
06440861
j
2015d.00555
Zhang, Xiaofen
Clements, M. A. (Ken)
Ellerton, Nerida F.
Conceptual mis(understandings) of fractions: from area models to multiple embodiments.
Math. Educ. Res. J. 27, No. 2, 233261 (2015).
2015
Springer Netherlands, Dordrecht; Mathematics Education Research Group of Australasia (MERGA), Wahroonga, New South Wales, Australia
EN
F43
D73
C33
unit fractions
multiple embodiments of fractions
areamodel representations of fractions
reification
doi:10.1007/s1339401401338
Summary: Areamodel 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 preteaching 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 nonareamodel scenarios. Analyses of postteaching 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.