problem solving approach in teaching

Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

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Why Every Educator Needs to Teach Problem-Solving Skills

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

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

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

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

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

Problem-Solving Skills Help Students…

develop resilience.

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

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

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

Set and Achieve Goals

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

Resolve Conflicts

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

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

Achieve Success

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

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

Problem-Solving Skills Can Be Measured and Taught

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

What Are Performance-Based Assessments?

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

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

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

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

Preview a Performance-Based Assessment

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

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

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

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

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

Explore CAE’s Problem-Solving Assessments

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

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

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

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

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

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

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

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

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

October 31, 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Teaching Problem-Solving Skills

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

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

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

Principles for teaching problem solving

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

Woods’ problem-solving model

Define the problem.

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

Think about it

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

Plan a solution

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

Carry out the plan

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

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

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

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

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

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

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

Daniel Kane - [email protected]

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Not getting stuck

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

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

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

What does it mean to explicitly teach problem solving?

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

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

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

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

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

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

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

Portrait of the Problem-Solving Curriculum

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

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

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

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

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

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

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

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

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

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

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

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

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Teaching problem solving

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

Introducing the problem

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

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

Working on solutions

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

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

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

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

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

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Evan Glazer (University of Georgia)

Editor’s Note: Dr. Glazer chose to use the term Problem-based Instruction and Inquiry, but my reading and other references to this chapter also use the term Problem-based Learning. The reader can assume the terms are equivalent.

Description

Problem-based inquiry is an effort to challenge students to address real-world problems and resolve realistic dilemmas.

Such problems create opportunities for meaningful activities that engage students in problem solving and higher-ordered thinking in authentic settings. Many textbooks attempt to promote these skills through contrived settings without relevance to students’ lives or interests. A notorious algebra problem concerns the time at which two railway trains will pass each other:

Two trains leave different stations headed toward each other. Station A is 500 miles west of Station B. Train A leaves station A at 12:00 pm traveling toward Station B at a rate of 60 miles per hour. Train B leaves Station B at 2:30 pm for Station A at a rate of 45 miles per hour. At what time will the trains meet?

Reading this question, one might respond, “Who cares?”, or, “Why do we need to know this?” Such questions have created substantial anxiety among students and have, perhaps, even been the cause of nightmares. Critics would argue that classic “story problems” leave a lasting impression of meaningless efforts to confuse and torment students, as if they have come from hell’s library. Problem-based inquiry, on the other hand, intends to engage students in relevant, realistic problems.

Several changes would need to be made in the above problem to promote problem-based inquiry. It would first have to be acknowledged that the trains are not, in fact, traveling at constant rates when they are in motion; negotiating curves or changing tracks at high speeds can result in accidents.

Further, all of the information about the problem cannot be presented to the learner at the outset; that is, some ambiguity must exist in the context so that students have an opportunity to engage in a problem-solving activity. In addition, the situation should involve a meaningful scenario. Suppose that a person intends to catch a connecting train at the second station and requires a time-efficient itinerary? What if we are not given data about the trains, but instead, the outcome of a particular event, such as an accident?

Why should we use problem-based inquiry to help students learn?

The American educational system has been criticized for having an underachieving curriculum that leads students to memorize and regurgitate facts that do not apply to their lives (Martin, 1987; Paul, 1993). Many claim that the traditional classroom environment, with its orderly conduct and didactic teaching methods in which the teacher dispenses information, has greatly inhibited students’ opportunities to think critically (Dossey et al., 1988; Goodlad, 1984; Wood, 1987). Problem-based inquiry is an attempt to overcome these obstacles and confront the concerns presented by the National Assessment of Educational Progress:

If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war. We have, in effect, been committing an act of unthinking, unilateral educational disarmament. (A Nation at Risk, 1983)

Problem-based inquiry emphasizes learning as a process that involves problem solving and critical thinking in situated contexts. It provides opportunities to address broader learning goals that focus on preparing students for active and responsible citizenship. Students gain experience in tackling realistic problems, and emphasis is placed on using communication, cooperation, and resources to formulate ideas and develop reasoning skills.

What is a framework for a problem-based inquiry?

Situated cognition, constructivism, social learning, and communities of practice are assumed theories of learning and cognition in problem-based inquiry environments. These theories have common themes about the context and the process of learning and are often associated.

Characteristics

Some common characteristics in problem-based learning models:

Activity is grounded in a general question about a problem that has multiple possible answers and methods for addressing the question. Each problem has a general question that guides the overall task followed by ill-structured problems or questions that are generated throughout the problem-solving process. That is, to address the larger question, students must derive and investigate smaller problems or questions that relate to the findings and implications of the broader goal. The problems or questions thus created are most likely new to the students and lack known definitive methods or answers that have been predetermined by the teacher.

Learning is student-centered; the teacher acts as facilitator. In essence, the teacher creates an environment where students take ownership in the direction and content of their learning.

Students work collaboratively towards addressing the general question . All of the students work together to attain the shared goal of producing a solution to the problem. Consequently, the groups co-depend on each other’s performance and contributions in order to make their own advances in reasoning toward answering the research questions and the overall problem.

Learning is driven by the context of the problem and is not bound by an established curriculum. In this environment, students determine what and how much they need to learn in order to accomplish a specific task. Consequently, acquired information and learned concepts and strategies are tied directly to the context of the learning situation. Learning is not confined to a preset curriculum. Creation of a final product is not a necessary requirement of all problem-based inquiry models.

Project-based learning models most often include this type of product as an integral part of the learning process, because learning is expected to occur primarily in the act of creating something. Unlike problem based inquiry models, project-based learning does not necessarily address a real-world problem, nor does it focus on providing argumentation for resolution of an issue.

In a problem-based inquiry setting, there is greater emphasis on problem-solving, analysis, resolution, and explanation of an authentic dilemma. Sometimes this analysis and explanation is represented in the form of a project, but it can also take the form of verbal debate and written summary.

Instructional models and applications

There is no single method for designing problem-based inquiry learning environments.

Various techniques have been used to generate the problem and stimulate learning. Promoting student-ownership, using a particular medium to focus attention, telling stories, simulating and recreating events, and utilizing resources and data on the Internet are among them. The instructional model, problem based learning will be discussed next with attention to instructional strategies and practical examples.

Problem-Based Learning

Problem-based learning (PBL) is an instructional strategy in which students actively resolve complex problems in realistic situations.

It can be used to teach individual lessons, units, or even entire curricula. PBL is often approached in a team environment with emphasis on building skills related to consensual decision making, dialogue and discussion, team maintenance, conflict management, and team leadership. While the fundamental approach of problem solving in situated environments has been used throughout the history of schooling, the term PBL did not appear until the 1970s and was devised as an alternative approach to medical education.

In most medical programs, students initially take a series of fact intensive courses in biology and anatomy and then participate in a field experience as a medical resident in a hospital or clinic. However, Barrows reported that, unfortunately, medical residents frequently had difficulty applying knowledge from their classroom experiences in work-related, problem-solving situations. He argued that the classical framework of learning medical knowledge first in classrooms through studying and testing was too passive and removed from context to take on meaning.

Consequently, PBL was first seen as a medical field immersion experience whereby students learned about their medical specialty through direct engagement in realistic problems and gradual apprenticeship in natural or simulated settings. Problem solving is emphasized as an initial area of learning and development in PBL medical programs more so than memorizing a series of facts outside their natural context.

In addition to the field of medicine, PBL is used in many areas of education and training. In academic courses, PBL is used as a tool to help students understand the utility of a particular concept or study. For example, students may learn about recycling and materials as they determine methods that will reduce the county landfill problem.

In addition, alternative education programs have been created with a PBL emphasis to help at-risk students learn in a different way through partnerships with local businesses and government. In vocational education, PBL experiences often emphasize participation in natural settings.

For example, students in architecture address the problem of designing homes for impoverished areas. Many of the residents need safe housing and cannot afford to purchase typical homes. Consequently, students learn about architectural design and resolving the problem as they construct homes made from recycled materials. In business and the military, simulations are used as a means of instruction in PBL. The affective and physiological stress associated with warfare can influence strategic planning, so PBL in military settings promotes the use of “war games” as a tactic for facing authentic crises.

In business settings, simulations of “what if” scenarios are used to train managers in various strategies and problem-solving approaches to conflict resolution. In both military and business settings, the simulation is a tool that provides an opportunity to not only address realistic problems but to learn from mistakes in a more forgiving way than in an authentic context.

Designing the learning environment

The following elements are commonly associated with PBL activities.

Problem generation: The problems must address concepts and principles relevant to the content domain. Problems are not investigated by students solely for problem solving experiences but as a means of understanding the subject area. Some PBL activities incorporate multidisciplinary approaches, assuming the teacher can provide and coordinate needed resources such as additional content, instructional support, and other teachers. In addition, the problems must relate to real issues that are present in society or students’ lives. Contrived scenarios detract from the perceived usefulness of a concept.

Problem presentation: Students must “own” the problem, either by creating or selecting it. Ownership also implies that their contributions affect the outcome of solving the problem. Thus, more than one solution and more than one method of achieving a solution to the problem are often possible. Furthermore, ownership means that students take responsibility for representing and communicating their work in a unique way.

Predetermined formats of problem structure and analysis towards resolution are not recommended; however, the problem should be presented such that the information in the problem does not call attention to critical factors in the case that will lead to immediate resolution. Ownership also suggests that students will ask further questions, reveal further information, and synthesize critical factors throughout the problem-solving process.

Teacher role: Teachers act primarily as cognitive coaches by facilitating learning and modeling higher order thinking and meta cognitive skills. As facilitators, teachers give students control over how they learn and provide support and structure in the direction of their learning. They help the class create a common framework of expectations using tools such as general guidelines and time lines.

As cognitive modelers, teachers think aloud about strategies and questions that influence how students manage the progress of their learning and accomplish group tasks. In addition, teachers continually question students about the concepts they are learning in the context of the problem in order to probe their understanding, challenge their thinking, and help them deepen or extend their ideas.

Student role: Students first define or select an ill-structured problem that has no obvious solution. They develop alternative hypotheses to resolve the problem and discuss and negotiate their conjectures in a group. Next, they access, evaluate, and utilize data from a variety of available sources to support or refute their hypotheses. They may alter, develop, or synthesize hypotheses in light of new information. Finally, they develop clearly stated solutions that fit the problem and its inherent conditions, based upon information and reasoning to support their arguments. Solutions can be in the form of essays, presentations, or projects.

Maine School Engages Kids With Problem-Solving Challenges (11:37)

https://youtu.be/i17F-b5GG94

[PBS NewsHour].(2013, May 6). Maine School Engages Kids with Problem Solving Challenges. [Video File]. Retrieve from https://youtu.be/i17F-b5GG94

Special correspondent John Tulenko of Leaning Matters reports on a public middle school in Portland, Maine that is taking a different approach to teaching students. Teachers have swapped traditional curriculum for an unusually comprehensive science curriculum that emphasizes problem-solving, with a little help from some robots.

Effectiveness of Problem and Inquiry-based learning.

Why does inquiry-based learning only have an effect size of 0.31 when it is an approach to learning that seems to engage students and teachers so readily in the process of learning?

When is the right and wrong time to introduce inquiry and problem based learning?

Watch video from John Hattie on inquiry and problem-based learning, (2:11 minutes).

[Corwin]. (2015, Nov. 9). John Hattie on inquiry-based learning. [Video File]. Retrieved from https://youtu.be/YUooOYbgSUg.

Glazer, E. (2010) Emerging Perspectives on Learning, Teaching, and Technology, Global Text, Michael Orey. (Chapter 14) Attribution CC 3.0. Retrieved from https://textbookequity.org/Textbooks/Orey_Emerging_Perspectives_Learning.pdf

Instructional Methods, Strategies and Technologies to Meet the Needs of All Learners Copyright © 2017 by Evan Glazer (University of Georgia) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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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. 

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

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

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

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

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

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

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

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

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

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

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

Key features of a good mathematics problem includes:

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

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

But look at the b ack.

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

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

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Choosing the Right Task

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

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

Low Floor High Ceiling Tasks

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

The strengths of using Low Floor High Ceiling Tasks:

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

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

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

Math in 3-Acts

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

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

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

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

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

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

Number Talks

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

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

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

Inside Mathematics Number Talks
Number Talks Build Numerical Reasoning

Saying “This is Easy”

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

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

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

Instead, you and your students could say the following:

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

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

Using “Worksheets”

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

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

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

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

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

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

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

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

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

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

when we teach students how to problem solve

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

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

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

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Problem-Based Learning (PBL)

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

By working with PBL, students will:

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

How to Begin PBL

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

Designing Classroom Instruction

How to Orchestrate a PBL Activity

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

Teacher’s Role in PBL

The Role of the Students

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Elementary teachers’ experience of engaging with Teaching Through Problem Solving using Lesson Study

Original Article
Published: 13 May 2022
Volume 35 , pages 901–927, ( 2023 )

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Mairéad Hourigan ORCID: orcid.org/0000-0002-6895-1895 1 &
Aisling M. Leavy ORCID: orcid.org/0000-0002-1816-0091 1

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For many decades, problem solving has been a focus of elementary mathematics education reforms. Despite this, in many education systems, the prevalent approach to mathematics problem solving treats it as an isolated activity instead of an integral part of teaching and learning. In this study, two mathematics teacher educators introduced 19 Irish elementary teachers to an alternative problem solving approach, namely Teaching Through Problem Solving (TTP), using Lesson Study (LS) as the professional development model. The findings suggest that the opportunity to experience TTP first-hand within their schools supported teachers in appreciating the affordances of various TTP practices. In particular, teachers reported changes in their beliefs regarding problem solving practice alongside developing problem posing knowledge. Of particular note was teachers’ contention that engaging with TTP practices through LS facilitated them to appreciate their students’ problem solving potential to the fullest extent. However, the planning implications of the TTP approach presented as a persistent barrier.

Lesson Study and Its Role in the Implementation of Curriculum Reform in China

Learning to Teach Mathematics Through Problem Solving

Avoid common mistakes on your manuscript.

Introduction

A fundamental goal of mathematics education is to develop students’ ability to engage in mathematical problem solving. Despite curricular emphasis internationally on problem solving, many teachers are uncertain how to harness students’ problem solving potential (Cheeseman, 2018 ). While many problem solving programmes focus on providing students with step-by-step supports through modelling, heuristics, and other structures (Polya, 1957 ), Goldenberg et al. ( 2001 ) suggest that the most effective approach to developing students’ problem solving ability is by providing them with frequent opportunities over a prolonged period to solve worthwhile open-ended problems that are challenging yet accessible to all. This viewpoint is in close alignment with reform mathematics perspectives that promote conceptual understanding, where students actively construct their knowledge and relate new ideas to prior knowledge, creating a web of connected knowledge (Hiebert, 2003 ; Lester, 2013 ; Takahashi, 2006 ; Watanabe, 2001 ).

There is consensus in the mathematics education community that problem solving should not be taught as an isolated topic focused solely on developing problem solving skills and strategies or presented as an end-of-chapter activity (Takahashi, 2006 , 2016 ; Takahashi et al., 2013 ). Instead, problem solving should be integrated across the curriculum as a fundamental part of mathematics teaching and learning (Cai & Lester, 2010 ; Takahashi, 2016 ).

A ‘Teaching Through Problem Solving’ (TTP) approach, a problem solving style of instruction that originated in elementary education in Japan, meets these criteria treating problem solving as a core practice rather than an ‘add-on’ to mathematics instruction.

