, with a large effect size at 0.388 (see row 1). However, when time was interacted with the groups (PBL with trained teacher, PBL with untrained teacher and TTM) the result showed a statistically significant effect, F (3, 121) = 4.333, p  = 0.015. The partial eta squared effect size for this statistically significant result was medium, at 0.067 (see row 2). This effect shows that there was an effect on at least one group, but further analysis was needed to identify which group(s) might be affected. Tukey’s post hoc test was applied to determine which of the groups was statistically significantly different from the others. This test found that the mean scores of the group of students taught using the PBL teaching strategy by the trained teacher were statistically significantly different only from the scores of the students taught using TTM, p  = 0.009 (see row 3). This indicates that the average of the PBL group’s scores with the trained teacher significantly improved more than the average of the traditional group’s scores did in ‘applying mathematics’.

Attitudes towards mathematics

From Table 5 , it can be seen that the mean score for ‘attitudes towards mathematics’ increased in groups A and C, while the scores of group B, the traditional group, decreased.

From the mixed-measures ANOVA analysis, as shown in Table 6 , there was no statistically significant improvement occurring for the average of students’ scores in attitudes towards mathematics, F (2, 121) = 0.480, p  = 0.490 (see row 1). However, when time was interacted with groups (PBL with trained teacher, PBL with untrained teacher, and TTM), the result showed a statistically significant effect, F (3, 121) = 12.486, p  = 0.000. The partial eta squared effect size for this statistically significant result was large, at 0.171 (see row 2). Tukey’s post hoc test was applied to determine which of the groups was significantly different from the others in attitudes towards mathematics. This test showed that using PBL with the trained teacher group was significantly different from using TTM, p  = 0.000; using PBL with the untrained teacher group was also significantly different from using TTM, p  = 0.008. However, there was no statistically significant difference between using PBL with the trained and untrained teachers (see row 3). This means that there was a statistically significant difference between the groups attributed to the types of treatment (PBL and TTM) in ‘attitudes towards mathematics’ and in favour of the PBL group, regardless of the different abilities of teachers in PBL implementation.

The study aimed to assess the effect of teacher training on students’ knowledge application and attitudes towards mathematics. The trained teacher demonstrated his ability to facilitate his students’ learning processes by using more metacognitive strategies than the untrained teacher. This result was expected, as many scholars think that training teachers on PBL implementation is critical for success (Barrows, 1996 ; Hmelo-Silver and Barrows, 2006 ; Leary et al., 2009 ; Wosinski et al., 2018 ). The results of the analyses of the interview data and the class observations were convergent. No noticeable difference was identified between the data analyses of class observation and the teachers’ interviews. Below, we consider how the teacher training affected student outcomes. Below, we consider how the teacher training affected student outcomes.

The current study’s quantitative results suggest that when PBL is taught by a teacher who can facilitate the students’ learning processes by using more meta-cognitive strategies, this could improve the application of mathematical knowledge of third-grade students’ significantly more than when they are taught using TTM (see Table 4 ). PBL theorists claim that, when compared with TTM, PBL is more successful in improving knowledge application (Hmelo-Silver, 2004 ; Hmelo-Silver and Barrows, 2008 ). This is because, with PBL, students engage in SDL by using their meta-cognitive learning strategies to solve real-life and ill-structured problems as a way of learning (Chin and Chia, 2006 ). This should reflect some improvement in the students’ ‘application’ ability over TTM (Fogarty, 1994 ). However, for such a method to be effective, skilled teachers who are also able to effectively use meta-cognitive strategies must be present to activate students’ meta-cognitive learning strategies. The trained teacher in PBL is better able to do so.

The role of the teacher in PBL is to facilitate learning processes (Hmelo-Silver and Barrows, 2006 , 2008 ). The shift to PBL requires new teaching roles and skills (Wilkerson and Hundert, 1997 ). Teachers can facilitate PBL processes if they are using meta-cognitive strategies, such as ‘thinking aloud with students’ and ‘modelling behaviours’ (Delisle, 1997 ). In the current study, these skills were shown effectively by the trained teacher; consequently, such strategies were reflected in the improvements to the students’ ‘application’ achievements. However, when students were taught by an untrained teacher, their learning processes were less facilitated. He only responded to difficulties they were experiencing by explaining similar situations (i.e., an example). Even though this approach is considered a metacognitive activation strategy, the students’ solutions were led by these examples. Thus, the teacher’s performance is an important factor that will affect the application of mathematical knowledge among third-grade students.

In terms of teacher training, the findings of the present study are supported by the results of the meta-analysis conducted by Leary et al. ( 2013 ), which showed a statistically significant positive relationship between teacher training and student achievement. The study also suggested that untrained teachers resulted in student outcomes similar to those attained by teachers who use TTM. This is also supported by the results of the current study. Moreover, this study’s findings are in line with those of Maxwell et al. ( 2005 ); these researchers’ conclusion suggests that PBL instruction can improve learning more than TTM can when teachers are well trained in using the PBL strategy. However, the results of the current study support the conclusions of several studies that found students taught via PBL outperformed students taught via TTM in terms of application knowledge (see Tong et al., 2021 ; Wirkala and Kuhn, 2011 ; Wong and Day, 2009 ).

The current study’s results suggested that PBL could significantly improve third-grade students’ attitudes towards mathematics compared with TTM (see Table 6 ). This is supported by the findings of (Lou et al., ( 2011 ) and Tong et al. ( 2021 ). For example, Tong et al. ( 2021 ) suggested that students taught via PBL improved their attitudes towards mathematics more significantly than those taught via TTM. The reason for this is that the students liked active learning and working in groups. This idea was supported by Goodnough and Cashion ( 2006 ), who suggested that young students like this strategy because it encourages active learning, supports working in groups and provides students with a variety of learning approaches and methods. In addition, real-life problems that interest students can be used to motivate students to engage deeply in learning processes when students fully understand them. These kinds of problems are expected to drive students’ curiosity and capture their interest, resulting in more effective student engagement in SDL in order to solve the problems (Schmidt et al., 2009 ).

In this study, the role of the problem was to motivate the students in all lessons taught by teachers trained in implementing PBL. Students became intrinsically motivated when they worked on tasks that stimulated their interests and sense of satisfaction or that challenged them (Hmelo-Silver, 2004 ). The possible reason for this is that the untrained teachers did not give students sufficient time to understand the problem, in contrast with the trained teacher (teachers’ interview and author’s observations).

In sum, PBL could be an effective teaching strategy for improving students’ attitudes towards learning mathematics; this effect is probably due to PBL content (i.e., real-life problems) and the nature of the PBL environment (i.e., eliciting active learning). In addition, PBL could be an effective teaching strategy for improving students’ mathematics application when students’ processes are effectively facilitated; without such facilitation, the effect of PBL instruction will not differ from that of TTM.

Limitations of the study

This study had several limitations. Because of the study design, results could be generated only for young students and for learning mathematics. The sample selection was not completely random, which could also decrease the opportunity to generalise the results of this study. Because of the gender segregation system that is currently operational in Saudi Arabia, the study participants were all male students. Therefore, the results of this study should be generalised with caution, taking these contextualising factors into account.

This study attempted to assess how training teachers in PBL implementation affects student outcomes, including knowledge application and students’ attitudes towards learning mathematics compared with TTM. Overall, the third-grade students who were taught using PBL showed more positive attitudes towards learning mathematics, regardless of whether they were taught by trained or untrained teachers. The study provides evidence that supports the necessity of training teachers to implement PBL effectively, as this will improve students’ mathematics application.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abdalqader K (2014) The effect of problem-based learning strategy in constructing proofs of solid geometry problems and attitudes toward math among female tenth graders in Gaza Governorates. Int J Res Educ Psychol 2:2210–1780

Alshhrany M (2010) The effect of using Wheatly’s Model for teaching a mathematics on sixth grade’s achievement in and attitudes towards math, Umm Al-Qura University

Arani SMN, Zarei AA, Sarani A (2023) Problem-based language learning: why aren’t teachers using it? Soc Sci Humanit Open 8(1):100668

Google Scholar  

Barrows HS (1996) Problem‐based learning in medicine and beyond: a brief overview. N Dir Teach Learn 1996(68):3–12

Article   Google Scholar  

Barrows HS (1986) Taxonomy of problem based learning methods. Med Educ 20(6):481–486

Article   CAS   PubMed   Google Scholar  

Barrows HS (1998) The essentials of problem-based learning. J Dent Educ 62(9):630–633

Bokonjic D, Mimica M, Pranjic N (2007) Problem based learning. In: Bokonjić D, Steiner T, Sonntag HG (eds) Manual of teaching and learning in medicine. Available at: http://www.bristol.ac.uk/medine . Accessed

Bosse HM, Huwendiek S, Skelin S, Kirschfink M, Nikendei C (2010) Interactive film scenes for tutor training in Problem-Based Learning (PBL): dealing with difficult situations. BMC Med Educ 10(1):52

Article   PubMed   PubMed Central   Google Scholar  

Cerezo N (2004) Problem-based learning in the middle school: a research case study of the perceptions of at-risk females. RMLE Online 27(1):1–13

Article   MathSciNet   Google Scholar  

Chin C, Chia LG (2006) Problem‐based learning: using Ill‐structured problems in biology project work. Sci Educ 90(1):44–67

Collins A, Brown JS, Newman SE (1989) Cognitive apprenticeship: teaching the crafts of reading, writing, and mathematics. In: LB Resnick (ed.), Knowing, learning, and instruction: essays in honor of Robert Glaser. Hillsdale NJ: Erlbaum, p 453–494

Delisle R (1997) How To Use Problem-Based Learning in The Classroom. Association for Supervision and Curriculum Development, Alexandria, VA

Dolmans DH, Gijselaers WH, Moust JH, Grave WSD, Wolfhagen IH, Vleuten CPVD (2002) Trends in research on the tutor in problem-based learning: conclusions and implications for educational practice and research. Med Teach 24(2):173–180

Article   PubMed   Google Scholar  

El-Aziz El Naggar MAA, Maklady FAH, Hamam AM, Omar AS (2013) Effectiveness of implementing a tutor training workshop for problem based learning class tutors at the Faculty of Medicine. Suez Canal Univ Intel Prop Rights 1(1):2

English MC, Kitsantas A (2013) Supporting student self-regulated learning in problem- and project-based learning. Interdiscip J Probl -Based Learn 7(2):6

Eviyanti CY, Surya E, Syahputra E, Simbolon M (2017) Improving the students’ mathematical problem solving ability by applying problem based learning model in VII grade at SMPN 1 Banda Aceh Indonesia. Int J Nov Res Educ Learn 4(2):138–144

Fernandes HV (2021) From student to tutor: a journey in problem-based learning. Curr Pharm Teach Learn 13(12):1706–1709

Field A (2013) Discovering statistics using IBM SPSS statistics. 4th Ed. London. Sage Publications

Flick D, Kardorff EV, Steinke I (2004) A Comparison To Qualitative Research. Sage, London

Fogarty R (1994) The mindful school: how to teach for metacognitive reflection. IRI/Skylight Publishing, Inc., 200 East Wood Street, Suite 274, Palatine, IL 60067

Friedman A, Woodhead S (2008) Approaches to CPD Measurement. Professional Associations Research Network. Retrieved on 26 October, 2008 From website: http://www.ifac.org/education/meeting-filedl.php?FID=3653

Gallagher SA, Stepien WJ (1996) Content acquisition in problem-based learning: depth versus breadth in American Studies. J Educ Gifted 19(3):257–275

Goodman RJB (2010) Problem-based learning: merging of economics and mathematics. J Econ Financ 34(4):477–483

Goodnough K, Cashion M (2006) Exploring problem‐based learning in the context of high school science: design and implementation issues. Sch Sci Math 106(7):280–295

Hmelo CE (1998) Problem-based learning: effects on the early acquisition of cognitive skill in medicine. J Learn Sci 7:173–208

Hmelo CE, Lin X (2000) Becoming self-directed learners: strategy development in problem-based learning. In: D Evensen & CE Hmelo (eds), Problem-based learning: a research perspective on learning interactions, Mahwah, NJ: Erlbaum, p 227–250

Hmelo-Silver CE, Barrows HS (2006) Goals and strategies of a problem-based learning facilitator. Interdiscip J Probl -Based Learn 1(1):4

Hmelo-Silver CE, Barrows HS (2008) Facilitating collaborative knowledge building. Cognit Instr 26(1):48–94

Hmelo-Silver CE (2004) Problem-based learning: what and how do students learn? Educ Psychol Rev 16(3):235–266

Howell D (2012) Statistical methods for psychology. 8th edn. Belmont, CA: Wadsworth, Cengage Learning

Hung W (2011) Theory to reality: a few issues in implementing problem-based learning. Educ Technol Res Dev 59(4):529–552. https://doi.org/10.1007/s11423-011-9198-1

Hung W (2006) The 3C3R model: a conceptual framework for designing problems in PBL. Interdiscip J Probl -Based Learn 1(1):6

Hung W, Jonassen DH, Liu R (2008) Problem-based learning. Handb Res Educ Commun Technol 3:485–506

Leary H, Walker A, Shelton BE, Fitt MH (2013) Exploring the relationships between tutor background, tutor training, and student learning: a problem-based learning meta-analysis. Interdiscip J Probl -Based Learn 7(1):6

Leary HM, Walker AE, Fitt MH, Shelton BE (2009) Expert Versus novice tutors: impacts on student outcomes in problem-based learning. Utah State University. ITLS Faculty Publications

Lou SJ, Shih RC, Diez CR, Tseng KH (2011) The Impact of problem-based learning strategies on STEM knowledge integration and attitudes: an exploratory study among female taiwanese senior high school students. Int J Technol Des Educ 21(2):195–215

Maxwell NL, Mergendoller JR, Bellisimo Y (2005) Problem-based learning and high school macroeconomics: a comparative study of instructional methods. J Econ Educ 36(4):315–329

Merritt J, Lee MY, Rillero P, Kinach BM (2017) Problem-based learning in K-8 mathematics and science education: A literature review. Interdiscip J Probl Based Learn 11(2):3–15. https://doi.org/10.7771/1541-5015.1674

Mullis IVS, Martin MO, Foy P (2008) TIMSS 2007 International Mathematics Report: Findings from IEA‟s Trends in International Mathematics and Science Study for the Fourth and Eighth Grades. Chestnut Hill, MA: TIMSS and PIRLS International Study Center, Boston College

Mullis IV, Martin MO, Foy P, Arora A (2012) TIMMS 2011 International Results in Mathematics. International Association for the Evaluation of Educational Achievement. Herengracht 487, Amsterdam, 1017 BT, The Netherlands

Mullis IV, Martin MO, Smith TA, International Association for the Evaluation of Educational Achievement (2003) TIMSS: Assessment frameworks and specifications 2003. https://pirls.bc.edu/timss2003i/PDF/t03_AF_preface.pdf‏

Mumcu HY (2016) Using mathematics, mathematical applications, mathematical modelling, and mathematical literacy: a theoretical study. J Educ Pract 7(36):80–96

Neuman W (2000) Social research methods: qualitative and quantitative approaches. 4th edn. Boston Mass and London: Ally and Bacon

Nowak JA (2001) The implications and outcomes of using problem-based learning to teach middle school science. Ph.D. Indiana University

Patton MQ (1990) Qualitative Evaluation and Research Methods. Sage Publications, Newbury Park

Polit DF, Beck CT (2004) Nursing Research. Principles and Methods. Lippincott Williams & Wilkins, Philadelphia, PA

Primadoni AB, Suharini E, Mulyono M (2020) Problem solving ability of the fourth grade students in problem based learning on two dimensional figures. J Prim Educ 9(2):155–161

Ronis DL (2008) Problem-based learning for math and science: integrating inquiry and the internet. 2nd edn. California: Corwin Press

Schmidt HG, Machiels-Bongaerts M, Hermans H, ten Cate TJ, Venekamp R, Boshuizen HPA (1996) The development of diagnostic competence: comparison of a problembased, an integrated, and a conventional medical curriculum. Acad Med 71:658–664

Schmidt HG, Van der Molen HT, Te Winkel WW, Wijnen WH (2009) Constructivist, problem-based learning does work: A meta-analysis of curricular comparisons involving a single medical school. Educ Psychol 44(4):227–249

Suparman S, Tamur M, Yunita Y, Wijaya TT, Syaharuddin S (2021) Using problem-based learning to enhance mathematical abilities of primary school students: A systematic review and meta-analysis. JTAM (J Teor Dan Aplikasi Matematika) 5(1):144–161

Tawfik AA, Kolodner JL (2016) Systematizing scaffolding for problem-based learning: a view from case-based reasoning. Interdiscip J Probl -Based Learn 10(1):6

Tong DH, Uyen BP, Nhu LKLTQ (2021) Application of Problem-Based Learning to Teaching the Relationships Within A Triangle And Solution Of Triangles. Int J Educ Change 7(7):486–503. https://doi.org/10.5281/zenodo.5137984

TRENDS IN INTERNATIONAL MATHEMATICS AND SCIENCE STUDY (TIMSS). (n.d.). National center for education statistics. Retrieved June 1, 2024, from https://nces.ed.gov/timss/released-questions.asp

Villegas-Reimers E (2003) Teacher Professional Development: An International Review of the Literature. International Institute for Educational Planning, Paris

Westwood P (2011) The problem with problems: potential difficulties in implementing problem-based learning as the core method in primary school mathematics. Aust J Learn Difficulties 16(1):5–18

Wilkerson L, Hundert EM (1997) Becoming a problem-based tutor: Increasing self-awareness through faculty development. In: Boud D, Feletti G (eds) The Challenge of Problem-Based Learning, 1st edn. Routledge, pp 160–172. https://doi.org/10.4324/9781315042039

Wirkala C, Kuhn D (2011) “Problem-based learning in K–12 Education is it effective and how does it achieve its effects?”. Am Educ Res J 48(5):1157–1186

Wong KKH, Day JR (2009) A comparative study of problem-based and lecture-based learning in junior secondary school science. Res Sci Educ 39(5):625–642

Wosinski J, Belcher AE, Dürrenberger Y, Allin AC, Stormacq C, Gerson L (2018) Facilitating problem-based learning among undergraduate nursing students: a qualitative systematic review. Nurse Educ today 60:67–74

Yew EH, Chng E, Schmidt HG (2011) Is learning in problem-based learning cumulative? Adv Health Sci Educ 16(4):449–464

Zan R, Di Martino P (2007) Attitude toward mathematics: overcoming the positive/negative dichotomy. Mont Math Enthus 3(1):157–168

Zimmerman BJ (1989) A social cognitive view of self-regulated academic learning. J Educ Psychol 81(3):329

Download references

Author information

Authors and affiliations.

College of Education, University of Ha’il, Ha’il, Saudi Arabia

Nawaf Awadh K. Alreshidi

College of Education, University of Glasgow, Glasgow, UK

Victor Lally

You can also search for this author in PubMed   Google Scholar

Contributions

The authors confirm contribution to the paper across all sections. Both authors reviewed the results and approved the version of the manuscript.

Corresponding author

Correspondence to Nawaf Awadh K. Alreshidi .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Ethical statements

Approval was obtained. The procedures used in this study adhere to the tenets of the Declaration of Helsinki. The approval obtained from the college ethics committee for non-clinical research involving human subject, at university of Glasgow, Number: 1105870A.

Informed consent

All participants include: the teachers, the students, and the students’ parents signed consent forms to participate.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ .

Reprints and permissions

About this article

Cite this article.

Alreshidi, N.A.K., Lally, V. The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: a mixed-method study. Humanit Soc Sci Commun 11 , 1137 (2024). https://doi.org/10.1057/s41599-024-03638-6

Download citation

Received : 03 December 2023

Accepted : 19 August 2024

Published : 05 September 2024

DOI : https://doi.org/10.1057/s41599-024-03638-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

• Campus Life
• ...a student.
• ...a veteran.
• ...an alum.
• ...a parent.
• ...faculty or staff.
• Class Schedule
• Crisis Resources
• People Finder
• Change Password

UTC RAVE Alert

Critical thinking and problem-solving, jump to: , what is critical thinking, characteristics of critical thinking, why teach critical thinking.

• Teaching Strategies to Help Promote Critical Thinking Skills

References and Resources

When examining the vast literature on critical thinking, various definitions of critical thinking emerge. Here are some samples:

• "Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action" (Scriven, 1996).
• "Most formal definitions characterize critical thinking as the intentional application of rational, higher order thinking skills, such as analysis, synthesis, problem recognition and problem solving, inference, and evaluation" (Angelo, 1995, p. 6).
• "Critical thinking is thinking that assesses itself" (Center for Critical Thinking, 1996b).
• "Critical thinking is the ability to think about one's thinking in such a way as 1. To recognize its strengths and weaknesses and, as a result, 2. To recast the thinking in improved form" (Center for Critical Thinking, 1996c).

Perhaps the simplest definition is offered by Beyer (1995) : "Critical thinking... means making reasoned judgments" (p. 8). Basically, Beyer sees critical thinking as using criteria to judge the quality of something, from cooking to a conclusion of a research paper. In essence, critical thinking is a disciplined manner of thought that a person uses to assess the validity of something (statements, news stories, arguments, research, etc.).

