ICME, the International Congress on Mathematical Education, in its eleventh edition, is to be held in Monterrey, Mexico from July 6th to 13th, 2008. The DG (Discussion Group) 13 is dedicated to challenges posed by different perspectives, positions, and approaches in mathematics education research.

As the name suggests, a Discussion Group (DG) is designed to gather congress participants who are interested in discussing, in a genuinely interactive way, certain challenging or controversial issues and dilemmas –of a substantial, non-rhetorical nature– pertaining to the theme of the DG. The team will identify more specific issues and questions for the DG, and participants in the group will be invited to propose responses to the issues thus raised, including answers to specific questions and possibly recommendations to relevant categories of policy or decision makers. There will be no oral presentations in a DG, except introductions by the organizers of the group to provide the background and framework for the discussion. Information or position papers are expected to be made available to group participants electronically through a web site forming part of the congress web site, in due time before the congress.

This webpage is dedicated to DG 13, which could also be found on the general ICME website.

The team of DG 13 is composed of:
Luc Trouche (France) – co-chair 
Susanne Prediger (Germany) - co-chair
Patricia Camarena Gallardo (Mexico)
Jana Trgalova (France)
Soledad Ulep  (Philippines)  

The International Program Comittee (IPC) has appointed Richard Noss as IPC liaison for DG 13.

Challenges and possibilities posed by different perspectives and theoretical approaches in mathematics education research. Aims and focus of DG13

The large diversity of different perspectives and theoretical approaches in the mathematics education research community has often been described. It poses challenges for international communication, for the integration of empirical results into a bigger corpus of scientific knowledge and in the long run for a cumulative and joint progress in the research field.

On the other hand, the diversity of different perspectives is unavoidable due to very different traditions and focuses. Even stronger, some researchers (including the organizing team) consider it to be a rich resource that enables researchers to grasp the complexity of the research objects.

The discussion group focuses not only on challenges, but also on possible strategies for connecting perspectives for a better understanding of complex phenomena in mathematics teaching and learning. In order to avoid a too abstract discussion without concrete basis, we will refer to concrete research projects in the field of mathematics teaching and learning (with most prefarably, but not only, a special attention paid to ICT, i.e. Information and Communications Technology, its design and use):

• How are different perspectives and theoretical approaches reflected in concrete research practices? (exemplify the expression of different theories on research practices)
• Where has the diversity of perspectives and theoretical approaches been used as a resource for a better understanding of complex phenomena? (Exemplify the use different perspectives for understanding empirical phenomena)
• What strategies can be used to connect different perspectives and approaches in concrete research projects? (connect different theories for their development)? How can different theoretical approaches learn from each other?

How to participate

Discussion Groups are expressly not about the presentation of research papers. How-ever, as starting points for discussions, the OT is calling for written contributions that bring forward examples of research projects and their general reflections due to one or more of the questions listed above.

Accepted contributions will be posted on the web page of DG13 and will be referred to during the discussions at ICME11. Contributors are expected to participate in all the sessions of the Discussion Group, together with others who are interested in the theme but have not entered a written contribution. The written contributions should include the following information:

• The author(s) names and location (town and country, school, or establishment) and contact details (if possible the address of the personal webpage);
• Explicit references to the addressed questions;
• A general reflection on the issues of the Discussion Group, rather than a classical research report;
• A concrete example from research practices.

The written preliminary contribution should be 2 to maximally 4 pages (A4 please) in length using 12-point font, single spaced, with 2 cm margins, and should be submitted electronically to both DG13 co-chairs Luc Trouche and Susanne Prediger.

Timeline

The deadline for submission of the preliminary short versions is January 20th 2008.

• By the end of February 2008 – Information about acceptance will be sent to contributors who will be asked to prepare an extended version of their text (6 pages maximum) by the end of March 2008.
• By the April 20th 2008 – The OT will prepare and publish an organising framework for the operation of DG13 based on the extended contributions received.

Preliminary plan for the sessions

• At this stage we envision devoting the first 2 sessions (of 2 hours each) to small group discussions after a brief introduction to the key issues by the members of the OT.
• For the final session (1 hour only) the OT is considering the possibility of a common report back session to share general observations and issues and possibly plan further cooperation.

