Information Is BeautifulApr 12
Quick! What's 6 x 8? 7 x 6? The trickiest multiplications for kids aged 5-8. How many do you still struggle with?
Show threadMichael WestergaardApr 12
The best part is it’s not 100% symmetrical along the diagonal
Show threadkasperdApr 12
I noticed that as well and think that’s an interesting result. The asymmetry tells us something about how kids learn to multiply, though I am not sure what that something is.
Show threadthe roamer

@kasperd @infobeautiful @michael

They "do the eights" and they "do the twelves", and these are distinct operations. Both are interrelated since 8x12 = 12x8, but swapping the order of the operation is a huge mental step that is costly to execute. So they stick with one and then make mistakes if multiplication in that order is more error-prone.

In a sense the students' seemingly limited behaviour reflects deeper mathematical truths. Multiplication need not be commutative, in many algebraic systems it is not, and here we see the students acting in a way that pays due respect to the fact that we must not take commutativity for granted! :-)

Apr 12 at 2:02pmWeb