Is "what we're going to do is + verb" grammatical?

The lecturer is saying

What we're going to do is translate the understanding about gradients that we saw in the previous video into ...

What we are taught at school is "be + to + verb" or "be + verb + ing".

It seems that "be + verb" is NOT grammatical.

Although, I heard a lot people say "what we're going to do is + verb", even college professors. So, in particular, is "what we're going to do is + verb" grammatical?

Yes, this is perfectly grammatical, and even common. The forms you have been taught are the most common forms, but they are not the only forms that can be grammatical.