## Center for Teaching

Teaching problem solving.

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## Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

## Encourage Independence

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

## Be sensitive

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

## Encourage Thoroughness and Patience

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

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

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

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## 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

## Teaching Problem-Solving Skills

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

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

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

## Principles for teaching problem solving

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

## Woods’ problem-solving model

Define the problem.

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

## Think about it

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

## Plan a solution

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

## Carry out the plan

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

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

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

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

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

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## Teaching problem solving

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

## Introducing the problem

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

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

## Working on solutions

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

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

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

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

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

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

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

October 31, 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Where can I learn more?

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

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## Center for Teaching Innovation

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## 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.

## Principles for Teaching Problem Solving

- January 1998
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## Probability and statistics

- Handling, Processing and Representing Data
- Probability

## Working mathematically

- Thinking mathematically
- Mathematical mindsets
- Cross-curricular contexts
- Physical and digital manipulatives

## For younger learners

- Early Years Foundation Stage

## Advanced mathematics

- Decision Mathematics and Combinatorics
- Advanced Probability and Statistics

Published 2018

## The Problem-solving Classroom

- Visualising
- Working backwards
- Reasoning logically
- Conjecturing
- Working systematically
- Looking for patterns
- Trial and improvement.

- stage of the lesson
- level of thinking
- mathematical skill.
- The length of student response increases (300-700%)
- More responses are supported by logical argument.
- An increased number of speculative responses.
- The number of questions asked by students increases.
- Student - student exchanges increase (volleyball).
- Failures to respond decrease.
- 'Disciplinary moves' decrease.
- The variety of students participating increases. As does the number of unsolicited, but appropriate contributions.
- Student confidence increases.
- conceptual understanding
- procedural fluency
- strategic competence
- adaptive reasoning
- productive disposition

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

## 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.

## Share This Book

## The Lesson Study Group

at Mills College

## Teaching Through Problem-solving

- TTP in Action

## What is Teaching Through Problem-Solving?

In Teaching Through Problem-solving (TTP), students learn new mathematics by solving problems. Students grapple with a novel problem, present and discuss solution strategies, and together build the next concept or procedure in the mathematics curriculum.

Teaching Through Problem-solving is widespread in Japan, where students solve problems before a solution method or procedure is taught. In contrast, U.S. students spend most of their time doing exercises– completing problems for which a solution method has already been taught.

## Why Teaching Through Problem-Solving?

As students build their mathematical knowledge, they also:

- Learn to reason mathematically, using prior knowledge to build new ideas
- See the power of their explanations and carefully written work to spark insights for themselves and their classmates
- Expect mathematics to make sense
- Enjoy solving unfamiliar problems
- Experience mathematical discoveries that naturally deepen their perseverance

## Phases of a TTP Lesson

Teaching Through Problem-solving flows through four phases as students 1. Grasp the problem, 2. Try to solve the problem independently, 3. Present and discuss their work (selected strategies), and 4. Summarize and reflect.

Click on the arrows below to find out what students and teachers do during each phase and to see video examples.

- 1. Grasp the Problem
- 2. Try to Solve
- 3. Present & Discuss
- 4. Summarize & Reflect
- New Learning

## WHAT STUDENTS DO

- Understand the problem and develop interest in solving it.
- Consider what they know that might help them solve the problem.

## WHAT TEACHERS DO

- Show several student journal reflections from the prior lesson.
- Pose a problem that students do not yet know how to solve.
- Interest students in the problem and in thinking about their own related knowledge.
- Independently try to solve the problem.
- Do not simply following the teacher’s solution example.
- Allow classmates to provide input after some independent thinking time.
- Circulate, using seating chart to note each student’s solution approach.
- Identify work to be presented and discussed at board.
- Ask individual questions to spark more thinking if some students finish quickly or don’t get started.
- Present and explain solution ideas at the board, are questioned by classmates and teacher. (2-3 students per lesson)
- Actively make sense of the presented work and draw out key mathematical points. (All students)
- Strategically select and sequence student presentations of work at the board, to build the new mathematics. (Incorrect approaches may be included.)
- Monitor student discussion: Are all students noticing the important mathematical ideas?
- Add teacher moves (questions, turn-and-talk, votes) as needed to build important mathematics.
- Consider what they learned and share their thoughts with class, to help formulate class summary of learning. Copy summary into journal.
- Write journal reflection on their own learning from the lesson.
- Write on the board a brief summary of what the class learned during the lesson, using student ideas and words where possible.
- Ask students to write in their journals about what they learned during the lesson.

## How Do Teachers Support Problem-solving?

Although students do much of the talking and questioning in a TTP lesson, teachers play a crucial role. The widely-known 5 Practices for Orchestrating Mathematical Discussions were based in part on TTP . Teachers study the curriculum, anticipate student thinking, and select and sequence the student presentations that allow the class to build the new mathematics. Classroom routines for presentation and discussion of student work, board organization, and reflective mathematics journals work together to allow students to do the mathematical heavy lifting. To learn more about journals, board work, and discussion in TTP, as well as see other TTP resources and examples of TTP in action, click on the respective tabs near the top of this page.

## Additional Readings

## Can’t find a resource you need? Get in touch.

- What is Lesson Study?
- Why Lesson Study?
- Teacher Learning
- Content Resources
- Teaching Through Problem-solving (TTP)
- School-wide Lesson Study
- U.S. Networks
- International Networks

## Problem-Solving

Add to Folder | |
---|---|

creative writing | |

children's book | |

activities | |

classroom tools | |

language arts and writing | |

vocabulary |

## Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

## Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

- List all related relevant facts.
- Make a list of all the given information.
- Restate the problem in their own words.
- List the conditions that surround a problem.
- Describe related known problems.

## It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

## Featured High School Resources

## Related Resources

## About the author

## TeacherVision Editorial Staff

The TeacherVision editorial team is comprised of teachers, experts, and content professionals dedicated to bringing you the most accurate and relevant information in the teaching space.

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

The positive impact of an innovative UC San Diego problem-solving educational curriculum continues to grow

- Daniel Kane - [email protected]

## Published Date

Share this:, article content.

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

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

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

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

What was noticeably absent from this laboratory classroom: frustration.

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

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

## Not getting stuck

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

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

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

## What does it mean to explicitly teach problem solving?

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

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

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

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

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

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

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

## Portrait of the Problem-Solving Curriculum

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

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

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

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

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

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

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

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

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

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

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

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

## You May Also Like

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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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## Why Every Educator Needs to Teach Problem-Solving Skills

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

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

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

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

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

## Problem-Solving Skills Help Students…

develop resilience.

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

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

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

## Set and Achieve Goals

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

## Resolve Conflicts

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

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

## Achieve Success

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

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

## Problem-Solving Skills Can Be Measured and Taught

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

## What Are Performance-Based Assessments?

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

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

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

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

## Preview a Performance-Based Assessment

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

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

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

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

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

## Explore CAE’s Problem-Solving Assessments

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

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

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

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

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

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

## Ready to Get Started?

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

## Project-Based Learning Strategies

Table of contents.

## Active-Learning

The A ctive-Learning definition is “students doing things while thinking about what they are doing.” The range of what students “do” includes a diverse range of activities to construct their knowledge and understanding (i.e., develop higher-order thinking). Although not always explicitly required, student reflections about what they are learning and how they are learning are essential elements. The goal is to link the activity with learning. Active-learning is a broader educational strategy, within which many other project-based learning tactics reside.

