Yesterday a student of mine raised her hand and said, “I don’t really have a question. I just wanted to say that I’m not 100 percent on this yet.” Then she paused for a moment and continued, “Is that okay?”
I was introducing linear relationships,1 one of the foundational ideas of algebraic reasoning, and yes, it was okay. But it was so much more than okay. In fact, it was one of the most beautiful collections of words I’ve heard uttered in a mathematics classroom. It was all there: the going out on a limb, the admission of being a mere mathematical mortal, the final yet, showing confidence that someday she would be “100 percent.”
It was as if I’d paid her to help me teach a lesson about growth mindset and the power of mistakes and failure.
My gut reaction was to say: “What do you think we’re doing here? Do you think that everyone else in class is “100 percent” on linear relationships? That they thought to themselves, ‘I can’t wait to go to school today so that I can show off all the stuff I already know.’? What is the point of school if not to move from not knowing to knowing? And how can we make that transition without not knowing in the first place?”
But I didn’t say this, because I remembered that for many students (myself included), this is exactly what school feels like, especially math class. It feels like everyone else already knows all the material and you’re the only one who doesn’t. And while there’s certainly a dopamine boost when we volunteer an idea or answer that turns out to be correct, that’s not the point of education.
So I tried to show some compassion. I told her that while I have a pretty good handle on the material we were covering that day, it would be fantasy to believe that I knew everything about it. And if I can feel okay about not knowing everything, then she should feel okay about it, too. More than okay, in fact. She should feel great about it. Because given the choice between learning and knowing, I’ll choose learning every single day of the week.
A linear relationship between two variables means that doubling (or halving, or tripling, or whatever) one will result in a doubling (or halving, or tripling, or whatever) of the other. Take y = 3x and let x = 1, then y = 3. If we double x to be equal to 2, then y = 6. Doubling x (from 1 to 2) resulted in a doubling of y (from 3 to 6). When you graph linear relationships, they form a straight line. ↩