4 ms·

When I was a couple years into my actual math education (about midway through vector calculus) I had a crazy moment when I was really struggling to understand s

by mlsu 3y ago

When I was a couple years into my actual math education (about midway through vector calculus) I had a crazy moment when I was really struggling to understand some problem that required more manipulation than the 3 dimensional problems I'd been used to up until that point. My roommate was a postdoc and he told me the simplest, dumbest thing, which was, roughly "the math is a separate thing than the picture. You have to actually think about the math" That one sentence blew my mind. Until then I had relied almost entirely on the geometric representation of a concept or a problem, and never knew to reach for the the actual concept. I think about 75% of people check out of math completely super early; of the 25% that remain, 75% of those never quite "get" that math is a separate thing from graphs and charts. The rest are usually successful scientists, engineers, and similarly technical folk. (I won't venture my opinion on the difference between mere number manipulators vs. actual prov-ers of mathematics, but I think it's probably a similar ratio)

tremon 3y ago
Same here, but not with calculus and geometry. My problem was with statistics: I had always been able to solve high-school level problems by intuition alone, and never needed the theory. That is, until 3rd-year university, when the problems became too complex to grasp by intuition alone. I had a really hard time that year, because I basically had to re-learn 4 years of foundational theory. So I'd say that teaching intuition first is a dangerous path: students may fail to fully understand the theory if they can get by on intuition. And intuition is not a solid foundation to build on.
- StackOverlord 3y ago
  What do you guys think of https://blog.revolutionanalytics.com/2014/01/the-fourier-transform-explained-in-one-sentence.html https://blog.revolutionanalytics.com/2014/01/the-fourier-tra...

by mlsu 3y ago

tremon 3y ago

Same here, but not with calculus and geometry. My problem was with statistics: I had always been able to solve high-school level problems by intuition alone, and never needed the theory. That is, until 3rd-year university, when the problems became too complex to grasp by intuition alone. I had a really hard time that year, because I basically had to re-learn 4 years of foundational theory. So I'd say that teaching intuition first is a dangerous path: students may fail to fully understand the theory if they can get by on intuition. And intuition is not a solid foundation to build on.

StackOverlord 3y ago
What do you guys think of https://blog.revolutionanalytics.com/2014/01/the-fourier-transform-explained-in-one-sentence.html https://blog.revolutionanalytics.com/2014/01/the-fourier-tra...