id: 06418763
dt: j
an: 2015b.00691
au: Wang, Sasha; Kinzel, Margaret
ti: How do they know it is a parallelogram? Analysing geometric discourse at
van Hiele level 3.
so: Res. Math. Educ. 16, No. 3, 288-305 (2014).
py: 2014
pu: Taylor \& Francis (Routledge), Abingdon, Oxfordshire; British Society for
Research into Learning Mathematics (BSRLM)
la: EN
cc: G40 C30 C50
ut: mathematical discourse; geometry; van Hiele theory
ci: ME 2011d.00346
li: doi:10.1080/14794802.2014.933711
ab: Summary: In this article, we introduce {\it A. Sfard}’s discursive
framework [Thinking as communicating. Human development, the growth of
discourses, and mathematizing. Cambridge: Cambridge University Press
(2008; ME 2011d.00346)] and use it to investigate prospective
teachers’ geometric discourse in the context of quadrilaterals. In
particular, we focus on describing and analysing two participants’
use of mathematical words and substantiation routines related to
parallelograms and their properties at van Hiele level 3 thinking. Our
findings suggest that a single van Hiele level of thinking encompasses
a range of complexity of reasoning and differences in discourse and
thus a deeper investigation of students’ mathematical thinking within
assigned van Hiele levels is warranted.
rv: