teaching problem solving strategies

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Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

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Teaching problem solving

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 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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Math Fluency Is All About Problem-Solving. Do We Teach It That Way?

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To learn math, students must build a mental toolbox of facts and procedures needed for different problems.

But students who can recall these foundational facts in isolation often struggle to use them flexibly to solve complex, real-world problems , known as procedural fluency.

“Mathematics is not just normalizing procedures and implementing them when somebody tells you to use that procedure. Mathematics is solving problems,” said Bethany Rittle-Johnson, a professor of psychology and human development at Peabody College in Vanderbilt University, who studies math instruction. “To solve problems, we have to figure out what strategy to use when—and that tends to get too little attention.”

In a series of ongoing experiments, Rittle-Johnson and her colleagues find students develop better procedural fluency when they get opportunities to compare and contrast problem-solving approaches and justify the approaches they use in different situations. While some students may develop this skill on their own, most need explicit instruction, she found.

Rittle-Johnson spoke with Education Week about how teachers can use such comparisons to help students develop a deeper understanding of math. This interview has been edited for space and clarity.

For more on the best research-based strategies on improving math instruction, see Education Week’s new math mini-course .

How often do teachers talk to students about multiple strategies, and how to select them, in math problem-solving?

Students in the [United States] are very rarely doing rich contextual problems. Even more rarely, they’re being asked to compare strategies to solve them. I don’t hear teachers talk about [using different strategies] a lot, and textbooks tend to do a pretty bad job of explaining it.

For example, in Algebra 1, solving systems of equations, there are many standard solutions strategies that are taught in separate chapters and textbooks, ... but I see shockingly little time spent having students think and compare and choose which strategy to use. In one study where teachers were trained [to compare math strategies], only about 20 percent did in the classroom—and only about 5 percent of teachers who [did not receive training.]

Sometimes I hear teachers say, “Well, multiple strategies, that’s great for my high-end learners, but I don’t want to show that to my struggling learners. … So maybe multiple strategies is the ideal, but I’m not going to get to it because I’m tight on time and my kids are behind.” But we hear from struggling learners that they really appreciate the multiple strategies and we see that it helps them, too, across the grade bands and across contexts.

How can teachers decide when to bring in and compare different strategies while introducing a new math concept?

We find comparisons can be useful in all different phases of instruction.

It can be helpful for kids to have had some time to think about one strategy before they think about multiple strategies, maybe at most a lesson. But the risk is in general, if you wait too long, kids just get attached to one strategy. You run the risk of kids becoming really attached to one strategy, and then they become more resistant to wanting to think about and use multiple strategies.

What does this sort of comparison look like in the classroom?

One best practice is to have the steps of the different strategies written out. It can be kids’ strategies that they wrote on the board. It can be projecting strategies from textbooks or your solutions, but one thing we know is: Make sure both strategies are visible so that kids don’t have to remember. Then we ask kids to think about similarities and differences and think about, when is each a good strategy?

Sometimes we have students compare correct and incorrect strategies and explain the concepts that make the correct strategy correct. Just because you teach kids correct ways of doing things, that doesn’t mean the incorrect strategies disappear. Students really need help thinking and reasoning through why those are wrong.

What are the more common struggles for teachers to teach multiple strategies?

The No. 1 barrier we face is time. Teachers just feel they’re under so much pressure to cover so much content that they feel like they can’t take the time to do this, and that they see the value and the payoff in it. It does pay off for what is assessed [in standardized math tests], but it’s not directly assessed, and so that makes teachers nervous.

Also, sometimes teachers really don’t like to say this way is better than this other way. Even though mathematicians would say, “yeah, this way is clearly better in this context, and this other way is clearly better in that context,” ... sometimes teachers feel uncomfortable that they’re making a value judgment.

But the evidence is really clear that it’s helpful to show correct and incorrect examples and talk through them.

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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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Developing Problem-Solving Skills for Kids | Strategies & Tips

We've made teaching problem-solving skills for kids a whole lot easier! Keep reading and comment below with any other tips you have for your classroom!

Problem-Solving Skills for Kids: The Real Deal

Picture this: You've carefully created an assignment for your class. The step-by-step instructions are crystal clear. During class time, you walk through all the directions, and the response is awesome. Your students are ready! It's finally time for them to start working individually and then... 8 hands shoot up with questions. You hear one student mumble in the distance, "Wait, I don't get this" followed by the dreaded, "What are we supposed to be doing again?"

When I was a new computer science teacher, I would have this exact situation happen. As a result, I would end up scrambling to help each individual student with their problems until half the class period was eaten up. I assumed that in order for my students to learn best, I needed to be there to help answer questions immediately so they could move forward and complete the assignment.

Here's what I wish I had known when I started teaching coding to elementary students - the process of grappling with an assignment's content can be more important than completing the assignment's product. That said, not every student knows how to grapple, or struggle, in order to get to the "aha!" moment and solve a problem independently. The good news is, the ability to creatively solve problems is not a fixed skill. It can be learned by students, nurtured by teachers, and practiced by everyone!

Your students are absolutely capable of navigating and solving problems on their own. Here are some strategies, tips, and resources that can help:

Problem-Solving Skills for Kids: Student Strategies

These are strategies your students can use during independent work time to become creative problem solvers.

1. Go Step-By-Step Through The Problem-Solving Sequence 

Post problem-solving anchor charts and references on your classroom wall or pin them to your Google Classroom - anything to make them accessible to students. When they ask for help, invite them to reference the charts first.

2. Revisit Past Problems

If a student gets stuck, they should ask themself, "Have I ever seen a problem like this before? If so, how did I solve it?" Chances are, your students have tackled something similar already and can recycle the same strategies they used before to solve the problem this time around.

3. Document What Doesn’t Work

Sometimes finding the answer to a problem requires the process of elimination. Have your students attempt to solve a problem at least two different ways before reaching out to you for help. Even better, encourage them write down their "Not-The-Answers" so you can see their thought process when you do step in to support. Cool thing is, you likely won't need to! By attempting to solve a problem in multiple different ways, students will often come across the answer on their own.

4. "3 Before Me"

Let's say your students have gone through the Problem Solving Process, revisited past problems, and documented what doesn't work. Now, they know it's time to ask someone for help. Great! But before you jump into save the day, practice "3 Before Me". This means students need to ask 3 other classmates their question before asking the teacher. By doing this, students practice helpful 21st century skills like collaboration and communication, and can usually find the info they're looking for on the way.

Problem-Solving Skills for Kids: Teacher Tips

These are tips that you, the teacher, can use to support students in developing creative problem-solving skills for kids.

1. Ask Open Ended Questions

When a student asks for help, it can be tempting to give them the answer they're looking for so you can both move on. But what this actually does is prevent the student from developing the skills needed to solve the problem on their own. Instead of giving answers, try using open-ended questions and prompts. Here are some examples:

2. Encourage Grappling

Grappling  is everything a student might do when faced with a problem that does not have a clear solution. As explained in this article from Edutopia , this doesn't just mean perseverance! Grappling is more than that - it includes critical thinking, asking questions, observing evidence, asking more questions, forming hypotheses, and constructing a deep understanding of an issue.

There are lots of ways to provide opportunities for grappling. Anything that includes the Engineering Design Process is a good one! Examples include:

• Engineering or Art Projects
• Design-thinking challenges
• Computer science projects
• Science experiments

3. Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset . Getting an answer "wrong" doesn't need to be a bad thing! What matters most are the steps they took to get there and how they might change their approach next time. As a teacher, you can support students in learning this reflection process.

4. Model The Strategies Yourself! 

As creative problem-solving skills for kids are being learned, there will likely be moments where they are frustrated or unsure. Here are some easy ways you can model what creative problem-solving looks and sounds like.

• Ask clarifying questions if you don't understand something
• Admit when don't know the correct answer
• Talk through multiple possible outcomes for different situations 
• Verbalize how you’re feeling when you find a problem

Practicing these strategies with your students will help create a learning environment where grappling, failing, and growing is celebrated!

Problem-Solving Skill for Kids

Did we miss any of your favorites? Comment and share them below!

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• Problem Solving in STEM

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

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

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

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

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

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

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

What are some benefits of having students work in groups?

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

What are some strategies for helping students to form groups?  

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

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

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

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

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

What happens if a student gives a wrong answer?

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

How can you make your classroom inclusive?

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

A few final notes…

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

For more information...

Tipsheet: Problem Solving in STEM Sections

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

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The Will to Teach

4 Strategies to Build Your Students’ Problem Solving Skills

Every teacher understands the importance of fostering problem-solving skills in their students. These skills not only help students navigate academic challenges, but they also translate into valuable tools for life beyond the classroom. In this article, we’ll delve into the reasons why it’s crucial to develop these skills and provide practical strategies you can implement in your classroom right away.

Why is Developing Problem Solving Skills Important?

Strategies to develop problem solving skills, real-world example, concluding thoughts.

Problem-solving skills are a crucial part of a well-rounded education. They encourage critical thinking, enhance creativity and flexibility, and equip students with the resilience needed to tackle obstacles head-on.

• Real-World Application:  Problem-solving skills aren’t confined to solving math problems or decoding a science experiment. They are applicable in everyday life situations, from resolving conflicts to making important decisions.
• Enhances Creativity and Critical Thinking:  Problem-solving activities often require students to think outside the box and use their critical thinking abilities. This stimulates creativity and fosters innovative thought.
• Boosts Confidence:  As students improve their problem-solving abilities, they gain confidence in their skills. This confidence can positively influence their academic performance and personal life.

There are numerous ways to incorporate problem-solving skill development into your classroom. Here are a few effective strategies:

• Project-Based Learning:  Projects that require planning, execution, and evaluation naturally involve problem-solving. For example, a project where students need to build a model bridge within a budget encourages them to solve logistical and financial problems.
• Group Work :  Group work allows students to face and solve problems together. It encourages communication, cooperation, and collective problem-solving. For example, a group assignment on preparing a presentation on an environmental issue can encourage problem-solving related to information gathering, presentation design, and time management.
• Encourage Questions :  Encourage students to ask and answer their own questions. This promotes independent thinking and problem solving. For example, instead of giving the answer to a complicated math problem, guide them towards the solution by prompting them with questions.
• Role-play Scenarios:  Role-play scenarios can help students develop problem-solving skills by putting them in hypothetical situations and asking them to come up with solutions. For example, a role-play scenario where a student has to navigate a disagreement between friends can help them develop conflict resolution skills.

As a school leader, I’ve seen the power of problem-solving skills firsthand. I remember a group of students who were working on a community garden project. They faced numerous challenges, like budget constraints and unpredictable weather. Despite the hurdles, they didn’t give up. Instead, they came up with creative solutions, such as fundraising to cover costs and building a small greenhouse for year-round gardening. This project not only enhanced their problem-solving skills but also their resilience and team collaboration.

Developing problem-solving skills in students is a crucial aspect of education that extends beyond academic success. By incorporating problem-solving activities into your teaching, you’re equipping your students with a tool that will serve them in all facets of life. Remember, the best learning happens when students are actively engaged , so make problem-solving a fun and integral part of your classroom culture.

1. What are problem-solving skills? Problem-solving skills are abilities that help individuals define problems, analyze potential solutions, and implement effective strategies to solve problems.

2. Why are problem-solving skills important for students? Problem-solving skills are important as they foster creativity, critical thinking, and resilience. They are applicable in real-world situations and can boost student confidence.

3. What are some strategies to develop problem-solving skills in students? Strategies can include project-based learning, group work, encouraging questions, and role-play scenarios.

4. How can I make problem-solving activities engaging for students? Making problem-solving part of a larger project or group work can make it more engaging. Also, try to relate problems to real-world situations that students find relevant.

5. How can I assess my students’ problem-solving skills? You can assess problem-solving skills through direct observation, group project participation, and individual assignments that require problem-solving.

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Problem-Solving

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?”

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

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

• Daniel Kane - [email protected]

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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. 

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Think back to the first problem in this chapter, the ABC Problem . What did you do to solve it? Even if you did not figure it out completely by yourself, you probably worked towards a solution and figured out some things that did not work.

Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

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).  He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985. [1]

 In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Looking back.

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

We have already seen one problem solving strategy, which we call “Wishful Thinking.” Do not be afraid to change the problem! Ask yourself “what if” questions:

• What if the picture was different?
• What if the numbers were simpler?
• What if I just made up some numbers?

You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started.

This brings us to the most important problem solving strategy of all:

Problem Solving Strategy 2 (Try Something!). If you are really trying to solve a problem, the whole point is that you do not know what to do right out of the starting gate. You need to just try something! Put pencil to paper (or stylus to screen or chalk to board or whatever!) and try something. This is often an important step in understanding the problem; just mess around with it a bit to understand the situation and figure out what is going on.

And equally important: If what you tried first does not work, try something else! Play around with the problem until you have a feel for what is going on.

Problem 2 (Payback)

Last week, Alex borrowed money from several of his friends. He finally got paid at work, so he brought cash to school to pay back his debts. First he saw Brianna, and he gave her 1/4 of the money he had brought to school. Then Alex saw Chris and gave him 1/3 of what he had left after paying Brianna. Finally, Alex saw David and gave him 1/2 of what he had remaining. Who got the most money from Alex?

Think/Pair/Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What did you figure out about the problem?

This problem lends itself to two particular strategies. Did you try either of these as you worked on the problem? If not, read about the strategy and then try it out before watching the solution.

Problem Solving Strategy 3 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric, like this one, thinking visually can help! Can you represent something in the situation by a picture?

Draw a square to represent all of Alex’s money. Then shade 1/4 of the square — that’s what he gave away to Brianna. How can the picture help you finish the problem?

After you have worked on the problem yourself using this strategy (or if you are completely stuck), you can watch someone else’s solution.

Problem Solving Strategy 4 (Make Up Numbers). Part of what makes this problem difficult is that it is about money, but there are no numbers given. That means the numbers must not be important. So just make them up!

You can work forwards: Assume Alex had some specific amount of money when he showed up at school, say $100. Then figure out how much he gives to each person. Or you can work backwards: suppose he has some specific amount left at the end, like $10. Since he gave Chris half of what he had left, that means he had $20 before running into Chris. Now, work backwards and figure out how much each person got.

Watch the solution only after you tried this strategy for yourself.

If you use the “Make Up Numbers” strategy, it is really important to remember what the original problem was asking! You do not want to answer something like “Everyone got $10.” That is not true in the original problem; that is an artifact of the numbers you made up. So after you work everything out, be sure to re-read the problem and answer what was asked!

Problem 3 (Squares on a Chess Board)

How many squares, of any possible size, are on a 8 × 8 chess board? (The answer is not 64… It’s a lot bigger!)

Remember Pólya’s first step is to understand the problem. If you are not sure what is being asked, or why the answer is not just 64, be sure to ask someone!

Think / Pair / Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What did you figure out about the problem, even if you have not solved it completely?

It is clear that you want to draw a picture for this problem, but even with the picture it can be hard to know if you have found the correct answer. The numbers get big, and it can be hard to keep track of your work. Your goal at the end is to be absolutely positive that you found the right answer. You should never ask the teacher, “Is this right?” Instead, you should declare, “Here’s my answer, and here is why I know it is correct!”

Problem Solving Strategy 5 (Try a Simpler Problem). Pólya suggested this strategy: “If you can’t solve a problem, then there is an easier problem you can solve: find it.” He also said: “If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?” In this case, an 8 × 8 chess board is pretty big. Can you solve the problem for smaller boards? Like 1 × 1? 2 × 2? 3 × 3?

Of course the ultimate goal is to solve the original problem. But working with smaller boards might give you some insight and help you devise your plan (that is Pólya’s step (2)).

Problem Solving Strategy 6 (Work Systematically). If you are working on simpler problems, it is useful to keep track of what you have figured out and what changes as the problem gets more complicated.

For example, in this problem you might keep track of how many 1 × 1 squares are on each board, how many 2 × 2 squares on are each board, how many 3 × 3 squares are on each board, and so on. You could keep track of the information in a table:

Problem Solving Strategy 7 (Use Manipulatives to Help You Investigate). Sometimes even drawing a picture may not be enough to help you investigate a problem. Having actual materials that you move around can sometimes help a lot!

For example, in this problem it can be difficult to keep track of which squares you have already counted. You might want to cut out 1 × 1 squares, 2 × 2 squares, 3 × 3 squares, and so on. You can actually move the smaller squares across the chess board in a systematic way, making sure that you count everything once and do not count anything twice.

Problem Solving Strategy 8 (Look for and Explain Patterns). Sometimes the numbers in a problem are so big, there is no way you will actually count everything up by hand. For example, if the problem in this section were about a 100 × 100 chess board, you would not want to go through counting all the squares by hand! It would be much more appealing to find a pattern in the smaller boards and then extend that pattern to solve the problem for a 100 × 100 chess board just with a calculation.

If you have not done so already, extend the table above all the way to an 8 × 8 chess board, filling in all the rows and columns. Use your table to find the total number of squares in an 8 × 8 chess board. Then:

• Describe all of the patterns you see in the table.
• Can you explain and justify any of the patterns you see? How can you be sure they will continue?
• What calculation would you do to find the total number of squares on a 100 × 100 chess board?

(We will come back to this question soon. So if you are not sure right now how to explain and justify the patterns you found, that is OK.)

Problem 4 (Broken Clock)

This clock has been broken into three pieces. If you add the numbers in each piece, the sums are consecutive numbers. ( Consecutive numbers are whole numbers that appear one after the other, such as 1, 2, 3, 4 or 13, 14, 15.)

Can you break another clock into a different number of pieces so that the sums are consecutive numbers? Assume that each piece has at least two numbers and that no number is damaged (e.g. 12 isn’t split into two digits 1 and 2.)

Remember that your first step is to understand the problem. Work out what is going on here. What are the sums of the numbers on each piece? Are they consecutive?

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What progress have you made?

Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

In this case, worrying about the clock and exactly how the pieces break is less important than worrying about finding consecutive numbers that sum to the correct total. Ask yourself:

• What is the sum of all the numbers on the clock’s face?
• Can I find two consecutive numbers that give the correct sum? Or four consecutive numbers? Or some other amount?
• How do I know when I am done? When should I stop looking?

Of course, solving the question about consecutive numbers is not the same as solving the original problem. You have to go back and see if the clock can actually break apart so that each piece gives you one of those consecutive numbers. Maybe you can solve the math problem, but it does not translate into solving the clock problem.

Problem Solving Strategy 10 (Check Your Assumptions). When solving problems, it is easy to limit your thinking by adding extra assumptions that are not in the problem. Be sure you ask yourself: Am I constraining my thinking too much?

In the clock problem, because the first solution has the clock broken radially (all three pieces meet at the center, so it looks like slicing a pie), many people assume that is how the clock must break. But the problem does not require the clock to break radially. It might break into pieces like this:

Were you assuming the clock would break in a specific way? Try to solve the problem now, if you have not already.

• Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons ↵

Mathematics for Elementary Teachers Copyright © 2018 by Michelle Manes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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Teaching Problem Solving in Math

• Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• read the problem carefully
• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• estimating the answer
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• check your work
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

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How to Teach Problem Solving Skills Like a Pro

Problem solving can be one of the most difficult things to teach children. It isn’t super cut and dry, and often times it can be simple to explain, but challenging for students to put into practice.

Here are the different ways I love to teach problem solving strategies to my students, and will make you a problem solving pro.

Problem Solving Strategies List

• Have a script
• Consistency, consistency, consistency
• Kelso’s Choices
• Realistic & Specific scenarios

Before we jump in- I am going to let you in on a little secret. When I am teaching my students problem-solving skills, I am typically referencing one of two things 1) my problem-solving posters and scenarios or 2) materials from Kelso’s choices. Kelso’s choices is a FANTASTIC, concrete way to give students action steps to take when they are trying to problem-solve.

I highly recommend incorporating Kelso’s choices from the beginning of the school year, and consistently teaching your students how to use it.

1. Have a Script

When you are teaching younger students how to problem solve, it may seem like they should know what to say and when to say it. You ask them, and they can tell you what should happen… and somehow, when that moment comes where there is disagreement…you still are hearing that yelling and screaming that you were hoping to avoid.

Here’s the thing- students need more help with these skills than we think, and that is why I believe it is crucial to have posted scripts for students to use to talk through their problems.

2. Consistency, consistency, consistency

Yup, you guessed it. You can’t just teach problem solving skills once or twice, and expect students to have it perfect. Just like with a new math or reading skill, problem solving takes time. LOTS of time- and lots of practice. Any time you can, have students practice their problem solving skills. Teach whole group and small group lessons on problem solving regularly. Choose one strategy, and teach it as often and consistently as you can.

Also- make sure to catch students working through problems IN THE MOMENT. Talking about it after is helpful, but not as helpful as if you can pull students aside as they are working through a problem, and guide them through it.

Some of the things I tell students before we do a ‘Talk it Out’ is:

-When student A is talking, you will wait to speak. I want you to focus on LISTENING to what they are saying. When Student B is talking, you will stay quiet, and focus on LISTENING.

-Then, I will have student A explain how THEY are feeling (and not what they think the other student did wrong). Then Student B shares their feelings.

-Afterwards, I help the students lead their own discussion on coming up with a solution to the problem.

3. Roleplay

How do actors memorize their lines? They act out their script until they have it memorized. Give your students opportunities to practice solving made up, but realistic, scenarios.

4. Kelso’s Choices

I love Kelso’s Choices . You can access the Kelso’s Choices poster (and other free resources) by clicking here , or, if you are feeling fancy, there is an entire curriculum that can give you some easy, low prep lessons to work on with students.

(If you are someone who prefers to have things ready to go, this is for you. For example, look at this Conflict Management kit! Tell your principal and counselor how awesome it is, and see if they can squeeze it into the budget.)

I introduce Kelso’s Choices at the beginning of the school year. I have the poster hung in the classroom, we look at the wheel, and I play this Kelso’s Choices Rap for students. (It is super silly and engaging.)

Over the first few weeks (or sets of lessons if you don’t see students every day), we really dig into what each choice looks like and means. I also love the motions that this counselor adds to her lessons.

Then, we use scenarios to practice which choice we might choose, and why.

Lastly, we act out those scenarios, so we get lots of practice.

Students know that they need to choose two Kelso’s Choices to try before they come get a teacher to help.

