I don’t teach children, I teach adults. Perhaps it is possible to teach every child, but I doubt it. It is not possible to teach every adult, particularly when they don’t act like adults. Students have to put in an effort. Many of them understand they have to study for exams, but relatively few realize that they have to study all semester. One of my colleagues has complained, “They understand it when they leave the class, but don’t know it three weeks later. How is that my problem?”
It has become our problem. The students don’t know they must keep doing math in order to keep knowing math. I am not even talking about the bigger problem of students who do not remember math from one course to the next, I am talking about students who walk out of class understanding something and never try the problems again until the test. Sometimes they look at the problems and think they can do them. That is about as useful as looking at sheet music and saying, “Yes, I’ve played this and won’t have any trouble playing it again.”
I spend more and more of my teaching time reviewing. A couple of days ago I gave them a worksheet containing mixed problems. Some were from the previous lesson and some were from more than a month ago. The older problems were originally taught the previous semester. Most students had trouble doing most of the problems.
There is a concept called “mastery learning.” The idea is not to advance students past a topic until they learn it. Ignoring the basic idea of mastery learning, it is sometimes misused to avoid teaching topics a second time. I have talked to people who claim they would not understand their own PhD thesis if they read it again. No one is exempt from forgetting. If I were teaching high school and had four times the number of classes, I could throw a little review into every class. But I am teaching at a community college and I don’t have time.