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Teachers’ Instrumental Geneses When Integrating Spreadsheet Software

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Book cover The Mathematics Teacher in the Digital Era

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 2))

Abstract

The spreadsheet is not a priori a didactical tool for mathematics education. It may progressively become such an instrument through the process of professional geneses on the part of teachers. This chapter describes the beginning of such a genesis, and presents some results concerning teachers’ professional development with ICT by examining the outcomes of two different sets of data. Theoretical notions, such as instrumental distance and double instrumental genesis supported the analysis of data leading to a comparison of a teacher integrating spreadsheets, for the first time in her practices, with the practices of teachers who are more expert with spreadsheets. The similarities found in the ways they use the tool leads to some hypotheses on the importance of these common elements as key issues in teachers’ ICT practices.

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Notes

  1. 1.

    The name taken in the initial French research is ‘Dan’; in this chapter, it is translated to ‘Ann’ as the teacher is a woman.

  2. 2.

    This term is explained in section 3.

  3. 3.

    There is no research at world scale comparing integration of geometry software and spreadsheets, but all local studies that can be found indicate a better penetration of geometry software than spreadsheets (see the examples cited in Haspekian 2005a).

  4. 4.

    The reader can find a brief explanation of the basic functionalities, in a didactic approach, in Haspekian 2005a, pp.18–23.

  5. 5.

    One can see in Coulange (1998) at which point the algebraic methods rest on rules of didactic contract and remain fragile for pupils ages 15–16 who, facing atypical problems, provide correct answers in rupture with the algebraic rules of the didactic contract.

  6. 6.

    Analyse/synthesis, trial/refinement and equations.

  7. 7.

    because the algebraic character of the formulas is restricted to their utility in carrying out and automating calculations, the focus is not on providing an operational language to analyse and handle relations (Capponi and Balacheff 1989).

  8. 8.

    Because of this dialectic “it is not possible to clearly distinguish between these two processes” (Trouche 2004).

  9. 9.

    We limit ourselves to the case of the material artefacts, but the ergonomic approach is extended to ‘psychological’ artefacts: symbols, signs, cards, etc.

  10. 10.

    This raises difficulties for teachers, see the experiment described in Haspekian 2005b.

  11. 11.

    Mathematical objects are not isolated, in educational institutions they live through mathematical and didactical organisations that are praxeologies: a quadruplet composed of tasks, techniques, technologies (discourse about the techniques: explanations, justifications…) and theories. See (Chevallard 2007).

  12. 12.

    The words ‘representation’ and ‘conception’ are not problematised in this chapter and used in their common senses.

  13. 13.

    Rabardel (2002) distinguishes the usage schemes (related to the material dimension of the tool) from the schemes of instrumented action (related to the global achievement of the task, with goals and intentions).

  14. 14.

    It may not be the case for all teachers: unlike Ann’s case, the first instrument can be already constituted in a more advanced way, long before trying to make it a didactical instrument.

  15. 15.

    The formula refers to the value 50 for the total. If one changes the value of any headcount, then the total will change and the formula becomes wrong.

  16. 16.

    Increment of references after filling makes the formula refer to empty cells. By default, empty cells are treated in formulas as if they contain the value 0, this option that can be changed.

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Acknowledgments

I would like to thank Rebecca Freund, and the anonymous second reviewer, who very carefully reviewed the English of the text.

Author information

Authors and Affiliations

  1. EDA, University Paris Descartes, Paris, France

    Mariam Haspekian

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  1. Mariam Haspekian
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Correspondence to Mariam Haspekian .

Editor information

Editors and Affiliations

  1. London Knowledge Lab Institute of Education, University of London, London, UK

    Alison Clark-Wilson

  2. Dipartimento di Matematica, Università di Torino, Turin, Italy

    Ornella Robutti

  3. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Nathalie Sinclair

Appendice-Extract of the Questionnaire Trainees and Experts

Appendice-Extract of the Questionnaire Trainees and Experts

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Haspekian, M. (2014). Teachers’ Instrumental Geneses When Integrating Spreadsheet Software. In: Clark-Wilson, A., Robutti, O., Sinclair, N. (eds) The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4638-1_11

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