Teaching problem solving skills in math class shouldn’t be something you squeeze into your curriculum when you happen to have an extra day. It also doesn’t have to mean adding another project, creating a complicated task, or giving students a giant word problem every Friday.
If we want students to become confident problem solvers, they need opportunities to practice problem solving skills throughout the entire math unit. They need to make decisions, choose strategies, interpret information, explain their reasoning, and determine whether their answers make sense instead of just following a procedure that has already been laid out for them. Keep reading to get strategies for building problem solving skills into the lessons you’re already teaching.
Start With Problem Solving Before You Teach the Skill
One of the easiest ways to incorporate problem solving in any math unit is to give students a chance to encounter a problem before you’ve taught them exactly how to solve it. This can feel uncomfortable at first. If students haven’t learned the procedure yet, how are they supposed to solve the problem, right?
When students encounter an unfamiliar problem, they’re forced to think about what they already know and consider how they might approach the situation. They might draw a picture, look for a pattern, estimate, write an equation, or try a strategy that doesn’t work.
For example, before formally teaching systems of equations, you could give students two different pricing plans and ask them to determine when the plans would cost the same amount. Students may not know the formal method for solving a system yet, but they can still reason about the situation and look for a way to find the answer.
Then, when you introduce systems of equations, students feel like they’re learning more than another set of steps to memorize.
This doesn’t need to take an entire class period. Even a short problem at the beginning of a lesson can give students an opportunity to think before they’re shown the “right” way to solve it.
Turn Daily Practice Into Problem Solving
Practice is an important part of learning math, but practice doesn’t have to mean giving students page after page of nearly identical problems. Students can practice a mathematical concept while also practicing problem solving skills.
Consider a basic equation such as 3x+7=25. Asking students to solve it gives you information about whether they can execute the procedure. But you can turn that same skill into a problem-solving opportunity by changing the question.
Instead, offer two different solutions to the equation and ask students to determine which one is correct and explain the error in the other solution. Now they’re still working with equations, but they also have to analyze the solution and communicate their thinking.
This same idea works across nearly every math topic. Students can compare two strategies, determine whether an answer is reasonable, decide which method would be most efficient, create an example that meets specific conditions, or explain why a particular approach works.
How to Build Problem Solving Skills into Review Days
Review is another place where problem solving can easily get lost. It’s tempting to create a review worksheet that includes five problems on equations, five on inequalities, five on functions, and so on. Students work through the worksheet, and you have a convenient way to see which skills they remember.
One of the most important parts of problem solving in math is determining where to start. A mixed review can become much more meaningful when students have to identify the strategy or skill they need instead of being told.
Give students a collection of problems where the topic isn’t labeled then ask them to determine which strategy makes sense and explain their choice. Include problems that can be approached in multiple ways or require students to connect two skills.
This kind of practice helps students move away from the question, “What steps do I use?” and toward the much more useful question, “What do I know, and what can I do with it?”
You Don’t Need Another Lesson to Teach Problem Solving Skills in Math Class
At this point, you might be thinking, “This all sounds great, but when am I supposed to fit it in?”
The answer is that you don’t necessarily need to fit in anything new. Problem solving can happen in just five or ten minutes.
At the beginning of a lesson, you might ask students how they would approach an unfamiliar situation. During practice, you might ask them to choose between two strategies. At the end of class, you might ask them to explain why their answer makes sense.
You don’t need to turn every lesson into a full-scale project, but rather create small opportunities for students to think critically instead of just automatically following directions. Ask these questions while reviewing your current units:
- At the beginning of the unit, can students explore the concept before being given the procedure
- During instruction, do students have opportunities to make mathematical decisions?
- During practice, are students doing more than repeating the same steps?
- During review, do students have to determine which skills or strategies they need?
- During assessment, do students have opportunities to independently apply what they’ve learned?
If you can answer yes to even a few of these questions, you’re already creating more opportunities for meaningful problem solving in math class.
What Problem Solving Can Look Like in an Algebra 1 Unit
Let’s take systems of equations as an example.
At the beginning of the unit, students could compare two pricing plans and investigate when the plans would cost the same. They don’t need to know the formal process for solving systems yet. They’re simply trying to make sense of the situation.
Once you begin teaching the formal methods, students can analyze different representations and discuss which method might be most useful for a particular system. During practice, they can solve equations while also analyzing incorrect solutions or comparing different approaches.
When it’s time to review, students can work through mixed problems without being told whether they should use substitution, elimination, or another representation. They have to identify the mathematical structure and decide how to approach each problem.
Finally, an assessment can include a real-world situation where students have to set up and solve a system, then interpret what the solution means in context.
Notice that this doesn’t require an additional “problem-solving lesson.” The problem solving practice is woven throughout the unit.
Final Thoughts About Adding Problem Solving Skills to Your Math Class
Students don’t become better problem solvers because we occasionally give them a challenging worksheet or dedicate one day to “real world applications.” They become better problem solvers when they’re regularly expected to think about what they’re doing.
Students need practice figuring out where to start with opportunities to choose strategies, work through unfamiliar situations, analyze mistakes, explain their reasoning, and decide whether their answers make sense.
Start by changing a few questions.
Give students a problem before teaching the procedure. Add an error-analysis question to your practice. Make a word problem require a decision. Add a real world application to your assessment.
Small changes like these can give students significantly more opportunities to practice the kind of critical thinking that matters beyond the classroom.