What I've found, is that often teachers (really anybody who's understood the subject and is willing to teach) will try to teach both the subject AND how they ha

What I've found, is that often teachers (really anybody who's understood the subject and is willing to teach) will try to teach both the subject AND how they have learned; i.e. they do not only tell you about the math but also the way in which they have arrived at understanding it (how they've related to it). to use an analogy, when describing the math they tell one about a place where they are (a 'place' where the math is there, already understood) and how they got there (the analogue of route they took to get there e.g. "took public transport line 4, get off at station Example and walk until you're there"). This leaves little room for those who may prefer to ride a bike all the way there (the analogy has been stretched to the breaking point), cuz the teacher will knock you off the bike and insist that you ride the line 4 then walk, same as they did.