who/whom

Who for both. No teacher is going to ask "whom are my pupils?". According to the rules of formal grammar, who should be used in the subject position in a sentence, while whom should be used in the object position, and also after a preposition. So from the formal rule it's "who" for both places in your sentence. In practice, most people never use whom anyway because it sounds extremely formal. They don't use whom at all, and instead use who in all contexts.

Thanks Tes Yeux

Aren't the pupils the object of the sentence, and the teachers the subject?

It's more complex than that.

There are four subjects in that sentence. "That's" is the abbreviation for "that is," and that is the first subject. In the second clause, the subject is "they," which refers to teachers (this is not a predicate nominative, but functions as a predicate nominative does--it renames "teachers" as "they"). Finally, the last two subjects are "who"--who are and who are not. Therefore, one uses the subjective form. Who is used as a pronoun and the subject of "who are," and "who are not."

To recapitulate, there are four subject/verb combinations:

That's (That is)

They forget

Who are

Who are not.

The proper places to use "whom" is something that bedevils even native English speakers.

Many native English speakers (me included) just use "who" no matter what.

Upper class and/or highly educated people often make a point of using "whom" and using it correctly.

If someone tries to use "whom" but they use it incorrectly, it makes them sound foolish and pretentious.

A good rule of thumb for the native speaker is asking oneself if one would use the third person objective:

We gave it to him. You gave it to whom?

I got it from her. You got it from whom?

She went with them. She went with whom?

Whom is never the subject acting with a verb. That must always be "who."

Lucy is the one who gave it to us. Brad asked who got that for you. We asked her who went with her.