What is the right preposition after teach

I could not find any information which of the following is correct:

  • To teach someone on a subject

  • To teach someone in a subject

What seems to be correct is "to teach someone about a subject". But "about" sounds to me as if you are casually teaching something. In contrast, Teaching "in" something sounds more like an active process over several lessons. What do you think?

Any hints apprectiated.


Generally, no preposition is needed.

I taught my son arithmetic.

Elementary school teachers must teach their students many subjects.