Abstract
The final purpose of this study is to develop the curriculum of geometric figure in the upper grades which promotes the mediating children's empirical recognition of the geometric figure to logical one. For attaining this purpose, this paper describes the usefulness and the theoretical framework of curriculum development to promote the awareness of the set of the relations among properties of geometric figure by applying Lampert's theory. Lampert insisted that the mathematical knowledge was made up of three mental components related to the learning content, and illustrated the interactive relationships among those components by using the idea of awareness and unawareness. We applied this theory to the lessons of geometric figure. The framework that we constructed is composed three components; concrete and intuitive understanding, (among the geometric figure) relational understanding, and logical understanding. The main purpose of teaching and learning of the geometric figure in elementary school is the understanding of properties. So we described the relationships and the mechanism among the three components for understanding the properties by the awareness and the unawareness of properties. Furthermore, for evaluating the framework, we designed the fifth grade's lessons "geometric congruence" as an application example and evaluated it. As a result, we could confirm that the three components and the interactive relationship we insisted in this paper became the theoretical framework to design the lesson which promoted to change children's understanding about geometrical figures from empirical one to logical one.
