数学学習における概念変容のモデル化に向けた基礎研究--概念変容の諸相についての考察を中心に A study on conceptual change in mathematics learning towards its theoretical model: relating to the phases of conceptual change
The purpose of this paper is to suggest theoretical basis towards a model of conceptual change in terms of the phases of conceptual change. For attaining this purpose, this paper consists of two main parts: in the former part some earlier theoretical framework of conceptual change are critically reviewed in terms of phases of conceptual change and an alternative characterization are shown; in the latter part the alternative framework are examined by means of preliminary analysis of one conceptual change situation, that is "multiplication with decimal numbers". Fundamentally speaking, the notion of "conceptual change" can be characterized as two different phases based on the frameworks of theory change in philosophy of science: T. Kuhn's "paradigm theory" and/or I. Lakatos's "scientific research programme". From the viewpoints of two phases, some earlier researches (e.g., Posner et al, 1982; Vosniadou & Verschaffel, 2004; Merenluoto & Lehitinen, 2004; Morimoto et al., 2006) can be summarized. On the other hand, such earlier researches on conceptual change tend to overlook the crucial differences between different claims about theory change in philosophy of science. This study tries to identify the differences and to show alternative views on the phases of conceptual change, particularly in the case of mathematics. That is to say, the phases of conceptual change in mathematics learning can be characterized as three different phases: "extensional enlargement", "internsional reduction" and "conceptual reconstruction". The three phases of conceptual change showed in this paper are explained and examined by means of preliminary analysis of one conceptual change situation: multiplication with decimal number. The teaching and learning of this content can be a problematic situation in the development form discrete to continuous quantity.
数学教育学研究 15(2), 29-39, 2009