数学的な考え方の再考 : Wittmannの数学教育学の視点から

抄録

Fostering 'mathematical thinking' has been intended as a goal of mathematics education in Japan. Since mathematical concepts are all abstructive, 'mathematical thinking' is the only way to deal with them. Therefore, it's essential in mathematics. But it cannot be clear by its very nature. Rather, the auther intendes that too much clarification of it can lose the freedom of it. So, we must bring out 'mathematical thinking' from the children. This paper studies the potentiality of the sources of mathematical thinking in children. The Review of studies in past shows the esential part of 'mathematical thinking' and the part which has to be extended. Nakajima (1981) describes that the 'value' on which mathematics was created is the base of 'mathematical thinking'. But, Because the concept of mathematics effects on it, we must start with the concept of mathematics which is relevant. Wittmann (1995) suggests MATHEMATICS as the concept of mathematics which includes mathematical works in the broadest sense which covers all sciences and daily life. The auther think that if the 'value' which is the source of 'mathematical thinking' is derived from MATHEMATICS, the extension described above will be done. And the auther concludes that mathematical thinking can be fostered by the 'tearing unit', which is the essential part of Wittmann's mathematics education. As an example of mathematical thinking, 'Symmetric Thinking' is elaborated. The extension is illustrated. And a 'teaching unit' which fosters childrens' 'Symmetric Thinking' is designd.