Learning the micro-steps well is like learning an abstraction in a program. Once you learn the abstraction to the point that your understanding of it is unconsc

Learning the micro-steps well is like learning an abstraction in a program. Once you learn the abstraction to the point that your understanding of it is unconscious, then your thought processes are lifted to a higher level. This is true understanding of math. Exactly. The argument is not to "do things in micro-steps", it's to do things in appropriately-sized steps. As your understanding of math improves, you can (and should!) take bigger and bigger steps. The point is that, for presumably a variety of reasons, a really large percentage of students don't drop down a level in abstraction when they get stuck--they get depressed and give up. I see a large part of education's role being the inculcation of good habits, and this is just a sucky, sucky habit.