Students’ calcs in the 70s/80s

[Johnh]

an aside on rote memorization:

10 years before we even knew what a calculator was, at age 6 or 7, we were having to stand up in class and recite:

"three threes are nine...
four threes are twelve...
five threes are fifteen..." etc

up to the 12x table

It's still pretty useful to have those results stuck in my head, but at the time I was hopeless at them because they were way too boring. So I secretly 'cheated' and made myself a table with a 12 x 12 grid with all the results on it, carefully adding up and checking each entry. And I noticed the easy results and the patterns along each row and column and down the diagonals. And then I didn't need my table anymore!

With more grown-up problems, a similar learning outcome is gained by programming a machine in some way, if you do it in a way that requires insight into the problem.