math by heart, not by execution

i want my children to learn the small 1x1 — the multiplication tables up to 10 — by heart. not because rote is good. because once it’s by heart, math stops being something you execute and starts being something you read.

when a 7-year-old hits “6 × 8” and has to compute it, the computation eats up working memory. the actual problem they were trying to solve — the word problem, the fraction, the area of the rectangle — has to wait. by the time the multiplication comes out, they’ve half-forgotten what they were calculating.

when “6 × 8” comes back instantly, working memory stays on the actual problem. math feels different. it feels more like reading a sentence than like running a program.

this is automaticity. the same reason we don’t sound out the letters of common words anymore — we recognise “the” or “and” as a unit and move on. the heavy lifting moved from decoding to comprehension.

grinding tables is unfashionable. people are afraid it kills the joy of math. i think it does the opposite — it removes the friction that was killing the joy.

for my own kids i print worksheets and we drill, gently, regularly, for short sessions. five minutes. not an hour. the worksheets live on this site.

i don’t think every part of education needs to be automated this way. but the parts that other parts of math depend on — the small 1x1, basic place value, common fractions — should be cheap and silent in the mind. then the actual maths gets all the attention.