## Inductive-Learning

Inductive learning is the process of learning by example and observation. Students induce a general rule, concept, or principle from a set of observed examples. Deductive learning presents the idea first and demonstrates how it works—but this process simply isn’t possible, or as effective, for the diversity of simultaneous explorations that occur with project-based learning. PBL exposes students to how a concept or principles happens in practice (through case-studies, system-thinking analysis, just-in-time teaching) so they can better understand the universal principles that build towards a rule or lesson. The flexibility of in-course activities in PBL allows for inductive learning to occur through specific examples, events, experiences crafted to the particular stage of development.

## Backward Design

The open-ended nature of day-to-day activities within a student-led PBL format can be uncomfortable for some instructors if used to control the process by which the lessons are presented and learned. Backward course design (or backward mapping) is essential for project-based learning because it provides a planning framework that works back from the module’s overall objectives, course, or project and creates a series of lessons built to help achieve these goals. PBL is a goal-focused approach with distinct phases which allows instructors to align short-term activities with long-term goals, content production, and student performance. Progress in PBL classes may not happen linearly with predictable results, but instructors can provide a framework for this advancement through lessons, problems, and goal-oriented assignments. Students work towards these deadlines, thus, crafting the process of teaching to support the goals of student learning.

## Experiential Activities

PBL courses frequently integrate a series of experiential-learning opportunities throughout the process. The purpose of these experiences is to expand opportunities for students to discover, empathize, and understand the problem in different ways. In these activities, students are exposed to, or create, a direct “experience” related to the course topic or project question (e.g., “What makes a shoe fit well?” or “How difficult is it to carry water long distances?”). This experience begins a process of reflection, discussion, analysis, and evaluation of the skills to guide further activities. Ideally, these experiences include exposure to circumstances, and people , not typically included in traditional classroom environments. The authenticity and significance of PBL problems cemented during this process.

## Haptic Engagement

Many experiential activities involve a haptic, hands-on approach to learning. Some learners look for ways to include the sense of touch in their educational process: drawing, building, fiddling with something, manipulating elements to complete a task. In project-based learning, these preferences are well-suited to aspects of the discovery and ideation process. Imagine how to learn about food safety practices through cooking or product design performance by testing it for failures.

## Retrieval Practice

The idea behind retrieval practice is to develop ways to turn passively-absorbed information into more embedded knowledge and understanding. Instead of re-reading books and notes, retrieval depends on one’s ability to “hack” their ability to recall information. This step occurs through visual note-taking, peer-to-peer teaching, or with hands-on experiences. As an example, imagine lifting two seemingly identical rods made of different densities; this one simple experience (“that’s heavier than the other one”) will immediately trigger an understanding of density and materiality. Explaining this lesson to others or drawing it would enhance the experience.

## Metacognition & Problem-Solving Strategies

For questions with right/wrong answers, solving a problem is embedded within the job (e.g., orders of operation, application of principles, etc.). Still, many of the problems used in the PBL model intentionally defy straightforward solutions. When problems are complex, multi-faceted, and vexing, a non-linear problem-solving method becomes necessary. PBL courses need to teach strategies for solving problems, ideally using best practices of metacognition (thinking about thinking). Specific tactics are essential to demonstrate: Students should be encouraged to articulate which principles and concepts are unclear and explain how their previous successful attempts at problem-solving might be useful. When students share their strategies by demonstrating their solutions aloud or graphically, they gain confidence in their efforts and foster a community mindset. Instructors should model problem-solving strategies rather than offering answers and ask directing questions to help students overcome obstacles.

## Just-in-Time Teaching

One of the challenges of teaching an open-ended educational practice is the potential variability in timing for when introducing specific lessons. Imagine a scenario in which student groups reach an impasse in their work because they lacked knowledge about a particular subject or the skills to manage one of their learning tools. Just-in-Time teaching tries to anticipate these impasses by creating a series of exercises that allow the instructor to survey and assess the students’ abilities and knowledge. This learning activity often takes the form of open-ended warm-up questions or surveys about the course material before class begins—the instructor can adjust the course activities to address any shortcomings or misunderstandings meaningfully. The learning happens just-in-time to apply it towards the PBL project. For example, an instructor asks students in a course about sustainable practices in landscape architecture to explain water retention principles. Then, they realize that most students don’t understand the relationship between soil types and drainage, so an in-class demonstration of the concept is created and shown at the start of class.

