By: Amy Buchheit, K-8 Math Instructional Coach at The Frances Xavier Warde School in Chicago
Growing up, I considered myself “good” at math. I was good at following the rules and procedures my teachers prescribed. I was good at taking notes and following steps. I was good at listening to a series of directions and then mimicking those steps.
When I went into math instruction, I desired to be this “good” math teacher. I wanted to explain the procedures so well that after my lesson, not a single question would need to be asked. I carefully selected the problems I used as examples so that they were clear and highlighted the rules students needed to remember. I wanted to send students off to do independent work and see that the whole class was working through the problems with ease and mistakes would be minimal.
Then, after work with Lesson Study and other teacher professional development, I realized I had it all wrong. Everything I thought about good math learning and good math teaching needed to be flipped on its head. Struggle was good. Mistakes were important. In class, I should be thinking less and students should be thinking a lot more.
The thinking classroom we want to create now, may be very different than the types of classrooms we were in as children, or even the types of classrooms we began instructing in with our pre-service teaching or the beginnings of our teaching careers. Thus, I found it essential to rewire my brain to teach math differently than I learned it.
Create Opportunities to Think and Persevere
Old wiring: Explain things so well that students don’t have questions or make mistakes.
New wiring: Create learning opportunities and tasks that require students to think, make mistakes, and persevere.
It is not the teacher’s job to explain the math.The teacher must facilitate a classroom in which students are making sense of mathematics and sharing these discoveries with their peers. A teacher should select problems that push students’ thinking. Mistakes should happen and opportunities to persevere through challenges should be frequent. Productive struggle should be embedded into every class period, rather than seen as something that suggests a weakness in the instruction.
There is No One Right Way
Old wiring: It’s the teacher’s job to explain the steps for the best way to solve a problem.
New wiring: There are many strategies to solve a problem and those ideas should come from the students.
Instead of being a “sage on the stage” explaining how to solve math problems, teachers should be a “guide on the side” supporting students as the students discover strategies to solve problems. Multiple strategies should be shared, connected, and celebrated. Students should internalize that there are many solution paths and that they have the autonomy to discern how to solve a problem.
It’s about the Journey, Not the Destination
Old wiring: Getting the right answer is key.
New wiring: Math is not an answer-getting exercise. It is about critical thinking, problem solving,and creativity.
Math teachers must actively work to devalue answer seeking. Creating a classroom culture that focuses on process and strategies highlights the importance of thinking and sense making.
Also important in developing this classroom culture is celebrating and learning from mistakes. Use errors as learning moments, as often a lot more can be understood from analyzing a mistake than a correctly worked problem.
Everyone Can Learn Math to High Levels
Old wiring: Some people are just “not math people.”
New wiring: Everyone can learn math to high levels.
There is no science behind the idea that some people are “math people” and some people are not. Yet, this was (and is) a commonly shared belief by many in our society. As teachers, we must actively work to dismiss this falsity by sharing that all students can learn math to high levels with our class.
We must also work to educate other adults as so often we hear comments from parents such as, “Oh I was never a math person, I always let his father help with the math homework,” or “My child has more of an artistic/writer mind; not a math and numbers brain.” We must rewire our own brain and those around us to dispel this myth and help all people believe that everyone can learn and be good at math.
Conclusion
Many teachers I talk to say that they went into math instruction because they like to explain math to students that are struggling and offer them help. It is a big shift to realize that explaining something may be doing a disservice to the student because you are not allowing the student to flex their problem solving skills. This is why as math teachers, we must rewire our brain and reframe what “help” and “support” really look like.
My ideal math classroom now has students doing a lot of thinking and discussing (and me as the teacher talking minimally). Students will be making mistakes and having opportunities to persevere. Students will be solving problems with multiple strategies and comparing and connecting across them. Students won’t be working to find the answer or finish the page, but rather deeply understand the concept. All students will feel like they are mathematicians and can be successful in math.