Back        

Wade (1995) identifies eight characteristics of critical thinking. Critical thinking involves asking questions, defining a problem, examining evidence, analyzing assumptions and biases, avoiding emotional reasoning, avoiding oversimplification, considering other interpretations, and tolerating ambiguity. Dealing with ambiguity is also seen by Strohm & Baukus (1995) as an essential part of critical thinking, "Ambiguity and doubt serve a critical-thinking function and are a necessary and even a productive part of the process" (p. 56).

Another characteristic of critical thinking identified by many sources is metacognition. Metacognition is thinking about one's own thinking. More specifically, "metacognition is being aware of one's thinking as one performs specific tasks and then using this awareness to control what one is doing" (Jones & Ratcliff, 1993, p. 10 ).

In the book, Critical Thinking, Beyer elaborately explains what he sees as essential aspects of critical thinking. These are:

• Dispositions: Critical thinkers are skeptical, open-minded, value fair-mindedness, respect evidence and reasoning, respect clarity and precision, look at different points of view, and will change positions when reason leads them to do so.
• Criteria: To think critically, must apply criteria. Need to have conditions that must be met for something to be judged as believable. Although the argument can be made that each subject area has different criteria, some standards apply to all subjects. "... an assertion must... be based on relevant, accurate facts; based on credible sources; precise; unbiased; free from logical fallacies; logically consistent; and strongly reasoned" (p. 12).
• Argument: Is a statement or proposition with supporting evidence. Critical thinking involves identifying, evaluating, and constructing arguments.
• Reasoning: The ability to infer a conclusion from one or multiple premises. To do so requires examining logical relationships among statements or data.
• Point of View: The way one views the world, which shapes one's construction of meaning. In a search for understanding, critical thinkers view phenomena from many different points of view.
• Procedures for Applying Criteria: Other types of thinking use a general procedure. Critical thinking makes use of many procedures. These procedures include asking questions, making judgments, and identifying assumptions.

Oliver & Utermohlen (1995) see students as too often being passive receptors of information. Through technology, the amount of information available today is massive. This information explosion is likely to continue in the future. Students need a guide to weed through the information and not just passively accept it. Students need to "develop and effectively apply critical thinking skills to their academic studies, to the complex problems that they will face, and to the critical choices they will be forced to make as a result of the information explosion and other rapid technological changes" (Oliver & Utermohlen, p. 1 ).

As mentioned in the section, Characteristics of Critical Thinking , critical thinking involves questioning. It is important to teach students how to ask good questions, to think critically, in order to continue the advancement of the very fields we are teaching. "Every field stays alive only to the extent that fresh questions are generated and taken seriously" (Center for Critical Thinking, 1996a ).

Beyer sees the teaching of critical thinking as important to the very state of our nation. He argues that to live successfully in a democracy, people must be able to think critically in order to make sound decisions about personal and civic affairs. If students learn to think critically, then they can use good thinking as the guide by which they live their lives.

Teaching Strategies to Help Promote Critical Thinking

The 1995, Volume 22, issue 1, of the journal, Teaching of Psychology , is devoted to the teaching critical thinking. Most of the strategies included in this section come from the various articles that compose this issue.

• CATS (Classroom Assessment Techniques): Angelo stresses the use of ongoing classroom assessment as a way to monitor and facilitate students' critical thinking. An example of a CAT is to ask students to write a "Minute Paper" responding to questions such as "What was the most important thing you learned in today's class? What question related to this session remains uppermost in your mind?" The teacher selects some of the papers and prepares responses for the next class meeting.
• Cooperative Learning Strategies: Cooper (1995) argues that putting students in group learning situations is the best way to foster critical thinking. "In properly structured cooperative learning environments, students perform more of the active, critical thinking with continuous support and feedback from other students and the teacher" (p. 8).
• Case Study /Discussion Method: McDade (1995) describes this method as the teacher presenting a case (or story) to the class without a conclusion. Using prepared questions, the teacher then leads students through a discussion, allowing students to construct a conclusion for the case.
• Using Questions: King (1995) identifies ways of using questions in the classroom:
• Reciprocal Peer Questioning: Following lecture, the teacher displays a list of question stems (such as, "What are the strengths and weaknesses of...). Students must write questions about the lecture material. In small groups, the students ask each other the questions. Then, the whole class discusses some of the questions from each small group.
• Reader's Questions: Require students to write questions on assigned reading and turn them in at the beginning of class. Select a few of the questions as the impetus for class discussion.
• Conference Style Learning: The teacher does not "teach" the class in the sense of lecturing. The teacher is a facilitator of a conference. Students must thoroughly read all required material before class. Assigned readings should be in the zone of proximal development. That is, readings should be able to be understood by students, but also challenging. The class consists of the students asking questions of each other and discussing these questions. The teacher does not remain passive, but rather, helps "direct and mold discussions by posing strategic questions and helping students build on each others' ideas" (Underwood & Wald, 1995, p. 18 ).
• Use Writing Assignments: Wade sees the use of writing as fundamental to developing critical thinking skills. "With written assignments, an instructor can encourage the development of dialectic reasoning by requiring students to argue both [or more] sides of an issue" (p. 24).
• Written dialogues: Give students written dialogues to analyze. In small groups, students must identify the different viewpoints of each participant in the dialogue. Must look for biases, presence or exclusion of important evidence, alternative interpretations, misstatement of facts, and errors in reasoning. Each group must decide which view is the most reasonable. After coming to a conclusion, each group acts out their dialogue and explains their analysis of it.
• Spontaneous Group Dialogue: One group of students are assigned roles to play in a discussion (such as leader, information giver, opinion seeker, and disagreer). Four observer groups are formed with the functions of determining what roles are being played by whom, identifying biases and errors in thinking, evaluating reasoning skills, and examining ethical implications of the content.
• Ambiguity: Strohm & Baukus advocate producing much ambiguity in the classroom. Don't give students clear cut material. Give them conflicting information that they must think their way through.
• Angelo, T. A. (1995). Beginning the dialogue: Thoughts on promoting critical thinking: Classroom assessment for critical thinking. Teaching of Psychology, 22(1), 6-7.
• Beyer, B. K. (1995). Critical thinking. Bloomington, IN: Phi Delta Kappa Educational Foundation.
• Center for Critical Thinking (1996a). The role of questions in thinking, teaching, and learning. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
• Center for Critical Thinking (1996b). Structures for student self-assessment. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univclass/trc.nclk
• Center for Critical Thinking (1996c). Three definitions of critical thinking [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
• Cooper, J. L. (1995). Cooperative learning and critical thinking. Teaching of Psychology, 22(1), 7-8.
• Jones, E. A. & Ratcliff, G. (1993). Critical thinking skills for college students. National Center on Postsecondary Teaching, Learning, and Assessment, University Park, PA. (Eric Document Reproduction Services No. ED 358 772)
• King, A. (1995). Designing the instructional process to enhance critical thinking across the curriculum: Inquiring minds really do want to know: Using questioning to teach critical thinking. Teaching of Psychology, 22 (1) , 13-17.
• McDade, S. A. (1995). Case study pedagogy to advance critical thinking. Teaching Psychology, 22(1), 9-10.
• Oliver, H. & Utermohlen, R. (1995). An innovative teaching strategy: Using critical thinking to give students a guide to the future.(Eric Document Reproduction Services No. 389 702)
• Robertson, J. F. & Rane-Szostak, D. (1996). Using dialogues to develop critical thinking skills: A practical approach. Journal of Adolescent & Adult Literacy, 39(7), 552-556.
• Scriven, M. & Paul, R. (1996). Defining critical thinking: A draft statement for the National Council for Excellence in Critical Thinking. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
• Strohm, S. M., & Baukus, R. A. (1995). Strategies for fostering critical thinking skills. Journalism and Mass Communication Educator, 50 (1), 55-62.
• Underwood, M. K., & Wald, R. L. (1995). Conference-style learning: A method for fostering critical thinking with heart. Teaching Psychology, 22(1), 17-21.
• Wade, C. (1995). Using writing to develop and assess critical thinking. Teaching of Psychology, 22(1), 24-28.

Other Reading

• Bean, J. C. (1996). Engaging ideas: The professor's guide to integrating writing, critical thinking, & active learning in the classroom. Jossey-Bass.
• Bernstein, D. A. (1995). A negotiation model for teaching critical thinking. Teaching of Psychology, 22(1), 22-24.
• Carlson, E. R. (1995). Evaluating the credibility of sources. A missing link in the teaching of critical thinking. Teaching of Psychology, 22(1), 39-41.
• Facione, P. A., Sanchez, C. A., Facione, N. C., & Gainen, J. (1995). The disposition toward critical thinking. The Journal of General Education, 44(1), 1-25.
• Halpern, D. F., & Nummedal, S. G. (1995). Closing thoughts about helping students improve how they think. Teaching of Psychology, 22(1), 82-83.
• Isbell, D. (1995). Teaching writing and research as inseparable: A faculty-librarian teaching team. Reference Services Review, 23(4), 51-62.
• Jones, J. M. & Safrit, R. D. (1994). Developing critical thinking skills in adult learners through innovative distance learning. Paper presented at the International Conference on the practice of adult education and social development. Jinan, China. (Eric Document Reproduction Services No. ED 373 159)
• Sanchez, M. A. (1995). Using critical-thinking principles as a guide to college-level instruction. Teaching of Psychology, 22(1), 72-74.
• Spicer, K. L. & Hanks, W. E. (1995). Multiple measures of critical thinking skills and predisposition in assessment of critical thinking. Paper presented at the annual meeting of the Speech Communication Association, San Antonio, TX. (Eric Document Reproduction Services No. ED 391 185)
• Terenzini, P. T., Springer, L., Pascarella, E. T., & Nora, A. (1995). Influences affecting the development of students' critical thinking skills. Research in Higher Education, 36(1), 23-39.

On the Internet

• Carr, K. S. (1990). How can we teach critical thinking. Eric Digest. [On-line]. Available HTTP: http://ericps.ed.uiuc.edu/eece/pubs/digests/1990/carr90.html
• The Center for Critical Thinking (1996). Home Page. Available HTTP: http://www.criticalthinking.org/University/
• Ennis, Bob (No date). Critical thinking. [On-line], April 4, 1997. Available HTTP: http://www.cof.orst.edu/cof/teach/for442/ct.htm
• Montclair State University (1995). Curriculum resource center. Critical thinking resources: An annotated bibliography. [On-line]. Available HTTP: http://www.montclair.edu/Pages/CRC/Bibliographies/CriticalThinking.html
• No author, No date. Critical Thinking is ... [On-line], April 4, 1997. Available HTTP: http://library.usask.ca/ustudy/critical/
• Sheridan, Marcia (No date). Internet education topics hotlink page. [On-line], April 4, 1997. Available HTTP: http://sun1.iusb.edu/~msherida/topics/critical.html

Walker Center for Teaching and Learning

• 433 Library
• Dept 4354
• 615 McCallie Ave
•   423-425-4188

• Grades 6-12
• School Leaders

Fill your classroom library 📚

44 Powerful Instructional Strategies Examples for Every Classroom

So many ways to help students learn!

Looking for some new ways to teach and learn in your classroom? This roundup of instructional strategies examples includes methods that will appeal to all learners and work for any teacher.

What are instructional strategies?

In the simplest of terms, instructional strategies are the methods teachers use to achieve learning objectives. In other words, pretty much every learning activity you can think of is an example of an instructional strategy. They’re also known as teaching strategies and learning strategies.

The more instructional strategies a teacher has in their tool kit, the more they’re able to reach all of their students. Different types of learners respond better to various strategies, and some topics are best taught with one strategy over another. Usually, teachers use a wide array of strategies across a single lesson. This gives all students a chance to play to their strengths and ensures they have a deeper connection to the material.

There are a lot of different ways of looking at instructional strategies. One of the most common breaks them into five basic types. It’s important to remember that many learning activities fall into more than one of these categories, and teachers rarely use one type of strategy alone. The key is to know when a strategy can be most effective, for the learners or for the learning objective. Here’s a closer look at the five basic types, with instructional strategies examples for each.

Direct Instruction Instructional Strategies Examples

Direct instruction can also be called “teacher-led instruction,” and it’s exactly what it sounds like. The teacher provides the information, while the students watch, listen, and learn. Students may participate by answering questions asked by the teacher or practicing a skill under their supervision. This is a very traditional form of teaching, and one that can be highly effective when you need to provide information or teach specific skills.

This method gets a lot of flack these days for being “boring” or “old-fashioned.” It’s true that you don’t want it to be your only instructional strategy, but short lectures are still very effective learning tools. This type of direct instruction is perfect for imparting specific detailed information or teaching a step-by-step process. And lectures don’t have to be boring—just look at the success of TED Talks .

Didactic Questioning

These are often paired with other direct instruction methods like lecturing. The teacher asks questions to determine student understanding of the material. They’re often questions that start with “who,” “what,” “where,” and “when.”

Demonstration

In this direct instruction method, students watch as a teacher demonstrates an action or skill. This might be seeing a teacher solving a math problem step-by-step, or watching them demonstrate proper handwriting on the whiteboard. Usually, this is followed by having students do hands-on practice or activities in a similar manner.

Drill & Practice

If you’ve ever used flash cards to help kids practice math facts or had your whole class chant the spelling of a word out loud, you’ve used drill & practice. It’s another one of those traditional instructional strategies examples. When kids need to memorize specific information or master a step-by-step skill, drill & practice really works.

Indirect Instruction Instructional Strategies Examples

This form of instruction is learner-led and helps develop higher-order thinking skills. Teachers guide and support, but students drive the learning through reading, research, asking questions, formulating ideas and opinions, and more. This method isn’t ideal when you need to teach detailed information or a step-by-step process. Instead, use it to develop critical thinking skills , especially when more than one solution or opinion is valid. ADVERTISEMENT

Problem-Solving

In this indirect learning method, students work their way through a problem to find a solution. Along the way, they must develop the knowledge to understand the problem and use creative thinking to solve it. STEM challenges are terrific examples of problem-solving instructional strategies.

Project-Based Learning

When kids participate in true project-based learning, they’re learning through indirect and experiential strategies. As they work to find solutions to a real-world problem, they develop critical thinking skills and learn by research, trial and error, collaboration, and other experiences.

Learn more: What Is Project-Based Learning?

Concept Mapping

Students use concept maps to break down a subject into its main points and draw connections between these points. They brainstorm the big-picture ideas, then draw lines to connect terms, details, and more to help them visualize the topic.

Case Studies

When you think of case studies, law school is probably the first thing that jumps to mind. But this method works at any age, for a variety of topics. This indirect learning method teaches students to use material to draw conclusions, make connections, and advance their existing knowledge.

Reading for Meaning

This is different than learning to read. Instead, it’s when students use texts (print or digital) to learn about a topic. This traditional strategy works best when students already have strong reading comprehension skills. Try our free reading comprehension bundle to give students the ability to get the most out of reading for meaning.

Flipped Classroom

In a flipped classroom, students read texts or watch prerecorded lectures at home. Classroom time is used for deeper learning activities, like discussions, labs, and one-on-one time for teachers and students.

Learn more: What Is a Flipped Classroom?

Experiential Learning Instructional Strategies Examples

In experiential learning, students learn by doing. Rather than following a set of instructions or listening to a lecture, they dive right into an activity or experience. Once again, the teacher is a guide, there to answer questions and gently keep learning on track if necessary. At the end, and often throughout, the learners reflect on their experience, drawing conclusions about the skills and knowledge they’ve gained. Experiential learning values the process over the product.

Science Experiments

This is experiential learning at its best. Hands-on experiments let kids learn to establish expectations, create sound methodology, draw conclusions, and more.

Learn more: Hundreds of science experiment ideas for kids and teens

Field Trips

Heading out into the real world gives kids a chance to learn indirectly, through experiences. They may see concepts they already know put into practice or learn new information or skills from the world around them.

Learn more: The Big List of PreK-12 Field Trip Ideas

Games and Gamification

Teachers have long known that playing games is a fun (and sometimes sneaky) way to get kids to learn. You can use specially designed educational games for any subject. Plus, regular board games often involve a lot of indirect learning about math, reading, critical thinking, and more.

Learn more: Classic Classroom Games and Best Online Educational Games

Service Learning

This is another instructional strategies example that takes students out into the real world. It often involves problem-solving skills and gives kids the opportunity for meaningful social-emotional learning.

Learn more: What Is Service Learning?

Interactive Instruction Instructional Strategies Examples

As you might guess, this strategy is all about interaction between the learners and often the teacher. The focus is on discussion and sharing. Students hear other viewpoints, talk things out, and help each other learn and understand the material. Teachers can be a part of these discussions, or they can oversee smaller groups or pairings and help guide the interactions as needed. Interactive instruction helps students develop interpersonal skills like listening and observation.

Peer Instruction

It’s often said the best way to learn something is to teach it to others. Studies into the so-called “ protégé effect ” seem to prove it too. In order to teach, you first must understand the information yourself. Then, you have to find ways to share it with others—sometimes more than one way. This deepens your connection to the material, and it sticks with you much longer. Try having peers instruct one another in your classroom, and see the magic in action.

Reciprocal Teaching

This method is specifically used in reading instruction, as a cooperative learning strategy. Groups of students take turns acting as the teacher, helping students predict, clarify, question, and summarize. Teachers model the process initially, then observe and guide only as needed.

Some teachers shy away from debate in the classroom, afraid it will become too adversarial. But learning to discuss and defend various points of view is an important life skill. Debates teach students to research their topic, make informed choices, and argue effectively using facts instead of emotion.

Learn more: High School Debate Topics To Challenge Every Student

Class or Small-Group Discussion

Class, small-group, and pair discussions are all excellent interactive instructional strategies examples. As students discuss a topic, they clarify their own thinking and learn from the experiences and opinions of others. Of course, in addition to learning about the topic itself, they’re also developing valuable active listening and collaboration skills.

Learn more: Strategies To Improve Classroom Discussions

Socratic Seminar and Fishbowl

Take your classroom discussions one step further with the fishbowl method. A small group of students sits in the middle of the class. They discuss and debate a topic, while their classmates listen silently and make notes. Eventually, the teacher opens the discussion to the whole class, who offer feedback and present their own assertions and challenges.

Learn more: How I Use Fishbowl Discussions To Engage Every Student

Brainstorming

Rather than having a teacher provide examples to explain a topic or solve a problem, students do the work themselves. Remember the one rule of brainstorming: Every idea is welcome. Ensure everyone gets a chance to participate, and form diverse groups to generate lots of unique ideas.

Role-Playing

Role-playing is sort of like a simulation but less intense. It’s perfect for practicing soft skills and focusing on social-emotional learning . Put a twist on this strategy by having students model bad interactions as well as good ones and then discussing the difference.

Think-Pair-Share

This structured discussion technique is simple: First, students think about a question posed by the teacher. Pair students up, and let them talk about their answer. Finally open it up to whole-class discussion. This helps kids participate in discussions in a low-key way and gives them a chance to “practice” before they talk in front of the whole class.

Learn more: Think-Pair-Share and Fun Alternatives

Independent Learning Instructional Strategies Examples

Also called independent study, this form of learning is almost entirely student-led. Teachers take a backseat role, providing materials, answering questions, and guiding or supervising. It’s an excellent way to allow students to dive deep into topics that really interest them, or to encourage learning at a pace that’s comfortable for each student.

Learning Centers

Foster independent learning strategies with centers just for math, writing, reading, and more. Provide a variety of activities, and let kids choose how they spend their time. They often learn better from activities they enjoy.

Learn more: The Big List of K-2 Literacy Centers

Computer-Based Instruction

Once a rarity, now a daily fact of life, computer-based instruction lets students work independently. They can go at their own pace, repeating sections without feeling like they’re holding up the class. Teach students good computer skills at a young age so you’ll feel comfortable knowing they’re focusing on the work and doing it safely.

Writing an essay encourages kids to clarify and organize their thinking. Written communication has become more important in recent years, so being able to write clearly and concisely is a skill every kid needs. This independent instructional strategy has stood the test of time for good reason.

Learn more: The Big List of Essay Topics for High School

Research Projects

Here’s another oldie-but-goodie! When kids work independently to research and present on a topic, their learning is all up to them. They set the pace, choose a focus, and learn how to plan and meet deadlines. This is often a chance for them to show off their creativity and personality too.

Personal journals give kids a chance to reflect and think critically on topics. Whether responding to teacher prompts or simply recording their daily thoughts and experiences, this independent learning method strengthens writing and intrapersonal skills.

Learn more: The Benefits of Journaling in the Classroom

Play-Based Learning

In play-based learning programs, children learn by exploring their own interests. Teachers identify and help students pursue their interests by asking questions, creating play opportunities, and encouraging students to expand their play.

Learn more: What Is Play-Based Learning?

More Instructional Strategies Examples

Don’t be afraid to try new strategies from time to time—you just might find a new favorite! Here are some of the most common instructional strategies examples.

Simulations

This strategy combines experiential, interactive, and indirect learning all in one. The teacher sets up a simulation of a real-world activity or experience. Students take on roles and participate in the exercise, using existing skills and knowledge or developing new ones along the way. At the end, the class reflects separately and together on what happened and what they learned.

