I have single-digit multiplications just kinda cached as ingrained associations between any two given digits and their product, but now I’m curious what algorithm you were using for them. Repeated addition maybe?
I would picture them as rectangles and count. Like, 2x3 would look like
xxx
xxx
in my head, and for small numbers I could use the size of it to feel whether I was close. I remember doing really well with ratios and fractions and stuff for that reason.
For larger numbers, like 8x8, I would often subdivide into smaller squares (like 4x4 or 2x2), and count those. Then it would be easy to subdivide the larger one and repeat-add. I would often get a sour taste if the answer just “popped” into my head and I would actively fight against it, so I think there was a part of me that really just viscerally hated the idea of letting ‘mere’ memorization into my learning at all.
Incidentally, my past memories are saying that’s why 6x7 and 7x7 gave me such trouble in particular; there was no “easy” way to decompose that in my head, it just looked like a square and another almost-maybe-a-square.
I have single-digit multiplications just kinda cached as ingrained associations between any two given digits and their product, but now I’m curious what algorithm you were using for them. Repeated addition maybe?
I would picture them as rectangles and count. Like, 2x3 would look like
xxx
xxx
in my head, and for small numbers I could use the size of it to feel whether I was close. I remember doing really well with ratios and fractions and stuff for that reason.
For larger numbers, like 8x8, I would often subdivide into smaller squares (like 4x4 or 2x2), and count those. Then it would be easy to subdivide the larger one and repeat-add. I would often get a sour taste if the answer just “popped” into my head and I would actively fight against it, so I think there was a part of me that really just viscerally hated the idea of letting ‘mere’ memorization into my learning at all.
Incidentally, my past memories are saying that’s why 6x7 and 7x7 gave me such trouble in particular; there was no “easy” way to decompose that in my head, it just looked like a square and another almost-maybe-a-square.