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An examination of middle school students’ representation practices in mathematical problem solving through the lens of expert work: towards an organizing scheme

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Abstract

Representation is viewed as central to mathematical problem solving. Yet, it is becoming obvious that students are having difficulty negotiating the various forms and functions of representations. This article examines the functions that representation has in students’ mathematical problem solving and how that compares to its function in the problem solving of experts and broadly in mathematics. Overall, this work highlights the close connections between the work of experts and students, showing how students use representations in ways that are inherently similar to those of experts. Both experts and students use representations as tools towards the understanding, exploration, recording, and monitoring of problem solving. In social contexts, experts and students use representations for the presentation of their work but also the negotiation and co-construction of shared understandings. However, this research also highlights where students’ work departs from experts’ representational practices, hence, providing some directions for pedagogy and further work.

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Notes

  1. As Presmeg (2006) noted, the term representation “became imbued with various meanings and connotations in the changing paradigms of the last two decades” (p. 206). She further notes that the mathematics education community has had difficulty articulating an accurate definition of this term. Presmeg continues to quote Kaput (1987) that “an indication of this difficulty is that definitions for the term ‘representation’ often include the word ‘represent’”. Hence several researchers prefer to use the term ‘inscriptions’ rather than representations. Here, I maintain the use of representation to stay closer to the majority of the literature; however, I use it as synonymous to ‘inscription’.

  2. Roth and McGinn (1997) use the terms “rhetorical objects” and “conscription devices”.

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Acknowledgments

The research reported here was supported in part by the National Science Foundation under Grant # REC-0447542. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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    Despina A. Stylianou

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Stylianou, D.A. An examination of middle school students’ representation practices in mathematical problem solving through the lens of expert work: towards an organizing scheme. Educ Stud Math 76, 265–280 (2011). https://doi.org/10.1007/s10649-010-9273-2

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