Teaching Through Problem Solving (TTP)

Teaching Through Problem Solving (TTP) is considered a powerful means of promoting mathematical understanding as a by-product of solving problems, where the teacher presents students with a specially designed problem that targets certain mathematics content (Stacey, 2018 ; Takahashi et al., 2013 ). The lesson implementation starts with the teacher presenting a problem and ensuring that students understand what is required. Students then solve the problem either individually or in groups, inventing their approaches. At this stage, the teacher does not model or suggest a solution procedure. Instead, they take on the role of facilitator, providing support to students only at the right time (Hiebert, 2003 ; Lester, 2013 ; Takahashi, 2006 ). As students solve the problem, the teacher circulates, observes the range of student strategies, and identifies work that illustrates desired features. However, the problem solving lesson does not end when the students find a solution. The subsequent sharing phase, called Neriage (polishing ideas), is considered by Japanese teachers to be the heart of the lesson rather than its culmination. During Neriage, the teacher purposefully selects students to share their strategies, compares various approaches, and introduces increasingly sophisticated solution methods. Effective questioning is central to this process, alongside careful recording of the multiple solutions on the board. The teacher concludes the lesson by formalising and consolidating the lesson’s main points. This process promotes learning for all students (Hiebert, 2003 ; Stacey, 2018 ; Takahashi, 2016 ; Takahashi et al., 2013 ; Watanabe, 2001 ).

The TTP approach assumes that students develop, extend, and enrich their understandings as they confront problematic situations using existing knowledge. Therefore, TTP fosters the symbiotic relationship between conceptual understanding and problem solving, as conceptual understanding is required to solve challenging problems and make sense of new ideas by connecting them with existing knowledge. Equally, problem solving promotes conceptual understanding through the active construction of knowledge (Hiebert, 2003 ; Lambdin, 2003 ; Takahashi, 2006 ). Consequently, students simultaneously develop more profound understandings of the mathematics content while cultivating problem solving skills (Kapur, 2010 ; Stacey, 2018 ).

Relevant research affirms that teachers acknowledge the merits of this approach (Sullivan et al., 2014 ) and most students report positive experiences (Russo & Minas, 2020 ). The process is considered to make students’ thinking and learning visible (Ingram et al., 2020 ). Engagement in TTP has resulted in teachers becoming more aware of and confident in their students’ problem solving abilities and subsequently expecting more from them (Crespo & Featherstone, 2006 ; Sakshaug & Wohlhuter, 2010 ).

Demands of TTP

Adopting a TTP approach challenges pre-existing beliefs and poses additional knowledge demands for elementary teachers, both content and pedagogical (Takahashi, 2008 ).

Research has consistently reported a relationship between teacher beliefs and the instructional techniques used, with evidence of more rule-based, teacher-directed strategies used by teachers with traditional mathematics beliefs (Stipek et al., 2001 ; Swan, 2006 ; Thompson, 1985 ). These teachers tend to address problem solving separately from concept and skill development and possess a simplistic view of problem solving as translating a problem into abstract mathematical terms to solve it. Consequently, such teachers ‘are very concerned about developing skilfulness in translating (so-called) real-world problems into mathematical representations and vice versa’ (Lester, 2013 , p. 254). Early studies of problem solving practice reported direct instructional techniques where the teacher would model how to solve the problem followed by students practicing similar problems (Chapman, 2015 ; Hiebert, 2003 ; Lester, 2013 ). This naïve conception of problem solving is reflected in many textbook problems that simply require students to apply previously learned routine procedures to solve problems that are merely thinly disguised number operations (Lester, 2013 ; Singer & Voica, 2013 ). Hence, the TTP approach requires a significant shift for teachers who previously considered problem solving as an extra activity conducted after the new mathematics concepts are introduced (Lester, 2013 ; Takahashi et al., 2013 ) or whose personal experience of problem solving was confined to applying routine procedures to word problems (Sakshaug &Wohlhuter, 2010 ).

Alongside beliefs, teachers’ knowledge influences their problem solving practices. Teachers require a deep understanding of the nature of problem solving, in particular viewing problem solving as a process (Chapman, 2015 ). To be able to understand the stages problem solvers go through and appreciate what successful problem solving involves, teachers benefit from experiencing solving problems from the problem solver’s perspective (Chapman, 2015 ; Lester, 2013 ).

It is also essential that teachers understand what constitutes a worthwhile problem when selecting or posing problems (Cai, 2003 ; Chapman, 2015 ; Lester, 2013 ; O’Shea & Leavy, 2013 ). This requires an understanding that problems are ‘mathematical tasks for which the student does not have an obvious way to solve it’ (Chapman, 2015 , p. 22). Teachers need to appreciate the variety of problem characteristics that contribute to the richness of a problem, e.g. problem structures and cognitive demand (Klein & Leiken, 2020 ; O’Shea & Leavy, 2013 ). Such understandings are extensive, and rather than invest heavily in the time taken to construct their mathematics problems, teachers use pre-made textbook problems or make cosmetic changes to make cosmetic changes to these (Koichu et al., 2013 ). In TTP, due consideration must also be given to the problem characteristics that best support students in strengthening existing understandings and experiencing new learning of the target concept, process, or skill (Cai, 2003 ; Takahashi, 2008 ). Specialised content knowledge is also crucial for teachers to accurately predict and interpret various solution strategies and misconceptions/errors, to determine the validity of alternative approaches and the source of errors, to sequence student approaches, and to synthesise approaches and new learning during the TTP lesson (Ball et al., 2008 ; Cai, 2003 ; Leavy & Hourigan, 2018 ).

Teachers should also be knowledgeable regarding appropriate problem solving instruction. It is common for teachers to teach for problem solving (i.e., focusing on developing students’ problem solving skills and strategies). Teachers adopting a TTP approach engage in reform classroom practices that reflect a constructivist-oriented approach to problem solving instruction where the teacher guides students to work collaboratively to construct meaning, deciding when and how to support students without removing their autonomy (Chapman, 2015 ; Hiebert, 2003 ; Lester, 2013 ). Teachers ought to be aware of the various relevant models of problem solving, including Polya’s ( 1957 ) model that supports teaching for problem solving (Understand the problem-Devise a plan-Carry out the plan-Look back) alongside models that support TTP (e.g., Launch-Explore-Summarise) (Lester, 2013 ; Sullivan et al., 2021 ). While knowledge of heuristics and strategies may support teachers’ problem solving practices, there is consensus that teaching heuristics and strategies or teaching about problem solving does not significantly improve students’ problem solving ability. Teachers require a thorough knowledge of their students as problem solvers, for example, being aware of their abilities and factors that hinder their success, including language (Chapman, 2015 ). Knowledge of content and student, alongside content and teaching (Ball et al., 2008 ), is essential during TTP planning when predicting student approaches and errors. Such knowledge is also crucial during TTP implementation when determining the validity of alternative approaches, identifying the source of errors (Explore phase), sequencing student approaches, and synthesising the range of approaches and new learning effectively (Summarise phase) (Cai, 2003 ; Leavy & Hourigan, 2018 ).

Supports for teachers

Given the extensive demands of TTP, adopting this approach is arduous in terms of the planning time required to problem pose, predict approaches, and design questions and resources (Lester, 2013 ; Sullivan et al., 2010 ; Takahashi, 2008 ). Consequently, it is necessary to support teachers who adopt a TTP approach (Hiebert, 2003 ). Professional development must facilitate them to experience the approach themselves as learners and then provide classroom implementation opportunities that incorporate collaborative planning and reflection when trialling the approach (Watanabe, 2001 ). In Japan, a common form of professional development to promote, develop, and refine TTP implementation among teachers and test potential problems for TTP is Japanese Lesson Study (LS) (Stacey, 2018 ; Takahashi et al., 2013 ). Another valuable support is access to a repository of worthwhile problems. In Japan, government-authorised textbooks and teacher manuals provide a sequence of lessons with rich well-tested problems to introduce new concepts. They also detail alternative strategies used by students and highlight the key mathematical aspects of these strategies (Takahashi, 2016 ; Takahashi et al., 2013 ).

Teachers’ reservations about TTP

Despite the acknowledged benefits of TTP for students, some teachers report reluctance to employ TTP, identifying a range of obstacles. These include limited mathematics content knowledge or pedagogical content knowledge (Charalambous, 2008 ; Sakshaug & Wohlhuter, 2010 ) and a lack of access to resources or time to develop or modify appropriate resources (Ingram et al., 2020 ; Russo & Hopkins, 2019 ; Sullivan et al., 2015 ). Other barriers for teachers with limited experience of TTP include giving up control, struggling to support students without directing them, and a tendency to demonstrate how to solve the problem (Cheeseman, 2018 ; Crespo & Featherstone, 2006 ; Klein & Leiken, 2020 ; Takahashi et al., 2013 ). Resistance to TTP is also associated with some teachers’ perception that this approach would lead to student disengagement and hence be unsuitable for lower-performing students (Ingram et al., 2020 ; Russo & Hopkins, 2019 ; Sullivan et al., 2010 ).

Problem solving practices in Irish elementary mathematics education

Within the Irish context, problem solving is a central tenet of elementary mathematics curriculum documents (Department of Education and Science (DES), 1999 ) with recommendations that problem solving should be integral to students’ mathematical learning. However, research reveals a mismatch between intended and implemented problem solving practices (Dooley et al., 2014 ; Dunphy et al., 2014 ), where classroom practices reflect a narrow approach limited to problem solving as an ‘add on’, only applied after mathematical procedures had been learned and where problems are predominantly sourced from dedicated sections of textbooks (Department of Education and Skills (DES), 2011 ; Dooley et al., 2014 ; National Council for Curriculum and Assessment (NCCA), 2016 ; O’Shea & Leavy, 2013 ). Regarding the attained curriculum, Irish students have underperformed in mathematical problem solving, relative to other skills, in national and international assessments (NCCA, 2016 ; Shiel et al., 2014 ). Consensus exists that there is scope for improvement of problem solving practices, with ongoing calls for Irish primary teachers to receive support through school-based professional development models alongside creating a repository of quality problems (DES, 2011 ; Dooley et al., 2014 ; NCCA, 2016 ).

Lesson Study (LS) as a professional development model

Reform mathematics practices, such as TTP, challenge many elementary teachers’ beliefs, knowledge, practices, and cultural norms, particularly if they have not experienced the approach themselves as learners. To support teachers in enacting reform approaches, they require opportunities to engage in extended and targeted professional development involving collaborative and practice-centred experiences (Dudley et al., 2019 ; Murata et al., 2012 ; Takahashi et al., 2013 ). Lesson Study (LS) possesses the characteristics of effective professional development as it embeds ‘…teachers’ learning in their everyday work…increasing the likelihood that their learning will be meaningful’ (Fernandez et al., 2003 , p. 171).

In Japan, LS was developed in the 1980s to support teachers to use more student-centred practices. LS is a school-based, collaborative, reflective, iterative, and research-based form of professional development (Dudley et al., 2019 ; Murata et al., 2012 ). In Japan, LS is an integral part of teaching and is typically conducted as part of a school-wide project focused on addressing an identified teaching–learning challenge (Takahashi & McDougal, 2016 ). It involves a group of qualified teachers, generally within a single school, working together as part of a LS group to examine and better understand effective teaching practices. Within the four phases of the LS cycle, the LS group works collaboratively to study and plan a research lesson that addresses a pre-established goal before implementing (teach) and reflecting (observe, analyse and revise) on the impact of the lesson activities on students’ learning.

LS has become an increasingly popular professional development model outside of Japan in the last two decades. In these educational contexts, it is necessary to find a balance between fidelity to LS as originally envisaged and developing a LS approach that fits the cultural context of a country’s education system (Takahashi & McDougal, 2016 ).

Relevant research examining the impact of LS on qualified primary mathematics teachers reports many benefits. Several studies reveal that teachers demonstrated transformed beliefs regarding effective pedagogy and increased self-efficacy in their use due to engaging in LS (Cajkler et al., 2015 ; Dudley et al., 2019 ; Fernandez, 2005 ; Gutierez, 2016 ). Enhancements in participating teachers’ knowledge have also been reported (Cajkler et al., 2015 ; Dudley et al., 2019 ; Fernandez, 2005 ; Gutierez, 2016 ; Murata et al., 2012 ). Other gains recounted include improvements in practice with a greater focus on students (Cajkler et al., 2015 ; Dudley et al., 2019 ; Flanagan, 2021 ).

Context of this study

A cluster of urban schools, coordinated by their local Education Centre, engaged in an initiative to enhance teachers’ mathematics problem solving practices. The co-ordinator of the initiative approached the researchers, both mathematics teacher educators (MTEs), seeking a relevant professional development opportunity. Aware of the challenges of problem solving practice within the Irish context, the MTEs proposed an alternative perspective on problem solving: the Teaching Through Problem Solving (TTP) approach. Given Cai’s ( 2003 ) recommendation that teachers can best learn to teach through problem solving by teaching and reflecting as opposed to taking more courses, the MTEs identified LS as the best fit in terms of a supportive professional development model, as it is collaborative, experiential, and school-based (Dudley et al., 2019 ; Murata et al., 2012 ; Takahashi et al., 2013 ). Consequently, LS would promote teachers to work collaboratively to understand the TTP approach, plan TTP practices for their educational context, observe what it looks like in practice, and assess the impact on their students’ thinking (Takahashi et al., 2013 ). In particular, the MTEs believed that the LS phases and practices would naturally support TTP structures, emphasizing task selection and anticipating students’ solutions. Given Lester’s ( 2013 ) assertion that each problem solving experience a teacher engages in can potentially alter their knowledge for teaching problem solving, the MTEs sought to explore teachers’ perceptions of the impact of engaging with TTP through LS on their beliefs regarding problem solving and their knowledge for teaching problem solving.

Research questions

This paper examines two research questions:

Research question 1: What are elementary teachers’ reported problem solving practices prior to engaging in LS?

Research question 2: What are elementary teachers’ perceptions of what they learned from engaging with TTP through LS?

Methodology

Participants.

The MTEs worked with 19 elementary teachers (16 female, three male) from eight urban schools. Schools were paired to create four LS groups on the basis of the grade taught by participating class teachers, e.g. Grade 3 teacher from school 1 paired with Grade 4 teacher from school 2. Each LS group generally consisted of 4–5 teachers, with a minimum of two teachers from each school, along with the two MTEs. For most teachers, LS and TTP were new practices being implemented concurrently. However, given the acknowledged overlap between the features of the TTP and LS approaches, for example, the focus on problem posing and predicting student strategies, the researchers were confident that the content and structure were compatible. Also, in Japan, LS is commonly used to promote TTP implementation among teachers (Stacey, 2018 ; Takahashi et al., 2013 ).

All ethical obligations were adhered to throughout the research process, and the study received ethical approval from the researchers’ institutional board. Of the 19 participating LS teachers invited to partake in the research study, 16 provided informed consent to use their data for research purposes.

Over eight weeks, the MTEs worked with teachers, guiding each LS group through the four LS phases involving study, design, implementation, and reflection of a research lesson that focused on TTP while assuming the role of ‘knowledgeable others’ (Dudley et al., 2019 ; Hourigan & Leavy, 2021 ; Takahashi & McDougal, 2016 ). An overview of the timeline and summary of each LS phase is presented in Table 1 .

LS phase 1: Study

This initial study phase involved a one-day workshop. The process and benefits of LS as a school-based form of professional development were discussed in the morning session and the afternoon component was spent focusing on the characteristics of TTP. Teachers experienced the TPP approach first-hand by engaging in the various lesson stages. For example, they solved a problem (growing pattern problem) themselves in pairs and shared their strategies. They also predicted children’s approaches to the problem and possible misconceptions and watched the video cases of TTP classroom practice for this problem. Particular focus was placed on the importance of problem selection and prediction of student strategies before the lesson implementation and the Neriage stage of the lesson. Teachers also discussed readings related to LS practices (e.g. Lewis & Tsuchida, 1998 ) and TTP (e.g., Takahashi, 2008 ). At the end of the workshop, members of each LS group were asked to communicate among themselves and the MTEs, before the planning phase, to decide the specific mathematics focus of their LS group’s TTP lesson (Table 1 ).

