If I had an extra minute, I’d also talk about how we shouldn’t only show the mathematics that’s useful — and statistics is useful for being an educated consumer and citizen. We could replace a lot of the drudgerous mathematics that’s being taught with math that’s purely fun, with no real promise of “you’re going to use this,” but just “this is beautiful stuff.”
You can go ape over patterns in Pascal’s triangle, in the Fibonacci numbers, in chaos, in fractals. These things that are just positively inspirational. We don’t make — I mean, I’m listening to this music. It’s inspirational. But I didn’t have to be drilled with how to draw my notes properly and learn all this music theory before I got exposed to that kind of music. I think the same sort of thing could happen in mathematics.
Why not give them a taste of beautiful mathematics in addition to the useful stuff?
He’s right, of course. But what’s most interesting is the interplay among the three different ideas of usefulness, fun, and beauty. Too often we end up with none of the above. Benjamin advocates more statistics and less calculus (and preparation for calculus). That path certainly wins on the usefulness score, though many would question it on grounds of fun and beauty. He cites wonderful examples for those, and we do find that a great many students enjoy studying chaos and fractals, finding both fun and beauty in them. Pascal’s Triangle and Fibonacci numbers are in our curriculum, but we could do more with them, especially if we want students to see their beauty and enjoy studying them.