problem solving as a method of teaching

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Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

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Teaching Problem-Solving Skills

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

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

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

Principles for teaching problem solving

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

Woods’ problem-solving model

Define the problem.

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

Think about it

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

Plan a solution

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

Carry out the plan

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

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

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

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

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

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Problem-Solving Method in Teaching

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

Table of Contents

Definition of problem-solving method.

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

Meaning of Problem-Solving Method

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

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

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

Benefits of Problem-Solving Method

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

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

Steps in Problem-Solving Method

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

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

Verification of the concluded solution or Hypothesis

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

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

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

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

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

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

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5 Most Important Benefits of Problem-Solving Method of Teaching

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

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

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

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

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

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

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

Know 6 Steps in the Problem-Solving Method of Teaching

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

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

Find Out Examples of the Problem-Solving Method of Teaching

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

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

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

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

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

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How to Choose: Let’s Draw a Comparison

The following table compares the different problem-solving methods:

Which Method is the Most Suitable?

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

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

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

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Some Unique Examples to Refer to Before We Conclude

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

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

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

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• Problem-Based Learning Clearinghouse of Activities, University of Delaware

Problem-Based Learning

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

Why Use Problem-Based Learning?

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

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

Considerations for Using Problem-Based Learning

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

Students generally must:

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

Getting Started with Problem-Based Learning

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

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

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

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

October 31, 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Teaching problem solving

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

Introducing the problem

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

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

Working on solutions

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

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

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

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

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

What is the most effective way to teach problem solving? A commentary on productive failure as a method of teaching

• Published: 04 May 2012
• Volume 40 , pages 731–735, ( 2012 )

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Jacobson, M. J., Thompson, K., Kennedy-Clark, S. & Hu, C. (2011) Failure and success in sequencing of model - based learning activities. Paper presented at the American Educational Research Association Annual Meeting, New Orleans.

Kapur, M. (2008). Productive failure. Cognition and Instruction, 26 (3), 379–424.

Article   Google Scholar  

Kapur, M. (2009). Productive failure in mathematical problem solving. Instructional Science, 38 (6), 523–550.

Kapur, M. (2010). A further study of productive failure in mathematical problem solving: Unpacking the design components. Instructional Science, 39 (4), 561–579.

Kapur, M. (2012). Productive failure in learning the concept of variance. Instructional Science . doi: 10.1007/s11251-012-9209-6 .

Google Scholar  

Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. Journal of the Learning Sciences, 21 (1), 45–83.

Koedinger, K. R., Aleven, V., Roll, I., & Baker, R. S. J. D. (2009). In vivo experiments on whether supporting metacognition in intelligent tutoring systems yields robust learning. In D. J. Hacker, J. Dunlosky, & A. C. Graesser (Eds.), Handbook of metacognition in education (pp. 383–412). New York: Routledge.

Roll, I., Holmes, N. G., Day, J., & Bonn, D. (2012). Evaluating metacognitive scaffolding in guided invention activities. Instructional Science . doi: 10.1007/s11251-012-9208-7 .

Salden, R. J. C. M., Koedinger, K. R., Renkl, A., Aleven, V., & McLaren, B. M. (2010). Accounting for beneficial effects of worked examples in tutored problem solving. Educational Psychology Review, 22 (4), 379–392.

Schoenfeld, A. J. (1985). Mathematical problem solving . New York: Academic Press.

Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16 (4), 475–522.

Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22 (2), 129–184.

Stigler, J. & Hiebert, J. (2009) The teaching gap: Best ideas from the world’s teachers for improving education in the classroom (paperback edition) . New York: Free Press.

Vygotsky, L. S. (1978). Mind in society. In M. Cole, V. John-Steiner, S. Scribner & E. Souberman (Eds.), The development of higher psychological processes. Cambridge: Harvard University Press.

Westermann, K., & Rummel, N. (2012). Delaying instruction: evidence from a study in a university relearning setting. Instructional Science . doi: 10.1007/s11251-012-9207-8 .

