id: 05264357
dt: j
an: 2008a.00309
au: Charalambous, Charalambos Y.; Pitta-Pantazi, Demetra
ti: Drawing on a theoretical model to study students’ understandings of
fractions.
so: Educ. Stud. Math. 64, No. 3, 293-316 (2007).
py: 2007
pu: Springer Netherlands, Dordrecht
la: EN
cc: F43 D63 C43
ut: equivalence; fraction subconstructs; fraction operations; measure;
operator; part-whole; problem-solving; quotient; ratio; structural
equation modeling
ci:
li: doi:10.1007/s10649-006-9036-2
ab: Summary: Teaching and learning fractions has traditionally been one of the
most problematic areas in primary school mathematics. Several studies
have suggested that one of the main factors contributing to this
complexity is that fractions comprise a multifaceted notion
encompassing five interrelated subconstructs (i.e., part-whole, ratio,
operator, quotient, and measure). Kieren was the first to establish
that the concept of fractions is not a single construct, but consists
of several interrelated subconstructs. Later on, in the early 1980s,
Behr et al. built on Kieren’s conceptualization and suggested a
theoretical model linking the five subconstructs of fractions to the
operations of fractions, fraction equivalence, and problem solving. In
the present study we used this theoretical model as a reference point
to investigate students’ constructions of the different subconstructs
of fractions. In particular, using structural equation modeling
techniques to analyze data of 646 fifth and sixth graders’
performance on fractions, we examined the associations among the
different subconstructs of fractions as well as the extent to which
these subconstructs explain students’ performance on fraction
operations and fraction equivalence. To a great extent, the data
provided support to the associations included in the model, although,
they also suggested some additional associations between the notions of
the model. We discuss these findings taking into consideration the
context in which the study was conducted and we provide implications
for the teaching of fractions and suggestions for further research.
rv: