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Third International Handbook of Mathematics Education pp 549–569Cite as

Modelling with Mathematics and Technologies

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Part of the book series: Springer International Handbooks of Education ((SIHE,volume 27))

Abstract

This chapter seeks to provide an integrating theoretical framework for understanding the somewhat disparate and disconnected literatures on “modelling” and “technology” in mathematics education research. From a cultural–historical activity theory, neo-Vygtoskian perspective, mathematical modelling must be seen as embedded within an indivisible, molar “whole” unit of “activity.” This notion situates “technology”—and mathematics, also—as an essential part or “moment” of the whole activity, alongside other mediational means; thus it can only be fully understood in relation to all the other moments. For instance, we need to understand mathematics and technology in relation to the developmental needs and hence the subjectivity and “personalities” of the learners. But, then, also seeing learning as joint teaching–learning activity implies the necessity of understanding the relation of these also to the teachers, and to the wider institutional and professional and political contexts, invoking curriculum and assessment, pedagogy and teacher development, and so on. Historically, activity has repeatedly fused mathematics and technology, whether in academe or in industry: this provides opportunities, but also problems for mathematics education. We illustrate this perspective through two case studies where the mathematical-technologies are salient (spreadsheets, the number line, and CAS), which implicate some of these wider factors, and which broaden the traditional view of technology in social context.

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Author information

Authors and Affiliations

  1. The University of Manchester, Manchester, UK

    Julian Williams

  2. The University of Queensland, St. Lucia, QLD, Australia

    Merrilyn Goos

Authors
  1. Julian Williams
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  2. Merrilyn Goos
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Correspondence to Julian Williams .

Editor information

Editors and Affiliations

  1. Illinois State University, n/a, Normal, 61790-4520, Illinois, USA

    M.A. (Ken) Clements

  2. Fac. Education, Centre for Science, Mathematics &, Monash University, Clayton, 3800, Victoria, Australia

    Alan J. Bishop

  3. FB Erziehungswissenschaft und, Psychologie, FU Berlin, Habelschwerdter Allee 45, Berlin, 14195, Germany

    Christine Keitel

  4. Dept. Mathematics Education, University of Georgia, Aderhold Hall 105, Athens, 30602-7124, Georgia, USA

    Jeremy Kilpatrick

  5. Fac. Education, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong SAR

    Frederick K.S. Leung

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Williams, J., Goos, M. (2012). Modelling with Mathematics and Technologies. In: Clements, M., Bishop, A., Keitel, C., Kilpatrick, J., Leung, F. (eds) Third International Handbook of Mathematics Education. Springer International Handbooks of Education, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4684-2_18

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