Patricia Camarena Gallardo

This theoretical position has some of the next references:
Ausubel, D. P., Novak, J. D. y Hanesian, H. (1990). Psicología educativa, un punto de vista cognoscitivo. Editorial Trillas.
Bucciarelli, L. (1996). Designing Engineers. The MIT Press, Cambridge, London, England.
Camarena, G. P. (2001). Reporte de investigación intitulado: Los modelos matemáticos como etapa de la matemática en el contexto de la ingeniería, con No. de registro: CGPI 2000731, IPN, México
Camarena, G. P. (2004). La formación de los profesores de las ciencias básicas en el nivel superior. Científica, The Mexican Journal of Electromechanical Engineering, Vol 8. No.1.
Olazábal, A. M. (2004). Categorías en la traducción del lenguaje natural al lenguaje algebraico de la matemática en contexto. Tercer Congreso Internacional “Retos y Expectativas de la Universidad”, México.
Muro, U. C. (2004). Análisis del conocimiento del estudiante relativo al campo conceptual de la serie de Fourier en el contexto de la transferencia de masa. Tesis de Doctorado. IPN, México.
Polya, G. (1976). Cómo plantear y resolver problemas. Editorial Trillas.
Salett, B. M. • Santos, T. L. M. (1997). Principios y métodos de la resolución de problemas en el aprendizaje de las matemáticas. Grupo Editorial Iberoamérica SA de CV.
Schoenfield, A. (1992). Learning to think mathematically: problem solving, metacognition and sense making in mathematics. In Handbook for Research on Matematics Teaching and Learning. New York: Macmillan.
Schön, D. (1998). El profesional reflexivo. Temas de Educación Paidós

Susanne Prediger

Susanne Prediger is full professor at the Institute for Development and Research in Mathematics Education in Dortmund, Germany.

My interest in the challenges posed by different theoretical perspectives has evolved in re-search projects on the development of students’ thinking from everyday conceptions to mathe-matical conceptions (e.g. in the domain of fractions, probability etc.) when I tried to coordinate different theoretical frameworks in order to make sense of my empirical data.

My tentative first reactions to the grand and difficult questions:

•    Is it possible to distinguish today main trends in mathematics education research? Are there divergent, or convergent processes? I am not sure if we should try to answer this question that!! This is a very huge question we could definitely not handle in our discussion group. My personal impression: the process is not convergent since the field is more and more dif-ferentiated and interconnected,
•    What are the roots of these different perspectives, positions, and approaches (Cul-tural? Technological? Political? Epistemological?…). I see the roots in cultural differences, but culture is a very huge word, including for exam-ple: the institutional situation of mathematics educators in different countries, typical phi-losophical and disciplinary traditions , different research practices and teaching cultures in schools, … Emphasizing the cultural roots of differences is operative in so far as I emphasize the exis-tence of a huge part of implicit factors.

The last two questions seem to be more instructive to answer:
•    What are the relationships between theoretical frameworks in mathematics, and more generally, science education? This is an important question which sometimes gets lost in all talking on differences! It would be worth to gather commonalities since it helps for the long term process  of estab-lishing an identity as a scientific discipline. I would like to work on this point at the discus-sion group.
•    How can different ‘schools of thought’ in mathematics education learn from one another? Here, I could bring in some answers from the CERME working group, which are basically systematized propositions for local answers, no general procedures. I would be interested in discussing different strategies of “learning from one another".

Prediger S., Ruthven K. (in press): From teaching problems to research problems. Proposing a way of comparing theoretical approaches, to appear in the Proceedings of CERME 5 (Larnaca, Zypern)
Arzarello F., Bosch M., Lenfant A., Prediger S. (2007): Different theoretical perspectives in research, to appear in the Proceedings of CERME 5 (2007 in Larnaca, Cyprus).
Bikner-Ahsbahs A., Prediger S. (2006): Diversity of Theories in Mathematics Education – How can we deal with it?, in: Zentralblatt für Didaktik der Mathematik 38(1), S. 52-57.
Dreyfus T., Artigue A., Bartolini-Bussi M., Gray E., Prediger S. (2006): Different theoretical perspectives and approaches in research in mathematics education, in: M. Bosch et al. (eds.): Proceedings of the 4th CERME, Sant Feliu de Guixols  2005, published at Fundemi IQS – Universitat 2006, S. 1239-1244. ( ISBN 84-611-3282-3
Prediger S. (2004): Intercultural Perspectives on Mathematics Learning – Developing a Theoretical Framework, in: International Journal of Science and Mathematics Education 2 (2004) 3, S. 377-406.

