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Computer Algebra as an Instrument: Examples of Algebraic Schemes

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The Didactical Challenge of Symbolic Calculators

Part of the book series: Mathematics Education Library ((MELI,volume 36))

Abstract

In this chapter, we investigate the relationship between computer algebra use and algebraic thinking from the perspective of the instrumental approach to learning mathematics in a technological environment, which was addressed in the previous chapter.

Data comes from a research study on use of computer algebra for developing algebraic insights. Teaching experiments were carried out in ninth- and tenth-grade classes in which the students used symbolic calculators to solve algebraic problems, and in particular for solving parameterized equations and substituting expressions.

We describe in detail instrumented action schemes for solving parameterized equations and substituting expressions. We observe that the approach which students take in their work in the computer algebra environment is closely related to their mental conceptions. The instrumental approach offers ways of making this connection more explicit and better understanding students’ difficulties. In particular, we note that students found it difficult to integrate the two schemes into one comprehensive scheme.

We argue that a relationship needs to be established and elaborated between the instrumental approach and other theoretical notions on learning such as the symbolization perspective.

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Author information

Authors and Affiliations

  1. Freudenthal Institute, Utrecht University, The Netherlands

    Paul Drijvers & Koeno Gravemeijer

Authors
  1. Paul Drijvers
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  2. Koeno Gravemeijer
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Editors and Affiliations

  1. Université Montpellier II, France

    Dominique Guin  & Luc Trouche  & 

  2. University of Cambridge, UK

    Kenneth Ruthven

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Drijvers, P., Gravemeijer, K. (2005). Computer Algebra as an Instrument: Examples of Algebraic Schemes. In: Guin, D., Ruthven, K., Trouche, L. (eds) The Didactical Challenge of Symbolic Calculators. Mathematics Education Library, vol 36. Springer, Boston, MA. https://doi.org/10.1007/0-387-23435-7_8

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