[cors-fls]

Learning by example is a thing in math too. Learning theorems and methods is not sufficient, they are tools and you need training to master them. Not everyone is able to generalize from one class example to other situations. For that you need to work with other examples. Not only the problems, the answers too.

Also if no one liked this course there is certainly a problem that can't be dismissed in a handwave like you did in your answer.

[strikelaserclaw]

Richard Borcherds, a field medal winner, stated that he approaches new topics by doing a lot of examples before trying to understand the theorems and such. There is no "right" way to do math, contrary to what OP claims.

[ivansavz]

> Not everyone is able to generalize from one class example to other situations.

I found the same thing in my tutoring experience. I had several students in physics whom I couldn't "reach" no matter how hard I tried to present "theory" using the equations in full generality (symbols instead of numebrs). I taught them this way because they this is the way I learned and because it seems OBVIOUS to me that learning the abstract thing is more powerful/efficient way to get through it.

Imagine spending dozens of hours with them and they still didn't "get" anything to the point I was feeling discouraged and was like this person will never pass this exam that they have next week. I felt bad because these were friends and I really wanted them to succeed (more friends in STEM, more STEM conversations with friends).

Lo and behold, these same people whom I thought were "physics dumb," were able to pick up all the material in literally minutes, as soon as we started the exercises (one person) or having tried some exercises on their own (the other person). I don't mean "imitate the steps"-know, I mean completely solve 80% of the problems on the practice exams and adapt the use of equations as needed for each problem. I mean it's still PHYS101, so there are only 10 or so equations, so they didn't turn savants or anything, but the transformation was so sudden and drastic that I realized people simply have different learning approaches.

Some people like the abstract/general approach. Some people like the hands-on approach. The latter kind of people often think they are "not good at X" but really they would have no problem picking up X if they had learning resources suitable for them (often lacking in traditional textbooks and courses). I think that's why Khan Academy videos are so popular. Sal does a fair bid of hands-on approach, and many people need that!