I think it is crucial for the math teacher to give a detailed description of anything he does, justifying any step he takes from definitions and axioms, from the start. Of course, before/later he should add a lot of intuitive explanations and examples about how and why the definitions are chosen and the results are going to be true; but the teacher should keep well in mind that, for every step he spares, he will get a bunch of students who will reach to the conclusion that maths is not a logical subject, but merely a collection of boring and inscrutable pieces of symbolic relations that they should memorize, even more if they are immersed in a program that teaches them more algorithms than theoretical results (as happens in the highschools of many countries, for example here in Spain, where I live).