White, B. Y., & Frederiksen, J. R. (1998). Inquiry, modeling, and metacognition: Making science accessible to all students. Cognition and Instruction, 16 (1), 3–118.

Wiedmann, M., Leach, R. C., Rummel, N., & Wiley, J. (2012). Does group composition affect learning by invention? Instructional Science . doi: 10.1007/s11251-012-9204-y .

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Collins, A. What is the most effective way to teach problem solving? A commentary on productive failure as a method of teaching. Instr Sci 40 , 731–735 (2012). https://doi.org/10.1007/s11251-012-9234-5

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Problem-Based Learning (PBL)

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

See also: Just-in-Time Teaching

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

By working with PBL, students will:

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

How to Begin PBL

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

Designing Classroom Instruction

See also: Inclusive Teaching Strategies

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

How to Orchestrate a PBL Activity

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

Teacher’s Role in PBL

See also: Flipped teaching

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

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

The Role of the Students

See also: ADDIE model

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

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

See also: Kirkpatrick Model: Four Levels of Learning Evaluation

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

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

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

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

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

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

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

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

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

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

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

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

Key features of a good mathematics problem includes:

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

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

But look at the b ack.

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

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

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Choosing the Right Task

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

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

Low Floor High Ceiling Tasks

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

The strengths of using Low Floor High Ceiling Tasks:

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

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

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

Math in 3-Acts

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

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

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

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

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

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

Number Talks

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

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

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

• Inside Mathematics Number Talks
• Number Talks Build Numerical Reasoning

Saying “This is Easy”

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

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

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

Instead, you and your students could say the following:

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

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

Using “Worksheets”

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

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

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

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

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

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

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

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

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

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

when we teach students how to problem solve

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

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

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

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

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Problem Solving Method Of Teaching

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."

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.

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.

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.

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.

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Key Tips On Problem Solving Method Of Teaching

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

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

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

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

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

The problem-solving method involves three basic functions

• Seeking information
• Generating new knowledge 
• Making decisions 

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

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

Woods' problem-solving model

Identify the problem .

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

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

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

Think about it

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

Plan a solution

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

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

Carry out the plan

Now that the major part of problem-solving has been done start executing the solution. There are possibilities that a plan may not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying. 

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

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

Other tips include

Ask open-ended questions.

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

Emphasize Process Over Product

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

Model The Strategies

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

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

Encourage Grappling

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

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

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

Make problem resolution relevant to the lives of your students

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

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

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Problem Solving as Teaching Method

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Are Real-World Problem-Solving Skills Essential for Students?

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Many school districts and policymakers are stepping up efforts to teach students the skills they need to be prepared for the jobs of the future.

One big area of focus is STEM.

Jobs in science, technology, engineering, and mathematics fields are expected to grow at a faster rate than all other occupations, according to the U.S. Department of Labor . But less than one-third of teens and young adults listed a role in those fields as their first-choice career, according to a 2023 Gallup/Walton Family Foundation survey .

“With increasingly rapid change being the only constant due to factors such as AI and climate change, yes, it’s important and essential for students to learn a [real-world] problem-solving approach to math and science,” said Maud Abeel, a director at Jobs for the Future, a national nonprofit that develops programs and public policies to boost students’ college and career readiness. “STEM is probably the best conduit for learning problem-solving available to all young people.”

Because of its focus on hands-on, problem-based learning, STEM education nurtures skills that are transferable to almost any field students pursue after graduation, experts say. These are skills that are highly valued by employers. The National Association of Colleges and Employers’ Job Outlook 2024 report found that nearly 90 percent of employers said they’re looking for people with proven problem-solving skills.

Most educators agree that, to be prepared for the jobs of the future, students need to learn math and science through a problem-solving approach that encourages them to tackle real-world challenges, according to a nationally representative EdWeek Research Center survey of 1,183 teachers, principals, and district leaders conducted in March and April. Most educators also say that this approach is important for all students, not just those who plan to go into STEM careers.

