[quadrifoliate]

Grew up in India. As the sibling commenter notes, this is likely an older British expression that has survived in Indian English.

It's hard to remember now, but I think the way I thought about it when I was taught is that "3 × 4" is combining 3 and 4 into a larger number 12. The "3 ÷ 4" was not special, and "by" there was just an abbreviation of "divided by" like you say.

For what it's worth, I think times usually should work in Indian English as well, as in "3 times 4" for 3 × 4.

[z3phyr]

We usually say "three fours are twelve"

Instead of "three times four is twelve"

[quadrifoliate]

Yep, that's true — but I think an oral question would be phrased as "What is three times four?", correct?

[z3phyr]

Yes, it could be phrased like the above, but from what I have experienced in day to day school life, people usually ask "What's three into four?" or even more likely an incomplete fill in the blank question "Three fours are?"