Though I might have written this article earlier, its writing was incited by the comment of an anonymous reader of an earlier version of "Telling the Truth." I wrote (and stand by) "One of the most important things an instructor can do for the students is to insist they learn mathematics in part from written sources, so they can get beyond the surface."

That person's reaction was "Most instructors feel a responsibility to at least mention, if not cover, whatever that means, everything considered essential in a class, and that his suggestion that this is not necessary since books do the job is a bit unrealistic."

That's not quite what I said. If you train the students not to pick up anything from the reading, they will probably oblige you. As I wrote in this article, there are things they can pick up. That includes partial understanding of material you must lecture on. The suggestion that one must cover every little thing in class is another one of those fixed ideas that might well be discarded. As is also in "Teaching freshmen to learn mathematics" (1999), it is of fundamental importance to force the student to learn how to learn; better learning of calculus (and other subjects, too) will then ensue.

Click here to read "Improving the learning of calculus."