What is the way of education based on discovering and experiencing things for oneself called?

A heuristic technique, self-discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal. 

The technical word that describes a way of learning based on the effort of the learner is the "aha" experience

I would suggest professor Richard Gardner's theory name; Multiple Intelligences" if I am sure about his name. You can Google search it for more information around it.

It seems to be Heuristic approach based on repeated and proven experience 

the heuristic way of learning