“I believe that problem-solving skills and critical thinking are imperative to the survival of students,” said an elementary teacher in Georgia in an open-ended response to the survey. “The skills will be needed to address issues that occur in everyday life. In addition, problem-solving and critical thinking are at the very core of the evolution of humanity and its continued existence.”

Still, there are plenty of educators who counter that students need to learn the basics before moving on to real-world problem-solving lessons.

“While learning math through ‘real problem-solving’ projects is interesting, engaging, and important, overlooking the foundational necessities is a huge, and common, mistake,” said a high school teacher in New York. “While this process can often feel like a repetitive grind full of rote, formulaic practice, it is nevertheless essential. First things must come first.”

Having solid foundational knowledge in science and math is important, because students could get discouraged if they aren’t good in those areas, experts agree. But a real-world problem-solving approach could help students be more engaged in the learning and gain a better understanding of how the topics they’re studying will be useful to them in the future, experts also point out.

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Question: What’s Your Favorite Tried-and-True Teaching Strategy?

Some teacher strategies are timeless. Share your favorite—and learn from other educators what works for them.

Teaching strategies are at the heart of effective education, and every educator has a go-to method that consistently yields positive results. Whether it's a technique to engage students deeply, a way to simplify complex concepts, or something else entirely, we want to hear about the strategy you rely on most. What makes it effective and how has it impacted your students' learning?

Please share your favorite tried-and-true teaching strategy and any tips for implementing it successfully.

How to align class discussions with learning objectives

A packed curriculum means it’s important to maximize the potential of every classroom activity — including class discussions ! You can transform discussions into meaningful learning opportunities by aligning them with clear learning objectives linked to curriculum standards.

With that in mind, we’re here to share our expertise to guide you in writing actionable learning objectives for class discussions (including ones you can do on Kialo Edu !). We even have free discussion resources to help you maximize student engagement and achievement.

Why is it important to write learning objectives for class discussions?

In class discussions, learning objectives act like a roadmap to guide students toward productive conversations while staying on topic. This makes discussions more purposeful to maximize learning time.

Moreover, learning objectives help focus discussions by targeting specific cognitive skills like critical thinking , language acquisition, and problem-solving. They can also address curriculum standards in subjects like reading, writing, and interdisciplinary literacy.

Finally, aligning discussions with learning objectives facilitates assessment. Educators can use these opportunities to assess students’ progress toward curriculum standards, with the added bonus of students self- and peer-evaluating their work.

How do I write good learning objectives for class discussions?

Learning objectives for class discussions should be specific, measurable, and actionable. Here are our top tips to achieve this:

• Use clear, concise language to facilitate student understanding.
• Use action verbs aligned with cognitive frameworks like Bloom’s Taxonomy or Webb’s Depth of Knowledge framework .
• Target specific cognitive skills or curriculum standards.
• Connect objectives to unit/course goals, making the discussion integral to students’ learning journeys.
• Ensure objectives are achievable within the timeframe.

Now, let’s take a look at examples of discussion learning objectives that target a range of skills and subjects.

Learning objectives for developing students’ critical thinking skills

To develop students’ critical thinking in discussions, objectives should target higher-order skills like synthesis, analysis, and evaluation. Students can apply these skills to construct evidence-based positions in arguments and debates . Below are some examples of subject-specific class discussions: 

Students will be able to argue for their position on the ethics of a scientific issue, using two scientific studies to justify their argument.

Try it in a Kialo discussion: Should cloning humans be legal?

Students will be able to collaboratively identify two potential biases in a news source and explain how these could affect the audience’s perception of the information. 

Social Studies: 

Students will be able to identify two logical fallacies used in a debate on a societal issue and explain how these weaken the arguments.

Try it in a Kialo discussion: Is democracy a good form of government?

Is democracy a good form of governme — kialo-edu.com

Learning objectives for developing students’ problem-solving skills

Discussions encourage collaboration , making them ideal for developing students’ problem-solving skills. Objectives should focus on having students analyze situations, explore causes, and develop solutions. Here are some examples:

Students will be able to present and defend a solution to a labor issue within an LMIC’s supply chain and reflect on alternative solutions from peers.

