id: 06589120
dt: a
an: 2016c.00756
au: Kageyama, Kazuya
ti: Students’ initial concepts of geometric transformations and underlying
cognitive abilities.
so: Tso, Tai-Yih (ed.), Proceedings of the 36th conference of the International
Group for the Psychology of Mathematics Education “Opportunities to
learn in mathematics education", PME 36, Taipei, Taiwan, July 18‒22,
2012, Vol. 3. Taipei: National Taiwan Normal University. 3-10 (2012).
py: 2012
pu: Taipei: National Taiwan Normal University
la: EN
cc: G50 C30 C40
ut: geometry; initial concepts; geometric transformations; underlying cognitive
abilities
ci:
li:
ab: Summary: The purpose of this study is to develop a teaching unit on
geometry for secondary school mathematics. In this paper, we focus on
transformation geometry and investigate secondary school students’
initial concepts of geometric transformations and underlying cognitive
abilities. A qualitative analysis of a series of mathematical lessons
about geometric transformations suggests that students tend not only to
move figures discursively but also to construct a comprehensive figure,
which is underlain by the cognitive abilities to make various composite
units of figures, including the pre-image and image of transformation
and make use of its figurative properties for the mathematical inquiry
into transformations.
rv: