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
Keywords:
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.