5. Realistic & Specific Scenarios

Last but not least, make your practice scenarios realistic . If you ask a student what they might do if someone has something they want, or they want to join into a game- that is important. But really dig into the specifics of these issues when you practice. Think of every day scenarios, and don’t just practice the original scenario, but what happens NEXT.

What if you ask someone if you can join their game, and they tell you no ? What if you left your homework at home and you already tried to call your grown-up, and they didn’t answer the phone ? If your friend says something mean to you multiple times and you already told them you didn’t like it ? I have a bunch of specific problem-solving scenarios in this product!

Be sure that when you have students practice, your scenarios are realistic and specific.

Overall, when you are teaching problem solving skills to your students, really focus on the specifics, your consistency, and regular practice!

11 of My Favorite Videos to Teach Gratitude

Principles for Teaching Problem Solving

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Resource library.

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

Problem-Based Learning

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

Why Use Problem-Based Learning?

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

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

Considerations for Using Problem-Based Learning

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

Students generally must:

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

Getting Started with Problem-Based Learning

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

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

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How to Teach Problem-Solving Skills to Children and Preteens

• By Ashley Cullins

Whether it’s a toy-related conflict, a tough math equation, or negative peer pressure, kids of ALL ages face problems and challenges on a daily basis.

As parents or teachers, we can’t always be there to solve every problem for our children. In fact, this isn’t our job. Our job is to TEACH our children how to solve problems by themselves . This way, they can become confident , independent, and successful individuals.

Instead of giving up or getting frustrated when they encounter a challenge, kids with problem-solving skills manage their emotions, think creatively, and persist until they find a solution. Naturally, these abilities go hand-in-hand with a  growth mindset .

Before you continue, we thought you might like to download our FREE Your Words Matter Volume 2 Kit . With these 10 one-page parenting guides, you will know exactly how to speak to your child to help them stand up for themselves, be more confident, and develop a growth mindset.

So HOW do you teach problem-solving skills to kids?

Well, it depends on their age . As cognitive abilities and the size of the child’s challenges grow/evolve over time, so should your approach to teaching problem-solving skills.

Read on to learn key strategies for teaching problem-solving to kids, as well as some age-by-age ideas and activities.

3 General Strategies to Teach Problem-Solving at Any Age

1. model effective problem-solving .

When YOU encounter a challenge, do a “think-aloud” for the benefit of your child. MODEL how to apply the same problem-solving skills you’ve been working on together, giving the real-world examples that she can implement in her own life.

At the same time, show your child a willingness to make mistakes . Everyone encounters problems, and that’s okay. Sometimes the first solution you try won’t work, and that’s okay too!  

When you model problem-solving, explain that there are some things that are out of our control. As we're solving a problem at hand we should focus on the things we CAN actually control.

You and your child can listen to Episode 35  of the Big Life Kids Podcast to learn about focusing on what you can control.

2. Ask for Advice

Ask your kids for advice when you have a problem. This teaches them that it’s common to make mistakes and face challenges. It also gives them the opportunity to practice problem-solving skills.

Plus, when you indicate that their ideas are valued ,  they’ll gain the confidence to attempt solving problems on their own.

3. Don’t Provide “The Answer”

As difficult as it may be, allow your child to struggle, sometimes fail , and ultimately LEARN  from experiencing consequences.

Now, let’s take a look at some age-specific strategies and activities. The ages listed below are general guidelines, feel free to choose any strategies or activities that you feel will work for YOUR child.

Use Emotion Coaching

To step into a problem-solving mindset, young children need to first learn to  manage their emotions . After all, it’s difficult for a small child to logically consider solutions to a problem if he’s mid-tantrum.

One way to accomplish this is by using the  emotion coaching process  outlined by John Gottman.

First,  teach your kids that ALL emotions are acceptable. There are NO “bad” emotions. Even seemingly negative emotions like anger, sadness, and frustration can teach us valuable lessons. What matters is how we  respond  to these emotions.

Second,   follow this process:

• Step One: Naming and validating emotions.  When your child is upset, help her process the way she’s feeling. Say something like,  “I understand that you’re upset because Jessica is playing with the toy you wanted.”
• Step Two:   Processing  emotions.  Guide your child to her  calming space. If she doesn't have one, it's a good idea to create one.  Let her calm her body and process her emotions so she can problem-solve, learn, and grow. 
• Step Three: Problem Solving.  Brainstorm solutions with your child, doing more   LISTENING   than talking during the conversation. This allows your child to practice her problem-solving skills, and she’s more likely to actually implement the solutions she came up with herself.

Say, “Show Me the Hard Part”

When your child struggles or feels frustrated, try a technique suggested by mom and parenting blogger Lauren Tamm . Simply say, “Show me the hard part.”

This helps your child identify the ROOT   of the problem, making it less intimidating and easier to solve.

Repeat back what your child says,  “So you’re saying…”

Once you both understand the real problem, prompt your child to come up with solutions . “There must be some way you can fix that…” or  “There must be something you can do…”

Now that your child has identified “the hard part,” she’ll likely be able to come up with a solution. If not, help her brainstorm some ideas. You may try asking the question, “If you DID  know, what would you think?” and see what she comes up with.

Problem-Solve with Creative Play

Allow your child to choose activities and games based on her  interests . Free play provides plenty of opportunities to navigate and creatively solve problems.

Children often learn best through play. Playing with items like blocks, simple puzzles, and dress-up clothes can teach your child the process of problem-solving.

Even while playing, your child thinks critically:  Where does this puzzle piece fit? What does this do? I want to dress up as a queen. What should I wear?   Where did I put my tiara? Is it under the couch?

Problem-Solve with Storybooks

Read age-appropriate stories featuring characters who experience problems, such as:

• Ladybug Girl and Bumblebee Boy by Jacky Davis: The story of two friends who want to play together but can’t find a game to agree on. After taking turns making suggestions, they arrive at a game they both want to play: Ladybug Girl and Bumblebee Boy.
• The Curious George Series by Margaret and H.E. Rey: A curious little monkey gets into and out of dilemmas, teaching kids to find solutions to problems of their own.
• Ira Sleeps Over by Bernard Waber: Ira’s thrilled to have a sleepover at his friend Reggie’s house. But there’s one problem: Should he or should he not bring his teddy bear? It may seem small, but this is the type of early social problem your child might relate to.

Connect these experiences to similar events in your child’s own life, and ASK your child HOW the characters in these stories could solve their problems. Encourage a variety of solutions, and discuss the possible outcomes of each.

This is a form of dialogue reading , or actively ENGAGING   your child in the reading experience. Interacting with the text instead of passively listening can “turbocharge” the development of literacy skills such as comprehension in preschool-aged children.

By asking questions about the characters’ challenges, you can also give your child’s problem-solving abilities a boost.

You can even have your child role-play the problem and potential solutions to reinforce the lesson.  

For book suggestions, refer to our Top 85 Growth Mindset Books for Children & Adults list.

Teach the Problem-Solving Steps

Come up with a simple problem-solving process for your child, one that you can consistently implement. For example, you might try the following five steps:

• Step 1: What am I feeling?  Help your child understand what she’s feeling in the moment (frustration, anger, curiosity, disappointment, excitement, etc.)  Noticing and naming emotions will diffuse  their charge and give your child a chance to take a step back.
• Step 2: What’s the problem?  Guide your child to identify the specific problem. In most cases, help her take responsibility for what happened rather than pointing fingers. For instance, instead of, “Joey got me in trouble at recess,” your child might say, “I got in trouble at recess for arguing with Joey.”
• Step 3:   What are the solutions?  Encourage your child to come up with as many solutions as possible. At this point, they don’t even need to be “good” solutions. They’re just brainstorming here, not yet evaluating the ideas they’ve generated.
• Step 4: What would happen if…? What would happen if your child attempted each of these solutions? Is the solution safe and fair? How will it make others feel? You can also try role-playing at this step. It’s important for your child to consider BOTH  positive and negative consequences of her actions.
• Step 5: Which one will I try?  Ask your child to pick one or more solutions to try. If the solution didn't work, discuss WHY and move on to another one. Encourage your child to keep trying until the problem is solved. 

Consistently practice these steps so that they become second nature, and model solving problems of your own the same way.  It's a good idea to   reflect :   What worked? What didn’t? What can you do differently next time?

Problem-Solve with Craft Materials

Crafting is another form of play that can teach kids to solve problems creatively.

Provide your child with markers, modeling clay, cardboard boxes, tape, paper, etc. They’ll come up with all sorts of interesting creations and inventive games with these simple materials.

These “open-ended toys” don’t have a “right way to play,” allowing your child to get creative and generate ideas independently .

Ask Open-Ended Questions

Asking open-ended questions improves a child’s ability to think critically and creatively, ultimately making them better problem-solvers. Examples of open-ended questions include:

• How could we work together to solve this?
• How did you work it out? or How do you know that?
• Tell me about what you built, made, or created.
• What do you think will happen next?
• What do you think would happen if…?
• What did you learn?
• What was easy? What was hard?
• What would you do differently next time?

Open-ended questions have no right answer and can’t be answered with a simple “Yes” or “No.”

You can ask open-ended questions even when your child isn’t currently solving a problem to help her practice her thinking skills, which will come in handy when she does have a problem to solve.

If you need some tips on how to encourage a growth mindset in your child, don't forget to download our FREE Your Words Matter Volume 2 Kit .

Break Down Problems into Chunks

This strategy is a more advanced version of “Show me the hard part.”

The bigger your child gets, the bigger her problems get too. When your child is facing a challenge that seems overwhelming or insurmountable, encourage her to break it into smaller, more manageable chunks.

For instance, let’s say your child has a poor grade in history class. Why is the grade so low? What are the causes of this problem?

As usual, LISTEN as your child brainstorms, asking open-ended questions to help if she gets stuck.

If the low grade is the result of missing assignments, perhaps your child can make a list of these assignments and tackle them one at a time. Or if tests are the issue, what’s causing your child to struggle on exams?

Perhaps she’s distracted by friends in the class, has trouble asking for help, and doesn’t spend enough time studying at home. Once you’ve identified these “chunks,” help your child tackle them one at a time until the problem is solved.

Show “ The Broken Escalator Video ”

Discuss the importance of embracing challenges and solving problems independently with the “broken escalator video.”

In the video, an escalator unexpectedly breaks. The people on the escalator are “stuck” and yelling for help. At this age, it’s likely that your child will find the video funny and immediately offer a solution: “Just walk! Get off the escalator!”

Tell your child that this is a simple example of how people sometimes act in difficult situations. Ask, “Why do you think they didn’t get off the escalator?” (they didn’t know how, they were waiting for help, etc.)

Sometimes, your child might feel “stuck” when facing problems. They may stop and ask for help before even attempting to find a solution. Encourage your child to embrace challenges and work through problems instead.

Problem-Solve with Prompts

Provide your child or a group of children with materials such as straws, cotton balls, yarn, clothespins, tape, paper clips, sticky notes, Popsicle sticks, etc.

With just these materials, challenge your kids to solve unusual problems like:

• Make a leprechaun trap
• Create a jump ramp for cars
• Design your own game with rules
• Make a device for two people to communicate with one another

This is a fun way to practice critical thinking and creative problem-solving. Most likely, it will take multiple attempts to find a solution that works, which can apply to just about any aspect of life.

