図形学習における数学的理解過程に関する研究 : 数学的理解を促進する証明行為に焦点をあてて

抄録

Numerous attempts have been made by researchers to answer "What is mathematical understanding?" and "How is it possible to capture individual understanding?" (e.g., Skemp, 1976; Beys & Herscovics, 1977; Herscovics & Bergeron, 1983; Pirie & Kieren, 1994). And a model of understanding in mathematics education has to consist with suitable components of the model and be used by researchers or mathematics teachers to analyze students' understanding. In this point, Koyama (1992) has studied mathematical understanding from a slightly different perspective and argues that we need to construct a process model of mathematical understanding. However, we need to pay attention to aspects of a cognitive function for promoting students deepen and expand their mathematical understanding. The aim of this paper is to define a cognitive function which could promote students deepen and expand their mathematical understanding. In this paper, the cognitive function is showed as an act which is observed clearly by researchers or mathematics teachers. As a result, I argue that if the act with conversations of students, "Why is that argument true?" or "Is that argument true or not?" are observed, students begin to deepen or expand their mathematical understanding. In this paper, with considerations of some previous researches, such act is explained in term of "proving act" by Harel & Sowder (1998).