## Guided Discovery

A cornerstone of all project-based learning models is the exceptional relationship between curiosity, critical thinking, and problem-solving. These strengthen connections through guided discovery problems . These are carefully constructed puzzles, challenges, or discrete questions that push students to learn how to solve the issues and build a framework of knowledge from these inquiries—before explaining the content to them. This type of discovery learning method based on the profound and straightforward notion that students are more likely to remember concepts and principles when they initially discover them. These “learning-by-doing” exercises are combining with experiential learning and haptic engagement exercises. Ideally, introducing these lessons in a collaborative setting in which individuals experience the learning, reflect upon it, and convey the lessons they’ve learned to their teammates. As an example, asking at a beginning astronomy course for students to speculate on how to explain the phases of the moon using physical models and a light source—they discover that the Earth’s shadow doesn’t cause the moon’s phases.

## Coached Ideation

At certain stages in the project-based learning/design thinking process, groups apply their knowledge of course content towards a project as they generate ideas. When the problems are complex, and the design process is collaborative, instructors must guide to facilitate these activities. A coached ideation process gives smaller groups of students a particular issue to address as it applies to the overall project (e.g., identifying options for non-conductive metals, prioritizing options for food distribution, etc.). The point isn’t to solve the broader problem of PBL, but perhaps a crucial stage in one of the branch problems. These exercises should be short, somewhat informal, and ungraded interactions where students present ideas, explore, and evaluate collaboratively. Instructors should encourage all students to interact (modeling inclusive classroom tactics) and provide just-in-time learning to clear misconceptions, suggest case studies, or provide technical expertise for concepts not apparent to student teams. The most important aspect of this process is that the work remains student-led. Doing so helps to emphasize student “voice and choice” while strengthening their engagement in the process. In a team-based learning process, this role of a “coach” may fall upon peer coaches or other team members.

## Visualizing Systems Thinking

The complexity and interdisciplinary nature of the problems used in PBL courses require participants to understand systems thinking. Systems thinking is the process of trying to understanding how constituent parts interrelate and influence each other within a whole system. Systems thinking looks for a holistic approach to the research, analysis, and design activities (e.g., how air, water, plants, and animals interact in an ecosystem). Systems thinking and visualizing the various means (e.g., causal loop diagrams (CLD), qualitative/quantitative (QQ) diagrams, Behavior Over Time (BOT) models, simulators), serves as a universal language that connects inter-disciplinary teams. Systems thinking deals with the variables, links, effects, and constraints that affect behaviors in complex systems—it is an ideal evaluative tool for the agile project-based learning approach. Although the visualization techniques and modeling can be advanced, the process need not be; consider these drawtoast examples of people have visually mapped “How To Make Toast.”

## Case-Study Method

Case-studies are real-world examples of situations, solutions, or failures that can provide valuable information during a project-based learning approach. Many professions rely upon case methods for continuing education because it is particularly useful in linking new learning to existing conditions. It is a valuable tactic in PBL courses in three primary ways:

- First, the PBL method relies extensively upon information gathering to define the problem, suggest potential solutions, and to understand the scope of on-going efforts either as a literature search or precedent study.
- Second, introduce specific case-studies as a way of provoking questions and challenging solutions. When students confront dilemmas from previous cases, they can assume the role decision-maker and weigh their potential choices against the real-world consequences.
- Finally, the case’s real-life nature brings relevance and authenticity to the project—the data sets and theories connect to an actual event with consequences.

