A Study on Operative Proof in Mathematics Education (IV): Cognitive Aspects of Instrumental Genesis on Operative Proof in Primary Level

Abstract

　　 The purpose of this study is to investigate how to realize explorative proving in schools by using Wittmann’s operative proofs.  In this paper we examine how elementary school children engage in exploratory proof activities with number pattern problems.

　　 In order to investigate dialectic relations between learners and the artifacts they use in operative proofs, we used ‘instrumental genesis’ as our main framework of analysis.  Data taken from 4 experimental lessons in  Japan and the UK suggest children in elementary schools can engage in productive proving activities with appropriate manipulatives.

　　 From an ‘instrumental  genesis’ point of view, we could observe ‘instrumentalized’ manipulatives offered ways for children to construct proofs and explain the patterns as well as produce new statements.  It was also observed that constructing proofs and producing new statements can occur simultaneously and this is a distinctive feature of proving activities in elementary school contexts.