LS phase 2: Planning

The planning phase was four weeks in duration and included two 1½ hour face-to-face planning sessions (i.e. planning meetings 1 and 2) between the MTEs and each LS group (Table 1 ). Meetings took place in one of the LS group’s schools. At the start of the first planning meeting, time was dedicated to Takahashi’s ( 2008 ) work focusing on the importance of problem selection and prediction of student strategies to plan the Neriage stage of the TTP lesson. The research lesson plan structure was also introduced. Ertle et al.’s ( 2001 ) four column lesson plan template was used. It was considered particularly compatible with the TTP approach, given the explicit attention to expected student response and the teacher’s response to student activity/response.

The planning then moved onto the content focus of each LS group’s TTP research lesson. LS groups selected TTP research lessons focusing on number (group A), growing patterns (group B), money (group C), and 3D shapes (group D). Across the planning phase, teachers invested substantial time extensively discussing the TTP lesson goals in terms of target mathematics content, developing or modifying a problem to address these goals, and exploring considerations for the various lesson stages. Drawing on Takahashi’s ( 2008 ) article, it was re-emphasised that no strategies would be explicitly taught before students engaged with the problem. While one LS group modified an existing problem (group B) (Hourigan & Leavy, 2015 ), the other three LS groups posed an original problem. To promote optimum teacher readiness to lead the Neriage stage, each LS group was encouraged to solve the problem themselves in various ways considering possible student strategies and their level of mathematical complexity, thus identifying the most appropriate sequence of sharing solutions.

LS phase 3: Implementation

The implementation phase involved one teacher in each LS group teaching the research lesson (teach 1) in their school. The remaining group members and MTEs observed and recorded students’ responses. Each LS group and the MTEs met immediately for a post-lesson discussion to evaluate the research lesson. The MTEs presented teachers with a series of focus questions: What were your observations of student learning? Were the goals of the lesson achieved? Did the problem support students in developing the appropriate understandings? Were there any strategies/errors that we had not predicted? How did the Neriage stage work? What aspects of the lesson plan should be reconsidered based on this evidence? Where appropriate, the MTEs drew teachers’ attention to particular lesson aspects they had not noticed. Subsequently, each LS group revised their research lesson in response to the observations, reflections, and discussion. The revised lesson was retaught 7–10 days later by a second group member from the paired LS group school (teach 2) (Table 1 ). The post-lesson discussion for teach 2 focused mainly on the impact of changes made after the first implementation on student learning, differences between the two classes, and further changes to the lesson.

LS phase 4: Reflection

While reflection occurred after both lesson implementations, the final reflection involved all teachers from the eight schools coming together for a half-day meeting in the local Education Centre to share their research lessons, experiences, and learning (Table 1 ). Each LS group made a presentation, identifying their research lesson’s content focus and sequence of activity. Artefacts (research lesson plan, materials, student work samples, photos) were used to support observations, reflections, and lesson modifications. During this meeting, teachers also reflected privately and in groups on their initial thoughts and experience of both LS and TTP, the benefits of participation, the challenges they faced, and they provided suggestions for future practice.

Data collection

The study was a collective case study (Stake, 1995 ). Each LS group constituted a case; thus, the analysis was structured around four cases. Data collection was closely aligned with and ran concurrent to the LS process. Table 2 details the links between the LS phases and the data collection process.

The principal data sources (Table 2 ) included both MTEs’ fieldnotes (phase (P) 1–4), and reflections (P1–4), alongside email correspondence (P1–4), individual teacher reflections (P1, 2, 4) (see reflection tasks in Table 3 ), and LS documentation including various drafts of lesson plans (P2–4) and group presentations (P4). Fieldnotes refer to all notes taken by MTEs when working with the LS groups, for example, during the study session, planning meetings, lesson implementations, post-lesson discussions, and the final reflection session.

The researchers were aware of the limitations of self-report data and the potential mismatch between one’s perceptions and reality. Furthermore, data in the form of opinions, attitudes, and beliefs may contain a certain degree of bias. However, this paper intentionally focuses solely on the teachers’ perceived learning in order to represent their ‘lived experience’ of TTP. Despite this, measures were taken to assure the trustworthiness and rigour of this qualitative study. The researchers engaged with the study over a prolonged period and collected data for each case (LS group) at every LS phase (Table 2 ). All transcripts reflected verbatim accounts of participants’ opinions and reflections. At regular intervals during the study, research meetings interrogated the researchers’ understandings, comparing participating teachers’ observations and reflections to promote meaning-making (Creswell, 2009 ; Suter, 2012 ).

Data analysis

The MTEs’ role as participant researchers was considered a strength of the research given that they possessed unique insights into the research context. A grounded theory approach was adopted, where the theory emerges from the data analysis process rather than starting with a theory to be confirmed or refuted (Glaser, 1978 ; Strauss & Corbin, 1998 ). Data were examined focusing on evidence of participants’ problem solving practices prior to LS and their perceptions of their learning as a result of engaging with TTP through LS. A systematic process of data analysis was adopted. Initially, raw data were organised into natural units of related data under various codes, e.g. resistance, traditional approach, ignorance, language, planning, fear of student response, relevance, and underestimation. Through successive examinations of the relationship between existing units, codes were amalgamated (Creswell, 2009 ). Progressive drafts resulted in the firming up of several themes. Triangulation was used to establish consistency across multiple data sources. While the first theme, Vast divide between prevalent problem solving practices and TTP , addresses research question 1, it is considered an overarching theme, given the impact of teachers’ established problem solving understandings and practices on their receptiveness to and experience of TTP. The remaining five themes ( Seeing is believing : the value of practice centred experiences ; A gained appreciation of the relevance and value of TTP practices ; Enhanced problem posing understandings ; Awakening to students’ problem solving potential ; and Reservations regarding TTP) represent a generalised model of teachers’ perceived learning due to engaging with TTP through LS, thus addressing research question 2. Although one of the researchers was responsible for the initial coding, both researchers met regularly during the analysis to discuss and interrogate the established codes and to agree on themes. This process served to counteract personal bias (Suter, 2012 ).

As teacher reflections were anonymised, it was not possible to track teachers across LS phases. Consequently, teacher reflection data are labelled as phase and instrument only. For example, ‘P2, teacher reflection’ communicates that the data were collected during LS phase 2 through teacher reflection. However, the remaining data are labelled according to phase, instrument, and source, e.g. ‘P3, fieldnotes: group B’. While phase 4 data reflect teachers’ perceptions after engaging fully with the TTP approach, data from the earlier phases reflect teachers’ evolving perceptions at a particular point in their unfolding TTP experience.

Discussion of findings

The findings draw on the analysis of the data collected across the LS phases and address the research questions. Within the confines of this paper, illustrative quotes are presented to provide insights into each theme. An additional layer of analysis was completed to ensure a balanced representation of teachers’ views in reporting findings. This process confirmed that the findings represent the views of teachers across LS groups, for example, within the first theme presented ( Vast divide ), the eight quotes used came from eight different teacher reflections. Equally, the six fieldnote excerpts selected represent six different teachers’ views across the four LS groups. Furthermore, in the second theme ( Seeing is believing ), the five quotes presented were sourced from five different participating teachers’ reflections and the six fieldnote excerpts included are from six different teachers across the four LS groups. Subsequent examination of the perceptions of those teachers not included in the reporting of findings confirmed that their perspectives were represented within the quotes used. Hence, the researchers are confident that the findings represent the views of teachers across all LS groups. For each theme, sources of evidence that informed the presented conclusions will be outlined.

Vast divide between prevalent problem solving practices and TTP

This overarching theme addresses the research question ‘What were elementary teachers’ reported problem solving practices prior to engaging in LS?’.

At the start of the initiative, within the study session (fieldnotes), all teachers identified mathematics problem solving as a problem of practice. The desire to develop problem solving practices was also apparent in some teachers’ reflections (phase 1 (P1), N = 8):

I am anxious about it. Problem solving is an area of great difficulty throughout our school (P1, teacher reflection).

During both study and planning phase discussions, across all LS groups, teachers’ reports suggested the almost exclusive use of a teaching for problem solving approach, with no awareness of the Teaching Through Problem Solving (TTP) approach; a finding also evidenced in both teacher reflections (P1, N = 7) and email correspondence:

Unfamiliar, not what I am used to. I have no experience of this kind of problem solving. This new approach is the reverse way to what I have used for problem solving (P1, teacher reflection) Being introduced to new methods of teaching problem solving and trying different approaches is both exciting and challenging (P1: email correspondence)

Teachers’ descriptions of their problem solving classroom practices in both teacher reflections (P1, N = 8) and study session discussions (fieldnotes) suggested a naïve conception of problem solving, using heuristics such as the ‘RUDE (read, underline, draw a picture, estimate) strategy’ (P1, fieldnotes) to support students in decoding and solving the problem:

In general, the problem solving approach described by teachers is textbook-led, where concepts are taught context free first and the problems at the end of the chapter are completed afterwards (P1, reflection: MTE2)

This approach was confirmed as widespread across all LS groups within the planning meetings (fieldnotes).

In terms of problem solving instruction, a teacher-directed approach was reported by some teachers within teacher reflections (P1, N = 5), where the teacher focused on a particular strategy and modelled its use by solving the problem:

I tend to introduce the problem, ensure everyone understands the language and what is being asked. I discuss the various strategies that children could use to solve the problem. Sometimes I demonstrate the approach. Then children practice similar problems … (P1: Teacher reflection)

However, it was evident within the planning meetings, that this traditional approach to problem solving was prevalent among the teachers in all LS groups. During the study session (field notes and teacher reflections (P1, N = 7)), there was a sense that problem solving was an add-on as opposed to an integral part of mathematics teaching and learning. Again, within the planning meetings, discussions across all four LS groups verified this:

Challenge: Time to focus on problems not just computation (P1: Teacher reflection). From our discussions with the various LS groups’ first planning meeting, text-based teaching seems to be resulting in many teachers teaching concepts context-free initially and then matching the concept with the relevant problems afterwards (P2, reflection: MTE1)

However, while phase 1 teacher reflections suggested that a small number of participating teachers ( N = 4) possessed broader problem solving understandings, subsequently during the planning meetings, there was ample evidence (field notes) of problem-posing knowledge and the use of constructivist-oriented approaches that would support the TTP approach among some participating teachers in each of the LS groups:

Challenge: Spend more time on meaningful problems and give them opportunities and time to engage in activities, rather than go too soon into tricks, rhymes etc (P1, Teacher reflection). The class are already used to sharing strategies and explaining where they went wrong (P2, fieldnotes, Group B) Teacher: The problem needs to have multiple entry points (P2, fieldnotes: Group C)

While a few teachers reported problem posing practices, in most cases, this consisted of cosmetic adjustments to textbook problems. Overall, despite evidence of some promising practices, the data evidenced predominantly traditional problem solving views and practices among participating teachers, with potential for further broadening of various aspects of their knowledge for teaching problem solving including what constitutes a worthwhile problem, the role of problem posing within problem solving, and problem solving instruction. Within phase 1 teacher reflections, when reporting ‘challenges’ to problem solving practices (Table 3 ), a small number of responses ( N = 3) supported these conclusions:

Differences in teachers’ knowledge (P1: Teacher reflection). Need to challenge current classroom practices (P1: Teacher reflection).

However, from the outset, all participating teachers consistently demonstrated robust knowledge of their students as problem solvers, evidenced in phase 1 teacher reflections ( N = 10) and planning meeting discussions (P2, fieldnotes). However, in these early phases, teachers generally portrayed a deficit view, focusing almost exclusively on the various challenges impacting their students’ problem solving abilities. While all teachers agreed that the language of problems was inhibiting student engagement, other common barriers reported included student motivation and perseverance:

They often have difficulties accessing the problem – they don’t know what it is asking them (P2, fieldnotes: Group C) Sourcing problems that are relevant to their lives. I need to change every problem to reference soccer so the children are interested (P1: teacher reflection) Our children deal poorly with struggle and are slow to consider alternative strategies (P2, fieldnotes: Group D)

Despite showcasing a strong awareness of their students’ problem solving difficulties, teachers initially demonstrated a lack of appreciation of the benefits accrued from predicting students’ approaches and misconceptions relating to problem solving. While it came to the researchers’ attention during the study phase, its prevalence became apparent during the initial planning meeting, as its necessity and purpose was raised in three of the LS groups:

What are the benefits of predicting the children’s responses? (P1, fieldnotes). I don’t think we can predict- we will have to wait and see (P2, fieldnotes: Group A).

This finding evidences teachers’ relatively limited knowledge for teaching problem solving, given that this practice is fundamental to TTP and constructivist-oriented approaches to problem solving instruction.

Perceived impacts of engaging with TTP through LS

In response to the research question ‘What are elementary teachers’ perceptions of what they learned from engaging with TTP through LS?’, thematic data analysis identified 5 predominant themes, namely, Seeing is believing : the value of practice centred experiences ; A gained appreciation of the relevance and value of TTP practices ; Enhanced problem posing understandings ; Awakening to students’ problem solving potential ; and Reservations regarding TTP.

Seeing is believing: the value of practice centred experiences

Teachers engaged with TTP during the study phase as both learners and teachers when solving the problem. They were also involved in predicting and analysing student responses when viewing the video cases, and engaged in extensive reading, discussion, and planning for their selected TTP problem within the planning phase. Nevertheless, teachers reported reservations about the relevance of TTP for their context within both phase 2 teacher reflections ( N = 5) as well as within the planning meeting discourse of all LS groups. Teachers’ keen awareness of their students’ problem solving challenges, coupled with the vast divide between the nature of their prior problem solving practices and the TTP approach, resulted in teachers communicating concern regarding students’ possible reaction during the planning phase:

I am worried about the problem. I am concerned that if the problem is too complex the children won’t respond to it (P2, fieldnotes: Group B) The fear that the children will not understand the lesson objective. Will they engage? (P2, Teacher reflection)

Acknowledging their apprehension regarding students’ reactions to TTP, from the outset, all participating teachers communicated a willingness to trial TTP practices:

Exciting to be part of. Eager to see how it will pan out and the learning that will be taken from it (P1, teacher reflection) They should be ‘let off’ (P2, fieldnotes: Group A).

It was only within the implementation phase, when teachers received the opportunity to meaningfully observe the TTP approach in their everyday work context, with their students, that they explicitly demonstrated an appreciation for the value of TTP practices. It was evident from teacher commentary across all LS groups’ post-lesson discussions (fieldnotes) as well as in teacher reflections (P4, N = 10) that observing first-hand the high levels of student engagement alongside students’ capacity to engage in desirable problem solving strategies and demonstrate sought-after dispositions had affected this change:

Class teacher: They engaged the whole time because it was interesting to them. The problem is core in terms of motivation. It determines their willingness to persevere. Otherwise, it won’t work whether they have the skills or not (P3, fieldnotes: Group C) LS group member: The problem context worked really well. The children were all eager and persevered. It facilitated all to enter at their own level, coming up with ideas and using their prior knowledge to solve the problem. Working in pairs and the concrete materials were very supportive. It’s something I’d never have done before (P3, fieldnotes: Group A)

Although all teachers showcased robust knowledge of their students’ problem solving abilities prior to engaging in TTP, albeit with a tendency to focus on their difficulties and factors that inhibited them, teachers’ contributions during post-lesson discussions (fieldnotes) alongside teacher reflections (P4, N = 9) indicate that observing TTP in action supported them in developing an appreciation of value of the respective TTP practices, particularly the role of prediction and observation of students’ strategies/misconceptions in making the students’ thinking more visible:

You see the students through the process (P3, fieldnotes: Group C) It’s rare we have time to think, to break the problem down, to watch and understand children’s ways of thinking/solving. It’s really beneficial to get a chance to re-evaluate the teaching methods, to edit the lesson, to re-teach (P4, teacher reflection)

Analysis of the range of data sources across the phases suggests that it was the opportunity to experience TTP in practice in their classrooms that provided the ‘proof of concept’:

I thought it wasn’t realistic but bringing it down to your own classroom it is relevant (P4, teacher reflection).