## Shared Solutions / Send-A-Problem

During the problem-solving phases of project-based learning, it becomes tricky to solicit multiple potential solutions to the same problem simultaneously. Some groups or individuals may dominate the conversation, and others become disengaged if no one pursues their solution. An excellent strategy to avoid these conflicts while still maintaining the cooperative problem-solving effort is to use a Send-A-Problem method (a variation of the Coached Problem-solving method). In this method, forming multiple student groups (2-4 each).

- Give each group a different discrete problem; the problems should be complicated and nuanced enough that no single right answer is possible.
- Teams discuss the issue, record their solution, and pass their resolution off to another group. Each group contributes a new or revised solution to the original.
- Eventually, after the problem has made its way through the class, a final resolution is selected (often a hybrid model of many suggestions). This process nurtures collaborative problem-solving and communication skills—groups have to learn to listen and consider other perspectives before offering their solution. It encourages creativity without demanding originality—set solutions are within the context of ideas that others have developed.
- In-person and online forums are equally useful for this process.

## Learning Artifacts & Portfolios

Learning artifacts/objects are tangible demonstrations of student learning. They are essential elements of a project-based learning course. The public presentations of learning artifacts often mark the transitions between the various stages of a project-based learning approach. As the stages progress from discovery to ideation, evaluation, and implementation, the artifacts change. The goal is to have students produce a series of expressions that showcases the process:

- Some elements demonstrate critical thinking, initial ideation and problem-solving, others to show a progression through design/problem-solving development.
- Eventually, all the artifacts can be linked together in a compelling story—ideally with demonstrations of work across format with a refined sense of resolution. The production of a portfolio at the end of the process is a critical learning tool. It promotes student self-reflection on learning and becomes evidence of the competencies required in the course’s learning objectives.
- The link between the visual representation of complex ideas is an essential professional communication skill to promote.
- Finally, portfolios are artifacts that extend the project’s life through publications, research funding, and as case-studies for other similar projects.

## Cooperative & Team-Based Learning

Collaboration is one of the essential components to successful project-based learning courses—but it is a soft skill that deserves specific instructional attention that it needs. PBL depends on the students’ ability to work as a team to produce a shared work. When students learn to work in a supportive, inclusive, and cooperative environment, they thrive. Teaching productive collaborative learning tactics involves a series of exercises presented to students that allows them to understand more about form teams, assess team members’ assets, refine roles and contributions to the project, and foster supportive intra-team communication. There are specific ways to model positive cooperation in the course: informal learning groups, think/pair/share exercises, peer instruction, jigsaw, etc. The PBL process has regular intervals built into the process for a routine sharing of ideas and formative evaluation of team-working efficacy. A more formalized model is the team-based learning (TBL) format. This small-group learning experience emphasizes student preparation out of class and application of knowledge in class. Students are organized strategically into diverse teams of 5-7 students that work together throughout the course.

## Role-Playing & Evaluation

A critical aspect of the project-based learning method is the ability to generate empathy and insight as an integral part of the initial information collection/discovery/research phase. One way of trying to instill an understanding of the process is to use a role-playing method. Simply put, ask a student (or groups of students) to assume the perspective of a particular character or user group. To do so, they’ll need to supplement their imagination with actual data, cultural competence training, and other research information about how the issues affect human interaction. Once the research is complete, the instructor facilitates an event (role-playing exercise) in which groups interact with questions and answers—during this event, raise concerns and present potential solutions, etc. as a way of evaluating progress. Specific feedback is essential for growth (“I don’t think that will work because…” vs. “I don’t like it”). Depending on the discipline or scenario, some vibrant online role-playing forums and simulations may lend additional feedback.

## Green applies problem-solving skills to service

- Facebook profile — external
- Twitter profile — external
- Email profile — external
- LinkedIn profile — external

Every year during awards season we hear talk of artistic types who have been named EGOTs for taking home the coveted combo of Emmy, Grammy, Oscar and Tony. Headlines scream, commentators gush because it is not easy to be good at so many things.

