Abstract
Teaching and learning of long division in Japanese elementary school more or less are based on the mapping theory. An analysis of the ten minutes episode on a typical introduction to the algorithm of division (3-digit number÷1-digit number) is presented to explore problems of that theory. The result is that behaviorism dominates the teaching and learning long division in Japan. Therefore the contextualist theories of truth on constructivism should receive more attention in our country. Even in our lessons, contexts in problems are also signified. But the problem is whether students make activity in those contexts. As in fact expressions are shown at first in a process of solving problems, students have not enough time to think the problem in the contexts. On these points of view, Lampert's lessons suggest our reconsideration to change learning theory to compensate our lessons for them, because they have a large gap. Gravemeijer (2002) points out faults of mapping instruction, which are also our problems to be conquered in Japanese lesson. What to be reformed is clear. If external factors are remedy, it is possible to improve teaching and learning of long division from Constructivist viewpoint in Japan.
