> The problem is that the culture of mathematics and the culture of mathematics education--elementary through lower-level college courses--are completely different ... I've had many conversations with such students [...] who by their third year decided they didn't really enjoy math. The story often goes like this: a student who was good at math in high school (perhaps because of its rigid structure) reaches the point of a math major at which they must read and write proofs in earnest. It requires an earnest, open-ended exploration they don't enjoy.
I found this interesting because I too discovered this difference in approach but had the complete opposite reaction. I absolutely hated math in middle and high school. It wasn't until I took a discrete math course for my CS program
that I got exposed to dealing with real proofs, which I found required a level of creative thinking, and I totally loved it. This admittedly wasn't an "advanced" university math class, but the difference from high school math was still quite stark.
I found this interesting because I too discovered this difference in approach but had the complete opposite reaction. I absolutely hated math in middle and high school. It wasn't until I took a discrete math course for my CS program that I got exposed to dealing with real proofs, which I found required a level of creative thinking, and I totally loved it. This admittedly wasn't an "advanced" university math class, but the difference from high school math was still quite stark.