Experienced Mechanical engineer gives Math and Physics class for High School students

Methodology

The secret is how to manage both technical rigor and structural intuitive explanation in a kind of inspired (and seminal) mix up. One has to repeat every time fundamental things (what is a real number, a line, a convergent sequence, a prime and so on). In order not to be boring, one must often repeat explanations of this kind using other words. In the same time, students must continue to develop their computation skills, and rigor must be kept in writing down proofs, lemmas, arguments. In fact, it is hard to find the good mix up which keeps the students attentive and curious until the lesson is closed. The best method is to be empathetic and feel what the students would like more in the sequel.