Why Would a Math Teacher Punish a Child for Saying 5 x 3 = 15?

[Ms. Toad]

177. Some of us who went on to get both undergraduate and graduate degrees in math

beg to differ.

The article explains reasonably well why the focus is on process, rather than results.

The challenge will be the same as it was when set theory was the "new math" when I was in elementary school: Ensuring that teachers who teach it (1) understand it and (2) know why it is extremely powerful in more advanced math. Absent these to factors, they will get it wrong and do more damage that good (both in terms of understanding and in terms of instilling a hatred for meaningless busy-work - as most of us felt set theory was until we hit about the second year of college math).

You are of course, correct, that the commutative property makes the two expressions equivalent. But having taught several levels of math for years, I'm pretty sure the person who answered that question didn't think, "Hmm...5 x 3 is equivalent to 3 x 5 because of the commutative property. It would be easier to write the equivalent addition expression 5 + 5 + 5, than it is to write 3 + 3 + 3 + 3 + 3." It is far more likely that they got the concept of repeated addition, but simply just didn't understand which factor designated how many addends, and which designated the value of each addend.