Storytelling

Ever since Aesop’s fables, we’ve been using storytelling as a way to teach. Stories grab students’ attention right from the start and keep them engaged throughout the learning process. Real-life stories and fiction both work equally well, depending on the situation.

Learn more: Teaching as Storytelling

Scaffolding

Scaffolding is defined as breaking learning into bite-sized chunks so students can more easily tackle complex material. It builds on old ideas and connects them to new ones. An educator models or demonstrates how to solve a problem, then steps back and encourages the students to solve the problem independently. Scaffolding teaching gives students the support they need by breaking learning into achievable sizes while they progress toward understanding and independence.

Learn more: What Is Scaffolding in Education?

Spaced Repetition

Often paired with direct or independent instruction, spaced repetition is a method where students are asked to recall certain information or skills at increasingly longer intervals. For instance, the day after discussing the causes of the American Civil War in class, the teacher might return to the topic and ask students to list the causes. The following week, the teacher asks them once again, and then a few weeks after that. Spaced repetition helps make knowledge stick, and it is especially useful when it’s not something students practice each day but will need to know in the long term (such as for a final exam).

Graphic Organizers

Graphic organizers are a way of organizing information visually to help students understand and remember it. A good organizer simplifies complex information and lays it out in a way that makes it easier for a learner to digest. Graphic organizers may include text and images, and they help students make connections in a meaningful way.

Learn more: Graphic Organizers 101: Why and How To Use Them

Jigsaw combines group learning with peer teaching. Students are assigned to “home groups.” Within that group, each student is given a specialized topic to learn about. They join up with other students who were given the same topic, then research, discuss, and become experts. Finally, students return to their home group and teach the other members about the topic they specialized in.

Multidisciplinary Instruction

As the name implies, this instructional strategy approaches a topic using techniques and aspects from multiple disciplines, helping students explore it more thoroughly from a variety of viewpoints. For instance, to learn more about a solar eclipse, students might explore scientific explanations, research the history of eclipses, read literature related to the topic, and calculate angles, temperatures, and more.

Interdisciplinary Instruction

This instructional strategy takes multidisciplinary instruction a step further, using it to synthesize information and viewpoints from a variety of disciplines to tackle issues and problems. Imagine a group of students who want to come up with ways to improve multicultural relations at their school. They might approach the topic by researching statistical information about the school population, learning more about the various cultures and their history, and talking with students, teachers, and more. Then, they use the information they’ve uncovered to present possible solutions.

Differentiated Instruction

Differentiated instruction means tailoring your teaching so all students, regardless of their ability, can learn the classroom material. Teachers can customize the content, process, product, and learning environment to help all students succeed. There are lots of differentiated instructional strategies to help educators accommodate various learning styles, backgrounds, and more.

Learn more: What Is Differentiated Instruction?

Culturally Responsive Teaching

Culturally responsive teaching is based on the understanding that we learn best when we can connect with the material. For culturally responsive teachers, that means weaving their students’ various experiences, customs, communication styles, and perspectives throughout the learning process.

Learn more: What Is Culturally Responsive Teaching?

Response to Intervention

Response to Intervention, or RTI, is a way to identify and support students who need extra academic or behavioral help to succeed in school. It’s a tiered approach with various “levels” students move through depending on how much support they need.

Learn more: What Is Response to Intervention?

Inquiry-Based Learning

Inquiry-based learning means tailoring your curriculum to what your students are interested in rather than having a set agenda that you can’t veer from—it means letting children’s curiosity take the lead and then guiding that interest to explore, research, and reflect upon their own learning.

Learn more: What Is Inquiry-Based Learning?

Growth Mindset

Growth mindset is key for learners. They must be open to new ideas and processes and believe they can learn anything with enough effort. It sounds simplistic, but when students really embrace the concept, it can be a real game-changer. Teachers can encourage a growth mindset by using instructional strategies that allow students to learn from their mistakes, rather than punishing them for those mistakes.

Learn more: Growth Mindset vs. Fixed Mindset and 25 Growth Mindset Activities

Blended Learning

This strategy combines face-to-face classroom learning with online learning, in a mix of self-paced independent learning and direct instruction. It’s incredibly common in today’s schools, where most students spend at least part of their day completing self-paced lessons and activities via online technology. Students may also complete their online instructional time at home.

Asynchronous (Self-Paced) Learning

This fancy term really just describes strategies that allow each student to work at their own pace using a flexible schedule. This method became a necessity during the days of COVID lockdowns, as families did their best to let multiple children share one device. All students in an asynchronous class setting learn the same material using the same activities, but do so on their own timetable.

Learn more: Synchronous vs. Asynchronous Learning

Essential Questions

Essential questions are the big-picture questions that inspire inquiry and discussion. Teachers give students a list of several essential questions to consider as they begin a unit or topic. As they dive deeper into the information, teachers ask more specific essential questions to help kids make connections to the “essential” points of a text or subject.

Learn more: Questions That Set a Purpose for Reading

How do I choose the right instructional strategies for my classroom?

When it comes to choosing instructional strategies, there are several things to consider:

• Learning objectives: What will students be able to do as a result of this lesson or activity? If you are teaching specific skills or detailed information, a direct approach may be best. When you want students to develop their own methods of understanding, consider experiential learning. To encourage critical thinking skills, try indirect or interactive instruction.
• Assessments : How will you be measuring whether students have met the learning objectives? The strategies you use should prepare them to succeed. For instance, if you’re teaching spelling, direct instruction is often the best method, since drill-and-practice simulates the experience of taking a spelling test.
• Learning styles : What types of learners do you need to accommodate? Most classrooms (and most students) respond best to a mix of instructional strategies. Those who have difficulty speaking in class might not benefit as much from interactive learning, and students who have trouble staying on task might struggle with independent learning.
• Learning environment: Every classroom looks different, and the environment can vary day by day. Perhaps it’s testing week for other grades in your school, so you need to keep things quieter in your classroom. This probably isn’t the time for experiments or lots of loud discussions. Some activities simply aren’t practical indoors, and the weather might not allow you to take learning outside.

Come discuss instructional strategies and ask for advice in the We Are Teachers HELPLINE group on Facebook !

Plus, check out the things the best instructional coaches do, according to teachers ..

You Might Also Like

Understanding Intrinsic vs. Extrinsic Motivation in the Classroom

What's the magic formula? Continue Reading

Copyright © 2024. All rights reserved. 5335 Gate Parkway, Jacksonville, FL 32256

• Our Mission

5 Strategies for Aligning PBL to Real-World Problem-Solving

The closer project-based learning comes to the messy, complicated problems of our world today, the more students benefit.

In March 2020, I faced a number of challenges as a school superintendent. Earlier in the month, I had read about a virus that was sweeping the world, and while American schools had not shuttered, the challenge seemed both eminent and far off.

Over the next several weeks, months, and years, I, and every other leader, faced a series of problems, including closing schools, redesigning in-person instruction, developing virtual learning programs, and working in partnership with public health organizations.

Interestingly, I learned that authentic, real-world problem-solving has a few key features:

• I was never given one problem but was presented with a number of problem situations in which I and my team needed to derive key questions that drove our decision-making.
• The problems we faced continued to change, requiring us to go back and learn new content, prepare for multiple contingencies, and communicate up-to-date information and our plans for multiple scenarios.

Contemporary learning frameworks and related methodologies can learn a lot from what we are experiencing with Covid-19. Applying the two features above to project-based learning (PBL) by using a more fluid rather than static, linear model may best prepare students for what the future of learning and work actually looks and feels like.

5 Strategies to Make PBL More Authentic

1: Students derive the driving question from multiple contexts or multiple issues within a context. In one third-grade class, students read the book We Are Water Protectors and discuss the challenges Native Americans face with the introduction of the Keystone pipeline. Next, the teacher presents two problems:

• The extraction of cobalt to build electric cars and the negative impact on rural African communities
• The development of wind farms and the decline of the golden eagle

Students then work together in this strategy to determine the key challenges facing Indigenous people and native species. Next, they develop core questions they want to answer and determine what they need to learn to answer those questions.

2: Students face changes in the problem(s) they are contemplating. Problem environments are fluid, not static. In an AP economics class, students are analyzing supply and demand of a new video game system and preparing to advise the company on what it should do to improve profits.

Every day at the beginning of class, their teacher asks them to scan reliable news sources to report any changes to supply chains, governmental restrictions such as embargoes, or any other factor that would influence their solutions to the client.

The students found out that there were major supply chain issues with essential parts needed to create the video game console. Moreover, some of the ships carrying current consoles are sitting in Asia awaiting passage to the United States because of a political dispute.

The students worked together in small groups and discussed the key factors that were impacting the company they were advising, along with what the students needed to learn and understand before meeting with the client, and finally developed multiple recommendations based on multiple contingencies.

The general strategy looks like this:

• Students learn about changes to the problem content (this could be via reading multiple news reports, listening to daily podcasts, or engaging with actual people in the field).
• In small groups, students share their key understanding of the changes and how that impacts their current understanding and strategy.
• Students determine key “need-to-knows” they have and work with the teacher and peers to gain competencies.
• Students plan for multiple contingencies and tentative solutions.

3: Presentations are short bursts of what students think and propose during the project with dollops of feedback to make adjustments. Seventh-grade students are sending in their persuasive essay on one of a number of topics (e.g., addressing the homelessness crisis, engaging with politicians on critical race theory).

As they are drafting their papers, students are randomly assigned to present their ideas and current drafts to other students and receive feedback on their writing as well as their persuasiveness to opposing views.

The strategy looks like this:

• Students have a mid-lesson stop in which they have 5 minutes to prepare to present their current work.
• Students conduct a feedback protocol (tuning or critical friends) in which one or two students receive feedback.
• Students who received feedback share what they have changed in a reflective journal or exit ticket.
• This process is repeated daily.

4: Authentic audiences engage with students throughout the project rather than just at the beginning and/or end. In a fifth-grade art class, students have been commissioned by the local town council to paint murals that represent voices that are largely marginalized in their community. During their work, students meet with a number of artists and community members who share their stories, offer feedback, and address questions.

In this strategy, students engage with people outside the classroom at the beginning, middle, and end of a project to hear stories that relate to the problem context, receive guidance on the technical aspects of the content they are learning, and ask questions.

5: Groups work together in small bursts of time to solve problems. Students in Algebra II are working with logarithms to solve a number of problems related to stomach acid, algae-filled hot tubs, soil composition, and buffalo teeth.

While each student may be solving a different problem, students form small groups to share their learning, evaluate the connections between each context, and give each other feedback. After approximately two weeks of solving complex math tasks, the teacher presents three new problems and forms new groups for students to solve the problem in one or two days.

In this strategy, students form temporary groups of two to three to solve a new challenge and work together for one to two days without forming task-specific roles.

