boring Saturday morning maths ramblings

Note: these posts are copied over from the ‘mathbucket’ section of my old tumblr blog and I haven’t put much effort into this, so there is likely to be context or formatting missing.

So yesterday I read about DragonBox, a game for learning algebra. I haven’t played it myself yet, just seen some videos, but it looks like you learn the rules by manipulating a bunch of pictures on a touch screen, and only later see the usual symbols and numbers.

Anyway I sent it to my sister, and it sounds like my 7-year-old nephew was happily playing it most of the evening. So that’s nice.

I read about it on Hacker News, and today there are a load of comments there probably duplicating a lot of the content of this one. I can’t be bothered to read them all right now, I’m in a writing mood more than a reading mood.

What interests me about this game is its complete focus on teaching the algorithmic component of algebra – cancelling factors, ‘throwing things over the equals sign’, multiplying both sides, whatever. Algebra as game mechanics. And that’s likely to be a good thing, as games are generally somewhat more fun than algebra classes. Learning the rules by playing around and seeing what happens is likely to be more successful than being told explicitly what the rules are, and being afraid to experiment too much in case you ‘get it wrong’.

Of course, the downside is that it’s completely divorced from a conceptual understanding of what you’re doing, and how it relates to the maths you already know. I’ve always been kind of annoyed at how late algebra is taught in schools, and how its separated so distinctly from arithmetic. I feel like a good start on the way to algebra is made right at the beginning of school, where you get those worksheets with the boxes to fill in:

1 + 3 = [ ]
2 + 4 = [ ]

and then for a bit of variety you might get

2 + [ ] = 5

later in the sheet. No big deal. Then somehow later in school the first two examples become ‘arithmetic’ and the third is some abstruse topic called ‘algebra’.

I feel like if it was introduced alongside arithmetic it might be easier to take in. E.g. when you first learn multiplication:

2 * 3 = [ ]

then why not also learn

2 * [ ] = 6 ?

It seems unfair to save all this stuff up for a few years and then intimidate you with the likes of

2 * [ ] + 3 = 7,

under the threatening new title of ‘algebra’, along with an array of confusing new algorithmic techniques for ‘solving’ an equation.

I’m not trying to criticise DragonBox. I think it’s a great idea. I guess what I’m wondering is what DragonBox’s twin looks like. The game that teaches conceptual understanding of algebra divorced from algorithmic understanding, with the same emphasis on playing around and not worrying too much about whether you’re doing the right thing. E.g. in the equation above you could just try some numbers and find that 2 works, or notice that 4 + 3 is 7 and work backwards, or anything else that helps. It would be nice to be able to use a bunch of examples like these to work towards finding a general algorithm for solving the equation, but one you’re using because it makes intuitive sense to you rather than because some teacher or some game told you to do it.

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