When are we ever going to use this?
Probably never
One of my favorite student questions is: “When are we ever going to use this?”
When I first started teaching I would whip out out some tangential connection between whatever we were talking about and the “real world,” all the while knowing that it was mostly a lie. It’s true that we wouldn’t have landed on the moon without calculus. And while I have no inside knowledge of what goes on at SpaceX, my guess is that they are not spending a lot of time factoring trinomials or scratching out derivatives. That’s what computers are for.
A more honest answer to the question, I think, and the one I respond with nowadays is: “Probably never.” This has two things going for it. One, it’s honest, depending on what we’re studying.1 Two, it sets up a more important question: “Why are we learning this?”
This is a much more interesting question. Why learn how to graph a function if you’ll eventually just rely on a computer to do it for you? I’m not the first person to ask this question, and there are countless good answers. Here’s mine: I think that learning math is valuable specifically because of what it teaches us about learning and about ourselves. Put another way, I’m less attracted to math because of its procedure or beauty (wonderful though they are), but rather because it’s a vehicle for proving to myself, over and over and through sustained dedication and focus, that I am capable of learning and doing difficult things.
I know those precise words won’t resonate with my students, and so I don’t say them. Instead, I tell them that learning math is a way of showing others, but more importantly themselves, that they can.
My grade 11 and 12 students need to know how to draw Voronoi diagrams, something I only learned how to do to teach them, so I feel confident saying that this is not a skill they are likely to use (except in the context of the class, of course).