LEARNING AND PROBLEM SOLVING: THE USE OF PROBLEM SOLVING METHOD TO ACHIEVE LEARNING IN PUPILS

• September 2020
• 9(3):239-250

• Ignatius Ajuru University of Education

Discover the world's research

• 25+ million members
• 160+ million publication pages
• 2.3+ billion citations
• Liudmyla Holubnycha
• Olena Kuznetsova
• Dina Demchenko

• Robert K. Atkinson

• Miriam Bassok
• J OPER RES SOC
• Thomas H. Cormen

• Clifford Stein

• Merlin C. Wittrock
• James F. Voss
• Timothy A. Post
• Charles C. Bonwell
• James A. Eison
• New Dir Teach Learn
• Marilla Svinicki
• Benjamin S. Bloom
• David R. Krathwohl
• Bertram B. Masia
• Recruit researchers
• Join for free
• Login Email Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google Welcome back! Please log in. Email · Hint Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google No account? Sign up

• Submit A Post
• EdTech Trainers and Consultants
• Your Campus EdTech
• Your EdTech Product
• Your Feedback
• Your Love for Us
• EdTech Product Reviews

ETR Resources

• Mission/Vision
• Testimonials
• Our Clients
• Press Release

Key Tips On Problem Solving Method Of Teaching

Problem-solving skills are necessary for all strata of life, and none can be better than classroom problem-solving activities. It can be an excellent way to introduce students to problem-solving skills, get them prepped and ready to solve real problems in real-life settings.  

The ability to critically analyze a problem, map out all its elements and then prepare a solution that works is one of the most valuable skills; one must acquire in life. Educating your students about problem-solving techniques from an early age can be facilitated with in-class problem-solving activities. Such efforts encourage cognitive and social development and equip students with the tools they will need to tackle and resolve their lives.  

So, what is  a  problem-solving method of teaching ?

Problem Solving  is the act of defining a problem; determining the cause of the problem; identifying, prioritizing and selecting alternatives for a solution; and implementing a solution. In a problem-solving method, children learn by working on problems. This skill enables the students to learn new knowledge by facing the problems to be solved. It is expected of them to observe, understand, analyze, interpret, find solutions, and perform applications that lead to a holistic understanding of the concept. This method develops scientific process skills. This method helps in developing a brainstorming approach to learning concepts. 

In simple words, problem-solving is an ongoing activity in which we take what we know to discover what we do not know. It involves overcoming obstacles by generating hypotheses, testing those predictions, and arriving at satisfactory solutions. 

The problem-solving method involves three basic functions

• Seeking information
• Generating new knowledge 
• Making decisions 

This post will include key strategies to help you inculcate problem-solving skills in your students. 

First and foremostly, follow the 5-step model of problem-solving presented by Wood

Woods' problem-solving model

Identify the problem .

Allow your students to identify the system under study by interpreting the information provided in the problem statement. Then, prepare a list of what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it. Once you have a list of known problems, identifying the unknown(s) becomes simpler. The unknown one is usually the answer to the problem; however, there may be other unknowns. Make sure that your students have a clear understanding of what they are expected to find. 

While teaching problem solving, it is very important to have students know how to select, interpret, and use units and symbols. Emphasize the use of units and symbols whenever appropriate. Develop a habit of using appropriate units and symbols yourself at all times. Teach your students to look for the words only and neglect or assume to help identify the constraints. 

Furthermore, help students consider from the beginning what a logical type of answer would be. What characteristics will it possess?  

Think about it

Use the next stage to ponder the identified problem. Ideally, students will develop an imaginary image of the problem at hand during this stage. They need to determine the required background knowledge from illustrations, examples and problems covered in the course and collect pertinent information such as conversion factors, constants, and tables needed to solve the problem. 

Plan a solution

Often, the type of problem will determine the type of solution. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards. 

Help your students choose the best strategy by reminding them again what they must find or calculate. 

Carry out the plan

Now that the major part of problem-solving has been done start executing the solution. There are possibilities that a plan may 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?  

Other tips include

Ask open-ended questions.

When a student seeks help, you might be willing to give them the answer they are looking for so you can both move on. But what is recommend is that instead of giving answers promptly, try using open-ended questions and prompts. For example: ask What do you think will happen if..? Why do you think so? What would you do if you get into such situations? Etc. 

Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset. Getting an 'incorrect' response does not have to be a bad thing! What matters most is what they have done to achieve it and how they might change their approach next time. As a teacher, you can help students learn the process of reflection. 

Model The Strategies

As children learn creative problem-solving techniques, there will probably be times when they will be frustrated or uncertain. Here are just a few simple ways to model what creative problem-solving looks like and sounds like. 

• Ask questions in case you don't understand anything.
• Admit to not knowing the right answer.
• Discuss the many possible outcomes of different situations. 
• Verbalize what you feel when you come across a problem.
• Practising these strategies with your students will help create an environment where struggle, failure and growth are celebrated!

Encourage Grappling

Grappling is not confined to perseverance! This includes critical thinking, asking questions, observing evidence, asking more questions, formulating hypotheses and building a deep understanding of a problem. 

There are numerous ways to provide opportunities for students to struggle. All that includes the engineering design process is right! Examples include: 

• Engineering or creative projects
• Design-thinking challenges
• Informatics projects
• Science experiments

Make problem resolution relevant to the lives of your students

Limiting problem solving to class is a bad idea. This will affect students later in life because problem-solving is an essential part of human life, and we have had a chance to look at it from a mathematical perspective. Such problems are relevant to us, and they are not things that we are supposed to remember or learn but to put into practice in real life. These are things from which we can take very significant life lessons and apply them later in life. 

What's your strategy? How do you teach Problem-Solving to your students? Do let us know in the comments. 

Latest EdTech News To Your Inbox

Stay connected.

Sign in to your account

Username or Email Address

Remember Me

We apologize for the inconvenience...

To ensure we keep this website safe, please can you confirm you are a human by ticking the box below.

If you are unable to complete the above request please contact us using the below link, providing a screenshot of your experience.

https://ioppublishing.org/contacts/

  Gender and Behaviour Journal / Gender and Behaviour / Vol. 19 No. 2 (2021) / Articles (function() { function async_load(){ var s = document.createElement('script'); s.type = 'text/javascript'; s.async = true; var theUrl = 'https://www.journalquality.info/journalquality/ratings/2409-www-ajol-info-gab'; s.src = theUrl + ( theUrl.indexOf("?") >= 0 ? "&" : "?") + 'ref=' + encodeURIComponent(window.location.href); var embedder = document.getElementById('jpps-embedder-ajol-gab'); embedder.parentNode.insertBefore(s, embedder); } if (window.attachEvent) window.attachEvent('onload', async_load); else window.addEventListener('load', async_load, false); })();

Article sidebar, article details, main article content, problem-solving as teaching strategy: promoting active learning in a south african university of technology, e.m. kgwete, k.s. malatji.

Education is expected to produce the workforce capable of problem solving and innovation. Application of problem-solving as a teaching strategy by lecturers in their teaching is another means of producing problem solvers and innovators at the workplace. The study investigated the application of problem-solving as a teaching strategy to promote active learning in South African university. In this study, the population consisted of lecturers in one South African universities. The research used purposive sampling to select two junior lecturers, two lecturers, two senior lecturers in the university. The study followed a qualitative approach with a case study as a research design. The research paradigm used was phenomenology because the study consisted of lecturers’ subjective experience of teaching at university. Kolb’s experiential learning theory underpinned the study. Semi structured Individual interviews were used to collect data. Data was analyzed through a thematic approach through identifying themes from the interviews. The results of this study have revealed that a problem-solving teaching is one of the good practices that promote active learning in universities. The study further revealed that the problem-solving encourages students to be self-reliant. The study recommends that lecturers should be trained on how to use problem-solving as a teaching strategy.

AJOL is a Non Profit Organisation that cannot function without donations. AJOL and the millions of African and international researchers who rely on our free services are deeply grateful for your contribution. AJOL is annually audited and was also independently assessed in 2019 by E&Y.

Your donation is guaranteed to directly contribute to Africans sharing their research output with a global readership.

• For annual AJOL Supporter contributions, please view our Supporters page.

Journal Identifiers

Bristol Institute For Learning and Teaching

2018-19 projects, approaches to active learning spaces .

Projects examine how pedagogy and learning needs can determine how to best configure digitally-enabled teaching spaces.

Accrediting Community Engagement: A Bristol Approach to Service-Learning

Project lead: Helen Thomas-Hughes (Cabot Institute)

Project summary: This project examines service-learning as a mechanism for bringing professional, industry-specific and community-engagement opportunities into taught curricula across the University through the piloting of a new curricula approach to teaching community-engagement within the English department’s English

Literature and Community Engagement programme (ELCE). ELCE is a unique offering within the university. It is a part-time, evenings and weekend taught, direct application programme which has an embedded, accredited approach to community and civic engagement combining teaching and practice. Students study with the programme for six years during which they design and run and are assessed upon a community-engaged literature or literacies-based project. ELCE has been an experimental programme for ten years and has only recently become a permanent feature of the English Department. The existing taught framework has been developed to draw more expansively on service-learning as a theoretical framework for community engaged and civic-learning (the new curricula will be launched in 2018/19). The proposed project will focus on the delivery of this developed curricula and assessment model in ELCE to examine how practise-based teaching of ‘community engagement’ can apply the service-learning model in the UK context. Through this, the project aims to create a demonstrative evidence base and framework for integrating accredited community-engaged projects within wider taught programmes within the University.

Evaluation of clinical skills lab as an active learning space: sharing best practice & identifying improvements

Project lead: Alison Catterall (Bristol Veterinary School)         

Project team: Rachel Christopher and Sam Brown (Bristol Veterinary School)

Project summary: The project aims to evaluate the Clinical Skills Lab (CSL) at Langford as an active learning space to identify best practice, new ideas and areas for further improvement. The findings will be used to continue to develop the CSL to support student learning and will be shared with others within and beyond the university.

Clinical skills are considered core competencies for all health professionals and the associated teaching is reviewed as part of accreditation visits. The veterinary CSL at Langford has evolved as an active, student-centred learning space that combines taught practicals with an open-access policy that allows students to practise ‘just in time’ i.e. as required. A variety of supporting learning resources are available including innovative uses of technology e.g. YouTube, tablets, QR codes and the Haptic Cow. The Bristol CSL is now considered one of the best veterinary examples in the world; it was described as ‘exemplary’ by the AVMA accreditation team and the transformative effect on student learning is evident in feedback from students, recent graduates and employers. The CSL regularly hosts visitors from overseas and the team have been invited to help others set up similar facilities and run workshops, including in Africa.

