
06639094
a
2016f.01040
Jones, Keith
Fujita, Taro
Miyazaki, Mikio
Learning congruencybased proofs in geometry via a webbased learning system.
Smith, C. (ed.), Proceedings of the British Society for Research into Learning Mathematics (BSRLM). Vol. 33, No. 1. Proceedings of the day conference, University of Bristol, UK, March 2, 2013. London: British Society for Research into Learning Mathematics (BSRLM). 3136 (2013).
2013
London: British Society for Research into Learning Mathematics (BSRLM)
EN
G43
G53
E53
U73
U53
Euclidean geometry
congruent figures
conceptions
congruent triangles
proving
similarity
congruent transformations
lower secondary
educational research
geometry software
webbased learning system
proof learning system
feedback
textbook analyses
http://www.bsrlm.org.uk/IPs/ip331/BSRLMIP33106.pdf
Summary: Congruence, and triangle congruence in particular, is generally taken to be a key topic in school geometry. This is because the three conditions of congruent triangles are very useful in proving geometrical theorems and also because triangle congruency leads on to the idea of mathematical similarity via similar triangles. Despite the centrality of congruence in general, and of congruent triangles in particular, there appears to be little research on the topic. In this paper, we use evidence from an ongoing research project to illustrate how a webbased learning system for geometrical proof might help to develop Year 9 pupils' capability with congruent triangles. Using the notion of `conceptions of congruency' as our framework, we first characterise our webbased learning system in terms of four different `conceptions' of congruency by comparing the online tasks with activities from a Year 9 textbook. We then discuss how the webbased learning system would aid pupils when they are tackling congruencybased proofs in geometry.