A Study on Abduction in Mathematics Learning (I): Focus on the Criterion of the Hypothesis Formation

Abstract

　　 In mathematics learning, we expect students’ activity that they create meaningful mathematical knowledge and make use of it by themselves.  In such activities, we need to distinguish the stage of guess and justification and we focus on the stage of guess.  Wada (2009) pointed out the importance role of the reasoning of abduction in the stage of guess.

　　 However, it is not fully clarified what types thinking are the basis of abduction.  Thus, we focus on the Yonemori (2007) because he argues about the nature of abduction.  According to him, there are the stage of insight and inference in the process of abduction, and both of them play essential role for to form a hypothesis. In the stage of inference, there are four criteria for to choose a hypothesis. When subjects form and choose a hypothesis, s/he use the criterion consciously and reflectively.  For this reason, we argue the criteria by to analyze examples and to compare Nakazima (1981).

　　 As a result, we propose three criteria (the criterion of the hypothesis formation) that played primary role for abduction.