Time to think

American elementary school students, watching a videotape of a Japanese mathematics lesson, inevitably react to the pace.: They perceive unbearable slowness. The pace is slow, but the outcome is impressive. Japanese teachers want their students to be reflective and to gain a deep understanding of mathematics. Each concept and skill is taught with great thoroughness, thereby eliminating the need to teach the concept again later. It also increases the likelihood that what children have learned in one lesson will help them understand another lesson. Competence in procedures such as calculation may be achievable through rapid drill, but thinking takes time, and Japanese teachers strive to allow their students time to think. Especially at the early grades, they frequently admonish students not to give a hasty answer, but to slow down and think.

In the United States, curriculum planners, textbook publishers, and teachers themselves seem to believe that students learn more effectively if they solve a large number of problems rather than if they concentrate their attention on only a few. The emphasis is on doing rather than on thinking. American teachers place a high premium on their ability to cover a large number of problems, and may regard that as the mark of an expert teacher. In a study comparing expert versus novice elementary school teachers in the United States, expert teachers were found to cover many more mathematics problems in a single lesson than novice teachers did, suggesting that with experience teachers grow more adept at getting students to cover a large amount of material. Contrast this with Japan and Taiwan, where teachers concentrate so intently on only a few problems.

Covering only a few problems does not mean that a lesson turns out to be short on content. In fact, this does not appear to be the case. When many problems are covered, the same mathematical content tends to be repeated with each new problem; when fewer problems are presented, there is time for the kind of discussion that transforms the solution of problems from something that must be memorized to something that is understood.

The Japanese emphasis on reflection appears not only in mathematics. Other researchers have noted the same phenomenon in reading instruction. Jana Mason and her colleagues had this to reports after studying reading instruction in forty Japanese kindergarten and primary school classrooms:

One's first impression is that instruction is rapid-fire, with little lost motion or wasted time. We remain confident that there is a sense in which these impressions are accurate. Yet the realization eventually dawned on us that progress through stories is very slow. In one first-grade class, for instance, we saw an entire 40-minute sent on 29 words describing a single episode from a 252-word story. We were shocked when a second-grade teacher whom we had seen teach an excellent lesson informed us in an after-school interview that his class covers about two stories a month.