Why learn calculus?

A young friend asked, why bother learning calculus, other than to get into college?

The answer is that calculus holds the keys to the secrets of the universe. If you don’t at least have an intuition for calculus, you’ll have a harder time building things that work (be they machines or organizations), and you’ll be prey to all kinds of crank theories. Of course, there are lots of other ways to go wrong in life too. Be grumpy. Don’t brush your teeth. Hang out in casinos. Wear white shoes after Labor Day. So, all is not lost if you don’t learn calculus. However, the world is less mystifying if you do.

The amazing thing is, calculus works. A couple of years ago, I found my kids busily engaged in a challenge, using a sheet of tinfoil of some fixed size to make a boat that would float as many marbles as possible. They’d managed to get 20 or 30 afloat so far. I surreptitiously went off and wrote down the equation for the volume of a rectangular prism, subject to the constraint that its area not exceed the size of the foil, and used calculus to maximize. They were flabbergasted when I managed to float over a hundred marbles on my first try.

The secrets of the universe come in two flavors. Mathematically, those are integration and differentiation, which are inverses of one another.

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Statistics >> Calculus ?

Another TED talk argues for replacing calculus with statistics at the pinnacle of mathematics education.

There’s an interesting discussion at Wild About Math!.

I’m a bit wary of the idea. First, I don’t think there needs to be a pinnacle – math can be a Bactrian camel. Second, some of the concepts are commingled anyway (limits and convergence, for example), so it hardly makes sense to treat them as competitors. Third, both are hugely important to good decision making (which is ultimately what we want out of education). Fourth, the world is a dynamic, stochastic system, so you need to understand a little of each.

Where the real opportunity lies, I think, is in motivating the teaching of both experientially. Start calculus with stocks and flows and physical systems, and start statistics with games of chance and estimation. Use both to help people learn how to make better inferences about a complex world. Then do the math as it gets interesting and necessary. Whether you come at the problem from the angle of dynamics or uncertainty first hardly matters.