The main Greek innovation in education was the Socratic Method. This mainly involved the teacher questioning the students, hopefully leading them to a better understanding of things that way.
I don't know much about Egyptian education, but between the times of Alexander and Mohammed the upper classes in Egypt were culturally Greek anyway.
By comparison you could say (and it has been said) that our Western method of lecturing and expecting students to memorize a lot of stuff and be able to regurgitate it back up correctly on exams doesn't encourage original thought as much. I suppose a lot depends on how far your instructors take that approach. I went to a school that put a lot of emphasis on essay writing (at least for non-math and science courses), which certianly did encourage good analysis skills.
In the Middle Ages in Europe (IMHO if you say "Middle Ages" you are talking about Europe) there really was no schooling outside of the Church. Pretty much everyone learned their trade in some kind of formal or informal (watch their parents) apprenticeship. Very few people were literate.