Encouraging Students to DO Mathematics
"Allowing students the opportunity to think creatively and bravely just by changing the medium was a small adjustment with a big impact."
“The only way to learn mathematics is to do mathematics” -Paul Halmos
When I think of going to school, I remember creating art, reading stories from history, writing papers, researching science, and replicating whatever my math teacher did. I don’t remember “doing” mathematics, I remember calculating, regurgitating procedures, and boxing my answers.
Now, I am not saying my students have discovery based lessons every day, but I do work to have my students DO mathematics every day. I try to make sure I am not doing the majority of the talking or controlling what they write, and to make sure each day, each student has the opportunity to do mathematics, rather than watch it.
Safe spaces to make mistakes
One of the first steps to having students do more mathematics in my classroom was to get them brave enough to try something unfamiliar and new. I didn’t have individual whiteboards when I started teaching, but my desks were shiny and I took a chance. Thankfully, they erased and I watched my students begin to do the process of try-fail-try again with less hesitation than they did with paper and pencil. I never went back. Allowing students the opportunity to think creatively and bravely just by changing the medium was a small adjustment with a big impact. The Wipebook Flipcharts raise the bar on vertical non permanent surfaces (vnps). When students are given a lot of space, they start to expand their writing, doodling, and thinking. They are more willing to work through ideas until they figure things out.
Shifting from duplicating procedures to generating ideas
I used Flipcharts this week to have them formalize the understanding of function notation. So often, function notation comes down to duplicating a process. “If f(x)=2x+1, find f(3).” As a check for understanding on day two, I had students work in groups at their Flipcharts to generate equations that satisfied a given constraint. For example, write an equation where f(-1)=5. Students not only had to understand the meaning of function notation, they also had to think creatively about how they were going to generate an equation that gave the desired results. Some students who were able to replicate procedures that could answer my initial questions struggled with this different perspective. By illuminating their unfinished learning, we were able to clarify incomplete understandings so students could deeply understand the concept of function notation.
After giving a constraint, I walked around the room asking questions to guide them when needed. Once groups were convinced they found an equation that satisfied the constraint, they rewrote it and erased the rest of their thinking. The whole class rotated to the next group’s equation and checked their work. Rinse and repeat.
Collaborative spaces to share thinking
My students enjoyed using the reusable Flipcharts so much, they begged for another opportunity to use them. We played a review game and with the Flipcharts, students were able to spread out their thinking, look across to their peer’s work, and work together to find the answer.
In each of these lessons, the students were working through problems, making mistakes, adjusting, and helping each other understand the mathematics. They were able to generate ideas that may or may not have been correct, but it was their thinking on a page, not mine. They were doing mathematics.
Lauren Johnson, Teacher, Sunny Hills High School
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