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Mathematics Education Research Journal

, Volume 27, Issue 2, pp 201–231 | Cite as

Enriching student concept images: Teaching and learning fractions through a multiple-embodiment approach

  • Xiaofen Zhang
  • M. A. (Ken) Clements
  • Nerida F. Ellerton
Original Article
First Online:

Abstract

This study investigated how fifth-grade children’s concept images of the unit fractions represented by the symbols \( \frac{1}{2} \), \( \frac{1}{3} \), and \( \frac{1}{4} \) changed as a result of their participation in an instructional intervention based on multiple embodiments of fraction concepts. The participants’ concept images were examined through pre- and post-teaching written questions and pre- and post-teaching one-to-one verbal interview questions. Results showed that at the pre-teaching stage, the student concept images of unit fractions were very narrow and mainly linked to area models. However, after the instructional intervention, the fifth graders were able to select and apply a variety of models in response to unit fraction tasks, and their concept images of unit fractions were enriched and linked to capacity, perimeter, linear and discrete models, as well as to area models. Their performances on tests had improved, and their conceptual understandings of unit fractions had developed.

Keywords

Unit fractions Concept images Multiple embodiments of fractions Area-model representations of fractions 
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Notes

Acknowledgments

The authors would like to thank Mr. X and his students for their enthusiastic participation in this study. We would also thank Dr. Jeffrey Barrett and Dr. Jennifer Tobias for their support and constructive advice.

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Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2014

Authors and Affiliations

  • Xiaofen Zhang
    • 1
  • M. A. (Ken) Clements
    • 1
  • Nerida F. Ellerton
    • 1
  1. 1.Department of MathematicsIllinois State UniversityNormalUSA

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