I never liked baseball as a kid. Maybe it’s because I wasn’t any good at it. Maybe it’s cause I never went to a professional game. Maybe it’s because it is quite boring when you watch it on TV. Then in the late 90’s the sabermetric revolution upended the stuck-in-the-50’s baseball establishment by using data to prove and disprove various myths that were pervasive in the game. From roster construction to in-game tactics, the sabermetric community was one or two steps ahead of the rest of the game. It was this data-driven analysis that served as my entry point into the game. Eventually the data-movement coalesced under the Baseball Prospectus name. Housed at baseballprospectus.com, the writers produce an annual that is my notice that Spring has arrived.
The annual contains copious amounts of raw numbers, advanced metrics, data tables, projections, as well as an approachable and easy-to-digest writing style that I blast through every March. This year was no different. This is one of my favorite books to read every year.
Here we have another book grounded in mathematics: Paul Lockhart’s Measurement. Here we have a rich text of mathematical creativity and imagination. In fact, pretty much everything in the book is developed in the author and reader’s imagination.
The problems posed (some of which even have Lockhart’s proof to accompany them), are decidedly abstract in nature. The problems rely on ingenuity for a solution. Lockhart is more likely to use mental shape-folding than a two-column proof to describe a mathematical concept, let alone a spreadsheet of data. This is one of my favorite books.
Both of these books (in Baseball Prospectus’ case, the annual publication) are quite dear to me. They also represent two entry paths through mathematics. One uses messy numbers and data to explain why things are the way they are. The other uses clean, imaginary shapes to explain why things are the way they are in our imagination. They both feature clever, humorous, conversational writing including analogies and storytelling.
Inherit the Wind
Then there is the final scene of Inherit the Wind. After psuedo-successfully defending a high school teacher who dared to teach evolution in the classroom, the protagonist of the true-story, defense attorney Henry Drummond picks up the Bible in one hand, Darwin’s The Descent of Man in the other, and exits the courtroom. Both of these books reveal things about the nature of man, and you’d be a fool to entirely discard either.
There are context-rich ways of posing mathematical tasks. There are entirely abstract ways of posing mathematical tasks. There are interesting and engaging ways of posing problems. There are dry and uninteresting ways of posing math problems.
I hated math in high school. All the way up until my integrated Physics/Calculus class threw an old computer off the football stadium and recorded it on video and we were able to successfully approximate the gravitational constant. I’m not sure if I had been presented abstract math in more interesting ways I’d have latched on to it. I was a pretty detached kid. It’s possible, but I was also more prone to think about mid-90’s Indians baseball and Carlos Baerga’s VORP. That would have been a way for me to engage with mathematics in High School. In fact, I did engage in it when Rob Neyer would publish a new column. But that was me.
I’m not saying that every task needs to be grounded in the real world. But the number of contextual mathematical tasks that should be provided any given year is certainly greater than zero. It’s probably greater than 10. Maybe the tasks need not even be that authentic. I mean, is throwing a computer off a building a “real-world” situation? Or was it just a fun thing to do that we then did a bunch of math on? It was “real-world” in the sense that we saw it happen. We interacted with it physically, visually, inter-personally and mentally. I have not, to this day, had a professional reason to toss a computer off a stadium.
Mathematics is so wonderful and ubiquitous that anyone can have some sort of entry point into the subject. It’s too vast to be constrained to a single context or a single person’s imagination. Our access points to the subject change from person to person, from age to age. You’d be foolish to eschew context-dependent scenarios to explore mathematics. You’d be foolish to toss aside all imagination from the content. You’d be foolish not to explore any and all avenues of all ways to provide access to this remarkable subject to your diverse students. You’d be inheriting the wind.