Computer Algebra as an Instrument: Examples of Algebraic Schemes View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2005

AUTHORS

Paul Drijvers , Koeno Gravemeijer

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. More... »

PAGES

163-196

References to SciGraph publications

  • 2002. Reflective Abstraction in Advanced Mathematical Thinking in ADVANCED MATHEMATICAL THINKING
  • 2000-03. La parabole du gaucher et de la casserole à bec verseur: ètude des processus d'apprentissage dans un environnement de calculatrices symboliques in EDUCATIONAL STUDIES IN MATHEMATICS
  • 2002-10. Learning mathematics in a computer algebra environment: obstacles are opportunities in ZENTRALBLATT FÜR DIDAKTIK DER MATHEMATIK
  • 2004. Learning to Reason About Distribution in THE CHALLENGE OF DEVELOPING STATISTICAL LITERACY, REASONING AND THINKING
  • 2002-10. Mastering by the teacher of the instrumental genesis in CAS environments: necessity of intrumental orchestrations in ZENTRALBLATT FÜR DIDAKTIK DER MATHEMATIK
  • 1999-10. Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus in INTERNATIONAL JOURNAL OF COMPUTERS FOR MATHEMATICAL LEARNING
  • 1991-02. On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin in EDUCATIONAL STUDIES IN MATHEMATICS
  • 2003. What can digital technologies take from and bring to research in mathematics education? in SECOND INTERNATIONAL HANDBOOK OF MATHEMATICS EDUCATION
  • 1991-04. Encouraging versatile thinking in algebra using the computer in EDUCATIONAL STUDIES IN MATHEMATICS
  • 2000-07. L'intégration d'instruments informatiques dans l'enseignement: Une approche par les techniques in EDUCATIONAL STUDIES IN MATHEMATICS
  • 2000-11. Students encountering obstacles using a CAS in INTERNATIONAL JOURNAL OF COMPUTERS FOR MATHEMATICAL LEARNING
  • 2000-02. Creating Meaning for and with the Graphing Calculator in EDUCATIONAL STUDIES IN MATHEMATICS
  • 1995-03. Cognition and artifacts: A contribution to the study of though in relation to instrumented activity in EUROPEAN JOURNAL OF PSYCHOLOGY OF EDUCATION
  • Book

    TITLE

    The Didactical Challenge of Symbolic Calculators

    ISBN

    0-387-23158-7

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/0-387-23435-7_8

    DOI

    http://dx.doi.org/10.1007/0-387-23435-7_8

    DIMENSIONS

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