There was an essay that came out last year (which I won’t mention directly) about how the modern school system is entirely wrong in it’s current form and should drop basically everything that it is now and start again. I was, when I read it, furious at it’s apparent blasphemy but since then internalizing and digesting it and have come full circle though perhaps not to quite the same extent as it’s brash denouncements. There are still these kinds of people who are, frankly, crazy but there are also studies like these that provide at least interesting alternatives.
The design of math
Today I went to the bank to deposit a paycheque and witnessed an event that stuck me as odd. Now, I’m somewhat unusual in how early I’ve achieved what I have but please take this anecdote as example of the public, not of me personally being a braggart. He was a well dressed kid and I noticed him initially because he actually seemed very similar to me, standing in line a few people up. Because of the way the queue snakes around I happened to be standing next to him facing the other direction but couldn’t help but overhear who I assumed was his mother standing beside him outside of the line: “You’re 18 now, you’re going to have to do this on your own” – he seemed nervous. He had his wallet, a cheque and his bank card at the ready, a sign of non-practice and underconfidence. As the line moved we shifted and I ended up farther away, effectively ending this story.
What hits me, here, is that I’ve been there. I’ve been that guy who nervously prepares all essential items before the kind lady motions ‘next, please’ and you prepare your speech as to what you want done. In fact (and I’ve done this out of experimentation) you can actually get through the entire process of depositing a cheque without talking at all. The nervousness is entirely internal. But I was that guy when I was ~13. I’m 19 now and have been living on my own for over two years in the big city to go to school. It strikes me as odd that he seemingly hadn’t done this before. “Where was he when they taught that in schools?” I thought “Oh. Wait. They don’t, do they? I learnt that from my parents too, just earlier”
So it occurs to me, as much as I disagree with anti-intellectualism, why are we teaching kids how to factor variables and not how to budget? This statement is a nervous one for me because it looks like a slippery slope. I really like math. Honestly, it’s a love language. It’s beautiful and flowing and works and can be used to do all sorts of things that English can’t. I wouldn’t be far to say “Well, we don’t factor variables anymore, maybe we should just drop variables altogether” which is alarming. Algebra, as much as people hate it, is actually one of the most useful things ever. A fictional subtraction statement: I make $20 a week and spend $15 on living expenses – how much do I have left? Third graders could figure that out. But let’s rewrite it: I make $20 a week and want to keep $5 for free money after living expenses – what’s the maximum I can spend on living? The interesting thing is it’s the exact same but uses a variable. For some reason we take until grade 8 to get the “you can move it across the equals sign and just solve normally” thing. We can make it more complicated. Maybe ‘living expenses’ is actually five different things adding up. Suddenly we’ve got brackets for organization. BEDMAS. We can learn to balance expenses and incomes. Real world things. We can see how banks work and instead of doing boom-bust cycle global economics, we can focus on the economics of how the root levels actually work. What’s interest? How do banks make money? It’s amazing how many people don’t know these things.
Conclusion: I’m not sure it’s about more or less math as much as reworking math and taking it from a beautiful abstraction (which, let’s face it, is only beautiful to a handful of us) and making it into a comfortable, practical thing.
The psychology of math
People brag about being bad at math. This blows my mind. There’s an XKCD for everything, and it doesn’t disappoint:
I’m terrible at playing guitar. It’s hard and doesn’t come naturally to me. Fortunately, I also don’t need it to live a functional life. It’s certainly not a bragging point to bring up.
There was, when I was in school, a sort of popularity complex in response to that fact. If you were good at math you must have been a nerd and therefore uncool, so it sort of was in your best interest to be bad at math. This is a shame.
Like science (which will be addressed in another part), the goal here is to foster genuine interest. The famous Antoine de Saint-Exupery quote:
If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.
It’s really not about rote memorization of multiplication tables. It’s really not about the discipline of not using calculators (this comes back to why that link in the first paragraph is insane) because we have computers now to do the heavy lifting. Wolfram Alpha is a gorgeous machine. Anyone can begrudgingly do 100 problems out of a textbook. The joy, the usefulness of math is seeing what you want to accomplish and then making up a method for getting there. It’s about problem solving by using a language that English can’t help you with, about distilling things down into known and unknown values and then massaging them until they spit out what you’d like. Teach them to long for the endless immensity of math itself.
Look! More awesome posts: