Analysis and Development of Constructive Abstraction:From Process of Collaborative Learning in Mathematics Class

Abstract

　　The aim of this paper is to clarify that mathematics is the most successful subject for collaborative learning. Abstraction and generalization are the essential characteristics of mathematics.  The separation model of generalization (Iwasaki 2007) based on Dörfler’s generalization theory and model is employed to analyze social and collective process of learning mathematics.  In that process, interactions develop effectively constructive abstraction toward generalization.  In other words, collaborative learning provides students with the opportunity for constructive abstraction in mathematics class.  Here they regard a symbol as object which contains meaning. Finally this paper identifies teacher’s roles in this construction: selection of tasks, designing of process and habituation of collaborative learning mode.