“Make sense of problems and persevere in solving them” is the first of the 8 Mathematical Practices we want all students to use within any domain. It is the keystone of mathematics. We want our children to be able to see a problem, figure out a way that makes sense for them to solve it, and arrive at an answer that makes sense. This is our goal.
We often have teachers ask us, “What can I do to help my students become better problem solvers?” After years of observations in classrooms, we have found five common instructional problems and developed solutions.
Problem 1: Addition/subtraction and multiplication/division are being taught separately. This is problematic. The kids know that all of the problems they are solving are going to be the operation they are learning. It takes the thinking out of problem solving so they have no attack skills.
Solution 1: If you are teaching operations in isolation, introduce the inverse operation through problem solving. Addition/subtraction and multiplication/division need to be taught at the same time. It helps kids examine the structure of problems, and not just calculate the numbers they see with the operation they are currently learning.
Problem 2: The teacher models how to solve the problem. The brain needs to learn math differently than it learns reading. While we need to model first in reading, the best thinking we should be modeling in math is questioning. The teacher may show lots of strategies for the students, and then give them a problem to “pick the strategy that works for them.” The students pick from a menu of strategies that might not make sense to them, and apply it but they aren’t sure why. We take the thinking out of problem solving when we model first.
Solution 2: Start with the problems. Let students share their own strategies in their own handwriting. When students have a chance to persevere through a problem, they are more likely to know the why and how. It gives them a chance to think, struggle, make conjectures and prove. This allows the students to do more talking about their thinking and less time practicing the strategies the teacher shares. Get a FREE Notice/Wonder JamBoard!
Problem 3: Problem solving is not the means of teaching. It is given quickly, like a number talk and not the mode of instruction. Another instructional problem is that word problems are given at the end of instruction instead of the beginning.
Solution 3: Problem solving needs to be the mode of instruction. The students should spend 30-45 minutes on 1 or 2 problems. They should be solving and discussing problems every day. One school I am working with has their virtual teachers assign the next day’s problem as their independent work. The students upload a picture of their work onto a google slide with their name. The teacher uses the time she has with them in virtual instruction to discuss the student strategies so they are still the ones doing the talking and the thinking. She has a strategy board in her virtual classroom that the kids can add to at any time.
Problem 4: The structure of problems is not taught and is not varied. The students get simple-result unknown problems for addition/subtraction and always get partitive division.
Solution 4: Keep students on their toes! Teach students to look for the structure of the problems (the bar model is amazing for this, in my opinion). They should be able to determine what they are finding and write a situation equation to represent the problem regardless of how they solve it. Teachers should be constantly presenting different problem types to them. If the students only see one type of problem structure for an extended time, the students don’t learn to think. They learn the formula for that structure of problems and just apply it. When they complete an assessment that gives mixed operations and different problem structures, they don’t know how to think through it.
Problem 5: Kids don’t have a way to keep track of their strategies. There is nothing that shows how to solve problems based on student thinking. They don’t have a reference for what works and what doesn’t work.
Solution 5: Create Strategy Walls based on student strategies. These can be personal in a math notebook or they can be posted in the classroom (or both). The important thing is that these come from the students, and are not the pre-printed kind you can get on Teachers Pay Teachers. It can be simple, but the strategy wall must be connected to the student who did that strategy. One way to connect the students is by naming the strategies and having the students write their names or draw a picture of themself when they try that strategy. For example, students use counting all and counting on to solve addition problems. A simple piece of paper with the name of the strategy and an example of that strategy is posted in the classroom, and the teacher draws the student’s face when they have tried the strategy.
Kids can solve problems when they are given the time and the chance to do it. We need to make sure that as the teacher, we are setting them up for success by allowing them to persevere, reason, talk, solve and connect mathematical ideas. We’ve witnessed teachers applying these solutions to their instruction, and the efforts create a classroom full of problem solvers.
