“Don’t just do something, stand there.”
That’s a line Dr. Bill McCallum, one of the writers of the Common Core State Standards, used in his presentation at the California Algebra Forum in San Jose, CA, which I attended last week. The focus of the Forum was California’s adoption and impending implementation of the Common Core State Standards for math.
Dr. McCallum used this memorable line—which suggests that students stop, think about, and fully understand a math problem before tackling it—while discussing the Standards for Mathematical Practice. As he described how he frequently uses this line in his teaching, I thought about how it might have worked in my classroom.
During my five years as a math teacher, I often asked students to come up to the board and solve a problem. Generally, my students’ immediate inclination was to try to manipulate the equation (combine like terms, factor …) before they understood what they had in front of them. If their initial manipulation did not work, they started over with another tool from their toolbox. They would continue trying different tools on the equation until they found a recognizable configuration that they could turn the crank and arrive at a solution.
There is no doubt that this approach both bolstered my students’ abilities to persist when they lacked clarity and increased their proficiencies with various math skills.
Unfortunately, because the students had not taken the time to fully embrace the initial question before trying to turn it into something that they recognized, their conceptual understanding of the initial mathematics was not complete. Therefore, they were less likely to understand WHY what they did worked, and they could not use the logic they’d applied to solve future problems.
I wish I’d used Dr. McCallum’s line and asked my students to explain the math problem and their ensuing approach prior to digging in. Mathematical Practice Standard #1 begs us to do exactly that:
“Make sense of problems and persevere in solving them.”
So, next time one of your students comes up to the board, try telling them, “Don’t just do something, stand there.” Just that little bit of noodling could lead to greater understanding of the material. I would love to hear how this works for you!