# Bugmaster comments on Rationality Games & Apps Brainstorming - Less Wrong Discussion

27 09 July 2012 03:04AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Sort By: Best

Comment author: 11 July 2012 08:37:56AM *  3 points [-]

Just because something doesn't teach everything about a subject doesn't make it a poor instructional aid. Algebra is more than rote memorization, but having the rules memorized does help a lot in getting to the stage where you truly understand it. Even if you do understand it and could in principle recreate the rules from scratch, recalling them from memory is faster than deriving them each time you need them - and since algebra is pretty much the foundation of all advanced math, you'll be needing them a lot if you want to study math at all. (Though if you end up struggling with the harder topics because you didn't have the rules of algebra appropriately memorized, you might never want to study more of it...)

Comment author: 11 July 2012 08:52:42PM -2 points [-]

Algebra is more than rote memorization, but having the rules memorized does help a lot in getting to the stage where you truly understand it.

I disagree. I think that memorizing the rules first, without understanding where they come from, discourages the student from attempting to understand anything to begin with. After all, his goal is to balance an equation, and look, he just balanced it... so what else is there to know ? Thus, the memorization approach creates the impression that math (or whatever subject you're studying) is all about arbitrary rules that make no sense; it's all about "guessing the teacher's password", and that's boring.

Contrast this with the approach of treating an equation like a puzzle. If "2x - 3 = 5", and we want to know what x is, there are many ways to approach the solution. We could ask, "someone did a bunch of stuff to x to get 5, how can we undo it ?", or we could say, "the equation is like a pair of scales that are balanced, so what can we do to get x by itself without unbalancing the scales ?", etc. Some possible partial answers are, "someone took away 3, so let's add it back", or "if we add 3 to both sides, the scales will still be balanced but we'll be one step closer to a solution". But "add 3 to both sides because that's how the game is programmed and you won't get the high score otherwise" isn't much of an answer. High scores don't mean anything, algebra does.

Comment author: 11 July 2012 09:52:37PM 5 points [-]

Well, I can't speak for others, but my personal experience with math tends to be that I only start properly learning why something works once I have the rules pretty well memorized. Before that, my working memory is so occupied with trying to just remember how to apply the rules that I don't have the space to remember why they work. Or alternatively, I can learn why the rules work - but in that case I don't have the memory capacity left for remembering how to apply them.

Of course, this is complicated by the fact that during the process of trying to memorize the rules, I often stop to think about why they work in an attempt to rederive them and make sure I'm not misremembering them. So it's not pure rote memorization, like the way it seems to be with DragonBox. But I would still expect that if somebody first learned them as meaningless rules in the game, and was then later taught math and the reasons for the rules, they'd have a good chance of being delighted at discovering where the rules came from, and could spend all of their cognitive capacity on developing an actual understanding.

Comment author: 11 July 2012 10:54:50PM 1 point [-]

Fair enough; it's possible that you and I simply think in different ways. I personally find it very difficult to memorize (seemingly) arbitrary rules, and I found it very difficult to un-teach the "guess the teacher's password" mentality to people. But it's quite likely that I'm making an unjustified generalization from a very small number of examples.

I wonder if there's any layman-accessible literature on this topic...