Passionately Promoting A More Perfect World

The Failure of Perfect Education

Today I realised that math education is an even worse/harder problem than I’d first anticipated.

So, for background, my brother is in the local equivalent of 8th grade. He’s brilliant and came first in the country for the pre-high school standardised tests. He now goes to one of the quartet of The Best Schools* in my country. His teacher was a friend of mine in college who majored in math and is quite good at explaining things. Basically, everything possible is in my brother’s favour.

My brother was home today, so my mother asked me to teach him some math, so that he can n̴̠̈͘é̸̲v̷̢̛̻̓e̵̪̔͗r̷̪̽͜͠ ̵͚̀͝e̶̪̻͒̕s̷̞͇͒̕č̶͓̚a̸͉̬͑̌p̸͉͈͂ẹ̷̇ education. To see where he was, in order to teach him from there, I decided to gradually give him progressively harder problems, starting with what I thought would be the absolute most basic thing possible.

I gave him 60 + x = 2x + 4x

He looked startled and asked how to do that. I asked if he knew how transposition worked. He said yes, but that he didn’t see what he could do there. I said to transpose the lone x…

…And he told me that you can only move terms from the right side of the equal sign to the left side.

I am told my “what the serious fuck” face was priceless but, alas, there was no one on sight to record it for posterity.

Anyway, after talking it through a little, it came to light that he had simply never realised transposition was symmetric. He had thought that “transposition” was basically a magic spell you cast to move a number from one place to another.

He didn’t know why this worked. He’d never seen someone transpose from left to right before, because all his example problems so far had been in the same format. He didn’t know why the sign of the number changed. He didn’t know what it meant for an equation to “balance”.

So I showed him the behind the scenes of transposition. I showed him that the actual process happening was:
60 + x = 2x + 4x
60 + x = 6x
60 + x [-x] = 6x [-x]
60 = 6x - x
60 = 5x
12 = x

That bold step? He didn’t know that was a thing. He didn’t realise subtraction was happening at all and just conceptualised transposition as picking something up from the right side and plopping it down on the left side. After I explained the “balance” of equations to him (including wtf “=“ meant), he had a look as if a dozen gears had clicked into place all at once. He was Enlightened.

Now, I’ve tutored kids before, so I knew all sorts of weird ideas could pop up. However, they’d never been the best students in their class, and they’d had lousy teachers, and they went to poor schools, etc. So it always made sense to me that they’d have wound up with misconceptions.

Today I learned that, even if you have the literal best student being taught by someone who fully understands what they’re teaching while in the one of the best schools -
- That, even then, sometimes learning just straight-up doesn’t happen. That, sometimes, that perfect student doesn’t know wtf an equals sign really means.

I don’t know what happened to lead here, to be honest. It wasn’t too much for him to understand - he completely got it under two minutes. He isn’t being taught by someone who can’t explain things, because his teacher did an excellent job of explaining physics stuff to me when we were both in college. His peers are some of the brightest kids in the country, because our school system rations students to schools by test score.

Maybe the classroom environment is just bad for learning? Maybe it’s too noisy for focus? Maybe the teacher can’t go into enough depth for everyone to fully get it? Maybe the students don’t ask enough questions when they’re missing something? Maybe no one quite realises that they don’t know something when it’s not being worked through one-on-one?

I don’t know! Learning is failing to occur under the best possible schooling conditions and I don’t know why! What I do know is that that is terrifying.

* They’re a quartet because they’re every intersection of [Catholic | Anglican]*[for boys | for girls] My brother goes to the Catholic boys’ school, my father went to the Anglican boys’ school, etc.

(The other place I’ve expressed concern about our schools)