id: 06140299
dt: a
an: 2013b.00589
au: Rahim, Medhat H.; Siddo, Radcliffe
ti: The use of visualization for learning and teaching mathematics.
so: Paditz, Ludwig (ed.) et al., Proceedings of the 10th international
conference “Models in Developing Mathematics Education”, Dresden,
Saxony, Germany, September 11‒17, 2009. Dresden: Hochschule für
Technik und Wirtschaft (ISBN 83-919465-9-2). 496-500 (2009).
py: 2009
pu: Dresden: Hochschule für Technik und Wirtschaft
la: EN
cc: G30 G50 D40 U60
ut: transformation geometry; area; visualization; visual justification;
diagrams; computer graphics; physical models
ci:
li:
ab: Summary: Based on dissection-motion-operations, DMO (decomposing a figure
into several pieces and composing the resulting pieces into a new
figure of equal area), a set of visual representations (models) of
mathematical concepts will be introduced. The visual models are
producible through manipulation and computer GSP/Cabri software. They
are based on the {\it P. M. van Hiele}’s levels [Structure and
insight: a theory of mathematics education. Orlando: Academic Press
(1989)] of thought development; in particular, level 2 (informal
deductive reasoning) and level 3 (deductive reasoning). The basic theme
for these models has been visual learning and understanding through
manipulatives and computer representations of mathematical concepts vs.
rote learning and memorization. The three geometric transformations or
motions: translation, rotation, reflection and their possible
combinations were used; they are illustrated in several texts. As well,
a set of three commonly used dissections or decompositions [{\it H.
Eves}, A survey of geometry. Boston: Allan and Bacon inc. (1972)] of
objects was utilized.
rv: