# Mathematics and technology: a CIEAEM source book

G.Aldon, F.Hitt, L.Bazzini, U. Gellert, Springer (2017)

## Technology, a tool for teaching and learning mathematics.

The 65th, 66th and the 67th conference of the Commission Internationale pour l’Ã‰tude et L’AmÃ©lioration de l’Enseignement des MathÃ©matiques (CIEAEM), the International Commission for the Study and Improvement of Mathematics Education (http://www.cieaem.org), gave in the years 2014 and 2015 grant importance to the role of technology in mathematics education. In every working group, presentations taking into account the technology show the importance of that topic either for teaching and learning mathematics or for communication within and outside classrooms.

The editorial team of the oultined volume – consisting of the chairs of CIEAEM65 (Bazzini & Hitt), CIEAEM66 and secretary of the commission (Aldon), the president of the commission (Gellert) and the vice-president (Hitt) – invited selected speakers to contribute to the volume by extending and, for some of them by translating into English, their conference papers.

A key question would be, how the proposed mathematical task in a technological environment influences the acquisition of knowledge? What elements are important to retain in the design of mathematical tasks in computing environments?

## Communication and Information

New paradigms of this century have highlighted the importance of communication both inside and outside the classroom, whether researchers or teachers follow a constructivist, socio-constructivist or sociocultural paradigm, communication is an essential part of their research program (Aldon, Artigue & al., 2009). Technology plays an important role in this communication, and simultaneously imposes its way of being used. In the past this communication outside the classroom was not fully efficient because we did not have mobile resources as we currently have. Then, the use of TBI, platforms as Moodle, tablets and smartphones has transformed the way we communicate both inside and outside the mathematics classroom. How to make an efficient use of these resources in the classroom and beyond?

Another important aspect detected by the editors of this volume, is on how teachers appropriate themselves the information to teach courses and to communicate with their colleagues. The issue of the documentation of teachers in the digital era has to be addressed as well as the documentation of students. Technology modifies the way information is transmitted and mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching with an extensive documentation (Aldon, 2010, Gueudet & Trouche, 2009, Trouche & Drijvers, 2010). The tools to learn and inform others are important in the process of teaching. The problems facing the educational environment for information to flow in both directions are huge. How the researchers can appropriate themselves about the teachers’ experiences and in turn, how the teachers can appropriate themselves about research results. Bilateral information represents one of the biggest problems to solve in the educational environment.

## Technology and teachers’ professional development

The last session, but not the least, is on the training of teachers in the digital era. Teacher education is a political issue that policy makers have to take into consideration in the cultural and social context of the society. The injunctions, often insistent, of introducing technology in the classroom have to face the reality of teachers' technological knowledge and the necessity of teachers' training (Clark-Wilson & al., 2014). It is well known that we can divide the teachers into three populations, those that completely reject the use of technology, those who believe that problems of teaching and learning mathematics are solved immediately with technology, and those who believe that they must make a rational use of technological resources in order to have a real impact on teaching and learning mathematics. How to convince the math teacher about the importance of the use of technological resources? How to convince the enthusiastic teacher who must make a rational use of technology? What problems of teaching and learning will have to confront future mathematics teachers in the use of technological resources?

## References

Aldon, G. (2009, 2010, 2011). MathÃ©matiques dynamiques. Paris : Hachette Education.

Aldon, G. (2010. Handheld calculators between instrument and document, in C. Bardini, P. Drijvers, & H.G. Weigand (eds.), Handheld technology in the mathematics classroom – theory and practice, special issue of ZDM (the International Journal on Mathematics Education).

Aldon, G., Artigue, M., Bardini, C. et Trouche, L., Ã©diteurs (2009). Une Ã©tude sur la conception et les usages didactiques d’une nouvelle plate-forme mathÃ©matique, potentialitÃ©, complexitÃ©. ExpÃ©rimentation collaborative de laboratoires mathÃ©matiques (e-CoLab). Rapport de recherche 2006-2008. , INRP (Ã©ditions Ã©lectroniques).

Artigue, M. (2000). Instrumentation issues and the integration of computer technologies into secondary mathematics teaching. Proceedings of the Annual Meeting of GDM. Potsdam. Retrieved on 3rd June, 2014 from

http://webdoc.sub.gwdg.de/ebook/e/gdm/2000.

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning 7: 245-274.

Artigue, M. (2002). L’intÃ©gration de calculatrices symboliques Ã l’enseignement secondaire : les leÃ§ons de quelques ingÃ©nieries didactiques. In D. Guin et L. Trouche (Eds), Calculatrices Symboliques transformer un outil en un instrument du travail mathÃ©matique : un problÃ¨me didactique (p. 277-349), Grenoble : La PensÃ©e Sauvage.

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Clark-Wilson, A., Robutti, O., Sinclair, N. (2014). The Mathematics Teacher in the Digital Era, Springer

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Gueudet, G., Trouche, L. (2009) Towards new documentation systems for teachers? Educational Studies in Mathematics 71/3, 199-218, DOI 10.1007/s10649-008-9159-8

Gueudet, G., Trouche, L. (2010). Des ressources aux genÃ¨ses documentaires. Ressources vives. Le travail documentaire des professeurs, le cas des mathÃ©matiques. In G. Gueudet & L. Trouche (Eds.), Ressources vives, le travail documentaire des professeurs, le cas des mathÃ©matiques. Rennes : Presses Universitaires de Rennes et Institut National de Recherche PÃ©dagogique. 57-74.

Hitt, F. (2007). Utilisation de calculatrices symboliques dans le cadre d’une mÃ©thode d’apprentissage collaboratif, de dÃ©bat scientifique et d’auto-rÃ©flexion. In M. Baron, D. Guin et L. Trouche (Ã‰diteurs), Environnements informatisÃ©s et ressources numÃ©riques pour l'apprentissage. conception et usages, regards croisÃ©s (pp. 65-88). Ã‰ditorial Hermes.

Hitt, F. (2011). Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom. International Journal of Mathematical Education in Science and Technologie, Vol. 42, No. 6, p. 723-735.

Hitt, F., & Kieran, C. (2009). Constructing knowledge via a peer interaction in a CAS environment with tasks designed from a Task-Technique-Theory perspective. International Journal of Computers for Mathematical Learning, 14, 121-152.

NCTM. (2008). The role of technology in the teaching and learning of mathematics. A position of the NCTM. Consulted (28 oct 2014).

http://www.nctm.org/about/content.aspx?id=14233

NCTM. (2011). Technology in teaching and learning mathematics. A position of the NCTM. Consulted (28 oct 2014). http://www.nctm.org/about/content.aspx?id=31734

Rabardel, P. (1995). Les hommes et les technologies, approche cognitive des instruments Contemporains. Armand Colin.

Trouche, L., & Drijvers, P. (2010), Handheld technology for mathematics education, flashback to the future, ZDM, The International Journal on Mathematics Education, 42(7), 667-681