Abstract
The purpose of this paper is to suggest the educational functions of geometric construction as an educational material on elementary school level mediating between elementary and secondary school mathematics to promote children's empirical recognition of the geometric figure to logical one. It is a general knowledge that geometric construction in elementary school mathematics has the educational functions to make children understand and apply the properties of geometric figures. Moreover, in this paper we stress that it has the educational function to change their recognition about the geometric figure. While they learn a geometric figure as the set of properties in elementary school mathematics, they need to grasp a geometric figure as the set of the relations among properties in secondary school mathematics. This conceptual gap between elementary and secondary school mathematics cases serious difficulties for the learning of proof in secondary mathematics. We focus on the educational functions of geometric construction to mediate these two sides, according to Okazaki & Iwasaki (2003). We designed the experimental lessons to confirm the educational functions of geometric construction for the fifth grade's teaching whose topics was the geometric construction of a rectangle by using the ruler and compass. When designing the teaching plan, we adopted the idea of Backward Design by Wiggins & McTighe (2005). The performance task was developed to evaluate the learner's cognitive changes about the geometrical figure. Thorough the quantitative and qualitative evaluations of the experimental lessons, it was suggested that the geometric construction had the educational function to promote learner's logical cognition about geometrical figure. The educational functions of geometric construction on elementary school mathematics that we confirmed through this study are as follows. (1) to promote the use and understanding of the properties of geometrical figures in the problem solving. (2) to give learners the chance to recognize geometric relations itself. (3) to change the recognition of geometrical figure from empirical to logical.
