
05197519
j
2007c.00285
Hackenberg, Amy J.
Units coordination and the construction of improper fractions: A revision of the splitting hypothesis.
J. Math. Behav. 26, No. 1, 2747 (2007).
2007
Elsevier, New York, NY
EN
F43
C33
improper fractions
units coordination
splitting
iterating
fractional schemes
teaching experiment
educational research
doi:10.1016/j.jmathb.2007.03.002
Summary: This article communicates findings from a yearlong constructivist teaching experiment about the relationship between four sixthgrade students' multiplicative structures and their construction of improper fractions. Students' multiplicative structures are the units coordinations that they can take as given prior to activity  i.e., the units coordinations that they have interiorized. This research indicates that the construction of improper fractions requires having interiorized three levels of units. Students who have interiorized only two levels of units may operate with fractions greater than one, but they don't produce improper fractions. These findings call for a revision in Steffe's hypothesis (Steffe, L. P. (2002). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20, 267307) that upon the construction of the splitting operation, students' fractional schemes can be regarded as essentially including improper fractions. While the splitting operation seems crucial in the construction of improper fractions, it is not necessarily accompanied by the interiorization of three levels of units.