The Dragon Every Math Teacher Has to Slay Eventually
One reason why students feel so much worse about math class than all others, and what one teacher did about it.
I want to understand why students feel so much worse about math class than other classes, why the residue of negative experiences in math class seem stickier than all others.
One hypothesis: in math class more than any other, students develop the idea that for every question they’re asked, there is one and exactly one correct answer. Moreover, they develop the idea that every step between the question and the answer is either correct or incorrect. Moreover, that there are lots of those steps, and all of them need to be memorized. They are irretrievable if forgotten.
This perception was summarized evocatively in Jo Boaler’s book “What’s Math Got to Do With It?” when an award-winning math student named Rebecca declared herself not a “math person” because “I can’t remember things well and there is so much to remember” (p 155).
Deconstructing those ideas about mathematics, helping students understand math as a creative discipline that needs human subjectivity, a discipline with as many correct applications as there are people in the world, takes intentional change to systems of curriculum, pedagogy, and belief.
Last week, I watched a teacher perform all three of those changes simultaneously. In this video clip, Jalah Bryant of Vancouver, WA, facilitates an activity called Equation Roundtable.
Bryant’s students perform one step of a solution to an equation and then pass their sheet to another student. That student will then have to understand the first student’s step and then perform the next step—essentially walking farther on a path initiated by someone else rather than thinking exclusively about their own.
When all of those different paths converge on the same destination, students will understand a little bit better that math accommodates and even needs human subjectivity just as much as the subjects in school that students like a lot more.
Question
Are there any particular routines or activities you use to help students deconstruct the idea that there is only one correct way to do math?
I worked with young children, mainly pr-k-5. When anything was being explored in math the question was always "How did You do it?" All the different ways were collected on the board for all the children to see. Young children like to see their work up on the board so they worked hard to think of a new or different way. Each volunteer explained how they thought about the work. Some methods were often more efficient and some more interesting. Children were then asked to choose someone else's method to use to solve the problem. At the end of the lesson kids were asked if they found a new way of working that they liked better than their own. Some did, some didn't.
Ah, this! Breaking the notion that there's only one way to do mathematics correctly takes intentionality, and this sort of "Write Around" activity is also one I love! (more here: https://www.mathycathy.com/blog/2012/11/revamping-a-writing-strategy-for-math/) Several others I like that promote discourse and not necessarily a direct route to the "right answer" are Stand & Talks (thank you Sara VanDerWerf... more here https://www.mathycathy.com/blog/2019/03/using-apple-classroom-for-stand-talks/ and here https://www.mathycathy.com/blog/2019/05/lead-learn-with-stand-talks-across-content-areas/) and "Find 'n Fix", which can be as simple as creating a template with 4 blocks, and a problem worked from start to finish in each block. Students are asked to "grade" the paper together, providing constructive feedback to the imaginary student for any errors... the fun part is, not EVERY worked problem contains errors! Again, promoting discourse regularly that considers multiple methods helps coach students away from the "one way" they may think they "MUST" do math. Finally, during lessons, I try to throw in exaggerated examples that make a silly, emotional impact. "Could I add 1,000,017 to both sides of this equation as my next step? Could I subtract 19.458 from both sides?" Guiding students to understand that these are "legal" algebraic moves that may not be HELPFUL, but they're also not WRONG, can encourage students who may later solve a problem less efficiently than a peer, but both got there... one just took the highway, and the other, the scenic route!