数学的な表現の主体的な活用における数学的にかくことと真実感の接点の一考察 ―数学的な表現の移行の考察を念頭において―

抄録

　　 The purpose of this study is to suggest the contact between drawing mathematically and its authenticity for considering the cue of expressive changing which will be expanded in the future.

　　 According to previous studies, the results of examining the relationship among the mind, the understanding, and the representation suggested that learners’ representations are the results of thinking and learners rethink with them.  Through such trial and error processes, “the mutual-beneficial relationship” which means thinking representations support mutually is suggested.  Moreover, better representations are as the results of trial and error processes.  This study suggests the powers of broad mathematical representation which can practice and utilize linguistic and symbolic expressions actively, properly, and flexibly with using graphical representations as the present question of mathematical education.  With considerations of previous studies, this study proposes the following three suggestions about the contact between drawing mathematically and its authenticity.  The first one is the teaching about teachers’ conscious drawing.  The second one is that the transformation of learners’ schema and cognitive aspect through trial and error processes is the contact.  The third one is that learners’ motivation of drawing actively is fostered by experiencing its authenticity through trial and error processes.