As math teachers, we’ve all had students who struggled with mathematical problem-solving. Now more than ever, this seems to be a rising cause for concern in the wake of the pandemic. Maybe it’s because students didn’t have as much exposure to mathematical situations due to being at home more, or maybe it stems from the lack of time to fill in learning that has been missed, so we rush more quickly through the concrete understanding within problems to the abstract part of solving.
Regardless of the reason, there are some things we can do to build up our students’ skills in this area.
When we break down learning into smaller, actionable steps, we can partner with our students and empower them to own their learning and see lasting results more quickly. It’s important for students to be aware of the processes they are building as problem solvers and how that will help them to be ready for the future in more than just the math classroom.
5 Ways to Boost Students’ Problem-Solving Skills
1. We can immerse students in problem-solving in all aspects of the math workshop: When teaching a specific computational strategy, embedding numbers in word problems helps students to build operational sense and reasoning behind using a skill. Even number sense and fact fluency can be sprinkled with context. During small group instruction, teachers can strategically and flexibly place students in groups that focus on building specific process skills, not only computation.
Using a simple chart can help you to sort through data and add students to specific groups based on the needs you see as you look through their work. Guided math groups could focus on teach points, such as being able to visualize the problem, utilize a representation to help them solve, or write an answer statement to help students recontextualize the problem after they’ve solved it.
Strategy groups would be focused more on computation or place value needs. If you’re unsure of a student’s understanding, you can place them in the conferring column. Conferring with students one-on-one provides space where the teacher can listen to students thinking out loud to get a better understanding of their mathematical ability.
2. We can give students consistent exposure to high-quality problem-solving: According to Peter Liljedahl, author of Building Thinking Classrooms in Mathematics, “Good problem-solving tasks require students to get stuck and then to think, to experiment, to try and to fail, and to apply their knowledge in novel ways in order to get unstuck.”
The go-to in our district for promoting productive math struggle is Exemplars. This resource encourages students to get stuck and power through really difficult, real-world, multistep situations. The tasks they provide encourage students to show their thinking processes in a variety of ways. You can really tell it’s a great task if all student thinking looks different. In a world where instant gratification has become the norm, we can remind students that when they get stuck, it’s exciting! This challenging moment is part of learning and making new connections in their brain.
3. We can be intentional about providing students with a variety of problems that contain a blend of previously learned skills: This makes it necessary for students to think and make sense of every problem they encounter, instead of being able to anticipate an operation based on current content or the title on the page.
For example, when students practice independently, one or two problems could be on a recently obtained skill, but there could also be a problem from a previous cluster of learning and one for an upcoming concept from a lower grade level. Not only does this provide students with an opportunity to practice their problem-solving skills; it gives the teacher the opportunity to ensure that students are retaining previously learned skills from earlier in the year and from the prior year.
Checking in on skills from the previous year can be a preassessment and helps the teacher to adjust future pacing, since they are informed about student needs before a new cluster of learning is started. Number sense routines are also the perfect time to offer a variety of problems within the math workshop because students get the daily opportunity to see peers solve problems flexibly, observe that computation can be approached in different ways, have a specific time to play with numbers, and build connections across concepts. I’ve compiled some great options for number sense (most of these are free).
4. We can make cross-content connections with reading and math: Utilizing a consistent reasoning routine across grade levels can create a habitual way of thinking for students as they make sense of problems. A good resource for this is Routines for Reasoning. The 3 Reads routine from this resource is great for making connections to reading comprehension. You could ask students, “Who are the characters in this problem? What are they doing? What is the setting? What happened in the beginning, middle, and end?” When students begin to think this way and train their brain to go through this process of visualization, it becomes more automatic, and students start to become sense makers.
5. We can ensure that our grading and assessment practices reflect our values: One way to do this is to bring students into the learning process by using a rubric, such as this one, as a self-assessment tool of the problem-solving processes. I have seen teachers utilize this as a whole class by focusing on one column at a time, where the teacher led the class in scoring teacher-created student work. Students would then later rate themselves and focus on how to move themselves to a higher level within the rubric on that skill. I’ve also seen teachers be very successful with using this rubric during one-on-one conferring.
According to the specific student’s understanding, the teacher can point them to analyze their work based on a specific column of the rubric. The teacher then guides the student to make a plan to focus on that one skill.
This might look like pointing the student to an anchor chart of representations in the classroom as a reference, helping the student with some sentence stems for communication, or even giving the student a word bank to help them learn how to use more math vocabulary within their justification. Teaching students how to use a tool like this one can give them a more concrete way of pushing themselves to deeper levels of learning, not just toward getting the correct answer.
I’ve also seen teachers display “expert”-level student work in the classroom as a guide for other students who are striving toward the same goal. Another encouraging tool could be a checklist with each problem, to give credit for correct representations and justification of thinking in addition to a correct answer.