After a lifetime of approaching math the wrong way, I took two college math courses this quarter with a newfound zest for math. These classes are integral calc and multivariable calc.
Integral calc started out okay, learning about Riemann sums and the Fundamental Theorem of calculus. But instead of spending a great deal of time gaining the intuition behind these things, we jumped into integration technique after integration technique.
Why on EARTH would we need to memorize and regurgitate a bunch of integration methods on toy problems for 6 weeks? It's absolutely bizarre. I'm not taking this at some random JC either, this is at a top research university. This class is single-handedly destroying my enthusiasm for calculus.
When we have software that can do much more difficult integrals than we can with pencil and paper, why would we waste time memorizing Trig substitutions or integration by partial sums? Doesn't that just make it a glorified algebra class?