Try it in a Kialo discussion: Should society reject fast fashion?

Geography: 

Students will be able to generate two potential solutions to an environmental problem, and use a decision-making framework to evaluate the potential consequences of each one.

Literature:

Students will be able to articulate the internal conflict faced by a novel’s main character and generate three possible solutions, considering the character’s motivations, limitations, and the context of the story.

Try it in a Kialo discussion: Was George right to kill Lennie in “Of Mice and Men?”

Learning objectives for developing students’ language acquisition skills

Discussions provide opportunities for students to acquire and apply new language. Objectives may target building students’ subject-specific disciplinary language, developing students’ fluency in a foreign language , or, for ESL students , applying their English language skills for different purposes. Here are some example objectives:

Students will be able to identify three key elements in an artwork and explain how they contribute to the artist’s intended meaning or message.

Try it in a Kialo discussion: Is “Fountain” really a work of art?

Religious Studies: 

Students will be able to critically evaluate opposing viewpoints using accurate religious vocabulary, and construct well-reasoned counter-arguments supported by relevant scripture or scholarly sources.

Try it in a Kialo discussion: Do all religions worship the same higher power?

Foreign language: 

Students will demonstrate fluency in using sentence structures and vocabulary from the unit when discussing the advantages and disadvantages of a topic.

Try it in a Kialo discussion ( available in 11 languages ): Which country would be the most interesting to visit?

Which country would be the most interesting to visit? — kialo-edu.com

English as a Second Language (ESL):

Students will demonstrate fluency in using transition words and phrases when summarizing key arguments for and against a topic from a class debate.

Try it in a Kialo discussion: Is it better to live in the city or the countryside?

Learning objectives for developing students’ reasoning and analysis of claims

Objectives to develop reasoning and claim analysis skills should center around having students evaluate the strength of claims and analyze relationships between factors to develop lines of reasoning. Try these examples:

Students will be able to analyze claims about the causes of a historical event from two different perspectives, citing primary or secondary sources to support each perspective.

Try it in a Kialo discussion: What was the main cause of the Great Depression?

Students will be able to evaluate evidence about the impact of four human activities on an environmental issue, ranking the activities based on the strength and credibility of supporting evidence.

Social Studies:

Students will analyze the pros and cons of a recent societal development, creating a cost-benefit assessment to analyze its potential impacts.

Try it in a Kialo discussion: Do the costs of AI outweigh the benefits?

Learning objectives for developing students’ communication skills

Classroom discussions provide a safe space for students to practice communicating respectfully and engaging with diverse perspectives . Objectives should aim to move students beyond “winning” arguments toward finding common ground. Try these with your students:

Students will be able to identify different perspectives and their supporting evidence on a scientific topic.

Try it in a Kialo discussion: Should we develop technology that can read minds?

English Language Arts:

Students will be able to articulate three perspectives on a recent news story and explain the reasoning behind each one in their own words.

In a Socratic seminar , students will be able to express their textual analysis and interpretations using appropriate tone, word choice, and organizational strategies, and provide constructive feedback to classmates.

Try it in a Kialo discussion: Does Never Let Me Go create a more effective sense of threat than The Handmaid’s Tale ?

Does Never Let Me Go create a more effective sense of threat than The Handmaid’s Tale? — kialo-edu.com

How can students achieve learning objectives in Kialo discussions?

1. kialo discussions greatly increase student participation.

The written format of Kialo discussions can help increase student participation and therefore opportunities to achieve learning objectives. That’s because all students can add their ideas simultaneously, while less confident students are free from the pressure of public speaking. Moreover, Anonymous Discussions mean all students can contribute freely, without fear of judgment.

2. Kialo discussions develop students’ critical thinking and problem-solving skills 

The branching format of Kialo discussions supports students in meeting critical thinking and problem-solving objectives. Students can visualize how ideas connect, enabling them to build sophisticated lines of reasoning. This format also prompts self-reflection, as students deconstruct their perspectives into step-by-step arguments, referencing sources to justify reasoning. 