If the academic world had a similar designation, Dr. Joe Green’s name would be right at the top of the list. During his career at Ohio State Lima, he has earned all the teaching, research and scholarly awards we have to offer, some of them twice. At Ohio State Lima’s 2024 Academic Celebration, he added the Outstanding Service Award, which recognizes individuals who demonstrate and support the Buckeye idea of care for others, as well as carrying out the mission of the university on an ongoing basis.

Green's approach to service is similar to the approach to general problem solving he developed as one of 11 kids. To stand out, you had to do more than come up with a good idea, you had to take action.

“Seeing things that could be improved is easy,” Green said. “Everybody notices things that could be improved, but taking the next step and trying to come up with a constructive solution that's doable and not just wishful, that is more complicated.”

Green has taken action to spread his service out from Ohio State Lima to include his hometown of Bellevue and the entire state of Ohio. During his time as faculty assembly president he helped develop a process for faculty and staff to evaluate administrators on our campus, a more detailed and layered process than any of us could have expected. Over the years, he and his colleagues have developed a cognitive-based approach to smoking cessation that includes hypnosis, mindfulness and acceptance-based approaches. The latest iteration was piloted at Ohio State Lima and included campus and community members. His ongoing efforts in his home community as president of the Gridiron Foundation support both the school and town and have resulted in an improved and expanded athletic complex, a more beautiful downtown, and a growing endowment for scholarships for high school students.

## Research mentor

Green applies the idea of turning abstract ideas into concrete action and knowledge to research and teaching as well. He models turning curiosity about a subject into a research question that you can collect empirical data on to strengthen the argument for or against its validity. As students in his classroom learn to how to do it as well, Green sees their confidence grow.

“That's all part of the goal of higher education is to instill greater confidence and assertiveness and willingness to insist upon good scientific evidence for claims that are being made as opposed to just accepting positions because a person in authority has stated them,” Green said.

Green realizes that he could do research more quickly and more efficiently if he wasn’t a mentor, but he is a mentor anyway. He has been in his undergraduates’ shoes and knows what it takes to help them become better students, researchers and community citizens.

“I was fortunate enough to have great mentors during my academic career and throughout my life more broadly,” Green said. “Having someone to take the time to explain is invaluable.”

Teaching has never become routine for Green in his 31 years at Ohio State. He preps for each lecture like it is a mini-performance with a lesson plan as the script and the ability to adjust to the students’ needs and questions as they develop.

“I try to script my lectures out to some extent,” Green said. “Once I get into the classroom, it's like improv because you never know where it's going to go or what questions are going to come out or what topics students are going to be interested in on a given day.”

While he sees the utility of offering online and hybrid classes, he misses a fully in person teaching load. It is easier to engage and hold the class in a live setting. It is a workout both mentally and physically.

“The biggest thing I miss about not being in a physical classroom is I used to get all my steps in every time I taught because I pace. Part of it was intentional,” Green said. “I want to change the site line that students are looking at. I want to change the volume level. I want to change the source of where my voice is coming from so going from the back of the class to the middle of the class to the front of the class to the left to the right, approaching students when they ask questions.”

Dr. Joe Green is a professor of psychology at The Ohio State University at Lima. In the course of his career he has earned the prestigious Alumni Award for Distinguished Teaching (2004), Outstanding Scholar Award (2022 and 2015), Faculty Award for Sustained Student Mentorship (2022 and 2017) and the Teaching Excellence Award (2011).

Photo captions (from top): Dr. Joe Green on the Quad at Ohio State Lima, Archie Griffin and Joe Green strike a Heisman pose when Griffin surprised Green with the Alumni Award for Distinguished Teaching in 2004.

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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.

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 ...

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. Be patient.

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 ...

Teaching problem solving: Let students get 'stuck' and 'unstuck'. This is the second in a six-part blog series on teaching 21st century skills, including problem solving , metacognition ...

Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and ...

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.

structured problem solving. 7) Use inductive teaching strategies to encourage synthesis of mental models and for. moderately and ill-structured problem solving. 8) Within a problem exercise, help ...

One of the benefits of the PBL model is the ease in which various teaching techniques integrated into the course activities: case studies, role-playing, just-in-time teaching, visualization techniques for systems thinking, and coached problem-solving, and guided discovery problems.

The Problem-solving Classroom. This article forms part of our Problem-solving Classroom Feature, exploring how to create a space in which mathematical problem solving can flourish. At NRICH, we believe that there are four main aspects to consider: • Highlighting key problem-solving skills. • Examining the teacher's role.

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 ...

Download. Teaching Through Problem-solving flows through four phases as students 1. Grasp the problem, 2. Try to solve the problem independently, 3. Present and discuss their work (selected strategies), and 4. Summarize and reflect. Click on the arrows below to find out what students and teachers do during each phase and to see video examples.

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically. Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving is the capacity to identify and describe a problem and generate solutions to fix it. Problem-solving involves other executive functioning behaviors as well, including attentional control, planning, and task initiation. Individuals might use time management, emotional control, or organization skills to solve problems as well.

It begins with the teacher introducing the problem-identification or problem-solving strategy of the day. The teacher then presents case studies of that particular strategy in action. Next, the students get introduced to the day's challenge project. Working in teams, the students compete to win the challenge while integrating the day's ...

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). ... Problem Solving Strategy 8 (Process of Elimination) This strategy can be used when there is ...

Instructional strategies used in teaching problem-solving skills include providing sufficient context, learning to think actively, and offering temporary supports. Review the examples of effective ...

These strategies are firmly grounded in educational research and learning principles. How does it work? Step 1: Identify a PROBLEM you encounter in your teaching. Step 2: Identify possible REASONS for the problem Step 3: Explore STRATEGIES to address the problem. This site supplements our 1-on-1 teaching consultations.

The problem-solving method involves three basic functions Woods' problem-solving model Identify the problem Think about it Plan a solution Carry out the plan Look back Other tips include Ask Open-Ended Questions Emphasize Process Over Product Model The Strategies Encourage Grappling Make problem resolution relevant to the lives of your students.

Resolve Conflicts. In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes "thinking outside the box" and approaching a conflict by searching for different solutions.

Instructors should model problem-solving strategies rather than offering answers and ask directing questions to help students overcome obstacles. Just-in-Time Teaching. One of the challenges of teaching an open-ended educational practice is the potential variability in timing for when introducing specific lessons. Imagine a scenario in which ...

So, in this case, it may be beneficial to teach the individual parts of the process in isolation first. 1. Clarify: Before beginning to seek creative solutions to a problem, it is important to clarify the exact nature of that problem. To do this, students should do the following three things: i. Identify the Problem.

Abstract This study uses the methodology of design-based research in search of ways to teach problem-solving strategies in mathematics in an upper secondary school. Educational activities are designed and tested in a class for four weeks. The design of the activities is governed by three design principles, which are based on variation theory.

These include low-stakes strategies like pausing for clarification up to more involved strategies such as problem-based learning (PBL) or classroom response systems (CRSs). Research generally supports the efficacy of active learning strategies, though impact varies widely based on context (Prince, 2004).

Critique of the Strategy. Using problem solving as a teaching strategy can engage students in developing deep understanding of important concepts and principles, developing skills relevant to authentic future applications (Killen,2009) despite the difficulty and time preparation involved in designing appropriate, relevant problems.

Teaching. Teaching has never become routine for Green in his 31 years at Ohio State. He preps for each lecture like it is a mini-performance with a lesson plan as the script and the ability to adjust to the students' needs and questions as they develop. "I try to script my lectures out to some extent," Green said.

You are capable! Don't know where to start? Think about this What is that ONE THING that people always come to you for? What could you talk...