Discrete mathematics occupy a rather variable place in math education : in some countries, only a very small number of discrete mathematics concepts are taught, except perhaps those related with combinatorics and the basics of number theory. In a few other countries, for example in Hungary (as far as Europe is concerned), there has been a long tradition to introduce graph theory in secondary schools.

The TSG-15 group aims at collecting researches on math education in its aspects pertaining to discrete mathematics : teaching and learning strategies, for students at different levels, and training of teachers. Discrete mathematics can be introduced, either as a mathematical theory, or as a set of tools to solve problems (a graph is a basic and intrinsic modelling tool). For example, mathematical games are often based on problems in discrete mathematics.

The group will try to assess and analyze collectively the state-of-art of curricula in discrete mathematics. This leads to two general and fundamental questions :

- Why and how introduce discrete maths in schools ?

- How can discrete mathematics contribute to make students acquire the fundamental skills involved in defining, modelling and proving, at various levels of knowledge ?

The TSG-15 group will try to focus on short presentations which present original considerations about number theory, discrete geometry, or graph theory, in a didactical point of view, accompanied, wherever possible, by experimental results concerning student productions and the difficulties encountered.

The group will be particularly interested in papers related to the following themes :

-number theory at the elementary school level and for pre-service education of teachers,

-combinatorics and graph theory in the current training of junior college teachers,

-the use of the concept of graph in problems which involve defining, modelling and proving,

–the rôle of discrete maths in mathematical games.

Deadlines

The deadline for submissions is the end of January. Information about acceptance of the submissions, with recommendations for the final version(8-10 pages), will be available by the end of February. Final versions should be sent by April, 20th, 2008.

Grenier D. (2003) The concept of « induction » in mathematics, Mediterranean Journal For Research in Mathematics Education, vol.2.1, pp.55-64. ed. Gagatsis ; Nicosia Cyprus.

Grenier D., (2002), Different aspects of the concept of induction in school mathematics and discrete mathematics, European Research in Mathematics Education, Klagenfurt, august, 23-27.

Grenier D. (2001), Learning proof and modeling. Inventory of fixtures and new problems. Actes du 9ème International Congress for Mathematics Education,ICME 9, Tokyo, Août 2000.

Zazkis, R., & Campbell, S. R. (Eds.) (2006). Number theory in mathematics education: Perspectives and prospects. In A. H. Schoenfeld (Ed.) Studies in mathematical thinking and learning series. Mahwah, NJ: Lawrence Erlbaum Associates.

Campbell, S. R., & Zazkis, R. (Eds.) (2002). Learning and teaching number theory: Research in cognition and instruction. In C. Maher & R. Speiser (Eds.) Mathematics, learning, and cognition: Research Monograph Series of the Journal of Mathematical Behavior (vol. 2). Westport, CT: Ablex.

Campbell, S. R. (2002). Zeno’s paradox of plurality and proof by contradiction. Mathematical Connections. Series II (1), 3-16.

Session 1 : Tuesday,July 8, 12:00-13:00 (60 mn)

Introduction (Jerry Lodder)

Jerry Lodder, Janet BARNETT, Guram BEZHANISHVILI, Hing LEUNG, David PENGELLEY, Desh RANJAN Historical Projects in Discrete Mathematics and Computer Science

QUEK Khiok Seng, TOH Tin Lam, BOEY Kok Leong, TAY Eng Guan and DONG Fengming (Nanyang Technological University, Singapore) Teaching of Discrete Mathematics at Advanced Level in Singapore : Teachers’Perspectives

Ambat VIJAYAKUMAR (Cochin University, India ) Teaching and learning of Discrete mathematics – The Indian scenario

Session 2 : Wednesday,July 9, 12:00-13:30 (90 mn)

Michel SPIRA (Universidade Federal de Minas Gerais, Brazil) The role of the bijection principle on the teaching of combinatorics

Ulrich KORTENKAMP (University of Education Schwäbisch Gmünd, Germany) A technology-based approach to discrete mathematics in the classroom.

Stephan HUBMANN (Dortmund University, Germany) Doing mathematics -authentically and discrete. A perspective for teacher training

Cécile OUVRIER-BUFFET (DIDIREM et Paris 12, France) Discrete mathematics : a mathematical field in itself but also a field on experiments. A case study : displacements on a regular grid

Session 3 : Friday, July 11, 12:30-13:30 (60 mn)

Thierry DANA-PICARD (Jerusalem College of Technology, Israel) Graph isomorphism, matrices and a Computer Algebra System : switching between representations

Léa CARTIER & Julien MONCEL (Joseph Fourier University, Grenoble, France) Learners’ conceptions in different class situations around Königsberg’s bridges problem

Session 4 : Saturday, July 12, 12:00-13:30 (60 mn)

Nicolas GIROUD (Joseph Fourier University, Grenoble, France) Learning experimental approach by a discrete mathematic problem

Denise GRENIER (Institut Fourier and IREM, Grenoble University I, France) Some specific concepts and tools of discrete mathematics

Conclusion (Michel Spira, Jerry Lodder and Denise GRENIER)

Research Situations for classrooms, an example : tiling polyminos, by Maths-à-Modeler-team, University Grenoble 1, France.