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Peer reviewed
Direct linkNorton, Anderson; Boyce, Steven – Journal of Mathematical Behavior, 2013
The purpose of this paper is to illustrate cognitive challenges introduced by Common Core State Standards for Mathematics (2010) with regard to conceptualizing fractions. We focus on a strand of standards that appear across grades three through five, which is best represented in grade four, by standard 4.NF.4a: "[Students should] understand a…
Descriptors: State Standards, Mathematics Skills, Mathematics Achievement, Grade 6
Norton, Anderson; Wilkins, Jesse L. M. – Journal of Mathematical Behavior, 2010
In building models of students' fractions knowledge, two prominent frameworks have arisen: Kieren's rational number subconstructs, and Steffe's fractions schemes. The purpose of this paper is to clarify and reconcile aspects of those frameworks through a quantitative analysis. In particular, we focus on the measurement subconstruct and the…
Descriptors: Mathematics Instruction, Mathematical Logic, Correlation, Measurement Techniques
Norton, Anderson; Wilkins, Jesse L. M. – Journal of Mathematical Behavior, 2009
Teaching experiments with pairs of children have generated several hypotheses about students' construction of fractions. For example, Steffe (2004) hypothesized that robust conceptions of improper fractions depends on the development of a splitting operation. Results from teaching experiments that rely on scheme theory and Steffe's hierarchy of…
Descriptors: Methods, Mathematics Instruction, Children, Mathematics
