Remix.run Logo
IanCal 4 days ago

There's a load of things I think are things many kids could do much earlier in maths, though my personal feeling may be off. My son seems to be taking very quickly to the feeling of maths so I'm trying to share some parts that I only realised drastically later on.

Rules you learn in maths are often based on much simpler, truer (I'll get back to this), things. I learned loads of "move this denominator up to this side, like an escalator!" and such and only when I was something like 13 I nearly shouted "EQUALS MEANS THE TWO SIDES ARE THE SAME THING" as I realised why so many of these god damn rules existed. It also explained suddenly why some things are OK to do and some aren't (notably taking roots).

The other key thing was finding out that these things are decisions. We can choose whatever rules we want and see what happens, and keep whatever is useful. Lots of the more interesting things I've seen later in life have been "well there's no number you can square and get a negative number. What if there was?" or "What if there was a way to raise to a real number, what would that mean?". There's no magical reason we can't divide by 0 but there's not a neat useful answer really, but you can totally define a setup where you can do that and have fun if you want.

Imaginary numbers and Argand diagrams are things my 6 year old can mess about with. He's still developing reasoning so certain things trip him up about seeing the process for solving a thing (fascinating to see where his comprehension is up to and the leaps that happen, I remember the first time seeing him pick up a chess piece, go to move it and before putting it anywhere say "no, if I do that you'll do X") but lots of things are very accessible. Powers are fun because you can make big things quickly, factorials too. Basic solving of equations I was only taught in secondary school yet I was taught "two bananas cost 30p and one banana and one apple costs 40p, how much is one apple" years before and that's just swapping fruit for letters.

I was always good at maths, but I think it's far more fun now I've understood more about what you can mess about with and how simple parts are at times.