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 bullshit. 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.

A few weeks ago I learned that one of my students had several thousand unread emails in his inbox. There shouldn't be anything surprising about this. He's twelve years old and living in an era when everything that could go online, did. And he has, to put it mildly, a bit of trouble staying organized.

He's not alone. I began asking my other students what their inboxes looked like. I found an interesting trend: there were a handful of students with only a couple unread emails, and then there were many others with hundreds or thousands. I almost wrote this off as statistical noise, but the trend in inboxes tracked quite clearly with another trend I've noticed over the past year and a half: when it comes to online learning, there are students who can hack it (with few unread emails), and others who cannot (with thousands of unread emails). I'm becoming increasingly convinced that being able to hack it online probably has much more to do with managing email than it does with managing math.

When our schools moved to online instruction last year we took advantage of the tools that were available to us. Chief among them were email and video chat software like Google Meet. But implicit in that adoption was the idea that our students had the skills and self-control to manage tools that were actually built for adults, many of whom have a hard enough time managing them as it is.

It would be easy enough to put this on the students, to say that they need to develop their organization skills, that they need to practice more self control. And to a degree, that may be true. But we are the adults. It's up to us to design an educational experience in which our students can be successful. That means helping them preserve their limited resources of organization and willpower.

This is the most useful advice I've ever heard¹ about teaching math:

Do the math to teach the math.

The idea is that you'll teach the material better if you work through it yourself beforehand. But with tests to grade and emails to respond to, it can feel easy to skip. This is especially true since the product of your effort, at least at the planning stage, is intangible.

I can now thank COVID-19 for making this something that I never skip. Since my students cannot always attend my live classes, I record videos of the most important parts of my lessons before teaching them live.² These videos only take me 5 to 10 minutes to make, depending on the material.³