I never really liked Math in school. I got good grades in the math classes I took, but I’ve realized since that I was never really good at mathematics but was reasonably good at memorizing formulas and studying and following directions. Once I reached higher math classes in college I realized there was a whole world of mathematics that I just didn’t get. I fully admit to being one of those students who grumbled about how there was no way they were ever going use something like trigonometry in the real world.
I wish a book like Jordan Ellenberg’s How Not to be Wrong had been around then. (Well, to be fair, maybe there was a book like that around then. But maybe I had to wait until I in my forties and more open to having my mind changed to appreciate it.) Ellenberg covers probability and regression theory and non-Euclid geometry and basic calculus all while discussing real-life examples of how math is useful in the real world. He skips around from the MIT students who figured out how to beat the Massachusetts lottery to how a mathematician figured out how to design better planes in WWII to a discussion of the 2000 election results in Florida (remember Bush v. Gore). It’s not an easy book to read, Ellenberg doesn’t shy away from discussions of complex formulas and puzzles. But he has a very easy to read style of writing. It’s like having a really excited math professor in the room with you. Even if you don’t grasp everything he’s saying you get the idea. Math is really cool! And useful!
A few quotes:
One of the most painful parts of teaching mathematics is seeing students damaged by the cult of the genius. The genius cult tells students it’s not worth doing mathematics unless you’re the best at mathematics, because those special few are the only ones whose contributions matter. We don’t treat any other subject that way! I’ve never heard a student say, “I like Hamlet, but I don’t really belong in AP English- that kid who sits in the front row knows all the plays, and he started reading Shakespeare when he was nine!”…. p 412-413
Every time you observe that more of a good thing is not always better; or you remember that improbable things happen a lot, given enough chances….; or you make a decision based not just on the most likely futures, but on the cloud of all possible futures, with attention to which ones are likely and which ones are not; or you let go of the idea that the beliefs of groups should be subject to the same rules as beliefs of individuals; or simply, you find that cognitive sweet spot where you can let your intuition run wild on the network of tracks formal reasoning makes for it; without writing down an equation or drawing a graph, you are doing mathematics, the extension of common sense by other means. When are you going to use it? You’ve been using mathematics since you were born and you’ll probably never stop. Use it well. p 437