### HPM 2012 – The HPM Satellite Meeting of ICME

**We were there**

The HPM Group celebrated its 40^{th} anniversary with HPM 2012 – the 8^{th} quadrennial Satellite Meeting of ICME. It took place in Daejeon, Korea from 16 – 20 July, 2012, where more than 100 participants gathered for an interesting week with 7 plenary lectures, 60 oral presentations, 7 workshops, 2 panel discussions, a poster session, several exhibitions, and a special focus on Asian HPM and insights into Eastern Asia Mathematics History.

The seven plenary lectures concerned the seven themes of the meeting. The first one concerned history and epistemology implemented in mathematics education and was given by Tsang-Yi Lin from Taiwan. He gave three examples of projects, on ancient Greek geometry, on Brigg’s tables of Logarithm and on Cramer’s Rule. He concluded on the necessity for teachers to acquire knowledge on history. The second lecture, given by Tinne Hoff Kjeldsen from Denmark, was interested by the theoretical framework for integrating history of mathematics in mathematics education. It dealt with the difficult question of the results of history *for* and *about *the learning of mathematics. For this purpose, she analyzed two examples: Bernoulli’s catenary and Egyptian mathematics. The third lecture, given by Janette Barnett from USA, considered the use of original sources in the classroom and their educational effects. She described her own experiences with using papers of Boole and Cayley. These three lectures indicated that the purpose and ideas of HPM now has entered a new mature period.

Three other plenary lectures were interesting for seeing history of mathematics as an interdisciplinary and cultural tool for the teaching and learning of mathematics. Dominique Tournès from France gave a very complete panorama of mathematics for 19^{th} century engineers, and especially on their methods and instruments, which can be used in classrooms. Michel-Pajus from France proposed a historical voyage into the literary-mathematical Universe. Her very living voyage had five stops: a Greek theatre, the world of Romans, a castle in Middle Ages, Parisian salons of the 17^{th} and 18^{th} centuries and the machinist world of 19^{th} century. The last lecture of the meeting was devoted to mathematics from Eastern Asia, with the theory of equations in the history of Chosun mathematics presented by Sung Sa Hong from Korea.

For many years now, history of mathematics education has been a theme of International meetings of HPM. The number of oral presentations given in Daejeon on this theme shows the increasing interest among teachers and researchers. The plenary lecture of this theme concerned the social structures in mathematics education, more precisely the research on mathematics education with theories and methods from sociology of education. Johan Prytz, from Sweden, began to give motives for studying the history of mathematics education and argued for the use of a sociological perspective for this endeavor.

The oral presentations, workshops, and the poster session taken together showed the richness of on-going HPM related activities and research. From examples of how to teach history of mathematics to teaching mathematics through historical sources over a “journey to a proof”, issues about “trends on mathematics in novels”, “the ladder and the box problem”, “historical problems and mathematical knowledge for teachers” and “research on the Muk Sa Jib San Beob” we got a glimpse of the diversity of HPM activities and the multi-faceted perspectives through which History and Pedagogy of Mathematics is perceived and treated around the world in research, classrooms, art, culture, literature.

It is impossible to summarize and do justice to all the presentations in this short Newsletter contribution; for that we refer to the program and the papers that were submitted, all of which are available at the web site: http://www.hpm2012.org/?mid=announce_05. Instead we will make a few comments about the two panel sessions. Their themes were addressed towards practices: the first panel dealt with the problem of justification: Why do we require a “history of mathematics” course for mathematics teacher candidates? The second panel dealt with how we can get insights into effects of history in mathematics education through empirical research.

The intentions of the first panel session were twofold: to share experiences with ways in which history of mathematics is part of elementary and/or secondary mathematics teacher candidates’ education, and to provide a synthesis of group discussions during the panel session – this second part is going to be post-panel work based on records of the group discussions which were produced during the session. The presentations by the five panelists showed two things: 1) The status of history of mathematics in the curriculum in their different countries varies a lot from being explicit to being implicit at different levels, and 2) reflections about why history of mathematics should be part of teacher training and how that reflects back on the content and teaching of such a course for teacher candidates do not seem to be clearly developed. However, the two questions that were raised by the panel of why history of mathematics should be part of mathematics teacher training programs and (in case of a positive outcome of the why question) what it should look like, are key questions to be dealt with in the HPM-community.

The second panel discussed the question of empirical research on history in mathematics education through four lenses: 1) Lesson studies and the use of technology, 2) Original sources and recruitment, transition, retention, 3) Integrating history and teacher training, and 4) Mathematics education research frameworks and theoretical constructs in HPM. Several of these lenses were also addressed in some of the plenary lectures and the panelists managed to draw on these presentations and in doing so, they provided a sort of a common ground that initiated a very lively discussion in the audience. One of the suggestions for measuring the effects of history in mathematics education has come out of the New Mexico State University & Colorado State University – Pueblo programs of using primary sources for the teaching of mathematics. Their results show that maybe the use of primary sources can do more than function as a tool for teaching and learning of mathematics. They suggest addressing the specific aspect on student success consisting of recruitment, transition and retention – topics that educators, curriculum designers, and policy makers care about and pay attention to. Hereby linking to a group of people the HPM community needs to address, if we want to promote the explicit inclusion of history of mathematics in mathematics education curricula.

We would like to mention also that the meeting was very well organized, in a very agreeable and friendly atmosphere. We thank Sunwook Hwang, his colleagues, and students for all they did for the success of HPM 2012.

**Evelyne Barbin,**

IREM and Laboratory LMJL, University of Nantes, evelyne.barbin@wanadoo.fr

**Tinne Hoff Kjeldsen,**

IMFUFA, NSM, Roskilde University, Denmark, thk@ruc.dk

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