Jana Trgalova

My interest in the DG13 comes mainly from my participation to the European project TELMA (Technology Enhanced Learning of Mathematics) addressing the issue of design and use of ICT tools for the teaching and learning mathematics.

Within this project, 6 European teams started working towards understanding the role played by theoretical frames in design and research in this area, and building tools to improve communication between researchers from different cultures (TELMA ERT 2006). This collaborative work began by an identification of the main theoretical frames used by TELMA teams in their research: Theory of didactic situations (Brousseau 1997), Activity theory (Cole and Engeström 1993; Engeström 1987; Vygotsky 1978), Situated abstraction (Noss & Hoyles 1996), Constructionism (Harel & Papert 1991). A first attempt at understanding how these theoretical frames influence the visions they develop as regards technology enhanced learning in mathematics was done in this first phase. A specific methodology has been developed in order to deepen the reflection and to better understand the exact role played by the theoretical frames they use in their research: a cross-experimentation, where each team experimented an ICT tool developed by another team (Cerulli & al. 2007). A methodological tool for the systematic exploration of the theoretical frames used in technology enhanced learning in mathematics has been built, with the aim to support the analysis of the cross-experimentation, but also the understanding of the role played by theoretical frames in the design and analysis of uses of ICT tools and the search for interesting connections and complementarities between such frames (Cerulli & al., submitted).

DG13 offers an opportunity to share this experience with other participants and to learn about and discuss other approaches towards a comparing and networking of theoretical frameworks.

Brousseau, G. (1997). The Theory of Didactical Situations in Mathematics, N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Trans. & Eds.). Dordrecht: Kluwer Academic Publishers.
Cerulli, M., Georget, J.-P., Maracci, M., Psycharis, G., Trgalova, J. (2007). TELMA’s approach to integration of research teams. 5e Congrès de ERME (European Society for Research in Mathematics Education), Larnaca (Chypre), 22-26 février 2007.
Cerulli, M., Georget, J.-P., Maracci, M., Psycharis, G., Trgalova, J. (submitted). Comparing theoretical frameworks enacted in experimental research: TELMA experience.
Cole, M., & Engeström, Y. (1993). A cultural-historical approach to distributed cognition. In G. Salomon (Ed.), Distributed cognitions: psychological and educational considerations (pp. 1-47). Cambridge: Cambridge University Press.
Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.
Harel, I., & Papert, S. (1991). Constructionism. Norwood, NJ: Ablex Publishing Corporation.
Noss, R., & Hoyles, C. (1996). Windows on Mathematical Meanings. Dordrecht: Kluwer Academic Publishers.
TELMA ERT (2006). Developing a joint methodology for comparing the influence of different theoretical frameworks in technology enhanced learning in mathematics: the TELMA approach. In Le Hung Son, N. Sinclair, J.-B. Lagrange, C. Hoyles (eds.) Proceedings of the ICMI 17 Study Conference: background papers for the ICMI 17 Study. Hanoï University of Technology, December 3-8 2006.
Vygotsky, L. S. (1978). Mind and Society. The development of higher psychological processes. Harvard University Press.

Both research studies dealt with classroom practices.  I find it is interesting to note the diversity of theoretical perspectives and frameworks used to interpret or develop classroom practices. Some relate to the use of mathematical tasks (Marton’s theory of variation and Brosseau’s theory of didactical situations in mathematics), development of social and socio-mathematical norms (Cobb and Yackel’s emergent perspective), and mathematical thinking (Bishop’s socio-cultural framework). And I find that these are not only useful to research, but to teacher training and curriculum development, as well.