id: 06639094
dt: a
an: 2016f.01040
au: Jones, Keith; Fujita, Taro; Miyazaki, Mikio
ti: Learning congruency-based proofs in geometry via a web-based learning
system.
so: 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). 31-36 (2013).
py: 2013
pu: London: British Society for Research into Learning Mathematics (BSRLM)
la: EN
cc: G43 G53 E53 U73 U53
ut: Euclidean geometry; congruent figures; conceptions; congruent triangles;
proving; similarity; congruent transformations; lower secondary;
educational research; geometry software; web-based learning system;
proof learning system; feedback; textbook analyses
ci:
li: http://www.bsrlm.org.uk/IPs/ip33-1/BSRLM-IP-33-1-06.pdf
ab: 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 on-going research project to illustrate
how a web-based 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 web-based 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 web-based
learning system would aid pupils when they are tackling
congruency-based proofs in geometry.
rv: