図形・空間学習における学習者の知識体系とその活性化に関する研究 : 数学授業中の討議でなされる正当化について

概要

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The purpose of this research is to describe various modes of knowledge students construct in mathematics classroom. For this purpose I have focused on the objectification-justification process in this paper, which is the view of mathematics classroom based on the findings from the series of my research, and described various modes of justification and the value and status of propositions students used. Below, I described main findings from qualitative analysis and global consideration: (1) There are two views supporting justifacation by indivisual students. One is the perceptual view, which has the role of visually verifing results from conceptual thinking and making trial and error for grasping clues of problem solving. The other is the conceptual view, which has the role of recalling and using possible theorems or propositions by thinking the meaning of sentences in problem situation. These views are complement each other, because their functions are appeared alternately in problem solving process. (2) Students have the strong belief of the value and status used in argumentation. If they once use very efficient and concise way of thought, they do not develop it but tend to relate different ways of thought to it. (3) Significant or not, all students does not always take part in argumentation. If they could not been convinced of ideas others presented, they often consider those as special ones.
全国数学教育学会の論文