2003 Volume 44 Issue 1-2 Pages 61-71
:In ordinary math classes, it is necessary for the students to combine visual information with acoustic images corresponding to the teacher's oral explanation for constructing a mathematical reasoning flow. Again in traditional math classes, teachers routienly assume that all students already know certain facts that are necessary for understanding the teacher's explanations in a lesson.If there are some students that don't know these facts, these students cannot understand the teacher's explanation. These students might be called "under-prepared" for the class. On the other hand, if some students are already familiar with the mathematical reasoning flow, those students are unlikely to learn anything new during the teaching-learning process. They might be called "over-prepared" for the class.The purpose of the paper is to show the lesson principle of arithmetic and mathematics which uses the thinking activities based on tactile sense information as a base, _and fulfills the following two conditions (1)(2). (l)Both under-and over-prepared students can deduce new facts on the basis of (old)facts they know in their own way;and (2) Each student can construct a new line of reasoning (or flow of reasoning) by combining the results of his /her reasoning with those of other students.
