[tokenadult]

Those are well-framed responses. Thanks. Khan Academy elicits my response because SO FAR, among the online exercises I have tried there, the "enlighten the student on a conceptual level" hasn't happened as much as just the habit-clinching drill. As Lang wrote (as quoted in the grandparent post), "Of course, some rote drilling is necessary. The problem is how to strike a balance."

The "mathematical form of Socratic learning where none of the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own" is what I attempt to provide in my live, face-to-face mathematics classes. I'm not worried about Khan Academy reducing the market for those classes (and in fact encourage current and prospective students to try out Khan Academy) because providing that sort of instruction is very hard to automate. As your example of Silverman's book points out, it is more of an art than a settled science to decide just how many steps to show with Socratic guidance, not to mention that different learners need different steps drawn out for them.