The heuristic approach is based on

The heuristic approach places the learner in the role of a discoverer, based on the spirit of inquiry and self-investigation.

Rote memorization is the opposite, relying on repetition without understanding.

Home work is a task type, not the basis of the method.

"None of the above" fails since inquiry is clearly its foundation.

The word heuristic comes from the Greek heurisko, meaning I find or discover.

H. E. Armstrong is credited with the heuristic method of teaching science.