Discussion Groups
As their name suggests, the Discussion Groups are 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 organisers 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 as an introduction by the organisers 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. Each DG will be allotted two two-hour and one one-hour timeslots.

Some of the themes may appear to be closely related to topics for the TSGs, but the focus there is on the presentation and sharing of recent trends in research, development and practice, whereas the DGs focus on the examination and discussion of issues that can be dealt with in different ways depending on different experiences, values, norms, and judgements. To illustrate the focus of each DG, the IPC has listed some key questions and issues that the DG is supposed to consider. However, it is in the hands of the organising teams to frame the discussions and to prioritise between the different aspects of their themes. Thus the questions listed below are meant to give an idea of the questions to be faced by each DG and not necessarily to set out the final questions. The DG teams are responsible for establishing a scheme for paper presentation by distribution, see "How to contribute". Typically proposals should be put forward before January 1, but specific guidelines, if such apply, will be made available on the web site.

Movements, processes, and policy in curriculum reform
What are the forces that drive or inhibit curriculum reform, and what are the instruments for reform? How do we know whether reform is progress? How do the various agents responsible for mathematics education policy interact?

Team Chairs: Zalman Usiskin, University of Chicago, USA, z-usiskin@uchicago.edu
                    Huang Xiang, Chongqing Normal University, China, hx@cqnu.edu.cn
 
The relationship between research and practice in mathematics education
Can we or should we expect results that can be generalised from mathematics education research? How can such results lead to changes in practice? What can researchers learn from practitioners in mathematics education? What can practitioners learn from researchers? Where and how should the interaction between practitioners and researchers take place and be organised? What are the ultimate goals of mathematics education research? What are the forces that govern the evolution of mathematics education research? What are the forces that prevent mathematics teachers from benefiting adequately from research?

Team Chairs: Luciana Bazzini, University of Torino, Italy, luciana.bazzini@unito.it
                    Ken Ruthven, University of Cambridge, United Kingdom, kr18@cam.ac.uk

Mathematics education for whom and why? The balance between ‘mathematics education for all’ and ‘for high level mathematical activity’.
Who should receive what kinds of mathematics education, why, and with what goals? Is the dichotomy in the title a genuine one? How can ‘mathematics education for all’ embrace opportunities for high mathematical achievement? How can instructional practices support the development of highly motivated mathematics learners as well as mathematics education for all? Is there sometimes a tendency to tacitly say ‘what not everyone can learn, nobody should learn’? What is the future of mathematics as an education subject in a changing world dominated by technology? Is more better, or…? What is mathematical literacy?

Team Chairs: Martha Villavicencio, Ministry of Education, Lima, Peru, villavicencio.mr@pucp.edu.pe
                    Lena Lindenskov, Danish University of Education, Copenhagen, Denmark, lenali@dpu.dk

Philosophy of mathematics education
What is the significance of philosophy of mathematics education? To what extent are the authorities of mathematics education implicitly or explicitly influenced by ‘recognisable’ philosophies of mathematics education? What are the relations between philosophy of mathematics education and other kinds of philosophies, such as educational philosophy, philosophy of mathematics, social philosophy, etc.? In what ways do different philosophies of mathematics education influence its theory and practice?

Team Chairs: Maria Viggiani-Bicudo, UNESP, Rio Claro, Brazil, mariabicudo@uol.com.br
                     Susanne Prediger, Mathematics Education, FB Mathematics/Informatics, University of Bremen, Germany

International co-operation in mathematics education
What are the goals of international co-operation? Should co-operation be global or regional? What forms could such co-operation take, and how could it be organised and implemented? What are the barriers to international co-operation? Is there a danger that international co-operation may lead to excessive homogenisation of mathematics education?

Team Chairs: Bill Atweh, Queensland University of Technology, Brisbane, Australia, b.atweh@qut.edu.au
                    Paolo Boero, University of Genova, Italy, boero@dima.unige.it

The education of mathematics teachers
What would be an appropriate balance between the main components of teacher education – e.g. mathematical, educational, and pedagogical components - for different educational levels? In particular, what mathematical competencies should different kinds of teachers have? What are the advantages and disadvantages of teachers being educated predominantly as generalists with some mathematical background, or primarily in mathematics with separate educational and pedagogical components being added, or in an integrated manner? How should research on the teaching and learning of mathematics be dealt with in teacher education?

Team Chairs: Claire Margolinas, Université de Provence, IUFM d'Aix-Marseille, cmargolinas@auvergne.iufm.fr
                    Derek Woodrow, Manchester Metropolitan University, United Kingdom, derek.woodrow@ntlworld.com,
                    d.woodrow@mmu.ac.uk

Public understanding of mathematics and mathematics education
What are the problems associated with the prevalent public understanding of the nature, significance, and role of mathematics in culture and society? Does the general public have adequate perceptions of the nature of mathematical literacy, knowledge and competence and of what it means and takes to learn mathematics? What can we, in the mathematics education community, do to effectively counteract these problems? To what extent are attempts to popularise mathematics helpful in these respects? Can they be counter-productive?

Team Chairs: Chris J. Budd, University of Bath, United Kingdom, cjb@maths.bath.ac.uk
                    Lim Chap Sam, Malaysia University of Science, Penang, Malaysia, cslim@usm.my

Quality and relevance in mathematics education research
What are appropriate criteria for quality and relevance, respectively, in mathematics education research? In actual practice, where and by whom are such criteria established? Are there potential conflicts between the pursuit of quality and the pursuit of relevance in such research? How can criteria be established that pay due respect to the diversity of approaches to mathematics education research?

Team Chairs: Margaret Brown, King’s College London, United Kingdom, margaret.l.brown@kcl.ac.uk
                    Rosetta Zan, University of Pisa, Italy, zan@dm.unipi.it

Formation of researchers in mathematics education
What academic and professional backgrounds should individuals admitted to graduate studies aiming at mathematics education research have? What is an appropriate balance between course work and work for and on the dissertation? To what extent should research students obtain experiences from institutions abroad? Is international harmonisation of the formation of researchers in mathematics education a desirable goal?

Team Chairs: Gilah Leder, La Trobe University, Bundoora, Australia, g.leder@latrobe.edu.au
                    Luis Rico Romero, University of Granada, Spain, lrico@goliat.ugr.es

Different perspectives, positions, and approaches in mathematics education research
To what extent are the different perspectives, positions, and approaches that exist in mathematics education research mutually antagonistic? How can such different ‘schools of thought’ learn from one another? Are there fashion waves in mathematics education research, and, if so, what are the implications?

Team Chairs: Lyn English, Queensland University of Technology, Brisbane, Australia, l.english@qut.edu.au
                    Anna Sierpinska, Concordia University, Montreal, Canada, sierpan@alcor.concordia.ca

International comparisons in mathematics education
Do international comparisons of performance and achievement tend to produce excessive uniformity across countries with respect to curricula, teaching materials, approaches to teaching and learning, and assessment modes? How do international comparisons influence, for better or for worse, national traditions, values, cultures and approaches to mathematics education? How can international comparisons foster and further national development in mathematics education?

Team Chairs: Bao, Jian sheng, Suzhou University, China, jsbaod325@yahoo.co.uk
                    Michael Neubrand, Carl-von-Ossietzky - Universität Oldenburg, Germany
                    neubrand@mathematik.uni-oldenburg.de, michael.neubrand@uni-oldenburg.de

Assessment and testing shaping education, for better and for worse
Are current assessment and testing modes and instruments compatible with today’s goals and aims of mathematics education? How do these modes and instruments influence the teaching and learning of mathematics? How much is too much in assessment and testing? Do the costs of testing match the positive results? What is the balance of positive and negative outcomes of testing? How can assessment and testing be devised and organised so as to serve as means to develop and strengthen the teaching and learning of mathematics? What are the barriers to the adoption of innovative modes of assessment and testing?

Team Chairs: Glenda Lappan, Michigan State University, East Lansing, USA, glappan@math.msu.edu
                    Dylan Wiliam, Learning and Teaching Research Center, Educational Testing Service, United Kingdom, dwilliam@ets.org

Evaluation of teachers, curricula, and systems
How do current requirements for increased accountability in education, and the ensuing trends of widespread evaluation of teachers, curricula, and systems, influence the teaching and learning of mathematics, as well as teachers and learners? What forms of such evaluation can further and accelerate the development of mathematics education rather than distort it?

Team Chairs: Claude Gaulin, Laval University, Quebec, Canada, claude.gaulin@fse.ulaval.ca
                    Max Stephens, University of Melbourne, Victoria, Australia, m.stephens@unimelb.edu.au

Mathematics textbooks
To what extents do mathematics textbooks shape the actual teaching and learning of mathematics, for better or worse? What is the balance between textbook impact and that of other forces, e.g. curricula and assessment, which influence mathematics teaching? What are the interests and forces that drive the publication and adoption of textbooks in different countries? Who are the authors of mathematics textbooks in different countries, and what are their backgrounds?

Team Chairs: Fan, Lianghuo, National Institute of Education, Singapore, lhfan@nie.edu.sg
                    Stefan Turnau, Rzeszow University, Poland, sturnau@atena.univ.rzeszow.pl

Ethnomathematics
What is the relationship between ethnomathematics, mathematics and anthropology and the politics of mathematics education? What evidence is there, and how do we get more, that school programmes incorporating ethnomathematical ideas succeed in achieving their (ethnomathematical) aims? What are the implications of existing ethnomathematical studies for mathematics and mathematics education? What is the relationship of different languages (or other cultural features) to the production of different mathematics?
Team Chairs: Franco Favilli, University of Pisa, Italy, favilli@dm.unipi.it
                    Abdulcarimo Ismael, Pedagogical University,Maputo, Mozambique, abdulcarimoismael@hotmail.com

The role of mathematical competitions in mathematics education
Do mathematical competitions contribute to widening the gap between ‘mathematics for all’ and ‘mathematics for the élite’, or can the opposite be the case? How can competitions motivate and foster mathematical creativity with students at large? To what extent do problems typically set in mathematical competitions adequately reflect the variety and richness of mathematical activity in problem solving? What should the relations be between competitions and mathematics education?

Team Chairs: André Deledicq, University of Paris VII, France, adeledicq@wanadoo.fr
                    Peter Taylor, University of Canberra, Australia, pjt@amt.canberra.edu.au

Current problems and challenges in pre-school mathematics education
To what extent is it desirable to expose pre-school children to structured or institutionalised mathematics teaching? What are the most important current problems, issues and challenges pertaining to the mathematical education of pre-school children?

Team Chairs: Ann Anderson, University of British Columbia, Vancouver, Canada, anders@interchange.ubc.ca
                    Robert D. Speiser, Brigham Young University, Provo, USA, speiser@mathed.hyu.edu

Current problems and challenges in primary mathematics education
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics at the primary level and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Giancarlo Navarra, University of Modena and R. Emilia, Italy, ginavar@tin.it
                    Catherine P. Vistro-Yu, Ateneo de Manila University, The Philippines, cvistro-yu@ateneo.edu

Current problems and challenges in lower secondary mathematics education
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics at the lower secondary level and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Maryvonne Le Berre, IREM of Lyon, France, leberre.maryvonne@free.fr
                    Gard Brekke, Telemark University College, Notodden, Norway, gard.brekke@hit.no

Current problems and challenges in upper secondary mathematics education
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics at the upper secondary level and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Olive Chapman, University of Calgary, Alberta, Canada, chapman@ucalgary.ca
                    Ornella Robutti, University of Torino, Italy, ornella.robutti@unito.it

Current problems and challenges in non-university tertiary mathematics education
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics at the non-university tertiary level and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Sergiy Klymchuk, Auckland University of Technology, New Zealand, sergiy.klymchuk@aut.ac.nz
                    Marilyn Mays, North Lake College, Irving, USA, memays@dcccd.edu

Current problems and challenges in university mathematics education
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics at the university level and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Oh-Nam Kwon, Seoul National University, Korea, onkwon@snu.ac.kr.
                    Stavros Papastavridis, University of Athens, Greece, spapast@cc.uoa.gr

Current problems and challenges concerning students with special needs
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics for students with special needs and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Ann Gervasoni, Australian Catholic University, Ballarat, Australia, a.gervasoni@aquinas.acu.edu.au
                    Jens Holger Lorenz, University of Education, Frankfurt, Germany, lorenz_jens@ph-ludwigsburg.de

Current problems and challenges in distance teaching and learning
What are the most important current problems and challenges pertaining to distance teaching and learning of mathematics and where are they located? Are there issues or dilemmas of a controversial nature? How should these problems, issues and challenges be dealt with?

Team Chairs: Alexander Afanasiev, The Russian Academy of Science, Moscow, Russia, apa@isa.ru
                    Nerida Ellerton, Illinois State University, Normal, USA, nellert@ilstu.edu