It's been a long time since I've sat in classrooms on a regular basis but I do attend a lot of conference events. For the most part, I find presentations that get into a lot of very detailed step by steps and the like cause me to zone out. I'm far more interested in learning enough to cause me to check out something later and to understand some of the motivations, thinking, etc. It's also a reason I think that conference presentations are generally longer than is optimal.

Having said that, people do differ. And with a smaller and more interactive group, getting into the nuts and volts can make a lot of sense. But it should IMO be done sparingly in more of a lecture format.

Turn by turn is what "the book" and it's handful of reference examples before the actual test questions are supposed to be about.

The classroom time is for general theory and the QnA part for debugging errors in the understanding of students.

(In High School I found it way more useful to spend most of the in-class time doing homework... even if for another class.)

> 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.

Right, its one of my biggest frustration with my university experience. Why am I paying you large sums of money for instruction that feels like it equates to a list of practice problems.

All of my math classes derived things and went through some problems step by step, and then often later a problem would be given and you have 5 minutes to try to solve it then compare with what was done on the board. It worked well and I don't see why you'd do it differently.

Very true and unfortunately all to frequently ignored.