trivial, i know (or: the old, the new, and the lazy)

according to NPR, the old way of doing math is

i was trained to do it this way, myself. the '0' makes sense, as long as you realise that

$$36 \times 20 = (36 \times 2) \times 10 = 72 \times 10 = 720.$$

apparently the "new" way of doing math is

to be honest, this looks like teachers have (at least) one of two things in mind:

1. they want a more conceptual, obvious method of why multiplication works, which is fine;
2. they don't trust kids to multiply non-simple numbers. instead, it is preferable to perform more additions, which is less error prone. if you believe, like nichοlas carr, that modern informational society and internet search engines are changing our cognitive abilities, then this teaching approach makes sense as a computational safeguard against increasingly bad memories.

now that i think about it, it's not clear to me what would be less error prone, when multiplying several 3- or 4-digit numbers ..

anyways, the rationale:

"You cannot become good at algebra without a mastery of arithmetic," Devlιn says, "but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers.

at any rate, i must be weird. i would have done it as ..

$$ 36 \times 24 = 36 \times 25 - 36 \times 1 = \frac{3600}{4}-36 = 900 - 40 + 4 = 864.$$

sure, there are more steps, but each step feels faster, to me.