머리가 나쁘다 = (The) head is bad. = (somebody) is stupid.
I think that meaning can be clear to most of our native languages.
Conjugating this verbal phase into an adjective to make "stupid professor", we get [머리가 나쁜 교수]를...
I will teach professor with a bad head is not accepted. (2017/09/28). Translation can be considered idiomatic.
머리 (head) + 가 (subject marker) + 나쁜 (bad) = "stupid." I didn't know this myself until just now.
Durolingo said "... the stupid professor." I said "... that stupid professor." I believe, in this instance usiage of either pronoun should be accepted in that "that" and "the" both appear to point toward a specific individual.