id: 05587842
dt: j
an: 2009d.00352
au: Laborde, Colette
ti: Experiencing the multiple dimensions of mathematics with dynamic 3D
geometry environments: Illustration with Cabri 3D.
so: Electron. J. Math. Technol. 2, No. 1, 39-53, electronic only (2008).
py: 2008
pu: Mathematics and Technology, Radford, VA
la: EN
cc: G40 C30 R20 U70 U50
ut: iconic and non-iconic visualization; geometry software
ci:
li: https://php.radford.edu/~ejmt/ContentIndex.php
ab: Summary: The paper analyzes how 3D dynamic geometry environments may be
used to foster the exploration of multiple dimensions of 3D geometry.
The notion of dimension is twofold: it refers, one the one hand to the
dimension of a geometrical object, on the other hand to the multiple
types of representation and expressions used in geometry. Two kinds of
processes are involved in problem solving in geometry: iconic and non
iconic visualization. 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. Iconic visualization is not always reliable
as it is in 2D geometry and 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 may enlarge the iconic visualization and assist the non
iconic visualization. 3D geometry computer environments may also offer
a textual description linked to the dynamic diagram. The interplay
between both representations not only facilitates the construction
process of figures but also may be used to move from construction tasks
to proof tasks. The example of Cabri 3D is used in the paper to
illustrate the argument.
rv: