Electronic Proceedings of the 12^th Asian Technology Conference in Mathematics

Abstract for 12925

Exploring Ellipses by Shuttling Between the Two and Three

Dimensional Worlds -Integrated Learning Function and Geometry to

Foster Function Sense

Authors: Chieko Fukuda, Kyoko Kakihana

Affiliations: Teikyo University, JAPAN, TSUKUBA GAKUIN University,

JAPAN

Keywords: K-12 Level, K-12 Level, Cabri3D, Cabri 2 plus, ellipses,

DGS, function sense, conic sections

The ellipse often appears in astronomy and we can see a lot of

ellipses in our daily lives. It has been studied for a long time by

researchers, and has deep roots in the history of science. Although

an ellipse is familiar to us, there are very few mathematics

teaching materials about them nor are ellipses usually included in

Japanese school curricula. It may be one of the reasons why Japanese

teachers and students have not been able to draw and explore figures

of ellipses and other conic sections easily, especially spatial

ones. The development of dynamic geometry software (DGS), for

example Cabri Geometry II Plus and Cabri3D , has helped the spatial

study of ellipses. In our research, we developed many teaching

materials for ellipses and we show them in an e-book (Kakihana,

2007). By using these materials, students are able to explore an

ellipse spatially and foster a gfunction sense" (Kyoko Kakihana,

Chieko Fukuda, & Katushiko Shimizu (2002); Fukuda, and Kakihana

(2005), etc.) in an integrated learning environment for functions

and geometry.