> One of the corollaries to this, if you're teaching, is that your time should be spent NOT on the details––not, for example, on the step-by-step algebra to solve some complicated algebra to solve some integral––but rather on the bigger concepts (e.g., the general strategy of how to solve that sort of integral). Give students the rough path and let them fill in the details, rather than just giving the turn-by-turn directions.

I'll argue the exact opposite of this in math class. I preferred lectures here the prof walked through the problem step by step and I could copy those steps down to my notes, and then apply those same steps for other problems.

The textbooks always skipped a lot of steps in the middle, making them hard to follow along. It ended up being the beginning, a bit in the middle, some magic, then the end.