[zck]

Here's a view of why it might make sense for a teacher to emphasize one way over the other that doesn't focus on "it's the definition and definitions are important":

> The teacher obviously knows (I’m assuming) that 5 + 5 + 5 is the same as 3 + 3 + 3 + 3 + 3.

> So why would one method be preferred over the other?

> Because thinking of 5 x 3 as, literally, “five groups of three” will help them when they learn how to divide. (That’s what the Common Core standard here is getting at.)

from http://www.patheos.com/blogs/friendlyatheist/2015/10/21/why-...

Also notable is the explicit assumption of good faith:

> Let’s assume for a second that this teacher isn’t an idiot. (I know. I know. Bear with me for a minute.)

> What possible explanation could there be for deducting points from this poor child’s exam?