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

[Chathamization]

409. I'd say that using a particular method can be pretty important, but this thread shows the serious

downsides to such an approach.

For instance, I think it makes sense to have the students write out 5+5+5 or 3+3+3+3+3, or draw a 4x6 or 6x4 rectangle, instead of just having them write down the answer. There are a lot of students who memorize the answer and don't understand what's actually going on, and it makes sense for the teachers to find some ways to make sure they understand the concepts.

The problem, as you can see in this thread, is that this can apparently lead people to think that a particular representation is the mathematical definition rather than, well, a representation. The student clearly understood the concept - that multiplication is repeated addition - but were marked down because the teacher (along with many in this thread) falsely believed that the 5x3 means 3 + 3 + 3 + 3 + 3 and not 5 + 5 + 5 (I've said elsewhere, the later is closer to the common definition, but both should work since they demonstrate the concept). You can also see the confusion this leads to - people thinking that this teaches order of operations (with only one operator?), or that if we act as if something that is commutative isn't commutative it will help kids when they run into things that aren't commutative (huh?).

Confusing the way that one can think of something with the way that something is defined seems to lead to a mess.