数学教師の知識とそれを顕在化させる方法

抄録

As L. S. Shulman (1986) have noted, there are content knowledge, pedagogical content knowledge, and curricular knowledge in teacher's knowledges. For Shulman, content knowledge is knowledge about the subject, for example mathematics, and its structure. Pedagogical content knowledge includes' the ways of representing and formulating the subject that make it comprehensible to others' and' an understanding of what makes the learning of topics easy or difficult; the concepts and preconceptions that students of different ages and backgrounds bring with them…' Finally curricular knowledge encompasses what might be called the 'scope and sequence' of a subject and material used in teaching. In this paper, I describe the knowledges in mathematics teacher, in paticular pedagogical content knowledge and a way to overt them. Pedagogical content knowledge is made up of several components; knowledge about the subject-matter, knowledge about students and knowledge about ways of presenting the subject-matter. Because they value quality above quantity, I concentrate on the relationship that knowledge about ways of presenting the subject-matter is due to knowledge about the subject-matter and knowledge about students. Shulman (1986) distinguishes between two kinds of understanding of subject-matter that teachers need to have - knowing "that" and knowing "why". I think that all three pedagogical content knowledges have two sides, knowing that and knowing why. To ask mathematics teacher a question on children's responses and subject-matter overt his or her knowledge about ways of presenting the subject-matter. After all knowledge about ways of presenting the subject-matter is due to 'knowing why' side of two other knowledge. The ways to overt pedagogical content knowledge in mathematics teacher connote the following three necessary condition; (1) to create conflict condition (2) to encounter children's errors and misconceptions (3) to be haven a keen awareness of a context in knowledges.