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*Brief history and statistics of the previous ESU*

The initiative of organizing a Summer Univeristy (SU) on *History and Epistemology in Mathematics Education* belongs to the French Mathematics Education community in the early 1980’s. It was the French IREM’s (*Institut des Recherches sur l’ Enseignement des Mathématiques*) that organized the first interdisciplinary SU on the History of Mathematics in 1984 in Le Mans, France. It was followed by other SU in France (1986 in Toulouse, 1988 in La Rochelle, and 1990 in Lille). The next one was organized in 1993 on a European scale, and was called the *1st European Summer University (ESU) on History and Epistemology in Mathematics Education*, (a name coined since then), but many participants in it and in the subsequent ESU came outside Europe.

The previous ESUs took place in July,

- 1993, Monpellier, France

- 1996, Braga, Portugal (conjointly with the HPM Satellite meeting of ICME 8)

- 1999, Louvain-la-Neuve & Leuven, Belgium

- 2004, Uppsala, Sweden (conjointly with the HPM Satellite meeting of ICME 10)

ESU |
Duration |
No of participants |
Number of talks, workshops etc |

1st Montpellier France |
19-23/7/1993, 5 working days |
254 from 29 countries (17 European) |
5PL, 2PN, 48WS, 37T |

2nd Braga, Portugal |
24-30/7/1996, 5 working days+a morning session |
548 from 33 countries (14 European) |
1PL, 28IL, 4PN, 33WS, 71T |

3rd Louvain-la-Neuve /Leuven, Belgium |
15-21/7/1999, 6 working days |
159 from 22 countries (16 European) |
6PL, 2PN, 37WS, 35T |

4th Uppsala, Sweden |
12-17/7/2004, 4 working days+ two half morning sessions |
120 from 32 countries (15 European) |
6PL, 2PN, 9WS, 59T |

PL=Plenary lecture

PN= Panel discussion

WS=Workshop

T= Talk/ oral presentation

IL=Introductory Lecture

Remarks:

(a) In the 2nd ESU there was only one plenary lecture, but many introductory lectures, which run in parallel and which were addressed to schoolteachers, providing an introduction to the topics elaborated in the workshops.

(b) The 2nd and 4th ESU have been organized conjointly with the HPM Satellite Meeting of the corresponding ICME (ICME 8 and ICME 10, respectively)

(c) In most ESU, more than half of the participants were local people: Portuguese in the 2nd ESU (310); French in the 1st ESU (134). In the 3rd ESU about 40% were Belgians (64). Thus, in general, there was a strong participation from local people, mainly primary and secondary schoolteachers.

(d) In general, a key element of the program was the great number of workshops, which gave the opportunity to presenters to explain their ideas, teaching practice, share their experience with participants and distribute relevant material. The workshops were of variable duration usually, from 1 to 3 hours.

(e) Non-local participants came from many countries, either European, or from other continents, although with a few exceptions, only a small number from each country (usually less than 5, or 6).

**Themes of the previous ESU**

The activities and the program of each ESU were structured around some main themes, which were the following:

*1st ESU Montpellier, France, 19-23/7/1993*

-The historical construction of mathematical knowledge

-Introducing a historical perspective into the teaching of mathematics

-The relationship between mathematics education and culture

-Epistemology and its relationship to didactics and pedagogy

-History of mathematics in initial teacher training and in-service courses

-Mediterranean mathematics

-Ethnomathematics

*2nd ESU Braga, Portugal, 24-30/7/1996*

Main themes:

-Mathematical cultures all over the world

-Mathematics as a science

-Mathematics, arts and technics

Special topics:

-History of mathematics education

-Epistemological obstacles

-Views on Mathematics

-Mathematics for all

-Mathematical proof in history

*3rd ESU Louvain-la-Neuve /Leuven, Belgium, 15-21/7/1999*

There were not any main themes specified a priori. However, themes proposed in due course included

Mathematical journals in Europe and their use in education

-The historical construction of mathematical knowledge

-The relation between mathematics and science in history; its in education

-Relations between mathematics and music up to Euler’s era; their use in education

-History of mathematics education

-Mathematicians in the Low Countries

-About the 19th century geometry: the Belgian theorems; what may be the insights for the education?

*4th ESU Uppsala, Sweeden 12-17/7/2004*

-The history of mathematics

-Integrating the history of mathematics into the teaching of mathematics

-The role of the history of mathematics in teacher's training

-The common history of mathematics, science and technology

-Mathematics and different cultures

-The philosophy of mathematics

An important aspect of the ESU has been the publication of its Proceedings. In the 2nd and 4th ESU the Proceedings became available in advance and were distributed to the participants on the spot.

1st ESU: *Actes de la première Université d’ Été Européenne sur l’ Histoire et Épistémologie dans l’ Éducation Mathématique*, F. Lalande, F. Jaboeuf, and Y. Nouazé (editors), IREM de Montpellier, Université Montpellier II, Montpelier, France, 1995 (598 pages in one volume).

2nd ESU: *Proceedings of the 2nd European Summer University on the History and Epistemology in Mathematics Education and the ICME 8Satellite Meeting of HPM*,M.J. Lagarto, A. Viera & E. Veloso (eds), Portuguese Association of the Teachers of Mathematics & Department of Mathematics, University of Minho, Braga, Portugal, 1996 (813 pages in two volumes).

3rd ESU:*Proceedings of the 3rd European Summer University on the History and Epistemology in Mathematics Education*, P. Radelet-de-Grave & C. Brichard (editors), Université Catholique de Louvain, Leuven and Louvain-la-Neuve, Belgium, 2001 (944 pages in two volumes).

4th ESU: *Proceedings of the HPM 2004: History and Pedagogy of Mathematics ICME 10 Satellite* *Meeting and 4th European Summer University on the History and Epistemology in Mathematics Education*, F. Furinghetti, S. Kaijer & A. Vretblad (editors), Uppsala University, Uppsala, Sweden, 2004 (482 pages in one volume).

"Appendix," *Convergence* (December 2005)