It is timely (at time of writing) to review the use of the CSL as the BVSc curriculum (and the use of the CSL) enters a period of greater stability, evolution rather than revolution. The aim of this project is to evaluate the CSL using a survey and focus groups and align questions with factors considered important when designing and running active learning spaces, including: the physical space; how students are using, and learning in, the CSL; how the variety of resources, including technology, support student learning. 

The project findings and outputs have potential to benefit students across the university. While specific findings related to clinical skills have most relevance to medicine, dentistry, veterinary science and nursing, by aligning the research with key factors related to active learning spaces, it is anticipated that many outputs will be generalisable. Additionally, the research will be disseminated to the international clinical skills community, informing similar developments elsewhere and will help to keep Bristol at the forefront of innovation in the field.

Developing the 'Criminology Skills Academy': A Framework Promoting Technology Enhanced Active Learning Spaces

Project lead: Joanna Large (School of Policy Studies)

Project summary: We (BSc Criminology team supported by Digital Education Office) aim to create a ‘Criminology Skills Academy’ (CSA) which provides an integrated and innovative space to promote active learning and skills progression. This project will create a searchable database of ‘just-in-time’ style 2-5 minute video content on academic and research skills supported by ‘Livecasts with Q&A’: with a focus of embedding these within specific disciplinary and programme examples. Content will be created by the teaching team and will be responsive to student needs.

Although the initial focus is on creating a Criminology Skills Academy, the project has a wider remit of developing a replicable framework which will see the model rolled out across the School for Policy Studies (SPS) undergraduate programmes (BSc Social Policy (SP)/BSc Childhood Studies (CS)), tailored by programme staff to pathways of study. This will allow the success of the model and its wider portability to be evaluated, whilst ensuring consistency in student experience across SPS undergraduate programmes.

In 2017/18, SPS introduced a Level 4 “Critical Skills” unit. Whilst students were positive about workshop style seminars, their feedback was critical of learning academic/research skills via lectures and many simply disengaged. Staff noted (similarly to Level 5 “Social Research Methods”) that students do not consider these as part of their degree programme as the cross-programme delivery lacks disciplinary specificity. In line with the broader development of Bristol Futures which aims to create ‘innovative learning resources’ and ‘development of academic skills’, we recognise problems of traditional and “bolt on” methods for teaching academic/research skills and the need for these to be embedded in curriculums (HEA, 2018; Wingate, 2007). Additionally, we recognise the need to engage students with taking an active approach to their own skills development (see HEA, 2018) and the increasing diversity of learners needs (Gordon, 2014). The Academy will create a space where students can drive their own personal development, embedded as part of their suite of learning opportunities in their wider degree programme. Drawing on the popularity of YouTube tutorials and the ‘prosumer’ interfaces of Web 2.0, the project takes advantage of technology enhanced learning (Gordon, 2014) and reinforces the movement towards a better integration of online and offline learning spaces (Peberdy, 2014). Focused video content allows students to select material when required, allows for differentiation in learning styles and needs, and is dynamic as we can respond to student feedback to adapt and update content.

Supporting post-graduate learners: optimising the environment for case-based learning in veterinary education

Project lead: Emma Love (Bristol Veterinary School)

Project team: Chloe Anderson, Lucy Squires, Sheena Warman, Simon Atkinson (all Bristol Veterinary School)

Project summary:  Enabling students to develop the skills and enthusiasm for independent learning is essential in veterinary medicine where lifelong learning is vital for career success and fulfilment. Case-based learning (CBL) is widely used in medical undergraduate education where it is perceived to motivate and engage students (Thistlethwaite et al 2012). Case-based learning in whole year (120-150 students) teaching sessions was successfully introduced into the existing undergraduate BVSc programme as part of the curriculum review (Crowther & Baillie 2015).

The Accelerated Graduate Entry BVSc programme (AGEP) is a four-year veterinary degree, exclusively for graduates, which will complement and feed into the existing five-year BVSc degree.  The AGEP students will join the 5-year cohort partway through the 2 nd   year of the AGEP (3 rd   year of the BVSc). The first cohort (35 students) started in September 2019. The introduction of an innovative new curriculum for Graduate Entry Students will be a unique selling point for Bristol Vet School and the programme will adopt many aspects of current best practice in andragogy with a focus on independent, self-directed, and/or cooperative learning, making it unique in veterinary education in the UK.

The learning outcomes for the first two years of the course will primarily be met using case-based learning in small tutor-facilitated groups of 8-10 students. Case material will be time-released, with students accessing materials electronically via iPads/iPhones and using interactive white boards to share resources and explore answers to questions.

The environment in which the students study is key, and will include small group teaching rooms and digital resources, providing a “home” for the students to study in.  As part of the development of the classroom environment we are engaging with the Digital Education office within the University.  This project will play a significant role in finalising the design of these spaces at Langford.

The aim of this pilot project is to ensure that a robust and effective strategy is used for the delivery of CBL in the new AGEP. 

Staff and student assessment literacy

Projects examine how assessment literacy is understood, defined, developed and encouraged in students and staff. In particular, they examine the impact of certain types of assessment or practice that create a shared understanding among staff and students on the "grammar" of assessment. 

Improving staff and student assessment literacy to aid development of problem solving skills

Project lead: Helen Health (School of Physics)

Project summary: The Institute of Physics, twice, lists problem solving as an essential attribute of the Physics Graduate in “The Physics Degree” which describes the content of accredited programmes. Enabling students to learn to solve problems and assessing that they can do this is therefore essential.  There is a wealth of literature on developing problem solving skills in students, however many staff are unaware of this and advocate for teaching methods that suited them as students. The literature describes differences between novice and expert problem solvers. Given the academic success of many staff it is likely that they moved quickly from the novice to expert mode and this affects their perception of how problem solving should be taught. For example, this leads to strong resistance to providing full solutions to problems when the literature strongly suggests that good worked examples are a good way to develop problem solving skills.

The aim of this project is to develop the understanding in the 1 st year and Foundation year Core Physics lecturers of the literature around problem solving and use these to design and develop materials for formative and summative assessment based on best practice. Through an understanding of the aims of the formative assessment, i.e. what skills are being developed and techniques are being taught, and the purpose of summative assessment should be clarified.

The objectives are

• To develop an understanding of the literature on problem solving in a selected group of staff with responsibility for delivering Core Physics in the 1 st and Foundation years through away days and development of an “early years” team.
• To produce guides for Physics staff to best practice in developing formative assessment materials to enable students to develop problem solving skills and summative materials which test these skills. The guides would focus on material relevant to our courses, but which could be adapted to other programmes.
• To develop materials based on best practice, these would include both online formative assessments and problems book material, for student use and as examples for staff to build on. So far, the adaptive release aspect of online testing has not been explored.

As an additional outcome working as a project team on the early years would provide a basis for moving towards a more programme level view of our courses and how to assess problem solving across the programme, linking to the Universities move towards programme level assessment.

Heterogeneous teaching–learning based optimization with local search for the covering delivering problem in last mile delivery

New citation alert added.

This alert has been successfully added and will be sent to:

You will be notified whenever a record that you have chosen has been cited.

To manage your alert preferences, click on the button below.

New Citation Alert!

Please log in to your account

• Information & Contributors
• Bibliometrics & Citations
• View Options

• Presentations
• Advanced Photonics
• Advanced Photonics Nexus
• Biophotonics Discovery
• Journal of Applied Remote Sensing
• Journal of Astronomical Telescopes, Instruments, and Systems
• Journal of Biomedical Optics
• Journal of Electronic Imaging
• Journal of Medical Imaging
• Journal of Micro/Nanopatterning, Materials, and Metrology
• Journal of Nanophotonics
• Journal of Optical Microsystems
• Journal of Photonics for Energy
• Neurophotonics
• Optical Engineering
• Photonics Insights
• DOWNLOAD PAPER SAVE TO MY LIBRARY

Show All Keywords

Keywords/phrases, publication years.

Solving time-delay issues in reinforcement learning via transformers

• Published: 10 September 2024

Cite this article

• Bo Xia   ORCID: orcid.org/0009-0003-3507-9732 1 ,
• Zaihui Yang 1 ,
• Minzhi Xie 1 ,
• Yongzhe Chang 1 ,
• Bo Yuan   ORCID: orcid.org/0000-0003-2169-0007 2 ,
• Zhiheng Li 1 ,
• Xueqian Wang   ORCID: orcid.org/0000-0003-3542-0593 1 &
• Bin Liang 3  

The presence of observation and action delays in remote control scenarios significantly challenges the decision-making of agents that depend on immediate interactions, particularly within traditional deep reinforcement learning (DRL) algorithms. Existing approaches attempt to tackle this problem through various strategies, such as predicting delayed states, transforming delayed Markov Decision Processes (MDPs) into delay-free equivalents. However, both model-free and model-based methods require extensive online data, making them time-consuming and resource-intensive. To effectively handle time-delay challenges and develop a competent and robust RL algorithm, the Augmented Decision Transformer (ADT) is proposed as the first offline RL algorithm designed to enable agents to manage diverse tasks with various constant delays. It transforms a deterministic delayed MDP (DDMDP) into a standard MDP by simulating trajectories in delayed environments using offline dataset from undelayed environments. The Decision Transformer, an autoregressive model, is then employed to train a decision model based on expected rewards, past state sequences and past action sequences. Extensive experiments conducted on MuJoCo and Adroit tasks validate the robustness and efficiency of the ADT, with its average performance across all tasks being 56% better than the worst-performing comparative algorithms. The results demonstrate that the ADT can outperform state-of-the-art RL counterparts, achieving superior performance across various tasks with different delay conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Explore related subjects

• Artificial Intelligence

Availability of data and materials

Data will be made available on reasonable request.

Code availibility

Code will be made available on reasonable request.

