The fractional knowledge and algebraic reasoning of students with the first multiplicative concept

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Date

2013

Journal Title

Journal ISSN

Volume Title

Publisher

The Journal of Mathematical Behavior

Abstract

To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of three different multiplicative concepts participated. This paper reports on the fractional knowledge and algebraic reasoning of six students with the most basic multiplicative concept. The fractional knowledge of these students was found to be consistent with prior research, in that the students had constructed partitioning and iteration operations but not disembedding operations, and that the students conceived of fractions as parts within wholes. The students' iterating operations facilitated their work on algebra problems, but the lack of disembedding operations was a significant constraint in writing algebraic equations and expressions, as well as in generalizing relationships. Implications for teaching these students are discussed.

Description

Accepted manuscript, post print version

Keywords

Fractional knowledge, Algebraic reasoning, Struggling students, First multiplicative concept, Iterating operation, Disembedding operation

Citation

Hackenberg, A. J. (2013). The fractional knowledge and algebraic reasoning of students with the first multiplicative concept. Journal of Mathematical Behavior, 32(3), 538-563.

Journal

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Rights

This work is under a CC-BY-NC-ND license. You are free to copy and redistribute the material in any format, as long as you give appropriate credit to the original creator and provide a link to the license. You may not use this work for commercial purpose. If you remix, transform, or build upon the material, you may not distribute the modified material.

Type

Article