New Perspectives in Science Education

Edition 13

Accepted Abstracts

On the Impact of Different Representation Systems over the Construction of Triangles Using GeoGebra. A Study with Prospective Primary Education Teachers

Alberto Arnal-Bailera, University of Zaragoza (Spain)

Antonio Oller-Marcén, Centro Universitario de la Defensa de Zaragoza (Spain)

Abstract

In this work, we study the answers given by 18 couples of prospective primary education teachers when they transfer the construction process of a triangle given its three sides as described in two different versions of Euclid’s Elements (Proposition I.22): The classical one and a less known by Oliver Byrne. The representation systems in these two versions are dramatically different even if they present the same mathematical content. We analyze the impact of these different representation systems over the work of the students. In particular, we focus on the adherence to the instructions and on the correctness of the procedures. We also describe and discuss the mistakes and the difficulties shown by the students regarding the representation systems as well as the use of a Dynamic Geometry System. We find that statistically significant influence of the representation system over the correctness of the construction, with better results among those students following the classical instructions. We also detect mistakes related to the misuse of a graphic representation given with the instructions and to the processes of instrumentation and instrumentalization. 

Keywords: teacher training, GeoGebra, Representation Systems, Geometry;

References
[1] Arnal-Bailera, A. y Oller-Marcén, A. (2017). Construyendo cuadrados con GeoGebra a partir de diferentes sistemas de representación. Un estudio con maestros de primaria en formación. Libro de Actas del VIII Congreso Iberoamericano de Educación Matemática (pp. 231-239). Madrid, España: FESPM.
[2] Rabardel, P. (1995). Les hommes et les technologies, approche cognitive des instruments contemporains. París, Francia: Armand Colin.

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