International workshop on variations and series of mathematical problems

Problems are traditionally the focus of many researches in mathematics education as well as in history of mathematics. While in many cases these researches treat problems in isolation, some recent projects concentrate on sets of problems, their organization, their variations and the links between them. Thus, historians in the HASTEC project examine the coherency and meaning of mathematical texts written as series of problems and solutions – this kind of textual organization being attested from antiquity to the present day and found in many different cultural contexts. In mathematics education, these questions appear in several different ways. Projects like the French DREAM try to construct long term teaching processes based on problems. In Hungary, where a strong tradition based on problems and mathematical discovery exists, current projects examine the role of series of problems in these teaching traditions: the way in which teaching and learning activities depend on the coherent ordering of problems. Several current mathematics education researches gain inspiration in the Chinese “variation method”. In these cases, questions of cultural transmission arise: for example, an Italian project examines the possibilities to adapt this Chinese method to the Italian context.

The aim of the interdisciplinary and international meeting organized in Budapest is to exchange about these different projects and perspectives: while they have neither exactly the same objects of study nor the same methodologies, there is enough proximity between these points of view and approaches to confront them. This dialogue should yields new perspectives and cross fertilization of our research perspectives.

This meeting is also an opportunity for the concrete encounter between various mathematics teaching cultures. Each of the participating groups and projects are mixed groups, composed of teachers, teacher trainers and researchers ‑ these qualities being not exclusive from each other. This professional diversity will also contribute to the variety of views that the meeting aims to confront.

Five projects are represented: From Hungary, the MTA-ELTE Complex Mathematics Education Research Group and the MTA-Rényi Discovery Learning in Mathematics Research Group; From France, the HASTEC research project entitled “series of problems, a genre at the crossroad of traditions”, the group on history and epistemology within the IREM of Paris Nord (in close connection with the HASTEC project), and finally the DREAM group of the IREM of Lyon. The above mentioned Italian project also inspired the organization of this workshop, even if it will not be represented during the April meeting.

Two types of presentation will take place in the meeting. Researchers will present the different projects, their aims, research methodologies and current results. Teachers and teacher trainers will lead reading seminars while we discuss examples of collections and series of problems studied in the frame of each project and/or used in classroom or in training sessions by the presenting teacher. In addition, discussion sessions will give ample opportunity to confront the views of the various participants: teachers, teacher trainers and researchers from different disciplines and countries, on the presented examples. This will thus contribute to the collective reflection on the role of variations and series of problems in mathematics, in the history of mathematics and in mathematics education.

Supporting institutions