Hence from the teachers’ perspective, they witnessed the affordances of TTP practices in the implementation phase of the LS process.

A gained appreciation of the relevance and value of TTP practices

While during the early LS phases, teachers’ reporting suggested a view of problem solving as teaching to problem solve, data from both fieldnotes (phases 3 and 4) and teacher reflections (phase 4) demonstrate that all teachers broadened their understanding of problem solving as a result of engaging with TTP:

Interesting to turn lessons on their head and give students the chance to think, plan and come up with possible strategies and solutions (P4, Teacher reflection)

On witnessing the affordances of TTP first-hand in their own classrooms, within both teacher reflections (P4, N = 12) and LS group presentations, the teachers consistently reported valuing these new practices:

I just thought the whole way of teaching was a good way, an effective way of teaching. Sharing and exploring more than one way of solving is vital (P4, teacher reflection) There is a place for it in the classroom. I will use aspects of it going forward (P4, fieldnotes: Group C)

In fact, teachers’ support for this problem solving approach was apparent in phase 3 during the initial post-lesson discussions. It was particularly notable when a visitor outside of the LS group who observed teach 1 challenged the approach, recommending the explicit teaching of strategies prior to engagement. A LS group member’s reply evidenced the group’s belief that TTP naturally exposes students to the relevant learning: ‘Sharing and questioning will allow students to learn more efficient strategies [other LS group members nodding in agreement]’ (P3, fieldnotes; Group A).

In turn, within phase 4 teacher reflections, teachers consistently acknowledged that engaging with TTP through LS had challenged their understandings about what constitutes effective problem solving instruction ( N = 12). In both teacher reflections (P4, N = 14) and all LS group presentations, teachers reported an increased appreciation of the benefits of adopting a constructivist-oriented approach to problem solving instruction. Equally for some, this was accompanied by an acknowledgement of a heightened awareness of the limitations of their previous practice :

Really made me re-think problem solving lesson structures. I tend to spoon-feed them …over-scaffold, a lot of teacher talk. … I need to find a balance… (P4, teacher reflection) Less is more, one problem can be the basis for an entire lesson (P4, teacher reflection)

What was unexpected, was that some teachers (P4, N = 8) reported that engaging with TTP through LS resulted in them developing an increased appreciation of the value of problem solving and the need for more regular opportunities for students to engage in problem solving:

I’ve come to realise that problem solving is critical and it should be focused on more often. I feel that with regular exposure to problems they’ll come to love being problem solvers (P4, teacher reflection)

Enhanced problem posing understandings

In the early phases of LS, few teachers demonstrated familiarity with problem characteristics (P2 teacher reflection, N = 5). However, there was growth in teachers’ understandings of what constitutes a worthwhile problem and its role within TTP within all LS groups’ post-lesson discussions and presentations (fieldnotes) and teacher reflections (P4, N = 10):

I have a deepened understanding of how to evaluate a problem (P2, teacher reflection) It’s essential to find or create a good problem with multiple strategies and/or solutions as a springboard for a topic. It has to be relevant and interesting for the kids (P4, teacher reflection)

As early as the planning phase, a small group of teachers’ reflections ( N = 2) suggested an understanding that problem posing is an important aspect of problem solving that merits significant attention:

It was extremely helpful to problem solve the problem (P2, teacher reflection)

However, during subsequent phases, this realisation became more mainstream, evident within all LS groups’ post-lesson discussions and presentations (fieldnotes) and teacher reflections (P4, N = 12):

During the first planning meeting, I was surprised and a bit anxious that we would never get to having created a problem. In hindsight, this was time well spent as the problem was crucial (P4, teacher reflection) I learned the problem is key. We don’t spend enough time picking the problem (P4, fieldnotes: Group C).

Alongside this, in all LS groups’ dialogues during the post-lesson discussion and presentations (fieldnotes) and teacher reflections (P4, N = 15), teachers consistently demonstrated an enhanced awareness of the interdependence between the quality of the problem and students’ problem solving behaviours:

Better perseverance if the problem is of interest to them (P4, teacher reflection) It was an eye-opener to me, relevance is crucial, when the problem context is relevant to them, they are motivated to engage and can solve problems at an appropriate level…They all wanted to present (P3, fieldnotes: Group C)

The findings suggest that engaging with TTP through LS facilitated participating teachers to develop an enhanced understanding of the importance of problem posing and in identifying the features of a good mathematics problem, thus developing their future problem posing capacity. In essence, the opportunity to observe the TTP practices in their classrooms stimulated an enhanced appreciation for the value of meticulous attention to detail in TTP planning.

Awakening to students’ problem solving potential

In the final LS phases, teachers consistently reported that engaging with TTP through LS provided the opportunity to see the students through the process , thus supporting them in examining their students’ capabilities more closely. Across post-lesson discussions and presentations (fieldnotes) and teacher reflections (P4, N = 14), teachers acknowledged that engagement in core TTP practices, including problem posing, prediction of students’ strategies during planning, and careful observation of approaches during the implementation phase, facilitated them to uncover the true extent of their students’ problem solving abilities, heightening their awareness of students’ proficiency in using a range of approaches:

Class teacher: While they took a while to warm up, I am most happy that they failed, tried again and succeeded. They all participated. Some found a pattern, others used trial and error. Others worked backward- opening the cube in different ways. They said afterward ‘That was the best maths class ever’ (P3, fieldnotes: Group D) I was surprised with what they could do. I have learned the importance of not teaching strategies first. I need to pull back and let the children solve the problems their own way and leave discussing strategies to the end (P4, teacher reflection)

In three LS groups, class teachers acknowledged in the post-lesson discussion (fieldnotes) that engaging with TTP had resulted in them realising their previous underestimation of [some or all] of their students’ problem solving abilities . Teacher reflections (P4, N = 8) and LS group presentations (fieldnotes) also acknowledged this reality:

I underestimated my kids, which is awful. The children surprised me with the way they approached the problem. In the future I need to focus on what they can do as much as what might hinder them…they are more able than we may think (P4, reflection)

In all LS groups, teachers reported that their heightened appreciation of students’ problem solving capacities promoted them to use a more constructivist-orientated approach in the future:

I learned to trust the students to problem solve, less scaffolding. Children can be let off to explore without so much teacher intervention (P3, fieldnotes: Group D)

Some teachers ( N = 3) also acknowledged the affective benefits of TTP on students:

I know the students enjoyed sharing their different strategies…it was great for their confidence (P4, teacher reflection)

Interestingly, in contrast with teachers’ initial reservations, their experiential and school-based participation in TTP through LS resulted in a lessening of concern regarding the suitability of TTP practices for their students. Hence, this practice-based model supported teachers in appreciating the full extent of their students’ capacities as problem solvers.

Reservations regarding TTP

When introduced to the concept of TTP in the study session, one teacher quickly addressed the time implications:

It is unrealistic in the everyday classroom environment. Time is the issue. We don’t have 2 hours to prep a problem geared at the various needs (P1, fieldnotes)

Subsequently, across the initiative, during both planning meetings, the reflection session and individual reflections (P4, N = 14), acknowledgements of the affordances of TTP practices were accompanied by questioning of its sustainability due to the excessive planning commitment involved:

It would be hard to maintain this level of planning in advance of the lesson required to ensure a successful outcome (P4, teacher reflection)

Given the extensive time dedicated to problem posing, solving, prediction, and design of questions as well as selection or creation of materials both during and between planning meetings, there was agreement in the reflection session (fieldnotes) and in teacher reflections (P4, N = 10) that while TTP practices were valuable, in the absence of suitable support materials for teachers, adjustments were essential to promote implementation:

There is definitely a role for TTP in the classroom, however the level of planning involved would have to be reduced to make it feasible (P4, teacher reflection) The TTP approach is very effective but the level of planning involved is unrealistic with an already overcrowded curriculum. However, elements of it can be used within the classroom (P4, teacher reflection)

A few teachers ( N = 3) had hesitations beyond the time demands, believing the success of TTP is contingent on ‘a number of criteria…’ (P4, teacher reflection):

A whole-school approach is needed, it should be taught from junior infants (P4, teacher reflection) I still have worries about TTP. We found it difficult to decide a topic initially. It lends itself to certain areas. It worked well for shape and space (P4, teacher reflection)

Conclusions

The reported problem solving practice reflects those portrayed in the literature (NCCA, 2016 ; O’Shea & Leavy, 2013 ) and could be aptly described as ‘pendulum swings between emphases on basic skills and problem solving’ (Lesh & Zawojewski, 2007 in Takahashi et al., 2013 , p. 239). Teachers’ accounts depicted problem solving as an ‘add on’ occurring on an ad hoc basis after concepts were taught (Dooley et al., 2014 ; Takahashi et al., 2013 ), suggesting a simplistic view of problem solving (Singer & Voica, 2013 ; Swan, 2006 ). Hence, in reality there was a vast divide between teachers’ problem solving practices and TTP. Alongside traditional beliefs and problem solving practices (Stipek et al., 2001 ; Swan, 2006 ; Thompson, 1985 ), many teachers demonstrated limited insight regarding what constitutes a worthwhile problem (Klein & Lieken, 2020 ) or the critical role of problem posing in problem solving (Cai, 2003 ; Takahashi, 2008 ; Watson & Ohtani, 2015 ). Teachers’ reports suggested most were not actively problem posing, with reported practices limited to cosmetic changes to the problem context (Koichu et al., 2013 ). Equally, teachers demonstrated a lack of awareness of alternative approaches to teaching for problem solving (Chapman, 2015 ) alongside limited appreciation among most of the affordances of a more child-centred approach to problem solving instruction (Hiebert, 2003 ; Lester, 2013 ; Swan, 2006 ). Conversely, there was evidence that some teachers held relevant problem posing knowledge and utilised practices compatible with the TTP approach.

All teachers displayed relatively strong understandings of their students as problem solvers from the outset; however, they initially focused almost exclusively on factors impacting students’ limited problem solving capacity (Chapman, 2015 ). Teachers’ perceptions of their students’ problem solving abilities alongside the vast divide between teachers’ problem solving practice and the proposed TTP approach resulted in teachers being initially concerned regarding students’ response to TTP. This finding supports studies that reported resistance by teachers to the use of challenging tasks due to fears that students would not be able to manage (Ingram et al., 2020 ; Russo & Hopkins, 2019 ; Sullivan et al., 2010 ). Equally, teachers communicated disquiet from the study phase regarding the time investment required to adopt the TTP approach, a finding common in similar studies (Ingram et al., 2020 ; Russo & Hopkins, 2019 ; Sullivan et al., 2015 ). Hence, the transition to TTP was uneasy for most teachers, given the significant shift it represented in terms of moving beyond a teaching to problem solve approach alongside the range of teacher demands (Takahashi et al., 2013 ).

Nevertheless, despite initial reservations, all teachers reported that engagement with TTP through LS affected their problem solving beliefs and understandings. What was particularly notable was that they reported an awakening to students’ problem solving potential . During LS’s implementation and reflection stages, all teachers acknowledged that seeing was believing concerning the benefits of TTP for their students (Kapur, 2010 ; Stacey, 2018 ). In particular, they recognised students’ positive response (Russo & Minas, 2020 ) enacted in high levels of engagement, perseverance in finding a solution, and the utilisation of a range of different strategies. These behaviours were in stark contrast to teachers’ reports in the study phase. Teachers acknowledged that students had more potential to solve problems autonomously than they initially envisaged. This finding supports previous studies where teachers reported that allowing students to engage with challenging tasks independently made students’ thinking more visible (Crespo & Featherstone, 2006 ; Ingram et al., 2020 ; Sakshand & Wohluter, 2010 ). It also reflects Sakshaug and Wohlhuter’s ( 2010 ) findings of teachers’ tendency to underestimate students’ potential to solve problems. Interestingly, at the end of LS, concern regarding the appropriateness of the TTP approach for students was no longer cited by teachers. This finding contrasts with previous studies that report teacher resistance due to fears that students will become disengaged due to the unsuitability of the approach (challenging tasks) for lower-performing students (Ingram et al., 2020 ; Russo & Hopkins, 2019 ; Sullivan et al., 2015 ). Hence, engaging with TTP through LS supported teachers in developing an appreciation of their students’ potential as problem solvers.

Teachers reported enhanced problem posing understandings, consisting of newfound awareness of the connections between the quality of the problem, the approach to problem solving instruction, and student response (Chapman, 2015 ; Cai, 2003 ; Sullivan et al., 2015 ; Takahashi, 2008 ). They acknowledged that they had learned the importance of the problem in determining the quality of learning and affecting student engagement, motivation and perseverance, and willingness to share strategies (Cai, 2003 ; Watson & Oktani, 2015 ). These findings reflect previous research reporting that engagement in LS facilitated teachers to enhance their teacher knowledge (Cajkler et al., 2015 ; Dudley et al., 2019 ; Gutierez, 2016 ).

While all teachers acknowledged the benefits of the TTP approach for students (Cai & Lester, 2010 ; Sullivan et al., 2014 ; Takahashi, 2016 ), the majority confirmed their perception of the relevance and value of various TTP practices (Hiebert, 2003 ; Lambdin, 2003 ; Takahashi, 2006 ). They referenced the benefits of giving more attention to the problem, allowing students the opportunity to independently solve, and promoting the sharing of strategies and pledged to incorporate these in their problem solving practices going forward. Many verified that the experience had triggered them to question their previous problem solving beliefs and practices (Chapman, 2015 ; Lester, 2013 ; Takahashi et al., 2013 ). This study supports previous research reporting that LS challenged teachers’ beliefs regarding the characteristics of effective pedagogy (Cajkler et al., 2015 ; Dudley et al., 2019 ; Fernandez, 2005 ; Gutierez, 2016 ). However, teachers communicated reservations regarding TTP , refraining from committing to TTP in its entirety, highlighting that the time commitment required for successful implementation on an ongoing basis was unrealistic. Therefore, teachers’ issues with what they perceived to be the excessive resource implications of TTP practices remained constant across the initiative. This finding supports previous studies that report teachers were resistant to engaging their students with ‘challenging tasks’ provided by researchers due to the time commitment required to plan adequately (Ingram et al., 2020 ; Russo & Hopkins, 2019 ; Sullivan et al., 2015 ).

Unlike previous studies, teachers in this study did not perceive weak mathematics content or pedagogical content knowledge as a barrier to implementing TTP (Charalambous, 2008 ; Sakshaug & Wohlhuter, 2010 ). However, it should be noted that the collaborative nature of LS may have hidden the knowledge demands for an individual teacher working alone when engaging in the ‘Anticipate’ element of TTP particularly in the absence of appropriate supports such as a bank of suitable problems.

The findings suggest that LS played a crucial role in promoting reported changes, serving both as a supportive professional development model (Stacey, 2018 ; Takahashi et al., 2013 ) and as a catalyst, providing teachers with the opportunity to engage in a collaborative, practice-centred experience over an extended period (Dudley et al., 2019 ; Watanabe, 2001 ). The various features of the LS process provided teachers with opportunities to engage with, interrogate, and reflect upon key TTP practices. Reported developments in understandings and beliefs were closely tied to meaningful opportunities to witness first-hand the affordances of the TTP approach in their classrooms with their students (Dudley et al., 2019 ; Fernandez et al., 2003 ; Takahashi et al., 2013 ). We suggest that the use of traditional ‘one-off’ professional development models to introduce TTP, combined with the lack of support during the implementation phase, would most likely result in teachers maintaining their initial views about the unsuitability of TTP practices for their students.

