Turin – 23-26 septembre 2015
Studying teaching journals and journals for teachers: a fruitful perspective for the history of circulation of mathematics
Hélène Gispert (GHDSO – University of Paris Sud)
Since 2014 an international group of historians of mathematics works on the circulation of mathematics in and by journals, over a long time period (18th – 20th centuries) and in various geographical and cultural areas, with a focus on the questions of territories and publics. In this talk, studying some specific journals, I will consider the way we have chosen to build our corpus of periodicals, questioning the very notion of circulation among and inside different milieus, choosing to analyse the processes of acculturation and appropriation of mathematics by various audiences, considering, beyond the professional and academic mathematical sphere, those which read, produce and use mathematics. From this point of view training and teaching are crucial forms of circulation of mathematics, teachers who teach mathematics – whatever the level, whatever the institutional context one of the major segments of the audience (authors as readers) we have to consider. This very teachers sphere, even if heterogeneous, has strong heuristic virtues which I will develop in this talk, as for the choices of the journals to be considered, the questions to be posed, the way of questioning circulation and the territories.
Number theory in teaching mathematical journals : the case of Nouvelles annales de mathématiques (1842-1927)
Jenny Boucard (Centre Viete – University of Nantes)
Teaching of mathematics in school periodicals: the case of the Piedmont (1849-1894)
Chiara Pizzarelli (University of Turin)
In the first half of the 19th century in the Sardinia Kingdom the teaching of mathematics was restricted to elementary Arithmetic and generally Geometry wasn’t taught to students less than 15 years old. Furthermore the 3/5 of the population hadn’t a primary education and few towns of the Kingdom had schools for teachers training.
After the Boncompagni law (1848) there was an improvement of the technical-scientific education, thanks to wider and more detailed programs in the boarding schools and to the establishment of the R. Istituto tecnico (1852-1859), then R. Politecnico (1906).
Two periodicals, the monthly Giornale della Società d’Istruzione e di Educazione (Turin, 1849-1852) and the weekly L’Istitutore (Turin, 1853-1894), which yearly collected their issues in a volume of about 800 pages, played an important role in raising the debates on the school. They were born under the initiative of the first Piedmontese association of teachers, which in 1855 had as members the 2/7 of all teachers in Sardinia Kingdom. Educators, mathematicians, chemists, physicists, ministers and politicians participated to the society’s conventions and published articles in these periodicals. In 1873, L’Istitutore and six other journals, such as La guida del maestro elementare italiano (1864-1897) and L’osservatore scolastico (1865-1899), reached the first place per number of copies (37,3%) among educational magazines published in Italy (Chiosso 1997).
Until 1879 none of the Italian educational periodicals was dedicated exclusively to the mathematics. However, by analyzing the articles published in the above mentioned journals by directors, educators, teachers and authors of mathematics textbooks it emerges that the problems of the teaching of mathematics were faced in different forms. There were articles about the programs and the methods, the foreign school systems, textbooks reviews and translations of some French books. There were also exercises with solutions and the exam themes given in local schools. Riddles and problems were addressed to the readers, and sometimes their solutions were published. Among the main subjects there was the teaching of Arithmetic (in particular fractions and the rule of the three), the decimal metric system, the first elements of plane and solid Geometry. The use of intuitive methods was prevalent. Algebraic exercises and some popularizing pieces on the history of mathematics were given for teachers.
My aim is to analyze the role of these educational journals in renewing mathematics programs and their implementation in schools, and in promoting new textbooks dedicated to the teaching of Arithmetic and Geometry from 1848 to 1859, i.e. the period between the two most important Italian educational reforms. Finally I’ll intend to examine if and how these periodicals improved their mathematical contents, in particular after the 1880s, when specialized journals in the teaching of mathematics get started to blossom.
Il Giornale della Società d’Istruzione e di Educazione (1849-1852),Torino, Paravia, vols. 1-4
L’Istitutore (1853-1894), Torino, Paravia, vols. 1-42.
Chiosso G. (ed.), La stampa pedagogica e scolastica in Italia (1820-1943), Brescia, La Scuola, 1997; TESEO. Tipografi e editori scolastico-educativi dell’Ottocento, Milano, Editrice Scolastica, 2003.
Chiosso G., Sani R. (eds.), Dizionario Biografico dell’Educazione 1800-2000, 2 v., Milano, Editrice Bibliografica, 2013. De Fort E., L’istruzione primaria e secondaria e le scuole tecnico-professionali, in U. Levra (ed.), Storia di Torino. La città nel Risorgimento, 1798-1864, VI, Torino, Einaudi, 2000, pp. 596-618.
Giacardi L. (ed.), Da Casati a Gentile: momenti di storia dell’insegnamento secondario della matematica in Italia, La Spezia, Agorà, 2006.
Lacaita C.G., Fugazza M., L’istruzione secondaria nell’Italia unita 1861-1901, Milano, Angeli, 2013.
The rise of „Stoffdidaktik“ in Germany 1950 – 1980 and the role played in it by the journal „Mathematisch-physikalische Semesterberichte“
Klaus Volkert (Bergische Universität Wuppertal)
After world war II, there was a rise of didactics in Western Germany. This development is mirrored (and was triggered) by the journal Mathematisch-physikalische Semesterberichte which published many important articles on the subject of “Stoffdidaktik” (this means the analysis of the subjects thought at school – like fractions or the rule of three – from a mathematical and didactical point of view). This journal was founded by H. Behnke and O. Tœplitz at the beginning of the 1930s in order to strengthen the ties between the universities and the highschools (Gymnasien). After the war the journal became one of the most influential for a for a specific type of didactical research – the just cited “Stoffdidaktik”. In my contribution, I want to analyze this development in particular in relation to the ideas behind this “didactical turn”.
Tietz H. 1973, Reformen im Spiegel der Semesterberichte – ein programmatischer Rückblick, Mathematisch-physikalische Semesterberichte, 20, 141-150.
Periodicals for mathematics teachers: the Netherlands, 1754-1904
Jenneke Krüger (University of Utrecht)
Towards the end of the 16th century many teachers of mathematics migrated to the Northern Netherlands, especially to the growing towns in Holland (Van Maanen & Vanpaemel, 2006). They taught a variety of mathematical subjects. The local schools for primary education taught reading, writing and occasionally arithmetic. During a large part of the 18th century the situation was similar: usually in towns and villages there was at least one school for primary education. By the mid-18th century learning arithmetic had become more common and schoolteachers were expected to know mathematics. There still were many private schools and teachers. In 1863 legislation on secondary education was introduced (Krüger, 2014). After 1815 mathematics gradually became a more important subject in Latin schools (Smid, 1997) and from 1863 it was an important subject in secondary schools, especially the HBS.
The rather strong interest in mathematics and the greater knowledge of teachers in the 18th century resulted in the publication of a periodical, Mathematische Liefhebberye (Mathematical Pastimes), between 1754 and 1769. Though the title suggests a periodical for mathematical recreation, the full title was: Mathematical Pastimes, with news of the French and Dutch Schools. ‘Dutch schools’ was the name of the basic primary schools, in French schools more subjects were taught. The content of these periodicals makes it clear that they were intended as a periodical for professionals: teachers who taught mathematics. One may conclude that in the Netherlands already in the 18th century there was a tendency to consider mathematics as an autonomous school discipline (Chervel, 1988; Matos, 2015).
After the disappearance of Mathematische Liefhebberye, there were no periodicals for mathematics teachers, until 1904, when the first national periodical for mathematics teachers in secondary education was published, Wiskundig Tijdschrift (Mathematical Magazine). In the foreword one of the editors stated that a major aim was communication between mathematics teachers, about mathematics and the teaching of mathematics. Not only mathematics teachers subscribed to this periodical, as is evident from the list of subscribers in 1904 and 1905.
The content of these two periodicals from different periods provide some insight in the topics which the editors considered important for mathematics teachers. .
Chervel, A. (1988). L’histoire des disciplines scolaires. Réflexions sur un domaine de recherche. Histoire de l’éducation, 38, 59-119.
Krüger, J. (2014). Actoren en factoren achter het wiskundecurriculum sinds 1600. PhD thesis, University of Utrecht.
Maanen, J.A. van & Vanpaemel, G. (2006). Migratiepatronen van wiskundigen in de Lage Landen. Scientiarum Historia, 32, 75- 98.
Mathematische Liefhebberye, vol 1 – vol. 17 (1754 – 1769). Purmerend: P. Jordaan.
Matos, J. (2015). The autonomy of secondary school mathematics culture (abstract). In K. Bjarnadóttir, F. Furinghetti, J. Prytz & G. Schubring (Eds.), Dig where you stand, vol.3. Proceedings of 3ICHME (pp. 406 – 407). University of Uppsala.
Smid, H. J. (1997). Een onbekookte nieuwigheid? Invoering, omvang, inhoud en betekenis van het wiskundeonderwijs op de Franse en Latijnse scholen 1815 – 1863. PhD thesis, University of Delft.
Wiskundig Tijdschrift, vol. 1 – 2 (1904 – 1906). Culemborg : Blom & Olivierse.
The problem section of El Progreso Matemático
Antonio M. Oller (Centro Universitario de la Defensa de Zaragoza)
During the XIX century “the number of journals dedicated to mathematics grew impressively” (Furinghetti, 2014, p. 545). They responded to the need to communicate and disseminate research results and new mathematical ideas.
Nevertheless, in some peripheral countries, where mathematical research was not a very important activity, periodicals were important in order to introduce new ideas and to improve the mathematical education of the society. In (Alpaslan, Schubring & Günergun, 2015) the case of the first periodical on Mathematical Sciences in the Ottoman Turkey (published from 1867 to 1869) was discussed.
In Spain, during the XIX century “the only mathematical activity was focused on the teaching, in particular of and engineers […] there is no noteworthy research” (Peralta, 2009, p. 219). In this context, Zoel García de Galdeano (Hormigón, 1991) started to publish in 1891 El Progreso Matemático. It was the first periodical entirely devoted to Mathematics to be published in Spain. The editor stated in the first number “it is surprising that in Spain, where so many periodicals devoted to the most diverse purposes are published, there is none whose main goal is the dissemination and development of Mathematical Sciences”.
The contents of this journal were quite diverse (Hormigón, 1981), ranging from bibliographical reviews to short research notes or articles on philosophy, pedagogy and history of Mathematics. Starting from number 8 (august 1891) a problem section was included in the journal. This new section, including problems proposed by readers and their solutions, appeared until the journal was closed in 1900.
351 problems were proposed and 252 were solved. They involved quite different topics: differential equations (Oller, 2012), the Fibonacci sequence (Oller & Meavilla, 2014), etc. Geometry being the most popular topic.
In this work, we analyze the contents of this problem section. We will focus, among others, on the following:
– Classify the problems according to their topic.
– Determine the proposers and solvers of the problems: their nationality, background, education, etc.
As a case study, we present and analyze the problems related to Fibonacci sequence, putting them in context with the mathematical work of their proposer.
Alpaslan, M., Schubring G & Günergun, F. (2015). ‘Mebahis-i ilmiye’ as the first periodical on Mathematcal Sciences in the Ottoman Turkey. In Krainer, K. & N. Vondrová (Eds.), Proceedings of CERME9. To appear.
Furinghetti, F. (2014). History of international cooperation in Mathematics Education. In Karp, A. & Schubring, G. (Eds.), Handbook on the history of Mathematics Education (pp. 543-564). New York: Springer.
Hormigón, M. (1981). El Progreso Matemático (1891-1900). Un estudio sobre la primera revista matemática española. Llull, 4, 87-115.
Hormigón, M. (1991). García de Galdeano’s Works on Algebra. Historia Mathematica, 18, 1-15.
Oller Marcén, Antonio M. & Meavilla, Vicente. (2014). La sucesión de Fibonacci en la sección de problemas de “El Progreso Matemático”. Revista Eletrônica de Educação Matemática, 9(1), 179-190.
Oller Marcén, Antonio M. (2012). Ecuaciones diferenciales en la sección de problemas de El Progreso Matemático. Boletín Electrónico de la Sociedad Española de Matemática Aplicada, 3, 9-14.
Peralta, J. (2009). La Matemática española del siglo XIX. In La Ciencia antes de la Gran Guerra (pp. 211-236). Canarias: Gobierno de Canarias.
The teaching of mathematics in the periodical press in Rio de Janeiro in the nineteenth century
Flavia Soares (Universidade Federal Fluminense)