Conference Report: 6th European Summer University on the History and Epistemology in Mathematics Education
6th European Summer University on the History and Epistemology in Mathematics Education
19-23 July 2010 Vienna
These Summer Universities started in Montpellier (France) in 1993 and from the beginning provided an occasion for researchers and teachers, not only to hear about new experiences and ideas and share their own, as in an ordinary international meeting, but above all to learn from each other, as in an open school inspired by cooperative learning. The main organizers were Evelyne Barbin, from University of Nantes (France); Manfred Kronfeller, from Vienna University of Technology (Austria); and Costantinos Tzanakis from University of Crete (Greece) and supported by the international Scientific Program Committee composed of 28 people from 18 different countries. There were 154 participants from 34 different countries, of whom about 75% made contributions (talks, workshops, posters). The conference was sponsored by the Austrian Federal Ministry of Science and Research, the Government of the City of Vienna, the Vienna Convention Bureau, Casio Europe and Texas Instruments.
This report is from a “teacher’s point of view” and summarises the reactions of about 30 classroom teachers who attended the conference. I would particularly like to thank Alexandra Lux from BRG Purkersdorf (Austria) in helping to prepare the report.
The main themes of this 6th ESU were:
- Theoretical and or conceptual frameworks for integrating history in mathematics education;
- History and epistemology implemented in mathematics education: Classroom experiments & teaching materials, considered from either the cognitive or/and affective point of view; survey of curricula and textbooks;
- Original sources in the classroom, and their educational effects;
- History and epistemology as tools for an interdisciplinary approach in the teaching and learning of mathematics and sciences;
- Cultures and Mathematics;
- Topics in the history of mathematics education.
Each theme had a plenary lecture, several workshops, oral presentations and posters, and some also had panel discussions. Since it was impossible to attend all the conferences and workshops, we shall only comment here on the ones we found most useful or interesting.
Of the plenaries, the most appreciated was that by Michael Glaubitz from the Albert Einstein Gymnasium in Hameln (Germany): The Use of Original Sources in The classroom – Empirical Research Findings (theme 3). He proposed the hermeneutic approach to the use of historical material claiming that reading an original source can be an especially rewarding enterprise which is capable of substantially deepening mathematical understanding, enriching classroom activities and developing learners’ beliefs in mathematics. He set out, from an empirical point of view, feasible conceptual designs, necessary preparations and prospective effects when reading an original source in class using the example of quadratic equations. This was judged as “probably the most important lecture for actual teaching in class”, and suggested further questions to be probed. We were really sorry that the same author’s workshop was cancelled.
Another successful plenary lecture was Michael Fried’s: History of Mathematics in Mathematics Education: Problems and Prospects (theme 1). The speaker from the Ben Gurion University of the Negev (Israel), suggested that teaching maths using history has to involve a redefinition of our general goals for mathematics education more than the concrete ways in which we bring history of mathematics into the classroom. History as a goal means history as a new view point on the mathematical landscape in which a central idea is the presence of original texts in a form or another.
Also the two plenary lectures given by Marc Moyon, from the Centre d’Histoire des Sciences et d’Epistémologie de Lille1 & IREM de Lille; and Fulvia Furinghetti from Università di Genova (Italy) together with Livia Giacardi from Università di Torino (Italy) were judged very interesting. The first one, titled Practical Geometries in Islamic Countries: the example of the division of plane figures (theme 4) presented different geometric problems linked to various other subjects as among others, the practices of craftsmen, architect or jurists. The interest for the class practice is the wide range of procedures in which the whole mathematical knowledge seems to be involved. The second one, named From Rome to Rome: Events, People, and Numbers during ICMI’s First Century (theme 6), was enjoyed because of his giving insights to some key ideas that led to the birth and to the growth of ICMI and to the changes in methodological approaches to problems that offered, especially to young teachers, a global perspective and a theoretical basis.
Our favourite panel discussion was the one chaired by Costantinos Tzanakis with contributions from Anne Boyé from Centre François Viète, Université de Nantes (France), Adriano Dematté from Università di Genova (Italy), and Ewa Lakoma from Military University of Technology Warsaw (Poland). The title was The history of mathematics in school textbooks. The close link with teachers’ everyday practice together with the well constructed discussion appealed to us, even though some detected a lack of optimism in some panellists. For a future ESU it would be good to have a panel discussion on the use of history for students who find mathematics difficult. (Could history of maths help them to do better?)
The most interesting workshops we thought were: Maps, Narratives and Orientations: The use of Concept Maps for exploring our Mathematical Heritage in the Classroom (theme 2), by Leo Rogers from Department of Education, University of Oxford (UK); Defining derivatives, integrals and continuity in secondary school: a phased approach inspired by history (theme 2), by Hilde Eggermont from Sint-Pieterscollege, Leuven (Belgium) together with Michel Roelens from Katholieke Hogeschool Limburg (Belgium); Good Old arithmetic (theme 3), by Frédéric Metin from IREM of Dijon, Université de Bourgogne (France); Pedagogical and Mathematical Games throughout the Times: from Rithmomachia to Hex (theme 3) by Jorge Nuno Silva from University of Lisbon (Portugal); Digitising the past mathematics by the future mathematics (theme 3), by Snezana Laurence from Bath Spa University, Culverhay Campus (UK); Mathematisation of nature and new conceptions of curves in the years 1630 (theme 4), by Evelyne Barbin; The mediaeval geometries: a way to use the history of mathematics in the classroom of mathematics by Marc Moyon. The main reason why these were so popular was because they related directly to classroom work and/or offered useful material.
We have some critical comments and suggestions. There were rather too many short oral presentations. We noticed a really widespread range of quality, from rather poor, to quite useful. Since the Summer Universities declared aims are to provide a forum for presenting research in mathematics education and innovative teaching methods and to give the opportunity to mathematics teachers, educators and researchers to share their teaching ideas and classroom experience, it would be a good idea to reduce the number of oral presentations so as to make room for, say, “panel discussions workshops”, coordinated by the theme of the discussion’s proposer, in which each participant has the right to say his/her opinion. This would be an opportunity, especially for new comers, who often feel that they are the only ones not already known to everyone else, to be introduced to the researchers and teachers more interested in the same questions as them. It would help first-time teachers to identify and meet other teachers at the very beginning of the conference. Even though there should not be any real separation between researchers and teachers, a clearer indication of sessions of special interest to classroom teachers could help the absolute beginners to choose from such a widespread menu. Maybe, the workshops could be of two different types: the usual ones on one hand and some others more similar to the pre-service teachers trainee activities on the other. This would help young people or other new entries to participate in an active way and to make the experience more useful and nice.
To conclude, let me offer a suggestion about the arrangements. I think that the reason why in recent ESUs there have not been as many teachers participating is also a problem of sponsorship. The economic crisis has had the effect of drastically reducing the money available for these activities, especially for teachers (this is the case in Italy and must be the same for other European countries). So, even if personally I always was very happy when we stayed in a big city like Prague or, this year, Vienna (I really enjoyed the operas I’ve seen and listened to), it might be better for future meetings to take place in quieter and less expensive places. May be it also help if there were a cheaper registration fee for classroom teachers.
Finally, we would all like to thank Manfred Kronfeller and the local organizing committee for the marvellous work they did and for the kindness and the smiles they gave to all of us even if they sometimes were under stress. Thanks a lot to Evelyne Barbin and Costas Tzanachis too, for their giving the teachers the opportunity to contribute to the improvement of ESU’s.
Istituto d’Arte “Max Fabiani”, Gorizia (Italy)
Scienza under 18 isontina, Fogliano Redipuglia (Italy)
(Editor’s note: Impressions on the ESU6 can also be read at the blog Teacher Educator Bjørn from where the photos are taken.)