EXPRESSION FRAME OF THINKING ACTIVITY FOR LEARNING MATHEMATICS

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Main results of our research are given by the following (1) and (2)(1) In ordinary math classes, most of the teachers try to infuse mathematical concepts or knowledge written in the textbook to the students. They then encounter sometimes with serious difficulties to make students to form clear images of notions in their minds, We have developed , in this research, a new teaching-learning process where all students can construct the mathematical concepts and knowledge written in the textbook by themselves by making use of "Expression Frame" defined by the following (a) and (b) .(a)Students may construct a narrative of thinking activities by making use of an of "Expression Frame".(b)Any "Expression Frame" does not represent any narrative of thinking activities.(2) We may consider the" Three myself' M 1, M2 and MS corresponding to the following activities (1), (2) and (3) respectively. (1) Dialogue with visible object of attention. (2)Dialogue with object of attention in mind.(3) Construct a new dialogue by combining (1) and (2). Many researchers on mathematics education have emphasized that math class where the students can make Mathematical concepts and knowledge by their own efforts. But none of them shows a method by which the students can construct the mathematical concepts and knowledge by themselves. In this research, we have established a principle of teaching-learning process which satisfies the following.(A)" Three myself' Ml, M2 and M3 in students' mind are able to construct mathematical concept or knowledge written in the textbook.(B)A student is able to combine his/her thinking with other student's thinking by making use of the "Expression Frame".