In terms of study limitations, given that all data were collected during the LS phases, the findings do not reflect the impact on teachers’ problem solving classroom practice in the medium to long term. Equally, while acknowledging the limitations of self-report data, there was no sense that the teachers were trying to please the MTEs, as they were forthright when invited to identify issues. Also, all data collected through teacher reflection was anonymous. The relatively small number of participating teachers means that the findings are not generalisable. However, they do add weight to the body of relevant research. This study also contributes to the field as it documents potential challenges associated with implementing TTP for the first time. It also suggests that despite TTP being at odds with their problem solving practice and arduous, the opportunity to experience the impact of the TTP approach with students through LS positively affected teachers’ problem solving understandings and beliefs and their commitment to incorporating TTP practices in their future practice. Hence, this study showcases the potential role of collaborative, school-based professional development in supporting the implementation of upcoming reform proposals (Dooley et al., 2014 ; NCCA, 2016 , 2017 , 2020 ), in challenging existing beliefs and practices and fostering opportunities for teachers to work collaboratively to trial reform teaching practices over an extended period (Cajkler et al., 2015 ; Dudley et al., 2019 ). Equally, this study confirms and extends previous studies that identify time as an immense barrier to TTP. Given teachers’ positivity regarding the impact of the TTP approach, their consistent acknowledgement of the unsustainability of the unreasonable planning demands associated with TTP strengthens previous calls for the development of quality support materials in order to avoid resistance to TTP (Clarke et al., 2014 ; Takahashi, 2016 ).

The researchers are aware that while the reported changes in teachers’ problem solving beliefs and understandings are a necessary first step, for significant and lasting change to occur, classroom practice must change (Sakshaug & Wohlhuter, 2010 ). While it was intended that the MTEs would work alongside interested teachers and schools to engage further in TTP in the school term immediately following this research and initial contact had been made, plans had to be postponed due to the commencement of the COVID 19 pandemic. The MTEs are hopeful that it will be possible to pick up momentum again and move this initiative to its natural next stage. Future research will examine these teachers’ perceptions of TTP after further engagement and evaluate the effects of more regular opportunities to engage in TTP on teachers’ problem solving practices. Another possible focus is teachers’ receptiveness to TTP when quality support materials are available.

In practical terms, in order for teachers to fully embrace TTP practices, thus facilitating their students to avail of the many benefits accrued from engagement, teachers require access to professional development (such as LS) that incorporates collaboration and classroom implementation at a local level. However, quality school-based professional development alone is not enough. In reality, a TTP approach cannot be sustained unless teachers receive access to quality TTP resources alongside formal collaboration time.

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The authors acknowledge the participating teachers’ time and contribution to this research study.

This work was supported by the Supporting Social Inclusion and Regeneration in Limerick’s Programme Innovation and Development Fund.

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Hourigan, M., Leavy, A.M. Elementary teachers’ experience of engaging with Teaching Through Problem Solving using Lesson Study. Math Ed Res J 35 , 901–927 (2023). https://doi.org/10.1007/s13394-022-00418-w

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Problem Solving in STEM

Solving problems is a key component of many science, math, and engineering classes. If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems. Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.

How do I decide which problems to cover in section or class?

In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.

You have given your students a problem to solve in class. What are some strategies to work through it?

Try to give your students a chance to grapple with the problems as much as possible. Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems. This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question). Ask students to start solving the problem, either independently or in small groups. As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion. After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
If you have ample board space, have students work in small groups at the board while solving the problem. That way you can monitor their progress by standing back and watching what they put up on the board.
If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.

When do you want students to work in groups to solve problems?

Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others. This ensures that every student engages with the problem and is ready to contribute to a discussion.

What are some benefits of having students work in groups?

Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.

What are some strategies for helping students to form groups?

Instruct students to work with the person (or people) sitting next to them.
Count off. (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
Hand out playing cards; students need to find the person with the same number card. (There are many variants to this. For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
Based on what you know about the students, assign groups in advance. List the groups on the board.
Note: Always have students take the time to introduce themselves to each other in a new group.

What should you do while your students are working on problems?

Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.

After students work on a problem during class, what are strategies to have them share their answers and their thinking?

Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
Use online polling software for students to respond to a multiple-choice question anonymously.
If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
Have students write an answer on a notecard that they turn in to you. If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.
Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems. Students now are responsible for teaching the other students in their new group how to solve their problem.
Have a representative from each group explain their problem to the class.
Have a representative from each group draw or write the answer on the board.

What happens if a student gives a wrong answer?

Ask for their reasoning so that you can understand where they went wrong.
Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
Do make sure that you clarify what the correct answer is before moving on.
Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.

How can you make your classroom inclusive?

The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity.

A few final notes…

Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.

For more information...

Tipsheet: Problem Solving in STEM Sections

Tanner, K. D. (2013). Structure matters: twenty-one teaching strategies to promote student engagement and cultivate classroom equity . CBE-Life Sciences Education, 12(3), 322-331.

Designing Your Course
A Teaching Timeline: From Pre-Term Planning to the Final Exam
The First Day of Class
Group Agreements
Classroom Debate
Flipped Classrooms
Leading Discussions
Polling & Clickers
Teaching with Cases
Engaged Scholarship
Devices in the Classroom
Beyond the Classroom
On Professionalism
Getting Feedback
Equitable & Inclusive Teaching
Advising and Mentoring
Teaching and Your Career
Teaching Remotely
Tools and Platforms
The Science of Learning
Bok Publications
Other Resources Around Campus

Problem Solving Method Of Teaching

The problem-solving method of teaching is the learning method that allows children to learn by doing. This is because they are given examples and real-world situations so that the theory behind it can be understood better, as well as practice with each new concept or skill taught on top of what was previously learned in class before moving onto another topic at hand.

What is your preferred problem-solving technique?

Answers : - I like to brainstorm and see what works for me - I enjoy the trial and error method - I am a linear thinker

Share it with me by commenting.

For example, while solving a problem, the child may encounter terms he has not studied yet. These will further help him understand their use in context while developing his vocabulary. At the same time, being able to practice math concepts by tapping into daily activities helps an individual retain these skills better.

One way this type of teaching is applied for younger students particularly is through games played during lessons. By allowing them to become comfortable with the concepts taught through these games, they can put their knowledge into use later on. This is done by developing thinking processes that precede an action or behavior. These games can be used by teachers for different subjects including science and language.

For younger students still, the method of teaching using real-life examples helps them understand better. Through this, it becomes easier for them to relate what they learned in school with terms used outside of school settings so that the information sticks better than if all they were given were theoretical definitions. For instance, instead of just studying photosynthesis as part of biology lessons, children are asked to imagine plants growing inside a dark room because there is no sunlight present. When questioned about the plants, children will be able to recall photosynthesis more easily because they were able to see its importance in real life.

Despite being given specific examples, the act of solving problems helps students think for themselves. They learn how to approach situations and predict outcomes based on what they already know about concepts or ideas taught in class including the use of various skills they have acquired over time. These include problem-solving strategies like using drawings when describing a solution or asking advice if they are stuck to unlock solutions that would otherwise go beyond their reach.

Teachers need to point out in advance which method will be used for any particular lesson before having children engage with it. By doing this, individuals can prepare themselves mentally for what is to come. This is especially true for students who have difficulty with a particular subject. In these cases, the teacher can help them get started by providing a worked example for reference or breaking the problem down into manageable chunks that are easier to digest.

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Ultimately, the goal of teaching using a problem-solving method is to give children the opportunity to think for themselves and to be able to do so in different contexts. Doing this helps foster independent learners who can utilize the skills they acquired in school for future endeavors.

The problem-solving method of teaching allows children to learn by doing. This is because they are given examples and real-world situations so that the theory behind it can be understood better, as practice with each new concept or skill taught on top of what was previously learned in class before moving onto another topic at hand.

One way this type of teaching is applied for younger students particularly is through games played during lessons. By allowing them to become comfortable with the concepts taught through these games, they are able to put their knowledge into use later on. This is done by developing thinking processes that precede an action or behavior. These games can be used by teachers for different subjects including science and language.

For instance, a teacher may ask students to imagine they are plants in a dark room because there is no sunlight present. When questioned about the plants, children will be able to recall photosynthesis more easily because they were able to see its importance in real life.

It is important for teachers to point out in advance which method will be used for any particular lesson before having children engage with it. By doing this, individuals can prepare themselves mentally for what is to come. This is especially true for students who have difficulty with a particular subject. In these cases, the teacher can help them get started by providing a worked example for reference or breaking the problem down into manageable chunks that are easier to digest.

lesson before having children engage with it. By doing this, individuals can prepare themselves mentally for what is to come. This is especially true for students who have difficulty with a particular subject. In these cases, the teacher can help them get started by providing a worked example for reference or breaking the problem down into manageable chunks that are easier to digest.

The teacher should have a few different ways to solve the problem.

For example, the teacher can provide a worked example for reference or break down the problem into chunks that are easier to digest.

The goal of teaching using a problem-solving method is to give children the opportunity to think for themselves and to be able to do so in different contexts. Successful problem solving allows children to become comfortable with concepts taught through games that develop thinking processes that precede an action or behavior.

Introduce the problem

The problem solving method of teaching is a popular approach to learning that allows students to understand new concepts by doing. This approach provides students with examples and real-world situations, so they can see how the theory behind a concept or skill works in practice. In addition, students are given practice with each new concept or skill taught, before moving on to the next topic. This helps them learn and retain the information better.

Explain why the problem solving method of teaching is effective.

The problem solving method of teaching is effective because it allows students to learn by doing. This means they can see how the theory behind a concept or skill works in practice, which helps them understand and remember the information better. This would not be possible if they are only told about the new concept or skill, or read a textbook to learn on their own. Since students can see how the theory works in practice through examples and real-world situations, the information is easier for them to understand.

List some advantages of using the problem solving method of teaching.

Some advantages of using the problem solving method of teaching are that it helps students retain information better since they are able to practice with each new concept or skill taught until they master it before moving on to another topic. This also allows them to learn by doing so they will have hands-on experience with facts which helps them remember important facts faster rather than just hearing about it or reading about it on their own. Furthermore, this teaching method is beneficial for students of all ages and can be adapted to different subjects making it an approach that is versatile and easily used in a classroom setting. Lastly, the problem solving method of teaching presents new information in a way that is easy to understand so students are not overwhelmed with complex material.

The problem solving method of teaching is an effective way for students to learn new concepts and skills. By providing them with examples and real-world situations, they can see how the theory behind a concept or skill works in practice. In addition, students are given practice with each new concept or skill taught, before moving on to the next topic. This them learn and retain the information better.

What has been your experience with adopting a problem-solving teaching method?

How do you feel the usefulness of your lesson plans changed since adopting this method?

What was one of your most successful attempts in using this technique to teach students, and why do you believe it was so successful?

Were there any obstacles when trying to incorporate this technique into your class?

Did it take a while for all students to get used to the new type of teaching style before they felt comfortable enough to participate in discussions and ask questions about their newly acquired knowledge?

What are your thoughts on this method?

“I have had the opportunity to work in several districts, including one where they used problem solving for all subjects. I never looked back after that experience--it was exciting and motivating for students and teachers alike."

"The problem solving method of teaching is great because it makes my subject matter more interesting with hands-on activities."

Active Learning, Teaching through problem-solving allows for active learning, Children understand the theory better by getting involved in real-world situations, Practice, Continuous practice is integral to problem-solving teaching, Each new skill or concept is practiced after being learned in class, Relevance, Problem-solving techniques make learning more relevant, Real-world examples related to the topic are presented, Incremental Learning, Each new topic builds on previous lessons, Relating new problems to ones solved in previous sessions, Overcome Challenges, Enhances ability to overcome real-world situations, Children understand the application of skills learned, Variety, Problem-solving allows flexibility in teaching methods, Problems can be practical, conceptual, or theoretical, Critical Thinking, Improves children's critical thinking skills, Adding alternative paths to a solution, Confidence, Boosts children's confidence in handling problems, Children feel empowered after successfully solving a problem, Adaptability, Increases adaptability to new learning situations, Children can apply learned strategies to new problems, Engagement, Problem-solving increases engagement and interest, Children find solving real-world examples interesting

What is the role of educators in facilitating problem-solving method of teaching?

Role of Educators in Facilitating Problem-Solving Understanding the Problem-Solving Method The problem-solving method of teaching encourages students to actively engage their critical thinking skills to analyze and seek solutions to real-world problems. As such, educators play a crucial part in facilitating this learning style to ensure the effective attainment of desired skills. Encouraging Collaboration and Communication One of the ways educators can facilitate problem-solving is by promoting collaboration and communication among students. Working as a team allows students to share diverse perspectives while considering multiple solutions, thereby fostering an open-minded and inclusive environment that is crucial for effective problem-solving. Creating a Safe Space for Failure Educators must recognize that failure is an integral component of the learning process in a problem-solving method. By establishing a safe environment that allows students to fail without facing judgment or embarrassment, teachers enable students to develop perseverance, resilience, and an enhanced ability to learn from mistakes. Designing Relevant and Engaging Problems The selection and design of appropriate problems contribute significantly to the success of the problem-solving method of teaching. Educators should focus on presenting issues that are relevant, engaging, and age-appropriate, thereby sparking curiosity and interest amongst students, which further improves their problem-solving abilities. Scaffolding Learning Scaffolding is essential in the problem-solving method for providing adequate support when required. Teachers need to break down complex problems into smaller, manageable steps, and gradually remove support as students develop the necessary skills, thus promoting their self-reliance and independent thinking. Providing Constructive Feedback Constructive feedback from educators is invaluable in facilitating the problem-solving method of teaching, as it enables students to reflect on their progress, recognize areas for improvement, and actively develop their critical thinking and problem-solving abilities. In conclusion, the role of educators in facilitating the problem-solving method of teaching comprises promoting collaboration, creating a safe space for failure, designing relevant problems, scaffolding learning, and providing constructive feedback. By integrating these elements, educators can help students develop essential life-long skills and effectively navigate the complex world they will experience.

The problem-solving method of teaching is a dynamic and interactive instructional strategy that engages students directly with challenges that resemble those they might encounter outside of the classroom. Within this framework, educators are not just conveyors of knowledge, but rather facilitators of learning who empower their students to think critically and deeply. Below, we look into the nuanced role educators play in making the problem-solving method impactful.Firstly, educators must curate an atmosphere that is conducive to inquiry and exploration. They set the tone by modeling an inquisitive mindset, posing thought-provoking questions, and encouraging students to ask why, how, and what if without hesitation. This intellectual curiosity promotes the kind of deep thinking that underpins successful problem-solving.Another key responsibility is to scaffold the complexity of problems. Educators do so by assessing the readiness of their students and designing tasks that are at the appropriate level of difficulty. They must ensure challenges are neither too easy – risking boredom and disengagement – nor too difficult – potentially causing frustration and disheartenment. By striking this balance, educators help students to experience incremental success and build their problem-solving capacities over time.Educators must also provide students with relevant tools and methodologies. This might involve teaching specific problem-solving strategies such as the scientific method, design thinking, or computational thinking. Educators help students to become conversant in these approaches, allowing them to tackle problems methodically and effectively.Assessment is another pivotal area where educators play a vital role in the problem-solving method. The traditional means of assessment may not always capture the depth of understanding and learning that occurs in problem-solving scenarios. Therefore, educators develop alternative forms of assessment, such as reflective journals, portfolios, and presentations, to better gauge student learning and thinking processes.Finally, educators must be adept at facilitating group dynamics. Collaborative problem-solving can be powerful, but it also invites a range of interpersonal challenges. Thus, educators need to guide students in conflict resolution, equitable participation, and recognizing the contribution of each member to the collective effort.Educators facilitate the problem-solving method by fostering inquiry, balancing problem difficulty, equipping students with methodologies, rethinking assessment, and nurturing group cooperation. In doing so, they are not simply providing students with content knowledge but are equipping them with crucial life skills that transcend educational settings and prepare them for real-world challenges.

