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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- 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).
References
Artigue, M. (2011). Challenges in basic mathematics education. UNESCO. Retrieved from http://unesdoc.unesco.org/images/0019/001917/191776e.pdf
Buisson, F. (Ed.). (1911). Nouveau dictionnaire de pédagogie et d’instruction primaire. Paris: Hachette. Retrieved March 2015, from http://www.inrp.fr/edition-electronique/lodel/dictionnaire-ferdinand-buisson/
Chevallard, Y. (1987). A theoretical approach to curricula. Communication to the seminar on Comparative Studies of Mathematical Curricula in Different Countries, held in Frascati (Italy).
Chevallard, Y. (1992). Intégration et viabilité des outils informatiques : le problème de l’ingénierie didactique. In B. Cornu (Ed.), L'ordinateur pour enseigner les mathématiques (pp. 183–203). Paris: PUF.
Cornu, B., & Ralston, A. (Eds.). (1992). The influence of computers and informatics on mathematics and its teaching. Paris: UNESCO. Science and Technology Education 44 (second edition of the 1985 ICMI study).
Drijvers, P. (2009). Tools and tests: Technology in national final mathematics examinations. In C. Winslow (Ed.), Nordic Research on Mathematics Education, Proceedings from NORMA08 (pp. 225–236). Rotterdam, The Netherlands: Sense.
Drijvers, P., Monaghan, J., Thomas, M., & Trouche, L. (2014). Use of technology in secondary mathematics (Report for the International Baccalaureat), London, IB.
Fort, M. (2007). Expérimentation d’une épreuve pratique de mathématiques au baccalauréat scientifique. Inspection générale de l’éducation nationale. Ministère de l’éducation nationale, de l’enseignement supérieur et de la recherche. Retrieved from http://media.education.gouv.fr/file/98/3/4983.pdf
George, A. R. (2005). In search of the é.dub.ba.a: The ancient Mesopotamian school in literature and reality. In Y. Sefati, P. Artzi, C. Cohen, B. L. Eichler, V. A. Hurowitz, & A. Experienced (Eds.), Scribe who neglects nothing. Ancient near eastern studies in honor of Jacob Klein (pp. 127–137). Bethesda, MD: CDL Press.
Gueudet, G., & Trouche, L. (2011a). ICT in France: Development of usages, institutional hesitations and research questions. In A. Oldknow & C. Knights (Eds.), Mathematics education with digital technologies (pp. 23–29). London: Continuum Press.
Gueudet, G., & Trouche, L. (2011b). Mathematics teacher education advanced methods: An example in dynamic geometry. ZDM, The International Journal on Mathematics Education, 43(3), 399–411. doi:10.1007/s11858-011-0313-x. Retrieved from http://www.springerlink.com/content/13733h7321658734/
Gutfreund, H., & Rosenber, Y. (Eds.). (2012). Knowledge and training of secondary school mathematics teachers. Jerusalem: The Israel Academy of Sciences and Humanities.
Hoyles, C., & Lagrange, J. B. (2010). Mathematical education and digital technologies: Rethinking the terrain. The 17th ICMI study. New York: Springer.
Hoyles, C., Noss, R., Vahey, P., & Roschelle, J. (2013). Cornerstone mathematics: Designing digital technology for teacher adaptation and scaling. ZDM, The International Journal on Mathematics Education, 45(7), 1057–1070.
Kahane, J.-P. (2002). L’enseignement des sciences mathématiques. Commission de reflexion sur l’enseignement des mathématiques. Paris: Odile Jacob.
Kahane, J.-P. (2008). The ICMI studies: their launch. In F. Furinghetti, L. Giacardi, & F. Arzarello (Eds.), The first century of the International Commission on Mathematical Instruction (1908-2008): Reflecting and shaping the world of mathematics education (pp. 18–19). Rome: Instituto della enciclopedia italiana.
Kelly, A. V. (1977). The curriculum, theory and practice. London: Sage publication.
Lagrange, J. B. (2005). Curriculum, classroom practices, and tool design in the learning of functions through technology-aided experimental approaches. International Journal of Computers for Mathematical Learning, 10(2), 143–189.
Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 239–271). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Lavoie, P. (1994). Contribution à une histoire des mathématiques scolaires au Québec: l’arithmétique dans les écoles primaires (1800–1920). Thèse de doctorat, Faculté des sciences de l’éducation, Université de Laval, Québec.
Maschietto, M., & Trouche, L. (2010). Mathematics learning and tools from theoretical, historical and practical points of view: The productive notion of mathematics laboratories. ZDM, The International Journal on Mathematics Education, 42(1), 33–47. doi:10.1007/s11858-009-0215-3. Retrieved from http://www.springerlink.com/content/48045470220u4073/
Pepin, B., Gueudet, G., & Trouche, L. (2015). Comfortable or Lost in Paradise? Affordances and constraints of mathematics E-textbooks in/for curriculum enactment, communication to the symposium. Mathematics Curriculum Contingencies: From Authoring to Enactment via Curriculum Resources, chaired by D. Clarke, K. Ruthven & M. K. Stein, in the frame of the AERA 2015 meeting, Chicago, 16–20 April.
Trouche, L. (2005). Calculators in mathematics education: A rapid evolution of tools, with differential effects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument (pp. 11–40). New York: Springer.
Trouche, L., Drijvers, P., Gueudet, G., & Sacristan, A. I. (2013). Technology-driven developments and policy implications for mathematics education. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 753–790). New York: Springer.
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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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