
06004018
j
2012b.00259
Fujita, Taro
Learners' level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon.
J. Math. Behav. 31, No. 1, 6072 (2012).
2012
Elsevier, New York, NY
EN
C33
D23
G43
geometrical thinking
investigations
cognitive development
lower secondary
geometry
inclusion
mathematical models
geometric concepts
teachers
trainees
theory of mathematics education
ME 2011b.00644
doi:10.1016/j.jmathb.2011.08.003
Summary: This paper reports on data from investigations on learners' understanding of inclusion relations of quadrilaterals, building on the ideas from our earlier study (Fujita \& Jones, 2007, see ME 2011b.00644 ). By synthesising past and current theories in the teaching of geometry (van Hiele's model, figural concepts, prototype phenomenon, etc.), we propose a theoretical model and method to describe learners' cognitive development of their understanding of inclusion relations of quadrilaterals, and in order to investigate the topic, data are collected from trainee teachers and lower secondary school students. The findings suggest that in general more than half of above average learners are likely to recognise quadrilaterals primarily by prototypical examples, even though they know the correct definition, and this causes them difficulty in understanding the inclusion relations of quadrilaterals.