\(\delta (x - x_0) = {\left\{ \begin{array}{ll} 1, & \text {if }x=x_0, \\ {0}, & \text {others.} \end{array}\right. }\)

\(c_i\) represents the action selected at time i before the first state is observed.

https://github.com/Farama-Foundation/D4RL

https://mujoco.org/

https://github.com/aravindr93/hand_dapg

https://gym.openai.com/

https://github.com/young-geng/CQL

https://github.com/sfujim/TD3_BC

https://github.com/rmst/rlrd

https://github.com/baimingc/dambrl

https://github.com/pranz24/pytorch-soft-actor-critic

van Dis EA, Bollen J, Zuidema W et al (2023) Chatgpt: five priorities for research. Nature 614(7947):224–226

Degrave J, Felici F, Buchli J et al (2022) Magnetic control of tokamak plasmas through deep reinforcement learning. Nature 602(7897):414–419

Article   Google Scholar  

Zhang R, Lv Q, Li J et al (2022) A reinforcement learning method for human-robot collaboration in assembly tasks. Robot Comput Integr Manuf 73:102227

Jiang W, Liu K, Charalambous T (2022) Multi-agent consensus with heterogeneous time-varying input and communication delays in digraphs. Automatica 135:109950

Article   MathSciNet   Google Scholar  

Jiang W, Chen Y, Charalambous T (2020) Consensus of general linear multi-agent systems with heterogeneous input and communication delays. IEEE Control Systems Letters 5(3):851–856

Chen H, Liu Z (2021) Time-delay prediction-based smith predictive control for space teleoperation. J Guid Control Dyn 44(4):872–879

Guerrero J, Chemori A, Torres J et al (2023) Time-delay high-order sliding mode control for trajectory tracking of autonomous underwater vehicles under disturbances. Ocean Eng 268:113375

Liu H, Wang L (2020) Remote human-robot collaboration: A cyber-physical system application for hazard manufacturing environment. J Manuf Syst 54:24–34

Zhou X, Yang Z, Ren Y et al (2023) Modified bilateral active estimation model: A learning-based solution to the time delay problem in robotic tele-control. IEEE Robot Autom Lett 8(5):2653–2660

Haarnoja T, Zhou A, Abbeel P et al (2018) Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In: International conference on machine learning, PMLR, pp 1861–1870

Deng Y, Léchappé V, Moulay E et al (2022) Predictor-based control of time-delay systems: a survey. Int J Syst Sci 53(12):2496–2534

Zhang XM, Han QL, Ge X (2022) The construction of augmented lyapunov-krasovskii functionals and the estimation of their derivatives in stability analysis of time-delay systems: A survey. Int J Syst Sci 53(12):2480–2495

Ali A, Zhu Y, Zakarya M (2022) Exploiting dynamic spatio-temporal graph convolutional neural networks for citywide traffic flows prediction. Neural Netw 145:233–247

Ali A, Zhu Y, Zakarya M (2021) Exploiting dynamic spatio-temporal correlations for citywide traffic flow prediction using attention based neural networks. Inf Sci 577:852–870

Ali A, Zhu Y, Zakarya M (2021) A data aggregation based approach to exploit dynamic spatio-temporal correlations for citywide crowd flows prediction in fog computing. Multimed Tools Appl 80(20):31401–31433

Walsh TJ, Nouri A, Li L et al (2009) Learning and planning in environments with delayed feedback. Auton Agent Multi-Agent Syst 18:83–105

Hester T, Stone P (2013) Texplore: real-time sample-efficient reinforcement learning for robots. Mach Learn 90:385–429

Derman E, Dalal G, Mannor S (2020) Acting in delayed environments with non-stationary markov policies. In: International conference on learning representations

Katsikopoulos KV, Engelbrecht SE (2003) Markov decision processes with delays and asynchronous cost collection. IEEE Trans Autom Control 48(4):568–574

Nath S, Baranwal M, Khadilkar H (2021) Revisiting state augmentation methods for reinforcement learning with stochastic delays. In: Proceedings of the 30th ACM international conference on information & knowledge management, pp 1346–1355

Ramstedt S, Pal C (2019) Real-time reinforcement learning. Adv Neural Inf Process Syst 32

Xiao T, Jang E, Kalashnikov D et al (2019) Thinking while moving: Deep reinforcement learning with concurrent control. In: International conference on learning representations

Bouteiller Y, Ramstedt S, Beltrame G et al (2021) Reinforcement learning with random delays. In: International conference on learning representations

Chen L, Lu K, Rajeswaran A et al (2021) Decision transformer: Reinforcement learning via sequence modeling. Adv Neural Inf Process Syst 34:15084–15097

Google Scholar  

Schuitema E, Buşoniu L, Babuška R et al (2010) Control delay in reinforcement learning for real-time dynamic systems: A memoryless approach. In: 2010 IEEE/RSJ International conference on intelligent robots and systems, IEEE, pp 3226–3231

Agarwal M, Aggarwal V (2021) Blind decision making: Reinforcement learning with delayed observations. Pattern Recogn Lett 150:176–182

Chen B, Xu M, Li L et al (2021) Delay-aware model-based reinforcement learning for continuous control. Neurocomputing 450:119–128

Prudencio RF, Maximo MR, Colombini EL (2023) A survey on offline reinforcement learning: Taxonomy, review, and open problems. IEEE Trans Neural Netw Learn Syst

Fujimoto S, Meger D, Precup D (2019) Off-policy deep reinforcement learning without exploration. In: International conference on machine learning, PMLR, pp 2052–2062

Kumar A, Fu J, Soh M et al (2019) Stabilizing off-policy q-learning via bootstrapping error reduction. Adv Neural Inf Process Syst 32

Fujimoto S, Gu SS (2021) A minimalist approach to offline reinforcement learning. Adv Neural Inf Process Syst 34:20132–20145

Kumar A, Zhou A, Tucker G et al (2020) Conservative q-learning for offline reinforcement learning. Adv Neural Inf Process Syst 33:1179–1191

Yu T, Kumar A, Rafailov R et al (2021) Combo: Conservative offline model-based policy optimization. Adv Neural Inf Process Syst 34:28954–28967

Janner M, Fu J, Zhang M et al (2019) When to trust your model: Model-based policy optimization. Adv Neural Inf Process Syst 32

Kidambi R, Rajeswaran A, Netrapalli P et al (2020) Morel: Model-based offline reinforcement learning. Adv Neural Inf Process Syst 33:21810–21823

Zhang R, Dai B, Li L et al (2020) Gendice: Generalized offline estimation of stationary values. Int Conf Learn Representations

Janner M, Li Q, Levine S (2021) Offline reinforcement learning as one big sequence modeling problem. Adv Neural Inf Process Syst 34:1273–1286

Li W, Luo H, Lin Z et al (2023) A survey on transformers in reinforcement learning. Transactions on Machine Learning Research pp 2835–8856

Vinyals O, Babuschkin I, Czarnecki WM et al (2019) Grandmaster level in starcraft ii using multi-agent reinforcement learning. Nature 575(7782):350–354

Parisotto E, Song F, Rae J, et al (2020) Stabilizing transformers for reinforcement learning. In: International conference on machine learning, PMLR, pp 7487–7498

Micheli V, Alonso E, Fleuret F (2023) Transformers are sample efficient world models

Ozair S, Li Y, Razavi A et al (2021) Vector quantized models for planning. In: international conference on machine learning, PMLR, pp 8302–8313

Paster K, McIlraith S, Ba J (2022) You can’t count on luck: Why decision transformers and rvs fail in stochastic environments. Adv Neural Inf Process Syst 35:38966–38979

Yang M, Schuurmans D, Abbeel P et al (2023) Dichotomy of control: Separating what you can control from what you cannot. The Eleventh International Conference on Learning Representations

Lee KH, Nachum O, Yang M et al (2022) Multi-game decision transformers. Adv Neural Inf Process Syst

Sutton RS, Barto AG (2018) Reinforcement learning: An introduction. MIT press

Hu K, Zheng RC, Gao Y et al (2023) Decision transformer under random frame dropping. The Eleventh International Conference on Learning Representations

Download references

Not applicable.

Author information

Authors and affiliations.

Shenzhen International Graduate School, Tsinghua University, Shenzhen, 518055, China

Bo Xia, Zaihui Yang, Minzhi Xie, Yongzhe Chang, Zhiheng Li & Xueqian Wang

Research Institute of Tsinghua University in Shenzhen, Shenzhen, 518057, China

Department of Automation, Tsinghua University, Beijing, 100084, China

You can also search for this author in PubMed   Google Scholar

Contributions

− Conceptualization: Bo Xia and Xueqian Wang− Methodology: Bo Xia and Xueqian Wang− Formal analysis and investigation: Bo Xia, Zaihui Yang, and Minzhi Xie− Writing - original draft preparation: Bo Xia, Minzhi Xie, Bo Yuan, and Yongzhe Chang− Writing - review and editing: Bo Xia, Bo Yuan, Zhiheng Li, and Xueqian Wang− Supervision: Yongzhe Chang, Bo Yuan, Zhiheng Li, Xueqian Wang, and Bin Liang− Funding acquisition: Xueqian Wang and Bin Liang

Corresponding author

Correspondence to Xueqian Wang .

Ethics declarations

Ethics approval and consent to participate, consent for publication, competing interests.

All authors disclosed no relevant relationships.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Expert rewards for different algorithms and tasks

For offline RL algorithms, including ADT, CQL, TD3_BC, and BC, the expert rewards for various tasks are sourced from D4RL. For the RLRD and SAC algorithms, the expert rewards for MuJoCo tasks are obtained from Tianshou, while the expert rewards for Adroit tasks (including pen, door, relocate, and hammer) are derived from the average experimental results of three different seeds. For the DATS algorithm, as reward functions for Adroit tasks are not designed, only MuJoCo tasks are considered, and the expert rewards are similarly obtained from the average of three different experiments.

Table 13 shows all the expert rewards in various environments with different algorithms.

Appendix B: More results and analysis

Tables 14 through 21 present the average normalized returns from ten test runs under delays 1 to 3, for eight tasks in MuJoCo and Adroit environments, using expert and medium-expert datasets. Each column’s “Dataset” string indicates the delay and dataset type, e.g., “1-e” represents a delay of 1 using the expert dataset. The “Average” value in the last row of each table reflects the overall performance of each algorithm, averaged across all delays and datasets for easier comparison.

From these tables, the following conclusions can be drawn: (1) For most tasks, the performance generally declines as the delay increases when using the same dataset and algorithm in a delay-free environment. This is due to the increasing discrepancy between the observed state and the actual state, impacting decision quality. However, ADT outperforms other algorithms in most tasks and exhibits a slower performance decline with increasing delay. This is attributed to ADT’s trajectory optimization approach and reward-guided updates, leveraging the Transformer architecture to deeply explore information context. (2) The experimental results indicate that for the same task and delay, policies trained on the expert dataset generally outperform those trained on the medium-expert dataset. This suggests that having more expert-level trajectories in the dataset, given a similar number of trajectories, is beneficial for policy learning. (3) Adroit tasks present significant challenges for conventional offline reinforcement learning methods due to their large action space and sparse reward settings. Further research is required to address the policy learning problem with limited expert trajectories in such tasks.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Xia, B., Yang, Z., Xie, M. et al. Solving time-delay issues in reinforcement learning via transformers. Appl Intell (2024). https://doi.org/10.1007/s10489-024-05830-2

Download citation

Accepted : 30 August 2024

Published : 10 September 2024

DOI : https://doi.org/10.1007/s10489-024-05830-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Deep reinforcement learning
• Deterministic delayed Markov Decision Process
• Offline reinforcement learning
• Decision transformer
• Find a journal
• Publish with us
• Track your research