Abstract
This chapter is dedicated to the analysis of the mutual influences between tools and mathematics curricula. Mathematics learning indeed develops ‘under the umbrella’ of the ‘really used’ tools. And the development of tools depends—partially—on the curricula intended as well as implemented: the design of calculators specially conceived ‘for the test’ is a clear illustration of this influence. This chapter aims to evidence that the integration of tools in mathematics curricula is far from being a linear and natural process. It depends on a set of conditions designing new tasks, new techniques; training teachers; finding new equilibrium for teachers’ and students’ mathematical activity.
This chapter is organised in three sections setting the scene: the first section proposes a vertical (historical) point of view, aiming to evidence the continuity of some issues over the time; the second gives an horizontal (international comparative) point of view, aiming to evidence, beyond the national peculiarities, some common features; the third section proposes a case study, the French policy on assessment, seen as paradigmatic. The conclusion addresses some questions and draws some perspectives for further studies.
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Notes
- 1.
For this analysis ‘over the time’, I have chosen, in this section, some particular moments appearing as critical: moments of transition for tools or/and curricula. This choice leads to jump over time, giving perhaps to the reader the impression of surfing over history: references are given for having means to analyse in more depth continuities and breaks.
- 2.
Such evolutions, linked to the writing tools, could also be analysed in the case or the transition from ‘pen and pencil’ to ‘keyboard and screen’, and then from ‘keyboard and screen’ to ‘touch screen’ (see Chap. 17).
- 3.
Founded at the end of the nineteenth century, the journal ‘L’enseignement mathématique’ was the place where mathematicians exchanged ideas about teaching. It became the official journal of the International Commission for Mathematical Instruction from its creation in 1908 (http://www.unige.ch/math/EnsMath/).
- 4.
The ICMI studies are launched by the International Commission on Mathematical Instruction, see http://www.mathunion.org/icmi/conferences/icmi-studies/introduction/.
- 5.
- 6.
The selected research papers were written from the years 2000 to 2014 (exceptions were made for key papers) from journals rated as A* and A (and some rated as B) in a recent European rating of mathematics education journals (Drijvers et al., 2014, p. 8).
- 7.
To be noticed: the French Ministry of education and research has launched a large study for analysing the use of educational resources in four disciplines (mathematics, english, physics/chemistry and technology): the ReVEA project (Ressources vivantes pour l’enseignement et l’apprentissage) will develop from 2014 to 2018.
- 8.
See the report of the history of this commission, the CREM (Commission de Recherche sur l’Enseignement des Mathématiques), written in 2006 by its secretary J.-C. Duperret: see http://educmath.ens-lyon.fr/Educmath/ressources/etudes/crem/.
- 9.
See the evocation of this experiment in the History of the CREM: http://educmath.ens-lyon.fr/Educmath/ressources/etudes/crem/.
- 10.
- 11.
This common core, proposed by the CSP to the discussion among teachers, is composed of five domains: languages for thinking and communicating; methods and tools for learning; the education of the person and of the citizen; observing and understanding the world; Representing the world and human activity.
- 12.
See the presentation of the mathematics strategy on the French Ministry website: http://cache.media.education.gouv.fr/file/12_Decembre/30/2/DP-l-ecole-change-avec-vous-strategie-mathematiques_373302.pdf.
- 13.
Particularly in the frame of the French Commission on Mathematics Teaching (CFEM).
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Trouche, L. (2016). Integrating Tools as an Ordinary Component of the Curriculum in Mathematics Education. In: Tools and Mathematics. Mathematics Education Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-02396-0_12
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