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An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

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Abstract

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings in spreadsheet environments and to understand better the questions of technological integration. Then, these theoretical elements are used in order to design an exploratory experiment with grade 7 pupils and analyse its results.

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References

  • J. Ainley (1999) Doing Algebra-Type Stuff: Emergent algebra in the primary school NumberInSeries2 Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education. Israel Institute of Technology Haifa 9–16

    Google Scholar 

  • J. Ainley E. Nardi D. Pratt (1999) Constructing meaning for formal notation in active g raphing. Proceedings of the 1st Conference of the European Society for Research in Mathematics Education NumberInSeries1 Forschungsinstitut fuer Mathematikdidaktik Osnabrueck 189–200

    Google Scholar 

  • J. Ainley L. Bills K. Wilson (2003) Designing tasks for purposeful algebra Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education Bellaria

    Google Scholar 

  • M. Artigue (2002) ArticleTitleLearning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work International Journal of Computers for Mathematical Learning 7 IssueID3 245–274 Occurrence Handle10.1023/A:1022103903080

    Article  Google Scholar 

  • F. Arzarello L. Bazzini G. Chiappini (1994) The process of naming in algebraic thinking Proceedings of the 18th International Conference for the Psychology of Mathematics Education NumberInSeries22 University of Lisbon Lisbon 40–47

    Google Scholar 

  • F. Arzarello L. Bazzini G. Chiappini (2001) A model for analysing algebraic processes of thinking R. Sutherland T. Assude A. Bell R. Lins (Eds) Perspectives on school algebra. Kluwer Academic Publishers Dordrecht 61–81

    Google Scholar 

  • N. Bednarz B. Janvier (2001) Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic N. Bednarz C. Kieran L. Lee (Eds) Approaches to Algebra: Perspectives for Research and Teaching. Kluwer Academic Publisher Dordrecht 115–136

    Google Scholar 

  • M. Bosch Y. Chevallard (1999) ArticleTitleLa sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique Recherches en Didactique des Mathématiques 19 IssueID1 77–124

    Google Scholar 

  • B. Capponi (1999) ArticleTitleLe tableur pour le collège, un outil pour l’enseignement des mathématiques Petit x 52 5–42

    Google Scholar 

  • B. Capponi (2000) Tableur, arithmétique et algèbre. L’algèbre au lycée et au collège, Actes des journées de formation de formateurs, 1999 IREM de Montpellier Boisseron 58–66

    Google Scholar 

  • Y. Chevallard (1992) Intégration et viabilité des objets informatiques dans l’enseignement des mathématiques B. Cornu (Eds) L’ordinateur pour enseigner les mathématiques. Presses Universitaires de France Paris 183–203

    Google Scholar 

  • Y. Chevallard (1998) Analyse des pratiques enseignantes et didactique des mathématiques: l’approche anthropologique, Actes de l’Université d’Été de Didactique de La Rochelle IREM de Clermont-Ferrand La Rochelle pp. 88–101 88–101

    Google Scholar 

  • H. Chick K. Stacey J. Vincent J. Vincent (Eds) (2001) The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conference University of Melbourne Melbourne

    Google Scholar 

  • G. Dettori R. Garuti E. Lemut L. Netchitailova (1995) An Analysis of the relationship between spreadsheet and algebra L. Burton B. Jaworski (Eds) Technology in Mathematics Teaching – a Bridge Between Teaching and Learning. Chartwell-Bratt Bromley 261–274

    Google Scholar 

  • Drouhard J.P., (1992). Les écritures symboliques de l’algèbre élémentaire. Thèse de Doctorat, Université Paris 7.

  • D. Guin L. Trouche (1999) ArticleTitleThe complex process of converting tools into mathematical instruments: The case of calculators International Journal of Computers for Mathematical Learning 3 IssueID3 195–227 Occurrence Handle10.1023/A:1009892720043

    Article  Google Scholar 

  • D. Guin K. Ruthven L. Trouche (Eds) (2004) The Didactical Challenge of Symbolic Calculators, Turning a Computational Device into a Mathematical Instrument Kluwer Academic Publisher Dordrechts

    Google Scholar 

  • J.B. Lagrange (1999) ArticleTitleComplex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculus International Journal of Computers for Mathematical Learning 4 IssueID1 51–81 Occurrence Handle10.1023/A:1009858714113

    Article  Google Scholar 

  • J.B. Lagrange (2000) ArticleTitleL’intégration d’instruments informatiques dans l’enseignement: Une approche par les techniques Educational Studies in Mathematics 43 IssueID1 1–30 Occurrence Handle10.1023/A:1012086721534

    Article  Google Scholar 

  • P. Rabardel (1993) Représentations dans des situations d’activités instrumentées A. Weill-Fassina P. Rabardel D. Dubois (Eds) Représentations pour l’action. Octares Toulouse 97–111

    Google Scholar 

  • P. Rabardel (1999) Eléments pour une approche instrumentale en didactique des mathématiques. Actes de l’Université d’été, Houlgate, 1999 IUFM de Caen Houlgate 2003–213

    Google Scholar 

  • T. Rojano (1996) Developing algebraic aspects of problem solving within a spreadsheet environment N. Bednarz C. Kieran L. Lee (Eds) Approaches to Algebra. Kluwer Academic Publishers Dordrecht 137–145

    Google Scholar 

  • T. Rojano (2001) Algebraic reasoning with spreadsheets. International Seminar on ‘Reasoning, explanation and proof in school mathematics and their place in the intended curriculum’ Cambridge England

    Google Scholar 

  • T. Rojano R. Sutherland (1997) Pupils’ strategies and the Cartesian method for solving problems: the role of spreadsheets Proceedings of the 21st International Conference for the Psychology of Mathematics Education University of Helsinki Lathi 72–79

    Google Scholar 

  • A. Sfard (1991) ArticleTitleOn the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin Educational Studies in Mathematics 22 1–36 Occurrence Handle10.1007/BF00302715

    Article  Google Scholar 

  • Trouche L., (2003a). Managing the Complexity of Human/Machine Interaction in a Computer Based Learning Environment: Guiding Student’s Process Command Through Instrumental Orchestrations. Communication presented at CAME 3: Learning in a CAS Environment: Mind-Machine Interaction. Reims, France, June 2003.

  • Trouche L., (2003b). Construction et conduite des instruments dans les apprentissages mathématiques: nécessité des orchestrations. Thèse d’habilitation, Université Paris 7.

  • G. Vergnaud A. Cortes P. Favre-Artigue (1988) Introduction de l’algèbre auprès des débutants faibles: problèmes épistémologiques et didactiques G. Vergnaud G. Brousseau M. Hulin (Eds) Didactique et acquisitions des connaissances scientifiques: Actes du Colloque de Sèvres, Mai 1987. La Pensée Sauvage Grenoble 259–280

    Google Scholar 

  • G. Vergnaud (1989) ArticleTitlePsychologie du développement cognitif et didactique des mathématiques Un exemple : les structures additives. Petit x n° 22 51–69

    Google Scholar 

  • G Vergnaud (1990) ArticleTitleLa théorie des champs conceptuels Recherches en Didactique des Mathématiques 10 IssueID2.3 133–170

    Google Scholar 

  • P. Vérillon P. Rabardel (1995) ArticleTitleCognition and artifacts: A contribution to the study of thought in relation to instrumented activity European Journal of Psychology of Education 10 IssueID1 77–101

    Google Scholar 

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Correspondence to Mariam Haspekian.

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Haspekian, M. An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets. Int J Comput Math Learning 10, 109–141 (2005). https://doi.org/10.1007/s10758-005-0395-z

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