Do Plato and Socrates ideas have an effect on the current education system?

Answer 1

Yes, of course. There's even a method of teaching called "the Socratic method" that's used every day by every teacher (except, perhaps, in P.E. and shop). It consists of asking questions which lead to the answer. Little by little the teacher gives clues in the questions. In the end, the student who gets it right thinks it was his/her own idea.