id: 06440861
dt: j
an: 2015d.00555
au: Zhang, Xiaofen; Clements, M. A. (Ken); Ellerton, Nerida F.
ti: Conceptual mis(understandings) of fractions: from area models to multiple
embodiments.
so: Math. Educ. Res. J. 27, No. 2, 233-261 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht; Mathematics Education Research Group of
Australasia (MERGA), Wahroonga, New South Wales, Australia
la: EN
cc: F43 D73 C33
ut: unit fractions; multiple embodiments of fractions; area-model
representations of fractions; reification
ci:
li: doi:10.1007/s13394-014-0133-8
ab: Summary: Area-model representations seem to have been dominant in the
teaching and learning of fractions, especially in primary school
mathematics curricula. In this study, we investigated 40 fifth grade
children’s understandings of the unit fractions, $\frac{1}{2}$,
$\frac{1}{3}$ and $\frac{1}{4}$, represented through a variety of
different models. Analyses of pre-teaching test and interview data
revealed that although the participants were adept at partitioning
regional models, they did not cope well with questions for which unit
fractions were embodied in non-area-model scenarios. Analyses of
post-teaching test and interview data indicated that after their
participation in an instructional intervention designed according to
{\it Z. P. Dienes}’ [Building up mathematics. London: Hutchinson
Educational (1960)] dynamic principle, the students’ performances on
tests improved significantly, and their conceptual understandings of
unit fractions developed to the point where they could provide
reasonable explanations of how they arrived at solutions. Analysis of
retention data, gathered more than 3~months after the teaching
intervention, showed that the students’ newly found understandings
had, in most cases, been retained.
rv: