A message from the new Chair of HPM


Dear colleagues,

I would like to take advantage of this newsletter to express my gratitude to Evelyne Barbin and the HPM Advisory Board for the trust and confidence they have placed in me by inviting me to chair our group. I will work hard with all of you to continue the work of our past chairs and members in order to ensure that HPM continues playing its important scientific role.

I joined HPM in the summer of 1992, when our quadrennial meeting was held in Toronto, just before ICME-7. The summer of 1992 was very important in my life. After spending one year at the Université du Québec à Montréal working with a remarkable team of mathematics educators, psychologists, and historians of mathematics, I had to decide whether or not to come back to my university — Universidad de San Carlos de Guatemala — or to accept an offer that Laurentian University in Ontario was making me to join its school of education. It was in this turmoil of feelings and uncertainties that I went to Toronto to participate in the HPM meeting.

The Toronto HPM meeting gave me the opportunity to meet people whose work I have read with great interest and passion. For instance, I met John Fauvel, whose natural curiosity and inquisitive mind impressed me tremendously. I remember that, during a coffee break, John came to me and invited me to sit on some stairs nearby so that I could tell him how we were trying to distinguish in Montreal between arithmetic and algebraic thinking. I mentioned that our approach was based on an investigation of ontogenetic and historical developments and synthesized, as best as I could, our findings. I was unaware of how this research problem and the way we tackled it in Montreal was going to affect me during the following years until now. If I see retrospectively the work that we did in Montreal, I find there, albeit in a nascent form, problems and topics that have become the major areas of my research— e.g., the emergence of algebraic symbolism, the development of algebraic thinking, the relationships between ontogenesis and phylogenesis, and the relationships between mathematical thinking and culture.

I found very inspiring and stimulating all the presentations that I attended at the HPM 1992 meeting. As you know, a selection of papers presented at that meeting and HPM talks at ICME-7 were published in Vita mathematica: historical research and integration with teaching by Ron Calinger. I read the book from its first page up the last one and ended up writing a review of it some years later (the review appeared in Revista Brasileira de História da Matemática, 4(7), 83-95).

This short overview of my first contact with HPM gives you, I hope, an idea of how important HPM has been in my academic life. Each one of the HPM meetings that I have attended has been profoundly inspiring and motivating. And I would like very much that young researchers have the same invaluable opportunity that the group has offered me to grow intellectually through the group’s meetings and network possibilities.

Our next meeting is still a few years ahead of us. Yet, we need to start planning it. We’ll do it. But I also feel that we could attempt to bring closer and in a more systematic manner our research interests. HPM can do that. With the development of new communication technologies, distances no longer pose the difficult problems they did in the past. So, what I have in mind is the creation of “research dossiers” that could facilitate exchange and joint work among our members. The idea is that each research dossier revolves around a research theme that would be investigated in the course of several years (2 or 3). The results could be presented at the HPM quadrennial meetings, with updates and short synopsis in each Newsletter. You are invited to organize a research dossier and to identify and invite researchers that you think can contribute to the dossier. I approached some colleagues to invite them to start this initiative.

Luis Puig will be in charge of the dossier “On the first books on Algebra written in Spanish.” The dossier starts from the fact that, during the second part of the 16th century, the first books written in Spanish containing chapters on Algebra were published: Marc Aurel’s Libro Primero de Arithmetica Algebratica, published in 1552 in Valencia, Juan Pérez de Moya’s Arithmetica Practica y Especulativa, published in 1562 in Salamanca, Pedro Nunes’s Libro de Algebra en Arithmetica y Geometria, published in 1567 in Anvers (today Antwerp), and Juan Pérez de Moya’s Tratado de Mathematicas, published in 1573 in Alcala de Henares. It is an interesting fact that only one of these authors, Pérez de Moya, had Spanish as his mother tongue: Marc Aurel was German, and Pedro Nunes was Portuguese. The goal of the research dossier is to compare the presentation of Algebra in these books.

Another dossier will be devoted to the Middle Age and Renaissance mathematics in the Classroom, featuring an investigation of Tartaglia Galigai and some other authors. This dossier will be carried out under the responsibility of Fulvia Furinghetti. So far, the participants include Adriano Demattè and myself.

A third dossier revolves around “Original sources in the teaching and learning of mathematics.” Participants include Uffe Thomas Jankvist, Tinne Hoff Kjeldsen, Hans Niels Jahnke, Renaud Chorlay, and Janet Barnett.

A fourth dossier is under the responsibility of Masami Isoda and will work towards the production of a Lesson Study Book for History of Mathematics.

Again, I invite you to identify a research dossier and invite people to participate in it. Of course, you can also try to recruit people who are not currently HPM members. By interacting and working with HPM people, they will become HPM members! One of the strengths of our group is the interdisciplinary composition—mathematicians, historians, epistemologists, mathematics educators, etc. Let’s try to keep building and capitalizing on that strength!


Luis Radford

Laurentian University, Canada

University of Manchester, UK


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