Kristín Bjarnadóttir, Fulvia Furinghetti, Jenneke Krüger, Fulvia Furinghetti, Jenneke Krüger, Kristín Bjarnadóttir, Johan Prytz, Gert Schubring, Harm Jan Smid (Eds.) Kristín Bjarnadóttir, Fulvia Furinghetti, Jenneke Krüger, Johan Prytz, Gert Schubring, Harm Jan Smid (Eds.) The First International Conference on the History of Mathematics Education took place in Iceland in 2009. In the Proceedings, the editors expressed their expectation that the research on history of mathematics education would be sufficiently productive to warrant the continuation of this conference every two years. And indeed, participation has grown, from 35 participants and 18 presentations in 2009, to 65 participants and 40 presentations in 2017, at the Fifth Internatio- nal Conference on the History of Mathematics Education. “DIG WHERE YOU STAND” 5 The venue of the Fifth Conference was the historical University Hall of the University of Utrecht PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE in the Netherlands. The Descartes Centre and the Freudenthal Institute, both part of the Univer- ON THE HISTORY OF MATHEMATICS EDUCATION sity of Utrecht, and the Dutch Association of Mathematics Teachers sponsored the organisation SEPTEMBER 19-22, 2017, AT UTRECHT UNIVERSITY, THE NETHERLANDS and the Proceedings of the conference. The Local Committee, consisting of Heleen van der Ree, Harm Jan Smid, Jan van Guichelaar and Jenneke Krüger, organized the conference in an excel- lent manner. The final editing of the Proceedings was in the capable hands of Nathalie Kuijpers. Previous international conferences on the history of mathematics education: 2009 Garðabær (Iceland) 2011 Lisboa (Portugal) 2013 Uppsala (Sweden) 2015 Torino (Italy) The Sixth International Conference on the History of Mathematics Education will be held in Marseille (France) in September 2019. CONFERENCE THE FIFTH INTERNATIONAL PROCEEDINGS OF “DIG WHERE YOU STAND” 5 YOU STAND” WHERE “DIG ON THE HISTORY OF MATHEMATICS EDUCATION OF MATHEMATICS THE HISTORY ON UTRECHT UNIVERSITY - FREUDENTHAL INSTITUTE 201905 - omslag final.indd All Pages 4-7-2019 13:06:35 “DIG WHERE YOU STAND” 5 bookfile.indb 1 11-Jun-19 12:37:08 bookfile.indb 2 11-Jun-19 12:37:08 “DIG WHERE YOU STAND” 5 Proceedings of the Fifth International Conference on the History of Mathematics Education September 19-22, 2017, at Utrecht University, the Netherlands Editors: Kristín Bjarnadóttir Fulvia Furinghetti Jenneke Krüger Johan Prytz Gert Schubring Harm Jan Smid bookfile.indb 3 11-Jun-19 12:37:09 “Dig where you stand” 5 Proceedings of the Fifth International Conference on the History of Mathematics Education September 19-22, 2017, at Utrecht University, the Netherlands Editors: Kristín Bjarnadóttir University of Iceland, School of Education, Reykjavík, Iceland Fulvia Furinghetti Dipartimento di Matematica, Università di Genova, Italy Jenneke Krüger Freudenthal Institute, Utrecht University, the Netherlands Johan Prytz Uppsala University, Department of Education, Sweden Gert Schubring Universidade Federal do Rio de Janeiro, Instituto de Matemática, Brazil Institut für Didaktik der Mathematik, Universität Bielefeld, Germany Harm Jan Smid Delft University of Technology, the Netherlands Front cover: The illustration is from the lecture notes by Frans van Schooten Sr. (1581-1645), manuscript BPL 1013, University Libraries, University of Leiden, the Netherlands. Back cover: Panoramic photo of the Utrecht city centre Printed by: Drukkerij Baas, Nieuwerkerk aan den IJssel Copyright © 2019 Authors ISBN: 978-908-236-796-6 bookfile.indb 4 11-Jun-19 12:37:09 Table of contents Introduction ..........................................................................................................................9 On French heritage of Cartesian geometry in Elements from Arnauld, Lamy and Lacroix ................................................................................................................................11 Évelyne Barbin Pólya and Dienes: Two men of one mind or one culture? ........................................31 András G. Benedek and Agnes Tuska Problems in the teaching of arithmetic: records in French school notebooks (1870- 1914) .....................................................................................................................................51 Luciane de Fatima Bertini Two textbooks on unconventional arithmetic: Reactions of influential persons ....67 Kristín Bjarnadóttir Attitudes toward intuition in calculus textbooks...........................................................85 Viktor Blåsjö Daily life traits in arithmetic word problems: a glance at 1950s school notebooks .95 Elisabete Zardo Búrigo Mathematical reasoning in trigonometric definitions, proofs, and calculations on early 19th century textbooks from Norway and Denmark ..................................... 113 Andreas Christiansen Mathématique moderne: A pioneering Belgian textbook series shaping the New Math reform of the 1960s ............................................................................................. 131 Dirk De Bock, Michel Roelens and Geert Vanpaemel John Leslie’s (1817) view of arithmetic and its relevance for modern pedagogy . 149 Andrzej Ehrenfeucht and Patricia Baggett Pedagogical value of the Russian abacus and its use in teaching and learning arithmetic in the 19th – early 20th century .................................................................... 163 Viktor Freiman and Alexei Volkov Jacob de Gelder (1765-1848) and his way of teaching cubic equations ................ 179 Henk Hietbrink v bookfile.indb 5 11-Jun-19 12:37:09 The mathematics teachers’ journal Euclides in the Netherlands in change, 1945-1976 ......................................................................................................................... 191 Martinus van Hoorn Dmitry Chizhov and the examination of mathematics textbooks in Russia during the 1820s-1830s ............................................................................................................... 207 Alexander Karp Differential calculus in a journal for Dutch school teachers (1754-1764) ............ 223 Jenneke Krüger Teaching mathematics in Moroccan high schools in the past fifty years ............... 241 Ezzaim Laabid Anton Dakitsch collection – the scope of mathematics teaching in Brazilian industrial education in the 1950s .................................................................................. 259 Regina de Cassia Manso de Almeida Didier Henrion, an enigmatic introducer of Dutch mathematics in Paris ............ 271 Frédéric Métin Arithmetic in Joan Benejam’s La Enseñanza Racional (1888) ................................. 285 Antonio M. Oller-Marcén Geometry for women in teacher training schools in the late 19th century in Spain ...................................................................................................... 303 Luis Puig Building new mathematical discourse among practitioners in restoration and enlightenment England 1650 – 1750 ........................................................................... 321 Leo Rogers Norms and practices of secondary teachers’ formation. The Portuguese case (1915-1930) ...................................................................................................................... 339 Ana Santiagoa and José Manuel Matosb Let them speak; hear them speak ─ old Chinese wisdom on mathematics education ................................................................................................... 357 SIU Man Keung Dutch mathematics teachers, magazines and organizations: 1904-1941 ................ 373 Harm Jan Smid vi bookfile.indb 6 11-Jun-19 12:37:09 Views on usefulness and applications during the sixties ........................................... 389 Bert Zwaneveld and Dirk De Bock Contributors ..................................................................................................................... 403 Index ................................................................................................................................. 411 vii bookfile.indb 7 11-Jun-19 12:37:09 viii bookfile.indb 8 11-Jun-19 12:37:09 9 Introduction The fifth International Conference on the History of Mathematics Education (ICHME-5) took place in the University Hall of the University of Utrecht, the Netherlands, from 19-22 September, 2017. The organisation of the conference and the production of the Proceedings were sponsored by the Descartes Centre and the Freudenthal Institute, both part of Utrecht University, and by the Dutch Association of Mathematics Teachers (NVvW). The local organising group con- sisted of Jan van Guichelaar (NVvW), Jenneke Krüger (NVvW, Freudenthal Institute), Heleen van der Ree (NVvW) and Harm Jan Smid (NVvW). The members of the International Program Committee were Kristín Bjarnadóttir (University of Iceland), Jan Hogendijk (Utrecht University), Jenneke Krüger (Utrecht University), Johan Prytz (Uppsala University), Gert Schubring (Universität Bielefeld, Germany/ Universidade Federal do Rio de Janeiro, Brazil) and Bert Theunissen (Utrecht University). Fulvia Furinghetti (University of Genoa, Italy) served as advisor to the International Program Committee. Nathalie Kuijpers (Freudenthal Institute) took care of the layout of these Proceedings. Altogether 65 participants from 21 countries registered for this conference. In the opening lecture Danny Beckers (Free University, Amsterdam) presented a light- hearted overview of mathematics education in the Netherlands from