My biggest issue with math education is that after we learned the theory we never went back and developed an actual plan for solving the problems. For example, we learned a dozen different ways to approach integration, but after all this we never really put together a workable strategy for approaching a problem and deciding what tools to use.
It's like trying to teach someone to swim by just throwing them in the water over and over and expecting them to eventually figure it out.
As a result, the primary emotion students learn to associate with math problems is fear. Instead of the sense of confidence that comes with having a plan, each problem feels like "will things work out or will I get lost and waste hours without actually ever finding a solution".
you face the exact same problems with coding, arguably more so as the trial and error and debugging process is worse than any proof i’ve ever had to do. if you can’t figure out how to apply basic integration techniques without a teacher formally sitting you down and saying exactly what situations to use each formula in, you haven’t learned shit
The best strategy is one suited to you because you came up with it yourself, in my opinion. Other than the big kludges (u-substitution, etc.), teaching specific/mechanistic integration processes directly would have been an uncomfortable way for me to learn.
It's like trying to teach someone to swim by just throwing them in the water over and over and expecting them to eventually figure it out.
As a result, the primary emotion students learn to associate with math problems is fear. Instead of the sense of confidence that comes with having a plan, each problem feels like "will things work out or will I get lost and waste hours without actually ever finding a solution".