I'd say two times two, two times three, my MIL says two twos, two threes etc
usage of two by three ( by four) is more common when referring to measurements/ dimensions
I do understand your annoyance, using "times by" is incorrect use of language. I'd point this problem out to the maths teacher and head - there can not be a confusion like this when teaching mathematical terms
I hate it when people say "like" as a speech filler - "I went to the shops, like, to buy bread" - what the hell does that mean?
English is not my first language btw, so learning it from scratch has its advantages!
Just throwing this one out there as it's something that irritates me daily at work where - due to working in financial sector - there are a lot of explanations of maths flying around and every time someone explains that something is "xx times by xx" I grind my teeth. I was always taught that it was "xx multiplied by xx" OR "xx times xx" - not both. Now my DH has started to say it when helping my DS with his homework and I'm lurking around correcting him every time, my main argument being you don't say your times' tables like this "2 times by 2 is" - or do you?!