Finish this sentence: Math class is about . . .

The New York Times recently ran an article about a professor at Carnegie Mellon University who stumbled upon an “amazing trick,” known to mathematicians in ancient Babylon, that improves upon the way we all learned to solve quadratic equations in algebra class (Chang & Corum, 2020). It’s a clever approach to factoring binomials that doesn’t require students to memorize and use the quadratic formula.

To me, though, what’s most interesting isn’t the trick itself so much as the way the professor, Po-Shen Loh, went about the process of figuring it out. Loh didn’t begin by analyzing the quadratic formula and looking for shortcuts. Rather, he began by asking himself what quadratic equations represent in the real world. What kind of problem do they allow us to solve, he wondered, and could there be another way to tackle that problem? That is, he gave himself a concrete challenge to overcome: Can I find a new and perhaps easier path to the solution than the formula we’ve all been taught in school?

Compare that to what I heard when I asked a handful of middle school students to finish the sentence, Math class is about . . .  “Math class,” said one, is about “getting the right answer.” It’s about “following the steps” and “learning stuff I will never use” and “doing what the teacher says,” others added. “It’s not like classes where we learn stuff we can use for other things,” another explained.