id: 05648591
dt: j
an: 2010a.00340
au: Hackenberg, Amy J.; Tillema, Erik S.
ti: Students’ whole number multiplicative concepts: a critical constructive
resource for fraction composition schemes.
so: J. Math. Behav. 28, No. 1, 1-18 (2009).
py: 2009
pu: Elsevier, New York, NY
la: EN
cc: F43 C33
ut: fractions; fraction multiplication; multiplicative concepts; schemes;
learning; educational research
ci:
li: doi:10.1016/j.jmathb.2009.04.004
ab: Summary: This article reports on the activity of two pairs of sixth grade
students who participated in an 8-month teaching experiment that
investigated the students’ construction of fraction composition
schemes. A fraction composition scheme consists of the operations and
concepts used to determine, for example, the size of 1/3 of 1/5 of a
whole in relation to the whole. Students’ whole number multiplicative
concepts were found to be critical constructive resources for
students’ fraction composition schemes. Specifically, the
interiorization of two levels of units, a particular multiplicative
concept, was found to be necessary for the construction of a unit
fraction composition scheme, while the interiorization of three levels
of units was necessary for the construction of a general fraction
composition scheme. These findings contribute to previous research on
students’ construction of fraction multiplication that has emphasized
partitioning and conceptualizing quantitative units. Implications of
the findings for teaching are considered.
rv: