No. 75 November 2010 This and earlier issues of the Newsletter can be downloaded from our website http://www.clab.edc.uoc.gr/hpm/ mathematician's scholarly work in the history Professor R. C. Gupta receives of mathematics. Kenneth O. May Prize Prof. Gupta's major contributions in the Professor Radha Charan Gupta received field include work on the history of the Kenneth O. May Prize for the History of development of trigonometry in India. He Mathematics at the International Congress of authored the chapter 'Historiography of Mathematicians (ICM) on 27 August 2010. Mathematics in India' in: Dauben and Scriba Prof. Gupta was chosen for the 2009 prize (eds.) Writing the History of Mathematics: Its jointly with Prof. Ivor Grattan-Guinness of Historical Development, Birkhauser, 2002. He UK by the International Commission for the was the President of the Association of History of Mathematics. Prof. Kim Plofker Mathematics Teachers of India from 1994 presented the award. until recently. He also founded the journal Ganita Bharati (meaning “Indian Mathematics”) and has written several articles in the journal. He is also a frequent contributor to the HPM Newsletter (including this issue). New Books De grands défis mathématiques: d’Euclide à Condorcet [On major challenges of mathematics: from Euclid to Condorcet] Evelyne Barbin (ed.) The Prize is named after the mathematician Paris: Vuibert; Adapt-Snes, 2010, 176pp, and historian Kenneth O. May, founder of the ISBN 9782356560100;9782311000191 International Commission for the History of Mathematics and its journal Historia The output of IREM colleagues is admirable Mathematica. The prize, instituted in 1989, and enviable. This latest volume, under the consists of a bronze medal and is given once editorship of Evelyne Barbin, provides nine in four years in appreciation of a incidents or problems that stimulated mathematical responses. The purpose of the HPM Newsletter No. 75 November 2010 HPM webpage: http://www.clab.edc.uoc.gr/hpm/ 1 descriptions here is to provide original ways of obtaining 5, something which students material that can be used in the classroom of can easily correct. Gérard Harmon treats early upper secondary schools, that is, in those years approaches to Bayes’ Theorem by Condorcet immediately preceding university entrance. (1805) and then Lacroix (1816) both The claim is slightly misleading in that the considering possible outcomes of taking black article by Evelyne Barbin describes work with or white balls from an urn. I also enjoyed third year university students preparing to reading the background to modern digital type teach and the historical time frame of the fonts and the use of Bézier curves which articles extends to before Euclid and after extended Loïc Le Corre’s lesson on Dürer’s Condorcet. The work is divided into four geometric representation of fonts. sections: measurement of magnitudes, The educational context – defending the representing magnitudes, probability, choice of material – makes us aware of French approximations to curves. concerns that would not trouble the British However entertaining and stimulating, I secondary mathematics teacher, more often feel that French studies linking history to accustomed to a pragmatic sloppiness of pedagogy would not appeal to the Anglo- approach to teaching mathematics, particularly Saxon reader and I even wonder how much with regard to notation. Vive la différence! they might be taken up in the French Chris Weeks, classroom, save for the enthusiasts who have Great Britain written these pieces. It is therefore encouraging to find, alongside suggested Tinhlelo exercises based on historical texts, or at least Interweaving Art and Mathematics: Colourful inspired by them, some illustrations of work Basket Trays from the South of Mozambique done by students themselves. Thus Dominique Paulus Gerdes Tournès from Réunion has examples of Lulu, 2010 students’ constructions of solution curves of differential equations, using Euler’s method, “Tinhlelo” exist in each family of the vast which they did following a guided reading of Mozambique. We need to know that there are an extract of Institutionum calculi integralis no factories for the production of the (1768). From Patrick Guyot of Bourgogne we “tinhlelo.” “Tinhlelo” knowledge is have an account of students working on the endogenous knowledge that repeats itself, problem of inscribing a square inside a recreates itself, and adorns itself in the triangle which includes images of the students’ multiplicity of its models, sizes, colours, and initial naïve attempts. Indeed, it is clear that in functions. No conventional school orients this almost all cases the writers are telling us of learning. The families, the remarkable, curious material they themselves have used. and master artisans, are the ones who are But this collection of articles is more than a creating and maintaining these products of description along the lines of a simple ‘these eloquent usefulness in our families. The have worked for us’. Each piece comes with families recreate the art of this mathematical an introduction of the mathematical, historical weaving! and educational context and some offer further (From the foreword) reflections and all have source bibliographies. There are some nice discoveries for me. Reports on new books are welcome. Leibniz does not appear among the founders of probability calculus but Renaud Chorlay has used a letter from him describing the expected outcomes of a simple game of dice which is easy to read and has the pedagogic advantage that his assumptions are wrong. He fails to count both (3,2) and (2,3) as distinct HPM Newsletter No. 75 November 2010 2 HPM webpage: http://www.clab.edc.uoc.gr/hpm/ Conference reports • History and epistemology as tools for an interdisciplinary approach in the teaching 6th European Summer University on the and learning of mathematics and sciences; History and Epistemology in Mathematics • Cultures and Mathematics; Education • Topics in the history of mathematics 19-23 July 2010 Vienna education. Each theme had a plenary lecture, several These Summer Universities started in workshops, oral presentations and posters, and Montpellier (France) in 1993 and from the some also had panel discussions. Since it was beginning provided an occasion for impossible to attend all the conferences and researchers and teachers, not only to hear workshops, we shall only comment here on about new experiences and ideas and share the ones we found most useful or interesting. 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 Of the plenaries, the most appreciated was Instruments. that by Michael Glaubitz from the Albert This report is from a “teacher’s point of Einstein Gymnasium in Hameln (Germany): view” and summarises the reactions of about The Use of Original Sources in The classroom 30 classroom teachers who attended the - Empirical Research Findings (theme 3). He conference. I would particularly like to thank proposed the hermeneutic approach to the use Alexandra Lux from BRG Purkersdorf of historical material claiming that reading an (Austria) in helping to prepare the report. original source can be an especially rewarding The main themes of this 6th ESU were: enterprise which is capable of substantially • Theoretical and or conceptual frameworks deepening mathematical understanding, for integrating history in mathematics enriching classroom activities and developing education; learners’ beliefs in mathematics. He set out, • History and epistemology implemented in from an empirical point of view, feasible mathematics education: Classroom conceptual designs, necessary preparations experiments & teaching materials, and prospective effects when reading an considered from either the cognitive original source in class using the example of or/and affective point of view; survey of quadratic equations. This was judged as curricula and textbooks; “probably the most important lecture for actual • Original sources in the classroom, and teaching in class”, and suggested further their educational effects; questions to be probed. We were really sorry HPM Newsletter No. 75 November 2010 HPM webpage: http://www.clab.edc.uoc.gr/hpm/ 3 that the same author’s workshop was Livia Giacardi from Università di Torino cancelled. (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