3. Kialo discussions help educators assess students against learning objectives

Contributions to Kialo discussions are automatically saved, providing valuable assessment evidence. The argument tree and sunburst visualizations offer an overview of the entire discussion, or you can view students’ individual contributions to assess their progress toward objectives. 

You can even provide personalized, targeted feedback on individual claims, helping students address areas for development and meet the intended learning objectives.

So, it’s time to empower students to achieve learning objectives through dynamic class discussions! Head to Kialo Edu’s Topic Library , a treasure trove of over 500 free ideas for discussions spanning history , science , liter a ture , and more. You’ll find discussion topics that not only spark conversation but also directly connect to your learning objectives. Try them out today!

We’d love to hear how you are transforming class discussions into purposeful learning opportunities. Contact us at [email protected] or on social media.

Want to try Kialo Edu with your class?

Sign up for free and use Kialo Edu to have thoughtful classroom discussions and train students’ argumentation and critical thinking skills.

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For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start – to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics – a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced How to Learn Math , the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users.

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer.

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 – but the most common answer 13-year-olds gave was 19. The second most common was 21.

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important?

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mindset. I think we all need a little more ish in our lives.

You also argue that mathematics should be taught in more visual ways. What do you mean by that?

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things – all of that contributes to our understanding of how it works.

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking.

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, “I’m in geometry class now, and I still remember that sugar cube, what it looked like and felt like.” His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing – elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

A depiction of various ways to calculate 38 x 5, numerically and visually. | Courtesy Jo Boaler

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them.

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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• diversity_3 2024 ASEE Annual Conference & Exposition
• Article Paper Management

2024 ASEE Annual Conference & Exposition

An autoethnography of the student experience solving an open-ended statics problem, presented at student division technical session 1: student experiences and support.

This research paper examines the student perception and experience of solving open-ended modeling problems (OEMPs) through an autoethnographic account of the student-authors’ personal reflections about an OEMP completed during an introductory level statics course. Currently, the student perspective is not represented in literature about engineering problem solving. This is significant as the student perspective is integral to understanding how students learn and develop an engineering mindset. By incorporating the student voice through autoethnographic techniques, this study can begin to fill this gap and provide meaningful insights about the student experience and perceived benefits surrounding an OEMP.

Autoethnography is an approach to research and writing that incorporates the researcher’s personal experience in conjunction with traditional research methods. The authors believe this is an underutilized research method within engineering education research that could provide additional insights to shift teaching and learning within engineering classrooms. The student-authors reflected on their personal experience solving an OEMP by retroactively responding to several written prompts. We analyzed our responses to determine possible patterns and emerging themes about the student perception of OEMPs.

While instructors make choices about course learning objectives, many times these are primarily based on what instructors historically believe students need to know. Rarely are students given a platform to voice the meaningful knowledge they constructed after course completion. Implications for this work include providing information to instructors on how students view innovative, problem-based work and the benefits to their development as novice engineers. This study also suggests that autoethnography can serve as a valuable research method in engineering education, allowing for a direct examination of students’ own experiences and perceptions.

Katelyn Churakos is an undergraduate research assistant in the Department of Engineering Education at the University at Buffalo. She is majoring in Mechanical Engineering with a minor in Law and is expected to graduate in December 2025. After graduation, Katelyn plans to pursue employment in the mechanical engineering field, preferably in project management.

• Jayden Mitchell University at Buffalo, The State University of New York

Jessica Swenson is an Assistant Professor at the University at Buffalo. She was awarded her doctorate and masters from Tufts University in mechanical engineering and STEM education respectively, and completed postdoctoral work at the University of Michigan. Her research work aims to improve the learning experience for undergraduate students by examining conceptual knowledge gains, affect, identity development, engineering judgment, and problem solving.

The full paper will be available to logged in and registered conference attendees once the conference starts on June 23, 2024, and to all visitors after the conference ends on June 26, 2024

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