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eli_sennesh comments on The Truth About Mathematical Ability - LessWrong
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Anecdata: I got an A in Calculus 1, a C+ in Calculus 2, and an A- in Calculus 3. Of them all, Calculus 2 seemed to be the most focused on "memorize this bunch of unjustified heuristics", and Calculus 3 was one of the first and only times I really experienced the Wonders of Math in an actual course.
Oh, and for further anecdata, without being able to convert to letter grades, I got a 75% in Statistics 1 and failed (post-grad level) Intro to Machine Learning last year due to taking the courses without the continuous probability-theory prereq, and then retook Machine Learning this year to get an 86%.
It seems to me that a lot of variation in math grades can be very easily explained by differences in previous preparation.
As someone whose day-job largely consists of teaching Calculus 1, 2, and 3, I heartily with you about what they are like! If I could redesign the curriculum from scratch, Calculus 3 would definitely come before Calculus 2 (for the most part), and far fewer people would be required to ever take Calculus 2 at all.
ETA: I'm talking about the curriculum in most colleges in the U.S., so I hope that you are too; other countries' curricula can vary a lot.
Calc 3 for me was Multivariate Calculus.
Actually, yeah, requiring more people to take Multivariate Calculus and fewer people to take Assorted Sequence/Series and Integration Heuristics sounds like a fine idea.
Yep, sounds like we're talking about the same curriculum.