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How visual representations participate in algebra classes’ mathematical activity

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Abstract

Our aim is to discuss how a visual display introduced in a classroom activity to represent a specific algebraic procedure is transformed, taking a central role and modifying the ongoing activity. To discuss how visualization comes about in this activity, we describe an illustrative example selected from observations carried out in a 9th grade classroom and analyze the class interaction from a cultural-historical perspective. Our analysis illuminates the tensions that emerge from a difference between the teacher’s way of signifying the algebraic procedure and the students’ overuse of a visual display they associate with it, and how these tensions impel changes in the activity. We further discuss some pros and cons of using visual displays in algebra classes, and we argue that it is very important for the teacher to be aware of them in order to realize the benefits of using such displays.

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Notes

  1. We use the term visual display as a general term to refer to all sorts of drawings and diagrams as well as to all graphic marks commonly used to represent and give meaning to mathematical ideas. In these, we do not include alphanumeric symbols and other frequently used mathematical symbols.

  2. Latour (2005) argues that objects (or things) too have agency and can be considered as participants in the course of social action.

  3. This is a widely, informally used expression in Brazilian schools: chuveirinho.

  4. The teacher is identified in the photos, with his permission, but all names mentioned have been changed.

  5. It can, however, be found in a quick Google search on several sites that present materials for teachers and/or solved problems for the students.

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Acknowledgments

The authors want to declare, first of all, their gratitude to the teacher and students involved in this study, for all we have learned with them. We also wish to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq, Fundação de Amparo à Pesquisa de Minas Gerais—FAPEMIG, and Pró-reitoria de Pesquisa da Universidade Federal de Minas Gerais—PRPq/UFMG for the financial support received.

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Authors and Affiliations

  1. Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Maria Manuela David, Vanessa Sena Tomaz & Maria Cristina Costa Ferreira

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  1. Maria Manuela David
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  2. Vanessa Sena Tomaz
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  3. Maria Cristina Costa Ferreira
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Correspondence to Maria Manuela David.

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David, M.M., Tomaz, V.S. & Ferreira, M.C.C. How visual representations participate in algebra classes’ mathematical activity. ZDM Mathematics Education 46, 95–107 (2014). https://doi.org/10.1007/s11858-013-0550-2

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