高校で可能な証明活動を組み入れた数学的活動についての考察 ― 証明の多面的機能のケーススタディ ―

抄録

　　 The author has been engaged in the study of structure-oriented mathematical activities.  In structure-oriented mathematics, there is emphasis on constructing mathematical concepts and developing mathematics.  Therefore, in the secondary education, proving should be the main method in those activities.  On the other hand, as De Villiers (1990, 1999) pointed out, the function of proof has been seen almost exclusively in terms of verification, although verification is only one aspect of proof, and to consider proving as mathematical-activities we should take the various functions of proof into account.  

　　 In this paper, we consider the mathematical activities involving proving in high school from the viewpoint of functions of proof argued by De Villiers (1990, 1999), and obtain some implications about developing such activities as structure-oriented mathematics.   　 

　　 Two previous studies, the mathematical activity model by Hamanaka & Kato (2012, 2013) and the mathematical activities involving “proofs and refutations” by Hayashi (2013) are considered and it is shown that the former focuses on verification and explanation, the latter on communication.  

　　 Then, as the mathematical activity focusing on proof as a means of discovery, we propose the activity taking up the mathematical classification problem.  Also its sample material is shown and the characteristics and the meanings of such an activity are considered.