doing a lot of killer sudoku has given me a knack for partitioning numbers into smaller ones that sum to them. maybe if we made puzzle games that required you to learn math concepts to play them at a high level, early math education would suck less. replace times tables with something fun that, as a side effect, makes you learn times tables over the course of doing it a lot
puzzle game with shapes that have rules about how they relate to each other and how to move them around, and the goal is to get one of them by itself on one side of the puzzle, and aha - we tricked you - you've been doing basic algebra this whole time
@octopus @typhlosion I never understood why order of operations isn't just the order they're in
@MPurpureus order of operations *is* pure convention; this way just happens to need fewer parentheses most of the time
ax² + bx + c vs. a * (x²) + (b * x) + c
but sometimes you see
(+ (* a (^ x 2)) (+ (* b x) c))
as well
@MPurpureus having them go strictly in order messes with commutativity laws
going strictly in order
2 + 3 × 5 = 60
3 + 2 × 5 = 60
2 + 5 × 3 = 21
2 × 3 + 5 = 11
3 × 2 + 5 = 11
2 × 5 + 3 = 13
if we "clump" multiplication harder than addition, though
2 + 3×5 = 17
3×5 + 2 = 17 (we can swap clumps across a +)
2 + 5×3 = 17 (we can swap numbers across ×)
2×3 + 5 = 11
5 + 2×3 = 11
3×2 + 5 = 11
ack that should be = 25 for the first two, not 60
@typhlosion I want this to exist and also I don't?
I'm bumping into students who are annoyed that their teacher told them x•x=x² ("there are two x's, so put a little ² over the x") but for some reason when they do the same thing and write x+x=x² their teacher takes off a bunch of points??
so there has to be some grounding the operations in a physical reality (or axioms) less arbitrary than "bishops/multiplication move diagonally and rooks/addition move orthogonally because that's what the rulebook says"
but there definitely seems to be something in this space that would be extremely helpful