## Mathematical Modeling in the Inquiry of Linkages Using LEGO and Graphic Calculator. Does New Technology Alternate Old Technology?

*ISODA Masami*

`msisoda@human.tsukuba.ac.jp`

Institute of Education

**University of Tsukuba**

*MATSUZAKI Akio*

`makio@human.tsukuba.ac.jp`

Graduate School of Education

**University of Tsukuba**

Japan

### Abstract

This study discussed the roles of old technology and new technology in the teaching of mathematical modeling. In this paper, a crank mechanism made of LEGO was used for teaching mathematical modeling. This paper, as the third phase of the research (Isoda, Matuzaki, Nakajima, 1998), discussed the changing roles of LEGO and a Graphic Calculator if we added the activity of making linkage (Matuzaki, 1999).From the case study, this paper distinguished the four cognitive phases through mathematical modeling: reasoning with the visual image in real world, reasoning with the mechanical structure, reasoning with the mathematical model without the mechanical structure and reasoning with the mathematical model and the mechanical structure. With comparing our results with Rose Mary Zbiek’s research (1998) which discussed the role of new technology in formulation of the model, this research discussed following: the real world activity should be distinguished before and after knowing the mechanical structure, and the mathematical activity with the model should be distinguished before and after synchronizing the parameters of the model and the parts of the mechanics. In this paper, graphic calculator as a piece of new technology helped mathematical works in the process of the mathematical modeling and LEGO as a piece of old technology helped the activity in real world. The synchronization of the model with the mechanics was supported by both technologies.

?1999, ATCM, Inc