ERIC Number: EJ796801
Record Type: Journal
Publication Date: 2007
Reference Count: 0
Units Coordination and the Construction of Improper Fractions: A Revision of the Splitting Hypothesis
Hackenberg, Amy J.
Journal of Mathematical Behavior, v26 n1 p27-47 2007
This article communicates findings from a year-long constructivist teaching experiment about the relationship between four sixth-grade 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, 267-307) 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.
Descriptors: Constructivism (Learning), Mathematics Instruction, Grade 6, Elementary School Students, Elementary School Mathematics, Mathematical Concepts, Arithmetic, Teaching Methods, Problem Solving
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: Elementary Education; Grade 6
Authoring Institution: N/A
IES Cited: ED512043