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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/319781200 2017 - "Dig where you stand" 4. Proceedings of the Fourth International Conference on the History of Mathematics Education Book · September 2017 CITATIONS READS 0 633 5 authors, including: Kristín Bjarnadóttir Fulvia Furinghetti University of Iceland Università degli Studi di Genova 41 PUBLICATIONS 59 CITATIONS 145 PUBLICATIONS 1,002 CITATIONS SEE PROFILE SEE PROFILE Marta Menghini Johan Prytz Sapienza University of Rome Uppsala University 40 PUBLICATIONS 142 CITATIONS 22 PUBLICATIONS 55 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Curriculum research View project Fundamental reasons View project All content following this page was uploaded by Fulvia Furinghetti on 22 September 2017. The user has requested enhancement of the downloaded file. “DIG WHERE YOU STAND” 4 Proceedings of the Fourth International Conference on the History of Mathematics Education September 23-26, 2015, at University of Turin, Italy Editors: Kristín Bjarnadóttir Fulvia Furinghetti Marta Menghini Johan Prytz Gert Schubring “Dig where you stand” 4 Proceedings of the Fourth International Conference on the History of Mathematics Education September 23-26, 2015, at University of Turin, Italy Editors: Kristín Bjarnadóttir University of Iceland, School of Education, Reykjavík, Iceland Fulvia Furinghetti Dipartimento di Matematica dell’Università di Genova, Italy Marta Menghini Dipartimento di Matematica, Sapienza Università di Roma, Italy 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 In the front cover: A classroom of a primary school (rural area of Northern Italy in the 1940s) In the back cover: View of Turin, venue of the conference These proceedings are published with the contribution of INdAM (Istituto Nazionale di Alta Matematica) Copyright © 2017 Edizioni Nuova Cultura - Roma ISBN: 9788868128647 DOI: 10.4458/8647 È vietata la riproduzione non autorizzata, anche se parziale, realizzata con qual- siasi mezzo, compresa la fotocopia, anche ad uso interno o didattico. Contents Introduction .................................................................................................................. 9 Preface ......................................................................................................................... 11 Ferdinando Arzarello The role of Reye’s Geometrie der Lage in the teaching of “modern geometry” ............................................................................................. 15 Evelyne Barbin The teaching of mathematics, architecture and engineering in the Ancien Régime in Turin .................................................................................... 31 Rita Binaghi Recommendations of the Royaumont Seminar on primary school arithmetic – Influences in the Nordic countries ......................................................................... 47 Kristín Bjarnadóttir John Dewey and mathematics education in Sweden ........................................... 61 Kajsa Bråting, Tove Österman Mathematics in the initial pre-service education of primary school teachers in Portugal (1926-1974) ............................................ 73 Rui Candeias Early geometry textbooks printed in Persian ........................................................ 87 Gregg De Young The mathematical journals for teachers and the shaping of mathematics teachers’ professional identity in post-unity Italy ............................................... 101 Fulvia Furinghetti Teaching and dissemination of mathematics in Beppo Levi’s work. From Italy to Argentina ......................................................................................... 117 Livia Giacardi, Margherita Raspitzu Half a century of Pythagoras, a mathematical magazine for students and teachers ....................................................................................... 133 Jan Guichelaar 6 Contents On the Russian national subcommission of the ICMI ...................................... 149 Alexander Karp Changing direction: The “Second Round” of the School Mathematics Study Group ........................................................................ 167 Jeremy Kilpatrick Mathematische Liefhebberye (1754-1769) and Wiskundig Tijdschrift (1904-1921): both journals for Dutch teachers of mathematics .............................................. 175 Jenneke Krüger Mathematics and race in Turin: the Jewish community and the local context of education (1848-1945) ................................................. 189 Erika Luciano Precision and approximation mathematics for teacher education: The lecture course of Guido Castelnuovo and the influence of Felix Klein ....... 203 Marta Menghini The standardisation of the place of problems in French geometry textbooks during the 19thcentury ...................................... 219 Guillaume Moussard The problem section of El Progreso Matemático .................................................... 235 Antonio M. Oller-Marcén The teaching of mathematics in the Italian artillery schools in the eighteenth century ........................................................................................ 247 Elisa Patergnani On the relationships between the geometric and the algebraic ideas in Duhre’s textbooks of mathematics, as reflected via Book II of Euclid’s Elements ....................................................... 263 Johanna Pejlare Mathematics textbooks for teachers training in Spain in the second half of 19th century: The metric system implementation ........ 275 Miguel Picado, Luis Rico, Bernardo Gómez Teaching of mathematics in educational journals of Turin (1849-1894) ........ 293 Chiara Pizzarelli The production of textbooks in mathematics in Sweden, 1930-1980 ............. 309 Johan Prytz Contents 7 New conceptions of mathematics and research into learning and teaching: Curriculum projects for primary and secondary schools in the UK (1960-1979) ........................................................................................... 325 Leo Rogers Mathematics teaching in the process of decolonization ................................... 349 Gert Schubring Johan Wansink and his role in Dutch mathematics education ........................ 369 Harm Jan Smid Marxism and mathematics. Paul Libois and intuitive geometry in Belgium .. 383 Geert Vanpaemel, Dirk De Bock Olivier string models and the teaching of descriptive geometry ..................... 399 João Pedro Xavier, Eliana Manuel Pinho The function of a preface: Contextual information and didactical foundation described in the preface and introduction of a textbook in arithmetic from 1825 (Abstract) .............................................. 415 Andreas Christiansen A case study on the teaching of mathematics in the Italian Renaissance: Niccolò Tartaglia and his General Trattato (Abstract) ......................................... 417 Veronica Gavagna Contributors ............................................................................................................. 419 Index .......................................................................................................................... 429 Introduction From 23 to 26 September 2015 the fourth International Conference on the His- tory of Mathematics Education (ICHME-4) was held at Academy of Sciences and University of Turin, Italy. The local organizers were Livia Giacardi and Erika Lu- ciano. The Scientific Program Committee was composed by Kristín Bjarnadóttir (University of Iceland), Fulvia Furinghetti (University of Genoa, Italy), Livia Gia- cardi (University of Turin, Italy), Erika Luciano (University of Turin, Italy), Johan Prytz (Uppsala University), Gert Schubring (Universität Bielefeld, Germany/Uni- versidade Federal do Rio de Janeiro, Brazil), with the scientific support of Ferdi- nando Arzarello (University of Turin, Italy), president of ICMI. Altogether there were 51 participants from 16 countries, 44 contributions (re- search reports and posters) were presented. After processing by peer reviews, 28 papers are published in these Proceedings. They may be categorized according to the following thematic dimensions: Ideas, people and movements Kristín Bjarnadóttir; Kajsa Bråting and Tove Österman; Livia Giacardi and Mar- gherita Raspitzu; Erika Luciano; Gert Schubring; Harm Jan Smid. Transmission of ideas Fulvia Furinghetti; Jan Guichelaar; Alexander Karp; Jenneke Krüger; Antonio M. Oller-Marcén, Chiara Pizzarelli. Teacher education Rui Candeias; Marta Menghini. Geometry and textbooks Evelyne Barbin; Gregg De Young; Guillaume Moussard; Johanna Pejlare. Textbooks – changes and origins Andreas Christiansen; Veronica Gavagna; Miguel Picado, Luis Rico, and Bernardo Gómez; Johan Prytz. Curriculum and reforms Jeremy Kilpatrick; Leo Rogers. 10 Introduction Teaching in special institutions Rita Binaghi; Elisa Patergnani. Teaching of geometry Geert Vanpaemel and Dirk De Bock; João Pedro Xavier and Eliana Manuel Pinho. To emphasize the continuity of the project behind the conference held in Turin the volume containing the proceedings keeps the original title of the first confer- ence, i.e. “Dig where you stand ” (followed by 4, which is the number of the confer- ence). This sentence, which is the English
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  • TOWARDS a HISTORY of the GEOMETRIC FOUNDATIONS of MATHEMATICS LATE Xixth CENTURY*

    TOWARDS a HISTORY of the GEOMETRIC FOUNDATIONS of MATHEMATICS LATE Xixth CENTURY*

    ARTICLES TOWARDS A HISTORY OF THE GEOMETRIC FOUNDATIONS OF MATHEMATICS LATE XIXth CENTURY* Rossana TAZZIOLI RÉSUMÉ : Beaucoup de « géomètres » du XIXe siècle – Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, et autres – ont joué un rôle important dans la discussion sur les fondements des mathématiques. Mais, contrairement aux idées d’Euclide, ils n’ont pas identifié « l’espace physique » avec « l’espace de nos sens ». Partant de notre expérience dans l’espace, ils ont cherché à identifier les propriétés les plus importantes de l’espace et les ont posées à la base de la géométrie. C’est sur la connaissance active de l’espace que les axiomes de la géométrie ont été élaborés ; ils ne pouvaient donc pas être a priori comme ils le sont dans la philosophie kantienne. En outre, pendant la dernière décade du siècle, certains mathématiciens italiens – De Paolis, Gino Fano, Pieri, et autres – ont fondé le concept de nombre sur la géométrie, en employant des résultats de la géométrie projective. Ainsi, on fondait l’arithmétique sur la géométrie et non l’inverse, comme David Hilbert a cherché à faire quelques années après, sans succès. MOTS-CLÉS : Riemann, Helmholtz, fondements des mathématiques, géométrie, espace. ABSTRACT : Many XIXth century « geometers » – such as Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, and others – played an important role in the discussion about the founda- tions of mathematics. But in contrast to Euclid’s ideas, they did not simply identify « physical space » with the « space of the senses ».