Development of Strategy for Theoretically Predicting Formation of Mathematical Conception: A Case of Function Concept

Abstract

　　 The purpose of this paper is to develop and propose the strategies for theoretical prediction of mathematical conception formation.  We elaborate the notion of hypothetical learning trajectory proposed by Simon (1995).  The paper mainly consists of three parts. First, we formulated the general strategies for predicting a hypothetical learning trajectory through the reviews of previous research. Second, we formulated the conditions of some types of mathematical conceptions, focusing on the operative origin of mathematical conceptions and on the educational implication from constructivism.  Third, in order to show the usefulness of our formulation of the strategies for theoretical prediction of mathematical conception formation, we predicted a hypothetical learning trajectory when a student reads a Japanese high school mathematics textbook, and discussed the implication from our analysis.