子どもたちの数学とその観察者としての教師の役割

抄録

Based on the constructivist principle of mathematics education, we focus on constructivist school mathematics that constructed by children. Constructivist school mathematics is called as children's mathematics in this paper. Steffe L.P. and Wiegel H.G. define "a constructivist school mathematics to be the results of the observer's experiential abstractions in the context of interacting with children mathematically". That is, the teacher needs to accept the principle of relativity (an admittion that there is a real world that is separate from one's experence of it) so that he or her establishes children's mathematics. In this paper, I suggest two roles of teacher as the obserber of children's mathematics constructed in their mathematics learing. The first is a role of the teacher as first-order observer. The teacher, as a first-order observer, tries to assume the point of view of the leaner. While to do, the teacher establishes children's mathematics as second-order observer. The teacher, as a second-order observer, is aware of his or her own activity in interaction with children, and of the influence that it may have on the children's activity. This teacher observers the teacher as a first-order observer constructing children's mathematics as a second-order model.