A Research on the Questioning of Refine & Elaborate in Elementary Mathematics Based on Argumentation

Abstract

　　A purpose of this paper is to show the structure of the questioning in refine & elaborate. In this paper, we focused on argumentation as a viewpoint for conducting a theoretical consideration of the questioning in refine & elaborate. Argumentation is a technique or method of establishing a claim, which is a concept focusing on the process of collective discussion. First, we considered refine & elaborate as a phase aimed at overcoming epistemological obstacles in the generalization process, and identified the static and dynamic states of the conception. Second, we modeled the argumentation that leads to overcoming the epistemological obstacles, and showed the aspect using concrete examples. Then, to derive some questionings in refine & elaborate, we focused on the rebuttal and the qualifier showing the acceptability of argument. Because of the consideration, it was shown that the questioning in refine & elaborate is to actualize rebuttal and qualifier. And we revealed that questionings to actualize rebuttal R₁, rebuttal R₂, qualifier Q₁ and qualifier Q₂ are requested when organizing argumentation. Rebuttal provides “criteria” which are grounds for reference in determining appropriateness of the qualifier. Finally, we concluded that the questioning in refine & elaborate has a relationship of “rebuttal R₁ ⇀ qualifier Q₁”, “rebuttal R₂ ⇀ qualifier Q₂”.