数学的リテラシーの育成に関する基礎的研究 : 「数学の方法」としての数学化と数学的モデル化の関係の考察

抄録

In this research, mathematical literacy is assumed to have fore components: "the nature of mathematics", "mathematical contents", "mathematical method", and "attitude". The purpose of this paper is to consider "mathematical method" as a component of mathematical literacy. "Mathematical method" has been told in various words and various ways. In this paper, in order to explore the essence of "mathematical method", it is focused the researches that are comparatively at an early stage and have affected the researches of "mathematical method" in Japan. According to the researcher's theoretical background, "mathematical method" is identified by three greatly positions: (1) The way that the main focus is construction of mathematical concepts and developing mathematics by mathematizing from a phenomenon (horizontal mathematization) and mathematizing within mathematics (vertical mathematization). (2) The way that the main focus is applying mathematics to reality by mathematizing from a phenomenon, making a mathematical model, and solving a problem. (3) The way includes the first and the second. The first is the stance of mathematization theory (e.g. Freudenthal, 1968, 1983; Treffers, 1987). The second is the stance of mathematical modelling theory and theory of application of mathematics (e.g. Pollak, 1970, 1997, 2003). And the third is the comprehensive stance which includes the both stance (e.g. Lange, 1987, 1996). Thus, "mathematical method" has two directivities: one go toward the development of mathematics and another go toward the application of mathematics to reality. Mathematical literacy should comprehend both. On that basis, it is necessary to identify "mathematical method" that is required today, and to foster this.