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Continuous Directed Scaling: How Could Dynamic Multiplication and Division Diagrams Be Used to Cross Mathematical Borders?

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Borders in Mathematics Pre-Service Teacher Education

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Abstract

We consider how dynamic diagrams can be used to model multiplication and division. This chapter begins with a review of how multiplication is conceptualized in elementary mathematics education. We consider the affordances of familiar representations of multiplication (e.g., repeated addition, the area representation) and highlight aspects of arithmetic (e.g., multiplication with signed numbers) that are difficult for them to represent. Next, we develop geometric models of multiplication and division by adapting compass-and-straightedge procedures to dynamic geometry. We argue that dynamic diagrams can model multiplication and division as continuous scaling operations on directed lengths, and we consider how dynamic diagrams could be used as virtual manipulatives in pre-service teacher education.

This research was supported in part by a College of Education and Human Development faculty research seed grant to both authors. Opinions expressed here are the authors’ and do not reflect the views of the University of Maine

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Notes

  1. 1.

    Such as would be found in My Math, Grade 3, Vol. 1 (2017, McGraw-Hill).

  2. 2.

    Pseudonyms.

  3. 3.

    See: https://en.wikipedia.org/wiki/Singly_and_doubly_even

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Author information

Authors and Affiliations

  1. School of Learning and Teaching and Research in STEM Education (RiSE) Center, 330 Shibles Hall, University of Maine, Orono, ME, USA

    Justin K. Dimmel

  2. School of Learning and Teaching and Research in STEM Education (RiSE) Center, 324A Shibles Hall, University of Maine, Orono, ME, USA

    Eric A. Pandiscio

Authors
  1. Justin K. Dimmel
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  2. Eric A. Pandiscio
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Correspondence to Justin K. Dimmel .

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Editors and Affiliations

  1. Department of Teacher Education, College of Charleston, Charleston, SC, USA

    Nenad Radakovic

  2. Department of Integrated Studies in Education, McGill University, Montreal, QC, Canada

    Limin Jao

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Dimmel, J.K., Pandiscio, E.A. (2020). Continuous Directed Scaling: How Could Dynamic Multiplication and Division Diagrams Be Used to Cross Mathematical Borders?. In: Radakovic, N., Jao, L. (eds) Borders in Mathematics Pre-Service Teacher Education. Springer, Cham. https://doi.org/10.1007/978-3-030-44292-7_2

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  • DOI: https://doi.org/10.1007/978-3-030-44292-7_2

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-44292-7

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