Starting from the most abstract principles is a good way to relearn something, but a bad way to learn something.
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Of course, and I am wondering now what a win-win for both students and teachers might be.
I think winning for teachers = students learn. So the win-win is just to do whatever's best for the student.
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Maybe it's best to give the students just enough examples so they will derive the abstract principle by themselves. That's how we learnt some spelling rules at school.
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The teacher asked us to find the pattern and replied with counterexamples until we found the right one. Not sure it works for math though.
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