# How I Teach Calculus: A Comedy (I Dreamed a Dream)

Can I come up with something so compelling that my students are powerless against its curiousness?

Like some sort of pedagogical epistemologist, can I distill down the essence of inquiry to a single statement?

Can I teach calculus by saying one thing, on the very first day, that forces my students to derive the rest with only mild shepherding?

Here are my candidates:

- How many humans have there been, total?
- How do ants work?

I read a lot about how to teach math. I worry a lot about how the narrative will go. I make sure each lesson is connected, and that students have the chance to come up with at least the impetus for new skills before I lay down the soul-crushing blow dealt by dry-erase-marker-cum-Thor’s-hammer that is “Notes: Chapter 2.3 – The Product Rule.”

Can a course be motivated by one, beautiful question? Will it grow and send chutes into the unploughed earth rendering it mathematically fruitful?

A teacher can dream, right?

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12 thoughts on “How I Teach Calculus: A Comedy (I Dreamed a Dream)”
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Why no love for the purely mathematical questions? Why not something like, “How should we describe the slope of a parabola?”

This is my dream too, so let me know when you’ve got it all figured out!

Gut reaction on the ?’s is same as Alemi’s. Not sure kids would be all that curious about either, actually. Probably more curious about the ants one is my guess.

If you haven’t read Understanding Analysis by Stephen Abbott, see if you can find a copy. The book won’t answer your request-for-a-single-question directly, but might give some inspiration.

Each of the (few) chapters has one of the best motivating questions I’ve seen in a math book. The motivation is a lot more mathematical than the kind of question you’re probably seeking, but it’s a similar idea: as his book’s website says, “the hard work of a rigorous study is justified by the fact that these questions are inaccessible without it.”

Or on the publisher’s website:

“The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.”

PS — thank you so much for the t-shirt!

Just a gut reaction, but I don’t like the first. Too closed. I don’t know why you need calculus to answer it either.

As for the second, I hate to say it, but maybe it’s too open. There are a lot of directions it could go that are not calculus. When you said that, you have in mind a whole line of reasoning that I don’t think is particularly natural.

But the second is much better than the first.

Why not embrace where calculus came from. Newton made the whole thing up in response to a single question, namely how does the world work, or more specifically I suppose, how come the heavens? or how come the world? I suppose modern students don’t really care about the stars or planet, so that approach has that going against it.

Maybe open up with Zeno’s paradoxes, all of which are only paradoxes to a pre-calculus mind. I think if one were attempting to win an argument against a stubborn Zeno-ist, sooner or later you’d be forced to think up calculus. Calculus is all about the in-betweens.

Before you do it with calculus, should you be able to do it with algebra?

@Cox: I think so?

I think this is all your need

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