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

  • Mariam HaspekianEmail author


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.


instrumental approach spreadsheet and mathematics education transition arithmetic-algebra 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ainley, J. 1999Doing Algebra-Type Stuff: Emergent algebra in the primary schoolProceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education. Israel Institute of TechnologyHaifa916Google Scholar
  2. Ainley, J., Nardi, E., Pratt, D. 1999Constructing meaning for formal notation in active g raphing. Proceedings of the 1st Conference of the European Society for Research in Mathematics EducationForschungsinstitut fuer MathematikdidaktikOsnabrueck189200Google Scholar
  3. Ainley, J., Bills, L., Wilson, K. 2003Designing tasks for purposeful algebraProceedings of the 3rd Conference of the European Society for Research in Mathematics EducationBellaria[Online Publication]: (∼didattica/CERME3/proceedings/Groups/TG6/TG6_ainley_cerme3.pdf)Google Scholar
  4. Artigue, M. 2002Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual workInternational Journal of Computers for Mathematical Learning7245274CrossRefGoogle Scholar
  5. Arzarello, F., Bazzini, L., Chiappini, G. 1994The process of naming in algebraic thinking Proceedings of the 18th International Conference for the Psychology of Mathematics EducationUniversity of LisbonLisbon4047Google Scholar
  6. Arzarello, F., Bazzini, L., Chiappini, G. 2001A model for analysing algebraic processes of thinkingSutherland, R.Assude, T.Bell, A.Lins, R. eds. Perspectives on school algebra.Kluwer Academic PublishersDordrecht6181Google Scholar
  7. Bednarz, N., Janvier, B. 2001Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmeticBednarz, N.Kieran, C.Lee, L. eds. Approaches to Algebra: Perspectives for Research and Teaching.Kluwer Academic PublisherDordrecht115136Google Scholar
  8. Bosch, M., Chevallard, Y. 1999La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématiqueRecherches en Didactique des Mathématiques1977124Google Scholar
  9. Capponi, B. 1999Le tableur pour le collège, un outil pour l’enseignement des mathématiquesPetit x52542Google Scholar
  10. Capponi, B. 2000Tableur, arithmétique et algèbre. L’algèbre au lycée et au collège, Actes des journées de formation de formateurs, 1999IREM de MontpellierBoisseron5866Google Scholar
  11. Chevallard, Y. 1992Intégration et viabilité des objets informatiques dans l’enseignement des mathématiquesCornu, B. eds. L’ordinateur pour enseigner les mathématiques.Presses Universitaires de FranceParis183203Google Scholar
  12. Chevallard, Y. 1998Analyse des pratiques enseignantes et didactique des mathématiques: l’approche anthropologique, Actes de l’Université d’Été de Didactique de La RochelleIREM de Clermont-FerrandLa Rochelle pp. 88–10188101Google Scholar
  13. Chick, H.Stacey, K.Vincent, J.Vincent, J. eds. 2001The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conferenceUniversity of MelbourneMelbourneGoogle Scholar
  14. Dettori, G., Garuti, R., Lemut, E., Netchitailova, L. 1995An Analysis of the relationship between spreadsheet and algebraBurton, L.Jaworski, B. eds. Technology in Mathematics Teaching – a Bridge Between Teaching and Learning.Chartwell-BrattBromley261274Google Scholar
  15. Drouhard J.P., (1992). Les écritures symboliques de l’algèbre élémentaire. Thèse de Doctorat, Université Paris 7.Google Scholar
  16. Guin, D., Trouche, L. 1999The complex process of converting tools into mathematical instruments: The case of calculatorsInternational Journal of Computers for Mathematical Learning3195227CrossRefGoogle Scholar
  17. Guin, D.Ruthven, K.Trouche, L. eds. 2004The Didactical Challenge of Symbolic Calculators, Turning a Computational Device into a Mathematical InstrumentKluwer Academic PublisherDordrechtsGoogle Scholar
  18. Lagrange, J.B. 1999Complex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculusInternational Journal of Computers for Mathematical Learning45181CrossRefGoogle Scholar
  19. Lagrange, J.B. 2000L’intégration d’instruments informatiques dans l’enseignement: Une approche par les techniquesEducational Studies in Mathematics43130CrossRefGoogle Scholar
  20. Rabardel, P. 1993Représentations dans des situations d’activités instrumentéesWeill-Fassina, A.Rabardel, P.Dubois, D. eds. Représentations pour l’action.OctaresToulouse97111Google Scholar
  21. Rabardel, P. 1999Eléments pour une approche instrumentale en didactique des mathématiques. Actes de l’Université d’été, Houlgate, 1999IUFM de CaenHoulgate2003213Google Scholar
  22. Rojano, T. 1996Developing algebraic aspects of problem solving within a spreadsheet environmentBednarz, N.Kieran, C.Lee, L. eds. Approaches to Algebra.Kluwer Academic PublishersDordrecht137145Google Scholar
  23. Rojano, T. 2001Algebraic reasoning with spreadsheets. International Seminar on ‘Reasoning, explanation and proof in school mathematics and their place in the intended curriculum’CambridgeEnglandGoogle Scholar
  24. Rojano, T., Sutherland, R. 1997Pupils’ strategies and the Cartesian method for solving problems: the role of spreadsheets Proceedings of the 21st International Conference for the Psychology of Mathematics EducationUniversity of HelsinkiLathi7279Google Scholar
  25. Sfard, A. 1991On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coinEducational Studies in Mathematics22136CrossRefGoogle Scholar
  26. 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.Google Scholar
  27. Trouche L., (2003b). Construction et conduite des instruments dans les apprentissages mathématiques: nécessité des orchestrations. Thèse d’habilitation, Université Paris 7.Google Scholar
  28. Vergnaud, G., Cortes, A., Favre-Artigue, P. 1988Introduction de l’algèbre auprès des débutants faibles: problèmes épistémologiques et didactiquesVergnaud, G.Brousseau, G.Hulin, M. eds. Didactique et acquisitions des connaissances scientifiques: Actes du Colloque de Sèvres, Mai 1987.La Pensée SauvageGrenoble259280Google Scholar
  29. Vergnaud, G. 1989Psychologie du développement cognitif et didactique des mathématiquesUn exemple : les structures additives. Petit x n°225169Google Scholar
  30. Vergnaud, G 1990La théorie des champs conceptuelsRecherches en Didactique des Mathématiques10133170Google Scholar
  31. Vérillon, P., Rabardel, P. 1995Cognition and artifacts: A contribution to the study of thought in relation to instrumented activityEuropean Journal of Psychology of Education1077101Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Université Denis Diderot (Paris 7) DIDIREMParisFrance

Personalised recommendations