I see many parallels with the post and my own experience. I got my PhD in math and taught many college math courses during that time. I was always saddened at the number of students that essentially viewed math as just an exercise in the memorization of algorithms (memorize differentiation and integration rules and chug away at problems). I would avoid teaching this way and instead give them fewer, "deeper" problems…
Indeed the math subject GRE was (when I took it) primarily many, many tricky calculus questions with a very strict time limit, because these problems are fairly straightforward to write and standard.