Graduation!

Congrats to everyone who’s graduating this week! A couple of my students worked really hard and got where they needed to go, and getting to contribute to that in even a tiny way really makes me smile.

Our relationship math changes is many ways when we graduate high school. For those of us tending toward add’l math study — math, sciences, engineering — we come to find that while we’re reasonably well-prepped in terms of the core mathematical ideas that we’ll need, we are far less-prepared for the manner in which we’ll approach them. As a math major, I was surprised and (eventually) thrilled to find that the entire major wasn’t about getting ‘an answer’ but rather reasoning through and proving out conclusions from base principles. To that point, the only place I’d seen proof as a notion was for a short period in geometry, and the fact that it’s most of what mathematicians actually do never really came up.

Most of us, though, bid good riddance to math after we graduate, and do as little structured study of math as possible after that. I don’t count this as a strike against learners; in fact, it’s why I’m here: most HS math instruction does a bad job helping people understand why they’d care about any of it — when’s the last time you had to numerically figure out when two trains were going to meet, or understand sand falling on a conical pile?

This is obviously a shame, and it’s also a feature: people who do know math well suffered through this, and now keeping it boring serves two emotional needs. First, it serves the ridiculous notion that ‘I suffered through it, you should too.’ This is dumb, but human. And second, it serves as a gate-keeping measure: if it’s difficult for you to get good at what I’m good at, then my skills are more in-demand, and my position more-secure.

Like I said, I get it. But I wish it were different, and I hope that some of the people I’ve taught have been able to find a path to engaging with math beyond high school that is both useful and gratifying.

Probability Primavera

I can’t believe that’s the title I’m going with, but it’s got alliteration, and it’s an accurate description of what I’m thinking on, so, here we are.

Spring is a great time to get in touch with how terribly-evolved we are as far as relating our own experience of variability to an accurate picture of reality. A few days of high or low temps, whatever that means, a very short memory about what last year was like, maybe a few snowflakes, a sptting-rain / 36 degree combo and we start saying things like, “WHAT THE HECK IS THIS I THOUGHT IT WAS SPRING??!?!”, or “OH THANK GOODNESS WINTER IS OVER AND IT WILL ONLY BE NICE FROM NOW ON!” I mean, maybe. My money’s on your simian brain having a limited ability to generalize from your own experience to larger weather trends, but that’s just me: proud and cognizant of my monkey heritage.

When I worked in retail analytics, one of the topics that I always wanted to dig into but never got up the energy for was a model of single-day events on perceptions of weather during Spring and Fall. What everyone’s going to tell you is, “When it’s warm, people shop for swimsuits,” and while that’s obviously true to some extent, what I was really interested in was “By observing shopping behavior, can I determine how people decide that ‘It’s warm’?” Because I think it’s possible that one 65 degree day in March might do the trick, as opposed to climbing slowly through the 50’s in April.

Point is, I got the SuperCub out of the basement today, so it is fully spring.

M.U.L.E.

Everything I know about economics, I learned when I was 10 from a video game called M.U.L.E.

M.U.L.E. is about mining on an alien planet, and there’s a phase where your plots of land generate goods, after which there’s an auction phase:

Sellers are at the top, buyers at the bottom. Here, brown is selling and blue is bidding by walking up the screen toward them (green and red aren’t interested). Their current bid of 75 is represented by a dotted line that moves with them.

When brown likes the price that blue is offering, they walk down the screen. This will create a dotted line for their offer price, and if his sell line meets blue’s buy line, there’s a transation. Simple! But as soon as you introduce two buyers or sellers, well, let’s just say no one in the computer lab at Bloomfield Middle School had any idea what they were unleashing.

Green and purple are both selling, but purple hesitates, because they want a higher price — and as a result, green makes the sale. Blue, buying, also hesitates — and if green runs out of stock, they’re in trouble because they’re going to have to pay purple’s higher price.

Two keyboard keys, four humans, one Apple IIe — all resulting in a shared, visceral experience with supply and demand, and how complex interactions around value and transactions happen.

M.U.L.E. is my north star of trying to help people understand math: if I can make a topic this concrete, you will learn it, you will never forget it, and you will feel a new organizing idea all around you. Your entire world will simply make more sense.

Real learning is moving from “When am I going to use this?”, to, “How did I not see this before?”