Comment by bwfan123
My abstract algebra class had it exactly backwards. It started with a lot of needless formalism culminating in galois theory. This was boring to most students as they had no clue why the formalism was invented in the first place.
Instead, I wished it showed how the sausage was actually made in the original writings of galois [1]. This would have been far more interesting to students, as it showed the struggles that went into making the product - not to mention the colorful personality of the founder.
The history of how concepts were invented for the problems faced is far more motivating to students to build a mental model than canned capsules of knowledge.
> This was boring to most students as they had no clue why the formalism was invented in the first place.
> The history of how concepts were invented for the problems faced is far more motivating to students to build a mental model than canned capsules of knowledge.
That's something I really like about 3blue1brown, and he says it straight up [0]:
> My goal is for you to come away feeling like you could have invented calculus yourself. That is, cover all those core ideas, but in a way that makes clear where they actually come from, and what they really mean, using an all-around visual approach.
[0]: https://www.youtube.com/watch?v=WUvTyaaNkzM