# On the Integration of Digital Technologies into Mathematics Classrooms

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## Abstract

Trouche’s [Third Computer Algebra in Mathematics Education Symposiums, Reims, France, June 2003] presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche’s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student’s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics.

## Keywords

Mathematical Expression Mathematical Knowledge Classroom Practice Digital Technology Computer Algebra## References

- Arcavi, A., Hadas, N. 2000Computer mediated learning: And example of an approachInternational Journal of Computers for Mathematical Learning52545CrossRefGoogle Scholar
- Artigue, M. (2000). Instrumentation issues and the integration of computer technologies into secondary mathematics teaching.
*Proceedings of the Annual Meeting of the GDM*.*Potsdam, 2000*: (download: http://webdoc.sub.gwdg.de/ebook/e/gdm/2000)Google Scholar - 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
- Balacheff, N. 1993Artificial intelligence and real teachingKeitel, C.Ruthven, K. eds. Learning from Computers: Mathematics Education and TechnologySpringer-VerlagBerlin131158Google Scholar
- Cobb, P., Stephan, M., McClain, K., Gravemeijer, K. 2001Participating in classroom mathematical practicesJournal of the Learning Sciences10113164CrossRefGoogle Scholar
- Cobb, P., Confrey, J., diSessa, A., Lehrer, R., Schauble, L. 2003Design experiments in educational researchEducational Researcher329131Google Scholar
- Cuoco, A. 2002Thoughts on reading artigue’s ‘learning mathematics in a CAS environment’International Journal of Computers for Mathematical Learning7293291CrossRefGoogle Scholar
- Defouad, B. (2000).
*Etude de genese instrumentals liees a l’utilisation d’une calculatrice symbolique en classe de premiere*These de doctorat, Universite Paris 7.Google Scholar - Dreyfus, T. 1993Didactic design of computer-based learning environmentsKeitel, C.Ruthven, eds. Learning from Computers: Mathematics Education and TechnologySpringer-VerlagBerlin101130(NATO ASI Series F, vol 121)Google Scholar
- Guin, D., Trouche, L. 1999The complex process of converting tools into mathematical instruments: The case of calculatorsInternational Journal of Computers for Mathematical Learning3195227CrossRefGoogle Scholar
- Healy, L., Pozzi, S., Hoyles, C. 1995Making sense of groups, computers and mathematicsCognition and Instruction13505523Google Scholar
- Hoyles, C. (2003). From instrumenting and orchestrating convergence to designing and recognising diversity: A response to luc trouche. Plenary presentation at the
*Third Computer Algebra in Mathematics Education Symposium*. Reims, France, June 2003.Google Scholar - Hoyles, C., Noss, R. 2003What can digital technologies take from and bring to research in mathematics education?Bishop, A.J.Clements, M.A.Keitel, C.Kilpatrick, J.Leung, F.K.S. eds. Second International Handbook of Mathematics EducationKluwer Academic PublishersDordrecht323349Google Scholar
- Hoyles, C., Noss, R., Pozzi, S. 2001Proportional reasoning in nursing practiceJournal for Research in Mathematics Education321427Google Scholar
- Kent, P. and Noss, R. (2002). The Mathematical Components of Engineering Expertise (End of project report). London: Institute of Education: (www.ioe.ac.uk/rnoss/MCEE)Google Scholar
- Koschmann, T.Hall, R.Miyake, N. eds. 2001CSCL2: Carrying Forward the ConversationLawrence ErlbaumMahwah, NJGoogle Scholar
- Lagrange, J.B. 1999Complex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculusInternational Journal of Computers for Mathematical Learning45181CrossRefGoogle Scholar
- Lagrange, J.B., et al. 2001A meta study on IC technologies in educationvan den Heuvel-Panhuizen, M. eds. Proceedings of the Twentyfifth Conference of the International Group for the Psychology of Mathematics EducationFreudenthal InstituteUtrecht111122vol. 1Google Scholar
- Nemirovsky, R., Tierney, C., Wright, T. 1998Body motion and graphingCognition and Instruction16119172Google Scholar
- Newman, D., Griffin, P., Cole, M. 1989The Construction Zone: Working for cognitive change in schoolCambridge University PressNew YorkGoogle Scholar
- Noss, R., Hoyles, C. 1996Windows on Mathematical Meanings: Learning Cultures and ComputersKluwer AcademicDordrechtGoogle Scholar
- Noss, R., Hoyles, C., Pozzi, S. 2002Abstraction in expertise: A study of nurses’ conceptions of concentrationJournal for Research in Mathematics Education33204229CrossRefGoogle Scholar
- Papert, S. 1972Teaching children to be mathematicians vs. teaching about mathematicsInternational Journal of Mathematics Education in Science and TechnologyVol. 3249262Google Scholar
- Rabardel, P. and Samurçay, R. (2001). From Artefact to Instrumented-Mediated Learning. New Challenges to Research on Learning: An international symposium organized by the Center for Activity Theory and Developmental Work Research, University of Helsinki, March 21--23.Google Scholar
- Roschelle, 1992Learning by collaboration: Convergent conceptual change.The Journal of the Learning Sciences2235276CrossRefGoogle Scholar
- Ruthven, K. 2002Instrumenting mathematical activity: Reflections on key studies of the educational use of computer algebra systemsInternational Journal of Computers for Mathematical Learning7275291CrossRefGoogle Scholar
- Star, S.L. (1989). The structure of ill-structured solutions: Boundary objects and heterogeneous distributed problem-solving. In L. Gasser and M.N. Huhns (Eds),
*Distributed Artificial Intelligence, volume 2*. London: Pitman / San Mateo, CA: Morgan Kaufmann.Google Scholar - Star, S.L., Griesemer, J. 1989Institutional Ecology, ‘translations,’ and boundary objects: Amateurs and professionals in Berkeley’s Museum of vertebrate zoologySocial Studies of Science193874201907--1939Google Scholar
- Trouche, L. (2003). Managing the Complexity of Human/Machine Interaction in a Computer Based Learning Environment: Guiding Student’s Process Command through Instrumental Orchestrations. Plenary presentation at the
*Third Computer Algebra in Mathematics Education Symposium*, Reims, France, June 2003.Google Scholar - Turkle, S., Papert, S. 1991Epistemological pluralism and the revaluation of the concreteHarel, I.Papert, S. eds. ConstructionismAblex Publishing Corp.Norwood, NJ161191Online version: http://www.papert.com/articles/ EpistemologicalPluralism.htmlGoogle Scholar
- Vérillon, P. (2000). Revisiting Piaget and Vygotsky: In Search of a Learning Model for Technology Education.
*The Journal of Technology Studies*XXVI 1: (download: http://scholar.lib.vt.edu/ejournals/JTS/Winter-Spring-2000)Google Scholar - Vérillon, P., Rabardel, P. 1995Cognition and Artefacts: A contribution to the study of thought in relation to instrumented activityEuropean Journal of Psychology of Education1077101CrossRefGoogle Scholar