Can interdisciplinary approaches be incorporated into problem-solving teaching methods, and if so, how?

Interdisciplinary Approaches in Problem-Solving Teaching Methods Integration of Interdisciplinary Approaches Incorporating interdisciplinary approaches into problem-solving teaching methods can be achieved by integrating various subject areas when presenting complex problems that require students to draw from different fields of knowledge. By doing so, learners will develop a deeper understanding of the interconnectedness of various disciplines and improve their problem-solving skills. Project-Based Learning Activities Implementing project-based learning activities in the classroom allows students to work collaboratively on real-world problems. By involving learners in tasks that necessitate the integration of diverse subjects, they develop the ability to transfer skills acquired in one context to novel situations, thereby expanding their problem-solving abilities. Role of Teachers in Interdisciplinary Teaching Teachers play a crucial role in the successful incorporation of interdisciplinary methods in problem-solving teaching. They must be prepared to facilitate student-centered learning and engage in ongoing professional development tailored towards interdisciplinary education. In doing so, educators can create inclusive learning environments that encourage individualized discovery and the application of diverse perspectives to solve complex problems. Benefits of Interdisciplinary Teaching Methods Adopting interdisciplinary teaching methods in problem-solving education not only enhances students' problem-solving abilities but also fosters the development of critical thinking, creativity, and collaboration. These essential skills enable learners to navigate and adapt to an increasingly interconnected world and have been shown to contribute to students' academic and professional success. In conclusion, incorporating interdisciplinary approaches into problem-solving teaching methods can be achieved through the integration of various subject areas, implementing project-based learning activities, and the active role of teachers in interdisciplinary education. These methods benefit students by developing problem-solving skills, critical thinking, creativity, and collaboration, preparing them for future success in an interconnected world.

Interdisciplinary approaches in problem-solving teaching methods present a contemporary framework for preparing students to tackle the complexities of real-world issues. This approach can bridge the gap between various academic disciplines, offering students a more holistic and connected way of thinking.**Embracing Complexity through Interdisciplinary Problem-Solving**Problem-solving in education is no longer confined to single-subject exercises. Interdisciplinary problem-solving recognizes the multifaceted nature of real issues and encourages students to tackle them by drawing from multiple disciplines. For instance, when examining the impacts of urbanization, students might incorporate knowledge from sociology, economics, environmental science, and urban planning.**Strategies for Implementing an Interdisciplinary Approach**Various strategies can be employed to incorporate interdisciplinary methods effectively:1. **Cross-Curricular Projects**: These require students to apply knowledge and skills across different subject areas, fostering an understanding of each discipline’s unique contribution to the whole problem.2. **Thematic Units**: By designing units around broad themes, educators can seamlessly weave multiple subjects into the exploration of a single topic, prompting students to see connections between different areas of study.3. **Collaborative Teaching**: When educators from different disciplines co-teach, they can provide a combined perspective that enriches the learning experience and demonstrates the value of integrating knowledge.4. **Inquiry-Based Learning**: Encourages students to ask questions and conduct research across multiple disciplines, leading to comprehensive investigations and solutions.**Outcome-Benefits of Interdisciplinary Teaching**The merits of an interdisciplinary approach within problem-solving teaching methods are manifold:1. **Complex Problem Understanding**: It can elevate a student’s ability to deconstruct complicated issues by understanding various factors and viewpoints.2. **Adaptability**: Students learn to apply knowledge pragmatically, enabling them to adapt to new and unforeseen problems.3. **Enhanced Cognitive Abilities**: The process can promote cognitive growth, supporting the development of higher-order thinking skills like analysis and synthesis.4. **Real-World Relevance**: Students find meaning and motivation in their work when they see its relevance outside the classroom walls.In summary, integrating interdisciplinary approaches into problem-solving methods is a highly effective way to provide students with robust and adaptable skills for the future. By engaging in project-based learning activities, enjoying the support of proactive educators, and seeing the interconnectivity across subjects, students can foster critical thinking, creativity, and collaborative abilities that transcend traditional learning boundaries. As we navigate a rapidly evolving and interrelated global landscape, such approaches to education become not just advantageous but essential.

In what ways can technology be integrated into the problem-solving method of instruction?

**Role of Technology in Problem-Solving Instruction** Technology can be integrated into the problem-solving method of instruction by enhancing student engagement, promoting collaboration, and supporting personalized learning. **Enhancing Student Engagement** One way technology supports the problem-solving method is by increasing students' interest through interactive and dynamic tools. For instance, digital simulations and educational games can help students develop critical thinking and problem-solving skills in a fun, engaging manner. These tools provide real-world contexts and immediate feedback, allowing students to experiment, take risks, and learn from their mistakes. **Promoting Collaboration** Technology also promotes collaboration among students, as online platforms facilitate communication and cooperation. Utilizing tools like video conferencing and shared workspaces, students can collaborate on group projects, discuss ideas, and solve problems together. This collaborative approach fosters a sense of community, mutual support, and collective problem-solving. Moreover, it helps students develop essential interpersonal skills, such as teamwork and communication, which are crucial in today's workplaces. **Supporting Personalized Learning** Finally, technology can be used to provide personalized learning experiences tailored to individual learners' needs, interests, and abilities. With access to adaptive learning platforms or online resources, students can progress at their own pace, focus on areas where they need improvement, and explore topics that interest them. This kind of personalized approach allows instructors to identify areas where students struggle and offer targeted support, enhancing the problem-solving learning experience. In conclusion, integrating technology into the problem-solving method of instruction can improve the learning process in various ways. By fostering student engagement, promoting collaboration, and facilitating personalized learning experiences, technology can be employed as a valuable resource to develop students' problem-solving skills effectively.

The integration of technology into the problem-solving method of instruction can significantly enhance the educational process, as it offers diverse opportunities for students to engage with challenging concepts and develop practical skills. The deliberate use of technology can stimulate student interaction with course material and encourage a more dynamic approach to learning.**Interactive Problem-Solving Scenarios**Technology can simulate complex scenarios requiring students to apply their knowledge creatively to solve problems. Through interactive case studies and gamified learning environments, students can engage with these scenarios in a manner that is both compelling and educative. Such simulations often incorporate branching choices, offering an exploration of consequences which creates a deeper understanding of the material.**Data Analysis Tools**Incorporating data analysis tools into problem-solving instruction can offer students hands-on experience with real-world data sets. By learning to manipulate and analyze data through software, students can identify patterns, test hypotheses, and make evidence-based conclusions. These skills are particularly valuable in STEM fields, economics, and social sciences.**Global Connectivity & Resources**Through global connectivity, technology enables access to a vast array of resources that can be utilized to enrich problem-solving tasks. Platforms such as IIENSTITU offer courses that are designed to incorporate technology into pedagogical strategies effectively. Moreover, access to international databases, research materials, and expert lectures from around the world ensures that students are exposed to diverse perspectives and approaches to problem-solving.**Interactive Whiteboards and Projection**Interactive whiteboards and projection technology make it possible to visualize complex problems and work though them interactively in the classroom. This technology allows for collaborative diagramming and mapping of ideas, which can aid in visual learning and the synthesis of information in group settings.**Adaptive Learning Software**Educational technology that adapts to individual student performance and preferences enables personalized instruction. Adaptive learning software assesses students' skills and tailors the difficulty of problems accordingly, ensuring that each student is engaged at the appropriate level of challenge.**Formative Assessment through Technology**Technology-enabled formative assessments give teachers and students real-time feedback on understanding and performance. These tools can help identify areas of difficulty, track progress, and adjust teaching strategies to help students develop their problem-solving abilities more effectively.**Facilitating Research and Inquiry**The ability to conduct research and inquiry is central to problem solving. When students are provided with the tools to explore, research, and verify information on the internet securely, they are empowered to seek out answers to their questions and develop solutions based on evidence.**Closing Thoughts**In integrating technology into problem-solving instruction, it's important to ensure that the use of any tool or platform is pedagogically sound, enhances the learning objectives, and actually serves to improve students' problem-solving capabilities. As education evolves with the digital age, so too does the art and science of teaching problem solving, where technology becomes an indispensable ally in preparing students for the challenges of the future.

I graduated from the Family and Consumption Sciences Department at Hacettepe University. I hold certificates in blogging and personnel management. I have a Master's degree in English and have lived in the US for three years.

A rectangular puzzle piece with a light green background and a blue geometric pattern sits in the center of the image. The puzzle piece has a curved edge along the top, and straight edges along the bottom and sides. The pattern on the piece consists of a thin green line that wraps around the outside edge and a thick blue line that follows the contours of the shape. The inside of the piece is filled with various shapes of the same color, including circles, triangles, and squares. The overall effect of the piece is calming and serene. It could be part of a larger puzzle that has yet to be solved.

What are Problem Solving Skills?

A woman in a white shirt is looking down and holding her head in her hands. She has long blonde hair and blue eyes. Her lips are slightly pursed, and her eyebrows are slightly furrowed. She looks sad and contemplative, as if she is lost in thought. Her arms are crossed in front of her chest, and her head is slightly tilted to the side. Her expression is thoughtful and her posture is relaxed. She is standing in front of a plain white wall, and the light casts shadows on her face. She appears to be alone in the room, and her posture conveys a sense of loneliness and introspection.

How To Solve The Problems? Practical Problem Solving Skills

A group of people, including a man holding a laptop, a woman with her hands in her pockets, and another woman wearing a striped shirt, are standing together in a closeknit formation. One woman is holding a cup of coffee, and another has their butt partially visible in blue jeans. Everyone is smiling, and the man with the laptop appears to be engaged in conversation. The group is bathed in warm sunlight, creating a friendly atmosphere.

A Problem Solving Method: Brainstorming

A close-up of a group of people holding puzzle pieces in their hands. A man is looking at the piece he is holding, while two other people are carefully looking at the pieces they are holding in their hands. The pieces have a wooden texture, and each one is a different color. One person is holding a light blue piece, while another person is holding a red piece. All the pieces are shaped differently, and some are curved while others are straight. The pieces all fit together to form a larger puzzle.

How To Develop Problem Solving Skills?

Discovery Method of Teaching: A Student-Centered Approach to Learning

Discovery Method of Teaching (Discovery Learning)

Table of Contents

The Discovery Learning or The Discovery Method of Teaching

It was introduced by an American Psychologist, Jerome Brunner, in the 1960s, who supported the constructivism paradigm and learning by doing. In his theory, Bruner’s Theory of Development clearly explains how students learn and the impact of the environment on the students learning.

The discovery learning method is a student-centred teaching approach that stresses problem-solving, critical thinking, and inquiry-based learning.

This strategy h as the potential to increase student engagement and motivation significantly. In this teaching method, the teachers must offer a supportive learning environment to ensure that all students benefit from this technique.

The discovery method of teaching, also known as discovery learning, is a form of education that places students at the centre of the learning process. Rather than depending on the teacher’s direct teaching, this technique enables students to actively participate in their learning process by investigating topics via inquiry and exploration.

Students can discover new ideas and concepts by problem-solving, questioning, and exploring their surroundings in exploration learning. The discovery teaching style features student-centeredness, critical thinking, problem-solving, exploration, and inquiry-based learning.

Discovery learning focuses on each student’s unique needs and talents, allowing them to explore new ideas and concepts in their distinctive manner. This strategy is ideal for naturally interested and self-motivated children since it helps them build critical thinking and problem-solving skills.

Discovery Method of Teaching (Discovery Learning)

The discovery teaching style has the potential to boost student involvement and motivation. Allowing students to participate actively in their learning makes them more involved in the topic and increases their chances of long-term retention.

Discovery learning may also assist students in developing a better knowledge of issues and ideas by allowing them to explore them more meaningfully.

But still, there are several drawbacks to using the discovery approach of teaching. Some children, for example, may struggle with the open-ended nature of discovery learning and get overwhelmed by the absence of structure.

Moreover, discovery learning takes time and may only sometimes result in the intended learning results. Instructors must balance guided and open-ended exploration learning to ensure that all children benefit from this method.

The discovery method of teaching may be implemented in various ways, depending on the subject matter and the individual requirements of the students. In mathematics, for example, students may be required to tackle a complicated issue by experimenting with several techniques and solutions independently.

Students in science may be encouraged to create their own experiments and observations about the natural world. Whatever the topic, the most important thing is to offer kids a secure and supportive learning environment where they can explore and learn at their speed.

What is the Discovery Method of Teaching?

The discovery teaching technique is a teaching and learning strategy that encourages students to learn via inquiry and experimentation. It is also known as the “investigative learning approach.” By providing students with opportunities to take an active role in their learning, this approach strongly focuses on developing critical thinking and problem-solving abilities.

Students are not simply told material; teachers encourage them to find ideas and principles independently through guided inquiry and investigation.

Types of Discovery Method of Teaching / Learning

There are two main types of discovery learning: unguided and guided discovery learning.

Unguided Discovery Learning

Students in an unguided discovery learning environment are free to autonomously explore and experiment without receiving any direction from the instructor. During guided discovery learning, the instructor offers students approaches and assistance to encourage them to investigate and uncover new ideas autonomously.

Guided Discovery Learning

Guided discovery learning is a more organized method that gives students help and direction as they explore and figure things out independently. This strategy often entails teaching students in their inquiry by asking questions, providing prompts, and providing clues to assist them in making connections between various ideas and concepts.

Steps in Discovery Method of Teaching

The discovery method of instruction consists of three phases to assist pupils in autonomously discovering and investigating various topics. The following items are normally included in these steps:

Exploration

Exploration is the first stage of the discovery method of teaching students. Students are allowed to investigate a subject or idea at this stage of the process by engaging in activities such as reading, watching, and participating in experiments, amongst other activities. In addition to laying a foundation of knowledge for the students to build upon in the next parts of the discovery process, this stage aims to foster a sense of natural curiosity and interest in the subject matter the class is studying.

As students are in the discovery phase of the unit, their instructors may utilise a range of materials, such as films, articles, and hands-on activities, to keep their attention and interest.

For instance, in a science lesson, the teacher would invite the students to watch a chemical reaction demonstration and write down their thoughts in a notebook about what they saw. Students taking a literature class may be assigned to read a short tale and then do an analysis of the narrative’s themes and characters.

The exploration phase is essential because it lets students get acquainted with the subject matter and develop a fundamental comprehension of the subject’s main ideas. Also, it helps to build interest and enthusiasm among students, which might drive them to participate in the succeeding parts of the discovery process.

The invention process is the second phase of the discovery method of teaching. At this stage, you will allow the students to apply their prior knowledge and imagination to develop original thoughts and answers to connect the subject.

This phase is intended to be completed for students to improve their ability to think critically and independently, as well as their problem-solving skills.

During the innovation phase, instructors may give students a provocation or challenge connected to the subject and then ask them to think of their ideas and develop their own answers. Students in a social studies class must devise a strategy for combating poverty in their neighbourhood as an assigned project.

Students in a math class could be invited to create a game that illustrates a mathematical subject via play.

Since it allows students to generate their concepts and approaches to the problem, the innovation phase is an essential part of the process. Students could benefit from this not just in terms of gaining self-assurance and independence but also in terms of developing a more in-depth comprehension of the material.

The actual process of discovery learning is the last stage in the discovery method of instruction. At this stage, you will guide students through putting their thoughts and ideas to the test by having them do experiments and conduct analyses.

Students will benefit from this phase by developing a more in-depth grasp of the material and strengthening their ability to solve problems in various contexts.

During the discovery phase, a teacher may give students a task or issue relevant to the subject and then invite students to use materials to solve the problem.

To put a theory to the test, for instance. The students in a science class can be asked to design and carry out their very own experiments. Throughout their history study, students are sometimes tasked with evaluating primary materials and drawing judgments on a particular historical occurrence.

Since it allows students to test their ideas and solutions in the context of the real world, the discovery phase is a crucial part of the process. Both their ability to solve problems and their grasp of the material may improve due to this activity.

