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Mathematics Education Research Journal

, Volume 27, Issue 2, pp 233–261 | Cite as

Conceptual mis(understandings) of fractions: From area models to multiple embodiments

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

Abstract

Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children’s understandings of the unit fractions, \( \frac{1}{2} \), \( \frac{1}{3} \) and \( \frac{1}{4} \), represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes’ (1960) dynamic principle, the students’ performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students’ newly found understandings had, in most cases, been retained.

Keywords

Unit fractions Multiple embodiments of fractions Area-model representations of fractions Reification 
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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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