Electronic Proceedings of the 12th Asian Technology Conference in Mathematics
Abstract for 13558
Experiencing the multiple dimensions of mathematics with dynamic 3D geometry environments:
Authors: Colette Laborde
Affiliations: University Joseph Fourier
Topics: Mathematics Education using Information & Communication Technology, Mathematics Teaching, Learning and Assessment using Technology
In this paper, we start from the distinction between two processes : iconic and non iconic visualization. Both are involved in solving problems in geometry. The non iconic visualization consists in breaking down an object into parts of same or lower dimension. This cognitive process is critical for solving problems in geometry as very often the reasoning consists in establishing relationships between elements of the figure. However this process is not spontaneous and must be learned. 3D geometry is the source of new problems regarding iconic and non iconic visualization. On the one hand, iconic visualization is not always reliable as it is in 2D geometry, on the other hand non iconic visualization is more complex since it deals with a larger number of kinds of objects, from dimension 0 to dimension 3. The paper examines how 3D dynamic geometry environments with direct manipulation and the tools they offer may enlarge the iconic visualization and assist the non iconic visualization. The example of Cabri3D is used to illustrate the analysis.