With those verbs that can take both the infinitive and the gerund:
Infinitives emphasize the possibility or potential for something and sound more abstract and philosophical. For that reason, they are used when we are talking generally about situations and events.
gerunds usually sound more like normal, spoken English, and so gerunds are used when we are speaking about a specific instance.
So:
[color=indigo]The best teachers do more than just go over the material in the class textbook.
and
[color=blue]He is a good teacher because he does more than just going over the material in the class textbook.
BOTH OF THESE ARE NOW CORRECT.