Make Them Work for It

When your child asks for a new toy, technology, or clothes, have her make a plan to obtain the desired item herself. Not only will your child have to brainstorm and evaluate solutions, but she’ll also gain confidence .

Ask your child HOW she can earn the money for the item that she wants, and encourage her as she works toward her goal .

Put It on Paper

Have your child write out their problems on paper and brainstorm some potential solutions.

But now, she takes this process a step further: After attempting each solution, which succeeded? Which were unsuccessful? Why ?

This helps your child reflect on various outcomes, learning what works and what doesn’t. The lessons she learns here will be useful when she encounters similar problems in the future.

Play Chess Together

Learning to play chess is a great way for kids to learn problem-solving AND build their brains at the same time. It requires players to use critical thinking, creativity, analysis of the board, recognize patterns, and more. There are online versions of the game, books on how to play, videos, and other resources. Don’t know how to play? Learn with your teen to connect and problem solve together!

Have Them Learn To Code

Our teens and tweens are already tech-savvy and can use their skills to solve problems by learning to code. Coding promotes creativity, logic, planning, and persistence . There are many great tools and online or in-person programs that can boost your child’s coding skills.

Encourage to Start a Meaningful Project

This project has to be meaningful to your teen, for example starting a YouTube channel. Your teen will practice problem-solving skills as they’re figuring out how to grow their audience, how to have their videos discovered, and much more. 

In the Big Life Journal - Teen Edition , there’s a section that guides them through planning their YouTube channel and beginning the problem-solving process.

Apply the SODAS Method

Looking for a game plan that your teen can employ when faced with a problem? The SODAS method can be used for big or small problems. Just remember this simple acronym and follow these ideas:

• D isadvantages
• A dvantages

Encourage to Join Problem-Solving Groups

Does your teen enjoy solving problems in a team? Have them join a group or club that helps them hone their skills in a variety of settings--from science and robotics to debating and international affairs. Some examples of groups include: 

• Odyssey of the Mind
• Debate team
• Science Olympiad

Looking for additional resources?  The Bestseller’s Bundle includes our three most popular printable kits packed with science-based activities, guides, and crafts for children. Our Growth Mindset Kit, Resilience Kit, and Challenges Kit work together as a comprehensive system designed specifically for children ages 5-11.

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25 thoughts on “ How to Teach Problem-Solving Skills to Children and Preteens ”

I love, love, love the point about emotional coaching. It’s so important to identify how children are feeling about a problem and then approach the solutions accordingly.

Thank you for putting this together. I wrote an article on problem-solving specifically from the point of view of developing a STEM aptitude in kids, if you like to check it out – https://kidpillar.com/how-to-teach-problem-solving-to-your-kids-5-8-years/

I feel that these techniques will work for my kid.. Worthy.. Thank you

I love you guys

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14 Effective Ways to Help Your Students Conquer Math Word Problems

If a train leaving Minneapolis is traveling at 87 miles an hour…

Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems.

1. Solve word problems regularly

This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process.

Learn more: Teaching With Jennifer Findlay

2. Teach problem-solving routines

There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.

Learn more: Word Problems Made Easy

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3. Visualize or model the problem

Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.

Learn more: Math Geek Mama

4. Make sure they identify the actual question

Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed. 

Learn more: Robert Kaplinsky

5. Remove the numbers

It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking. 

Learn more: Where the Magic Happens Teaching

6. Try the CUBES method

This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.

Learn more: Teaching With a Mountain View

7. Show word problems the LOVE

Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use. 

8. Consider teaching word problem key words

This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.

Learn more: Book Units Teacher

9. Determine the operation for the situation

Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.

Learn more: Solving Word Problems With Jennifer Findlay

10. Differentiate word problems to build skills

Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.

Learn more: Differentiating Math 

11. Ensure they can justify their answers

One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.

Learn more: Madly Learning

12. Write the answer in a sentence

When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.

Learn more: Multi-Step Word Problems

13. Add rigor to your word problems

A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.

Learn more: The Routty Math Teacher and Alyssa Teaches

14. Use a problem-solving rounds activity.

Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.

Learn more: Teacher Trap

Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .

Plus, 60+ Awesome Websites For Teaching and Learning Math .

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50+ Tips, Tricks, and Ideas for Teaching 4th Grade

Brilliant ideas from brilliant teachers (like you). Continue Reading

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4 Tips on Teaching Problem Solving (From a Student)

A student shares her insights into the most important skill you can teach. (Hint: It’s not perseverance.)

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Education is one of the most important things in the world, but at most schools, students are told to memorize facts, formulas, and functions without any applicability to the real challenges we will face later. Instead, give us challenges; give us problems that focus on real-world scenarios; give us a chance to understand the world we’re entering and to be prepared for it before we’re thrown in headfirst.

At Two Rivers Public Charter School, they taught us how to problem solve, and they made it relevant. Here are four tips that engaged me in my learning that you can adapt in your classroom:

1. Give Your Students Hard Problems

In the real world, we’re not going to have nice problems that will be easy to understand. We are going to have complex problems that require a lot more preparation than most math, science, or English classes will give us. The challenges in the real world won’t be simple, and the problems that are supposed to prepare us for that world shouldn't be either.

2. Make Problem Solving Relevant to Your Students’ Lives

In the seventh grade, we looked at statistics concerning racial murders and the jury system. That’s something that is going to affect students later in life, and we got a chance to look at it from a mathematical perspective. Problems like that are actually relevant to us, and they’re not things we’re supposed to just memorize or learn. They are things from which we can take very important life lessons, and then actually apply them later on in life.

Related Article: Solving Real World Issues Through Problem-Based Learning

In the eighth grade, we wrote policy briefs in relation to gene editing and presented them to the National Academies of Sciences, Engineering, and Medicine. We talked to researchers who worked with CRISPR-Cas9 (a gene editing tool used to modify specific genes in organisms), and we studied how gene editing is evolving and how we can use this modern technology for science applications. At the same time, in English, we read The Giver by Lois Lowry and analyzed whether the society in the book was ethical to gain an understanding of what ethical means and how it’s applicable in real situations, like gene editing.

This wasn’t something where we were being told, “Somebody’s going to buy 60 watermelons at a store.” This was actually happening in real life, and the only people really discussing this were people whom it wasn't even going to affect. This science won’t come into widespread use until much later, and we’re going to be the first ones who are actually in danger from the possible consequences of it. By presenting our policy briefs, we had a chance to make an impact and get our voice out there at only 14.

3. Teach Your Students How to Grapple (It’s More Powerful Than Perseverance)

Grappling is like perseverance, but it goes beyond that. Perseverance means trying again and again, even after you’ve failed. Grappling implies trying even before you fail the first time. It’s thinking, “First, I’ll work with it independently. Okay, I’m really not understanding it. Let me go back to my notes. Okay, I have solved for the first part of it. Now I have the second part of it. Okay, I got the question wrong; let me try again. Maybe I can ask my peer now.” Grappling is working hard to make sure you understand the problem fully, and then using every resource at your fingertips to solve it.

4. Put More Importance on Student Understanding Than on Getting the Right Answer

I am graduating from Two Rivers with a practical view of the world. I don’t think that many students come out of middle school saying, “It was great.” And I don’t think many students have had this introduction to our society and its benefits and drawbacks. I’m also coming out of here with incredible problem-solving skills and the ability to look at any problem and have 10,000 ways to solve it in my mind already—because we don’t just memorize functions or the periodic table. We understand why, and we work to understand how to solve a problem instead of just getting the answer.

As students preparing for the real world, it is so much more impactful for us if our learning is relevant and challenging than if it is just about memorizing the right answers.

Two Rivers Public Charter School

Per pupil expenditures, free / reduced lunch, demographics:.

This blog post is part of our Schools That Work series, which features key practices from Two Rivers Public Charter School .

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Math Problem Solving Strategies Posters

Subject: Mathematics

Age range: 11-14

Resource type: Visual aid/Display

Last updated

20 September 2024

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This set of posters is designed to help students develop and reinforce problem-solving strategies in mathematics. Each poster focuses on a different strategy, such as:

Guess and Check Work Backwards Break It Down (Decompose) Solve a Simpler Problem Make a List Use Logic Reasoning Work with a Friend Act It Out Use a Number Line Guess, Estimate, and Check Check for Extra Information Use Equations The posters include helpful examples, visuals, and a “Thinking Out Loud” section to encourage students to articulate their thought processes. These vibrant and easy-to-understand posters can be displayed in classrooms to support students in using a variety of methods to approach and solve math problems. Ideal for elementary and middle school settings, they provide students with key problem-solving techniques that are essential for success in math. Also included are colored and black and white bookmarks.

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Problem Posing Via Scriptwriting: What Instructional Flows Do Mathematics Teachers Use in Implementing the Problem-Posing Task?

• Published: 24 September 2024

Cite this article

• Tuğrul Kar   ORCID: orcid.org/0000-0001-8336-1327 1 ,
• Ferhat Öztürk   ORCID: orcid.org/0000-0003-2849-8325 2 ,
• Mehmet Fatih Öçal   ORCID: orcid.org/0000-0003-0428-6176 3 &
• Merve Özkaya   ORCID: orcid.org/0000-0002-0436-4931 4  

The present study aimed to describe teachers’ instructional flows when implementing a mathematical problem-posing task using scriptwriting technique. With matchsticks, a growing pattern that increases by a constant unit was created and presented to the teachers as a problem-posing situation. We analyzed the instructional flows in 50 scripts, taking into account situations recognized in the problem-posing field as critical for integrating problem posing into mathematics classrooms. We determined three instructional flows in the scripts: pose and solve cycle-based, observation-based, and problem-solving based, the first being the most common. We presented a new problem-posing instructional model and discussed its potential benefits for student learning.

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Data Availability

The data is available upon reasonable request from the corresponding author.

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College of Education, Department of Mathematics and Science Education, Recep Tayyip Erdoğan University, Rize, Türkiye

College of Education, Department of Mathematics and Science Education, Kırıkkale University, Kırıkkale, Türkiye

Ferhat Öztürk

College of Education, Department of Mathematics and Science Education, Ağrı İbrahim Çeçen University, Ağrı, Türkiye

Mehmet Fatih Öçal

College of Education, Department of Mathematics and Science Education, Atatürk University, Erzurum, Türkiye

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Each  Tuğrul Kar designed the study, conducted the literature review, contributed to data collection and data analysis, and drafted the initial manuscript. Ferhat Öztürk contributed to data collection, data analysis, and writing the methodology and discussion sections. Mehmet Fatih Öçal contributed to data collection, data analysis, and writing the discussion section. Merve Özkaya contributed to data collection and data analysis. All authors reviewed and approved the final version of the manuscript. 

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Kar, T., Öztürk, F., Öçal, M.F. et al. Problem Posing Via Scriptwriting: What Instructional Flows Do Mathematics Teachers Use in Implementing the Problem-Posing Task?. Int J of Sci and Math Educ (2024). https://doi.org/10.1007/s10763-024-10507-w

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Received : 04 January 2024

Accepted : 11 September 2024

Published : 24 September 2024

DOI : https://doi.org/10.1007/s10763-024-10507-w

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