
06589120
a
2016c.00756
Kageyama, Kazuya
Students' initial concepts of geometric transformations and underlying cognitive abilities.
Tso, TaiYih (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 1822, 2012, Vol. 3. Taipei: National Taiwan Normal University. 310 (2012).
2012
Taipei: National Taiwan Normal University
EN
G50
C30
C40
geometry
initial concepts
geometric transformations
underlying cognitive abilities
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 preimage and image of transformation and make use of its figurative properties for the mathematical inquiry into transformations.