It also allows children to take ownership of their work and feel pleasure in their accomplishments, which is a powerful motivator.

5 Principles of Discovery Learning Method

The Discovery Method of Instruction is an effective strategy that centres the educational experience on the student. Educators may assist students in developing critical thinking abilities, self-direction, and resilience by combining the five processes of Problem Solving, Learner Management, Integration and Connection, Information Analysis and Interpretation, and Failure and Feedback. This strategy empowers students to take charge of their own education , resulting in a more engaged and effective learning experience.

You want your students to succeed as teachers, yet conventional teaching approaches sometimes fall short. Here is where the Discovery Teaching Approach comes in. This method places the power in the hands of the students, enabling them to direct their education and enjoy the gratification that comes from self-discovery.

Principal 1: Problem-Solving

Problem-solving is the first phase of the Discovery method of instruction. Students must identify an issue, question, or difficulty and then brainstorm possible solutions or responses in this stage. The emphasis is on the mental process and critical thinking abilities required to arrive at a solution rather than the “correct” or “wrong” answer. Students grow more skilled at problem-solving and are better prepared to manage complicated situations in the future when they are encouraged to think creatively and evaluate some possibilities.

Principal 2: Learner Management

The second phase in the Discovery Way of Teaching is learner management. The significance of student autonomy and self-direction is emphasised at this level. Learners are empowered to take charge of their education by defining objectives and measuring their progress toward those goals. This stage also enables students to acquire time management skills and learn how to prioritize things to meet their objectives.

Principle 3: Integration and Connection

Integration and Connection is the third phase in the Discovery Way of Teaching. Students are encouraged to apply what they learn in other aspects of their lives at this level. This integration and connectivity may take numerous forms, such as using new information in real-world situations or integrating concepts across disciplines. Creating these connections gives students a more comprehensive grasp of the world and how various ideas fit together.

Principle 4: Information Analysis and Interpretation

Information analysis and interpretation are the fourth and final phases. In the classroom , students can explore the topic further and critically assess information sources. Students learn to recognize prejudice, analyse facts, and make sound decisions. This level promotes students becoming more selective information consumers while developing strong analytical and research abilities.

Principle 5: Failure and Feedback

Failure and feedback are the last steps in the discovery method of teaching. This stage highlights the significance of trial and error in learning. Teachers may help students learn from their mistakes and build resilience by allowing them to fail and offering constructive criticism. This phase also teaches pupils to see learning as a journey rather than a goal.

3 Modes of Representation in Jerome Bruner’s Constructivist Theory Of Learning And Cognitive Development

The Discovery Learning Method or Bruner’s 3 Steps of Learning in a Spiral Curriculum

Enactive Mode
Iconic Mode
Symbolic Mode

Jerome Bruner’s constructivist theory of learning and cognitive development is an outstanding contribution to education that has transformed how we think about teaching and learning. Bruner felt that learning should be an active process in which students actively develop their own knowledge via interaction with their surroundings. This educational technique empowers and frees pupils by giving them agency and control over their learning.

Bruner’s theory is intensely emotional since it recognizes each learner’s unique experiences and views. It acknowledges that everyone has a unique perspective on the world and that this perspective is continually developing and changing. Bruner thought education should be adapted to each learner’s requirements rather than a one-size-fits-all approach that overlooks the complexities of human intellect and growth.

The constructivist learning and cognitive development paradigm supports critical thinking, problem-solving, and creativity. It understands that education is more than simply gathering information; it is also about applying that information meaningfully. Bruner felt students should be allowed to investigate new ideas and concepts and participate in open-ended inquiry and experimentation.

Bruner’s constructivist approach also highlights the significance of social contact and cooperation in learning. It acknowledges that we learn not just from our own viewpoints and experiences but also from the perspectives and experiences of others. This social component of education is a strong source of emotional engagement and connection because it helps us to meaningfully connect with others and build a better knowledge of ourselves and the world around us. He introduced the tree models for discovery learning, which are explained below.

Enactive Mode In the Discovery Learning (0 to 1 Year)

The discovery learning technique relies on the active mode, which emphasises the value of hands-on experience and active participation in the learning process. It encourages students to learn by doing and to relate their experiences to the taught principles. This learning method is productive and exciting, enabling students to thoroughly immerse themselves in the subject matter and take ownership of their learning.

Learners participate in physical activities that assist them in understanding the topics being taught in the method of discovery learning. This might include creating models, performing experiments, or participating in simulations. By actively engaging in these activities, students may gain personal experience with the ideas and concepts being taught, resulting in a stronger grasp and recall of the information.

Enactive learning is especially effective for those who struggle with typical classroom learning approaches such as lectures and texts. It offers a different method that enables students to actively engage in their education and take charge of their learning. Learners may build a personal connection to the subject by leveraging their experiences and observations, which can help them better absorb and recall the content.

Iconic Mode In the Discovery Learning Method (1 to 6 Years)

For young learners aged 1 to 6 years, the iconic mode is essential to the exploration learning process. It enables individuals to learn via visual representation and investigate their surroundings through their senses. This learning method is interesting and engaging because it allows youngsters to use their ideas and creativity to find new things and relate their experiences to the topics taught.

Children employ visual aids such as drawings, diagrams, and movies to explore and comprehend the world around them in the iconic mode of exploration learning. They may use their senses to study and learn about many items and occurrences, including touch, smell, taste, sight, and sound. They may build a personal connection to the subject matter by engaging these senses, resulting in stronger comprehension and retention of the content.

The iconic mode is especially useful for young learners still working on their language abilities. It enables people to communicate and comprehend topics using visual signals rather than exclusively through spoken communication. This bridges the gap between their present level of language development and the subjects being taught, making it easier for children to learn and create connections.

Symbolic Mode In the Discovery Learning Method (for seven and Above Years)

For older learners to understand complex ideas and develop critical thinking abilities, the symbolic mode of the discovery learning approach is important. It teaches students to create links between abstract concepts and the actual world by representing ideas and theories using symbols and words. This form of learning is fascinating and powerful since it enables students to express themselves and comprehend complicated topics in innovative and relevant ways.

Students utilise symbols like letters, numbers, and mathematical formulae to express ideas and concepts in the symbolic style of discovery learning. They use language to explain and analyse these symbols and relate them to the actual world. Students may better comprehend complicated topics and apply this knowledge to real-world issues and circumstances by employing symbols and words.

The symbolic method is especially valuable for older students because it enables them to practice critical thinking and problem-solving abilities. Students may improve their analytical and problem-solving skills by using symbols and words to express abstract ideas. Students may also enhance their communication abilities by using language to express themselves clearly and effectively.

Discovery Method of Teaching Advantages and Disadvantages

Advantages:

Encourages Active Learning: Discovery learning enables students to actively participate in the learning process, which increases motivation and interest in the topic.
Students build critical thinking and problem-solving abilities through solving issues and exploring new ideas, which are vital for their future academic and professional success.
Customised Learning: By allowing students to explore ideas and answers quickly, personalized learning is promoted, and individual needs and interests are catered to.
Long-term Retention: Since discovery learning is hands-on, it enhances long-term knowledge retention and improves memory recall.
Encourages Curiosity: Since students actively research and study new ideas and concepts, the discovery learning technique fosters curiosity and a quest for knowledge.

Disadvantages:

Time-consuming: Compared to other teaching approaches, the discovery learning method may be time-consuming since students may need more time to investigate and discover topics.

Resources required: To perform experiments or investigations, discovery learning necessitates using resources such as equipment, materials, and enough space.

Students may feel overwhelmed or confused when investigating new concepts and ideas if they need to be properly guided and structured.

Possible Misconceptions: Students who explore subjects without good direction may acquire misconceptions or misunderstandings, leading to wrong conclusions and incomplete learning.

Assessment Difficulties: Evaluating student learning and comprehension in discovery learning may be difficult since quantifying a student’s understanding and knowledge level can be difficult.

Active learning and critical thinking abilities are encouraged.
Curiosity and drive to study are encouraged.
Improves idea retention and comprehension.
Aids in the development of problem-solving abilities.
It encourages independence and self-directed learning.
It promotes creativity and inventiveness.
Encourages the use of knowledge in real-world circumstances.
Opportunities for cooperation and communication are provided.
Improves student interest and participation in learning.
Allows learners to take charge of their learning.
Planning and execution need a large amount of time and resources.
It may only be appropriate for some learners, particularly those who demand structure and assistance.
It might be difficult for pupils who do not have previous knowledge or core abilities.
Sufficient supervision and feedback may result in a partial or accurate grasp of topics.
Learning outcomes assessment may require more work to evaluate and quantify.

What is Discovery Learning?

Discovery Learning is a student-centred teaching and learning strategy that promotes problem-solving, critical thinking, and discovery. Students actively participate in the learning process with this technique, finding topics via inquiry and exploration.

What are the benefits of using the Discovery Learning Method?

The Discovery Learning Method promotes active participation and critical thinking, fosters creativity, improves problem-solving abilities, encourages cooperation and teamwork, and provides a more real and meaningful learning experience.

What are the characteristics of Discovery Learning?

Discovery Learning has a student-centred approach, active involvement in the learning process, problem-solving and critical thinking, exploration and experimentation, and an emphasis on generating real and meaningful learning experiences.

What are the discovery method of teaching examples?

Pure discovery learning, guided discovery learning, and problem-based learning are all examples of discovery learning.

How does the Discovery Learning Method promote active learning?

The Discovery Learning Method encourages active learning by enabling students to take ownership of their education and actively participate in the learning process via inquiry and experimentation.

What are some examples of hands-on learning activities used in discovery learning?

Experiments, simulations, case studies, and problem-based learning activities are some hands-on learning activities utilised in Discovery Learning.

How does the Discovery Learning Method encourage collaboration among students?

The Discovery Learning Method promotes cooperation and group work activities, such as collaborative problem-solving and group presentations, to increase student participation.

How does the Discovery Learning Method promote problem-solving skills?

The Discovery Learning Method encourages students to participate in learning, develop critical thinking abilities, and apply problem-solving techniques to real-world situations and circumstances.

How can teachers evaluate student learning in the Discovery Learning Method?

Instructors may assess student learning using several assessment techniques in the Discovery Learning Method, such as formative assessments, self-assessments, and peer assessments. Teachers may also use rubrics to measure student performance on particular learning goals.

How does the Discovery Learning Method align with educational innovation?

The Discovery Learning Method promotes student-centred learning, active involvement, and real and meaningful learning experiences, which connect with educational innovation. This method of teaching and learning fosters creativity, critical thinking, and problem-solving abilities, all of which are necessary for success in today’s fast-changing world.

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Students’ performance, attitude, and classroom observation data to assess the effect of problem-based learning approach supplemented by YouTube videos in Ugandan classroom

Nicholus Gumisirizah 1 ,
Joseph Nzabahimana 1 &
Charles M. Muwonge 2

Scientific Data volume 11 , Article number: 428 ( 2024 ) Cite this article

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Metrics details

Applied physics

In response to global demands, Uganda’s Vision 2040 seeks to transform the country into a modern and prosperous nation by implementing Sustainable Development Goal (SDG) 4, focusing on equitable and quality education. The 21st-century workforce requires individuals who can effectively navigate complex workplace challenges. This dataset was gathered from Form-2 Ugandan secondary school students (aged 12 to 15) across 12 schools in the Sheema District. The dataset comprises three types of data: students’ performance in a physics topic (simple machines), their attitudes toward problem-solving and critical thinking when learning physics using Problem-Based Learning (PBL) supplemented by YouTube videos, and classroom observations documented with the reformed teaching observational protocol (RTOP). The intervention of teaching using PBL was executed in 2022, collecting data from 973 lower secondary school students. The intervention involved three approaches: one group (144 students) received PBL along with YouTube videos, another group of 482 students received PBL alone, and a third group (347 students) was taught using the traditional method. This data article explains the study’s data creation, collection, and analysis process. The dataset holds significance for secondary school teachers, policymakers, and researchers, offering insights into the impact of PBL with and without ICT resources on learning physics and students’ attitudes toward these learner-centered approaches.

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Background & summary.

Physics education in secondary schools plays a vital role in developing students’ social, physical, leadership, and problem-solving skills. Understanding physics concepts equips learners to know how things work, enabling them to apply this understanding to real-life situations 1 . The physics teaching is structured around activity-based 2 chapters and topics, emphasizing hands-on experiences 3 and practical applicability in everyday life. However, many students find physics challenging, necessitating an active teaching approach. Teaching in physics remains dynamic and interactive, with teachers adopting various strategies to engage students actively. Reciprocal teaching involves dialogues between the teacher and small student groups, while peer collaboration fosters cooperative work on class activities. Problem-Based Learning (PBL) 4 , 5 , 6 is a student-centered approach that encourages group-based learning and teacher facilitation. It has been widely adopted in various educational fields, promoting problem-solving in learning environments. Implementing PBL follows a five-stage process:

Finding a problem

The teacher prepares a task for students to investigate, stimulating problem-solving abilities.

Organizing ideas on the problem

Learners investigate the problem, generate ideas, and receive probing questions from the facilitator to stimulate critical thinking.

The teacher facilitates the distribution of learners into groups, each focusing on solving a particular problem related to the main task. Responsibilities are assigned within each group, promoting cooperation.

Present findings

Learners present solutions to the problem and receive feedback from peers, consolidating their learning outcomes.

Generalizing

Problem-solving leads to the development of skills essential for solving complex, real-world situations. These skills, including problem-solving, creativity, communication, cooperation, and innovation, prepare students to adapt to change and overcome 21st-century challenges.

Integrating YouTube videos as Information and Communication Technology (ICT) tools within a PBL approach offers a multifaceted strategy to enhance physics education 7 , 8 . High-quality videos aligned with curriculum objectives introduce real-world problems and cater to diverse learning styles. Interactive features and accessibility allow continuous learning, and educators can curate playlists to align with curriculum goals. The flipped classroom model 9 combines videos with problem-solving discussions 10 , creating a dynamic learning environment that deepens students’ understanding of physics concepts and their practical applications.

Physics is a subject that holds a significant position in promoting scientific literacy, critical thinking, and essential life skills. However, conventional teaching methods often struggle to engage and empower students in the subject matter effectively. This inadequacy is a pressing concern, as it can hinder students from developing a strong foundation in physics, which is essential for their academic and practical pursuits. This study was critically important due to the existing challenges within physics education in Ugandan secondary schools. Incorporating innovative teaching approaches, such as PBL supplemented by YouTube videos, becomes pivotal in addressing these challenges. These methods can enhance students’ comprehension of physics and nurture vital skills like problem-solving, creativity, communication, cooperation, and innovation. These skills are indispensable for students to thrive in a rapidly evolving, knowledge-driven world.

Sharing the data generated through this study is equally significant. It is a valuable resource for educators, policymakers, curriculum designers, and researchers. By making this data accessible, the study contributes to the ongoing efforts to improve the quality and relevance of secondary education in Uganda. Educators can utilize this data to adopt innovative and effective teaching methods that align with the goals of the educational system, ultimately enhancing students’ performance and fostering lifelong learning. Policymakers and curriculum designers can use the insights derived from this data to conduct essential reviews and make informed decisions about teacher competence and the adoption of innovative teaching methodologies. Furthermore, researchers in similar fields can leverage this data to understand better the impact of PBL and the use of multimedia resources in education. This data identifies gaps and challenges and offers potential solutions and avenues for further research.

This data-sharing article presents insights into the effects of Problem-Based Learning (PBL) supplemented by YouTube videos on students’ comprehension of simple machines in physics within Ugandan lower secondary schools. The research collected data from 973 students, encompassing both public and private schools in the Sheema district of Uganda. Three primary types of data were collected: students’ performance data, attitude data, and classroom observation data.

Performance data was acquired through a Physics Learning Achievement Test (PLAT), involving students from various school types and teaching methods. Attitude data were collected via two surveys, one focusing on problem-solving ability (AAPS) and the other on critical thinking ability (CTMS) under PBL with YouTube videos. The Approaches to Problem-Solving Survey (AAPS) and the Critical Thinking Motivational Scale (CTMS) are measurement tools commonly used in the field of physics. The AAPS assesses various strategies individuals employ when solving problems, while the CTMS evaluates motivational factors influencing critical thinking abilities. The Reformed Teaching Observation Protocol (RTOP) assessed classroom practices and teaching methods.

The dataset, available in raw, filtered, and analyzed formats, offers valuable insights into the impact of innovative teaching methods on student performance, attitudes, and classroom practices. It addresses critical questions about the effectiveness of PBL approaches, with potential implications for science education in Uganda.

This dataset intends to assess the impact of PBL when supplemented with YouTube videos on Ugandan form-2 lower secondary schools in learning simple machines. The following are the research questions:

To what extent do PBL and PBL supplemented with YouTube videos enhance students’ conceptual understanding of simple machines in physics?

What are the problem-solving and critical thinking levels brought by learning with PBL supplemented by YouTube videos?

How is physics teaching reformed when learning simple machines in physics with PBL supplemented by YouTube videos?

Are there differences in students’ academic achievement for school type (government alongside private school)?

Ethics statements

The research project rigorously adhered to ethical standards established by the University of Rwanda College of Education’s (UR-CE) Research and Innovation Unit under the ethical protocol number Ref. 03/DRI-CE/078/EN/gi/2021, dated 30th November 2021. All necessary permissions were obtained systematically and ethically, as outlined in the research project description. Here is a summary of the ethical considerations and recruitment process:

Ethical protocol

The research project adhered to the ethical standards and principles of the UR-CE)‘s Research and Innovation Unit. The protocol number and approval date are explicitly mentioned, demonstrating a formal ethical review.

Permissions from authorities

The Ministry of Education and Sports obtained formal permission to access schools through the Permanent Secretary’s (PS) office. The PS communicated with the Chief Administrative Officer (CAO), District Education Officer (DEO), and Resident District Commissioner (RDC) to secure the necessary support for the study.

Engagement with schools

With the approval from the CAO, the DEO contacted school heads to inform them about the research study. The school heads responded positively and even provided physics teachers with three-day problem-based learning (PBL) training as part of the research. It is worth noting that all participating teachers held teaching qualifications, and as part of the research process, we provided them with a three-day training session specifically focused on implementing PBL interventions. This training aimed to ensure consistent delivery of PBL across treatment classrooms and schools, thereby mitigating variations attributable to individual teaching styles.

Informed consent

Teachers and students, with parental consent, willingly participated in the research study. Informed consent forms were signed, indicating they fully understood the study’s purpose, procedures, potential risks, and benefits. Anonymity was ensured for students by not including their names on the test papers.

The research employed purposive sampling to select 973 students from 12 schools. These schools were divided into three groups, each with a different teaching method: PBL with YouTube videos, PBL alone, and Traditional teaching.

Geographic considerations

Schools were selected from different town councils at extreme ends of the district, sharing similar characteristics suitable for the study. This approach helps ensure that the study’s findings are robust and generalizable.

Research design

The study utilized a non-equivalent comparison group pre/post-test design (Creswell, 2012). The study involves Form 2 students from six Sheema District, Western Uganda schools. Three selected schools were public, while the remaining three were private, offering a diverse representation of school types in the district. The selection of schools was purposeful, aiming to ensure diverse representation and maximize the study’s validity. This approach allowed for the strategic allocation of schools to treatment or control groups based on specific criteria pertinent to the research objectives. Notably, the selection criteria considered factors such as geographical location, school size, academic performance, and availability of resources to ensure a balanced representation of different educational contexts. The traditional method, characterized by conventional lectures supplemented with textbooks and teacher-centered content delivery, was employed in control group schools. Students in this group primarily learned through note-taking with minimal demonstrations. Conversely, four other secondary schools were designated as the first treatment group, where Problem-Based Learning (PBL) was implemented. Four additional schools comprised the second treatment group, which utilized PBL supplemented by educational YouTube videos. These groups collectively engaged in constructing knowledge and enhancing conceptual understanding. The participants in the study were form-2 students, ranging in age from 12 to 15 years, who were already enrolled in the schools.

We provide a performance (achievement) test to all 973 students before and after teaching interventions in all groups. We administered an attitude survey (motivation scale) and observed classes in the group that used PBL and YouTube videos. Table 1 presents the sample size under the teaching intervention of design groups implemented.

The objective of the performance test was to gauge students’ grasp of conceptual understanding acquired through the implementation of a problem-based learning approach following the completion of the topic on simple machines. The test, spanning 25 minutes, consisted of ten questions sourced from practice exercises on simple machines within form-two secondary learners’ physics textbooks. The National Curriculum Development Center and the Ministry of Education and Sports in Uganda approved these textbooks. The examination encompassed themes outlined in the approved lower secondary curriculum physics syllabus, covering concepts like the applications of simple machines, mechanical advantage, velocity ratio, and efficiency of machines. Specific topics included levers (covering classes and applications), pulley systems (encompassing types, applications, mechanical advantage, velocity ratio, and efficiency), inclined planes (including applications, mechanical advantage, velocity ratio, and efficiency), wheel and axle (exploring understanding, applications, and velocity ratio), gears (addressing simplification of work, applications, and velocity ratio), and methods of enhancing machine efficiency. The test was validated by four researchers from Mbarara University of Science and Technology (MUST) and the University of Rwanda College of Education (URCE). Test 1 was scored in MS Excel with “IF EXCACT” function, while Test 2 was manually marked, and results were entered in the same software.

Attitude surveys were all adopted from existing literature. Critical Thinking Motivational Scale (CTMS) was used as our Survey 1 and was adapted from Valenzuela et al . 11 , while Attitudes and Approaches to Problem-Solving Survey (AAPS) was used as our Survey 2 and was adapted from Singh and Mason 12 and available at Physport ( https://www.physport.org/assessments/assessment.cfm?A=AAPS ). Problem-solving and critical thinking are integral to effective physics education. They deepen students’ understanding by connecting theoretical concepts to real-world situations 13 , 14 . These skills encourage active engagement and foster analytical abilities, allowing students to break down complex problems. Additionally, they promote creativity, help apply theory to practice, and cultivate logical reasoning. Problem-solving and critical thinking prepare students for future challenges in scientific and engineering fields, encourage collaboration, boost confidence, and instill a mindset for lifelong learning. Incorporating these skills into physics teaching enhances academic performance and equips students with valuable personal and professional growth tools. We adopted all 19 items from CTMS and only 31 items from AAPS to meet our research aim. Thus, the last two items (32 and 33) in AAPS were removed as they were not related to the content delivered in our study. All these surveys were rated on a Likert scale (from strongly disagree to strongly agree). Items 1–4 are related to expectancy, items 5-8 to attainment, items 9-12 to utility, items 13-16 to interest, and items 17-19 to cost.

Classroom observation data was collected with the famous standardized reformed teaching observation protocol (RTOP) from Pibun and Sawada 15 and is available at Pysport ( https://www.physport.org/assessments/assessment.cfm?A=RTOP ). RTOP proved its validity and reliable results across the globe 16 , 17 , 18 , 19 with its potential to reveal reformed teaching while implementing a new teaching method. It comprises 25 statements where each item is evaluated on a 5-scale. It is scored 0 when such practice was not found in a lesson and 4 when a certain practice was very well described or observed in a delivered lesson. During classroom observation, an observer sits in the classroom and observes what the teacher and student do. He/she may take notes on what is happening but wait until the class is over to rate these 25 items.

Data Records

All data described in this descriptor are deposited in figshare ( https://figshare.com/articles/dataset/RTOP_Data_for_the_implementation_of_Problem-based_learning_in_a_Physics_classroom_Uganda/23974902 ) 20

To evaluate the impact of PBL teaching intervention on students’ performance and attitude toward learning physics, we gathered three data types (performance, attitude, and observation) presented in five datasets (two performance tests, two attitude surveys, and one classroom observation).

Students’ performance data

The student performance data comprises two datasets or MS Excel files. The first file contains data for test one titled “Performance data _ Test 1 (Multiple choice) _ 12102022 figshare.” This file contains data from ten multiple-choice questions. The file contains three sheets. The first sheet shows test items (all ten questions), the second presents pretest answer choices, and the third presents post-test answer choices or results. Each results sheet shows the school code (column B), student code (column C), school type (column D), and treatment group (column E) as variables. From column “F” to column “O” we see student answer choices under each test question. From column “Q” to column “Z” we marked the test (one score for each correct question). Column “AB” shows the percent score. Row “3” shows the expected correct answer, while row “4” shows variables and the number of test items.

The second file contains data for test two titled “Performance data _ Test 2 (Problem solving) _ 12102022 figshare.” This file contains data from ten-word problem kinds of questions. The file contains three sheets. The first sheet shows test items (all ten questions), the second presents pretest scores, and the third presents post-test scores or results. Each results sheet shows the school code (column C), student code (column D), school type (column E), and treatment group (column F) as variables. From column “G” to column “P” we see student scores under each test question. Column “R” shows the total score, while column “S” shows percent score. Row “3” shows the assigned score when each question’s expected correct answer was provided. Row “4” shows variables and several test items.

Students’ attitude data

The student attitude data comprises two datasets or MS Excel files. The first file contains data for the first survey titled “Motivation data _ Survey 1 (Critical thinking ability) _ 12102022 figshare.” This file contains data from 19 items of critical thinking ability survey. The file contains two sheets. The first sheet shows the pre-test results, while the second shows the post-test results. Each sheet shows the school code (column C), student code (column D), school type (column E), and treatment group (column F) as variables. From column “F” to column “O” we see student answer choices under each test question. From column “G” to column “Y” we see student answers or agreement (1: STRONGLY DISAGREE, 2: DISAGREE, 3,: NEUTRAL, 4: AGREE, AND 5: STRONGLY AGREE) to each item of the survey. Row “2” shows the survey title, while row “4” shows the variables and number of survey items.

The second file contains data for the second survey titled “Attitude data _ Survey 2 (Problem solving ability) _ 12102022 figshare.” This file contains data from 31 items related to problem-solving ability in learning physics. The file contains two sheets. The first sheet shows the pre-test results, while the second shows post-test results. Each sheet shows the school code (column C), student code (column D), school type (column E), and treatment group (column F) as variables. From column “G” to column “AK” we see student answers or agreement (1: STRONGLY DISAGREE, 2: DISAGREE, 3,: NEUTRAL, 4: AGREE, AND 5: STRONGLY AGREE) to each item of the survey. Row “2” shows the survey title, while row “4” shows the variables and number of survey items.

Classroom observation data

The file for classroom observation data is titled “Classroom observation data _ RTOP for video & pbl group _ 12102022 figshare” and contains only one sheet. From column “B” to column “C” we see RTOP while the following columns (D-AA) present data. Row “10” shows school codes, while row “5” shows several observations and frequencies under each school supplied with PBL and YouTube videos teaching intervention. The data range from 0 (never occurred) to 4 (very descriptive).

Technical Validation

Initially, we had 20 problem-solving questions, but evaluators rated 10 as valid, which were included in the final administration. We also initially had 15 multiple-choice questions, and evaluators rated 10 as appropriate and aligned with the study objectives. A pilot study was conducted with 90 students to evaluate the face validity and reliability of the questions. We assessed the reliability of these items using a split-half method and obtained a high reliability (r = 0.87) for multiple-choice items and a medium reliability (r = 0.68) measured by the Pearson product-moment correlation coefficient for problem-solving items. The split-half reliability assumes that the two halves of the test are equivalent in difficulty and content 21 .

CTMS and AAPS

During our pilot phase, the internal consistency of CTMS, assessed using Cronbach’s alpha, was found to be high (0.793) for all 19 items, medium (0.428) for expectancy, (0.411) for attainment, (0.686) for utility, (0.574) for interest, and (0.594) for cost. The AAPS exhibited an internal consistency reliability of Cronbach’s alpha = 0.685. It is important to note that the AAPS contains nine items formulated negatively. Therefore, for a positive attitude, students were required to respond with ‘Disagree’ or ‘Strongly disagree’ to these items (1, 3, 5, 8, 11, 12, 16, 23, and 30). Consequently, the reliability of the 22 positively formulated items was 0.601, while that of the negatively formulated items was 0.480.

Before observing actual classes, we underwent a 2-hour training session and watched and coded a YouTube classroom video on physics. The inter-rater agreement between the first author and the assistant exceeded 80% on two occasions, indicating the reliability of the data.

Scope and potential limitations

In our study, we recognized the significance of investigating potential bias in the results obtained from students in both private and public schools. To ensure the credibility and robustness of our findings, we conducted a comparative analysis to determine whether any notable disparities existed between these two groups. Our data collection process was comprehensive, encompassing a diverse range of schools, including both private and public institutions. This approach allowed us to capture a broad spectrum of socioeconomic backgrounds and educational settings. The study itself involved Form-2 students who were enrolled in schools situated in different town councils at opposite ends of the district. Despite their geographical diversity, these schools shared pertinent characteristics relevant to our research objectives. To facilitate our investigation, we categorized these schools into distinct treatment groups, comprising PBL alone and PBL with videos, along with a control group following traditional teaching methods. Importantly, we deliberately chose to maintain the existing class arrangements in these schools. Our commitment to preserving each school’s established class organization and cultural norms guided this decision.

However, it is essential to acknowledge the limitations inherent in the research design. One notable limitation is the observation of attitudes, which was limited to the student group exposed to the PBL with the video teaching method. This restriction may impact the generalizability of the findings, as attitudes toward learning may vary among students exposed to different instructional methods. Future research endeavors could consider incorporating measures to assess attitudes across all treatment groups to provide a more comprehensive understanding of the intervention’s effects.

The current data files do not contain information on individual teachers due to the scope and focus of the study. These variables could include educators’ teaching experience, pedagogical approach, content knowledge, and instructional effectiveness. Since we recognize the significance of teacher impact, we would consider incorporating such variables in future research projects to provide a more comprehensive analysis of instructional effectiveness and its associated factors.

Regarding the decision to maintain existing class arrangements in schools, particularly considering cultural norms, it is crucial to recognize its potential influence on the study outcomes. The intervention’s impact may have been influenced by preserving the existing class structures, including student composition and dynamics. For instance, certain class arrangements may foster greater collaboration and engagement, while others may present challenges in implementing collaborative learning approaches such as PBL. Therefore, future studies could explore the relationship between class arrangements and instructional effectiveness to provide insights into optimizing learning environments.

Usage Notes

Value of the data.

The data presented is valuable and beneficial to science education in Uganda as it elucidates the status of students’ content knowledge and their perceptions about learning simple machines with PBL approaches.

Policymakers and curriculum designers have the opportunity to conduct essential reviews that highlight the competence of teachers. This process can pave the way for advocating innovative and relevant teaching methodologies, subsequently informing the identification of professional development requirements for educators.

Researchers in similar fields can re-use these data to measure the effect of PBL intervention on student achievement, identify gaps, and predict possible remedies. Thus, data can be analyzed using various variables such as teaching intervention and school type.

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Acknowledgements

We acknowledge the African Center for Excellence for Innovative Teaching and Learning Mathematics and Science (ACEITLMS) for funding this study and the authors of the research tools we used to free them to use. All study participants, teachers, and school headteachers are also well acknowledged.

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Gumisirizah, N., Nzabahimana, J. & Muwonge, C.M. Students’ performance, attitude, and classroom observation data to assess the effect of problem-based learning approach supplemented by YouTube videos in Ugandan classroom. Sci Data 11 , 428 (2024). https://doi.org/10.1038/s41597-024-03206-2

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