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Negotiating the Boundaries Between Mathematics and Physics

The Case of Late 1950s French Textbooks for Middle Schools

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Abstract

This paper examines physics and mathematics textbooks published in France at the end of the 1950s and at the beginning of the 1960s for children aged 11–15 years old. It argues that at this “middle school” level, textbooks contributed to shape cultural representations of both disciplines and their mutual boundaries through their contents and their material aspect. Further, this paper argues that far from presenting clearly delimited subjects, late 1950s textbooks offered possible connections between mathematics and physics. It highlights that such connections depended upon the type of schools the textbooks aimed at, at a time when educational organization still differentiated pupils of this age. It thus stresses how the audience and its projected aptitudes and needs, as well as the cultural teaching traditions of the teachers in charge, were inseparable from the diverse conceptions of mathematics and physics and their relationships promoted through textbooks of the time.

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Notes

  1. This reform concerned specifically secondary instruction. It also witnessed numerous debates regarding competing conceptions of physics. The latter resulted in the introduction of practical exercises and practical works (travaux pratiques) in physics teaching in relationship with the adoption of a more experimental pedagogy. The context, debates and stakes of the reform regarding physics are the subject of a volume edited by Hulin (2000).

  2. Until the 1959 reform, in France, the words “primary” and “secondary” did not refer to levels of education but to “orders”: this situation, known as the “educational duality”, established autonomous and parallel courses of study, which were more or less impenetrable (see Sect. 1.1). By calling the different types of schools which accommodated 11–15-year-old children the “middle school level” I follow Renaud D’Enfert’s introduction of a useful category for analysis.

  3. Such an interest is even stronger considering the relatively under-developed historiography on the second third of the twentieth century, when compared with the beginning of the Twentieth Century and 1970s reforms. In this paper, I follow a quite recent trend of scholarship which focuses on the period from the interwar years to the 1960s (see especially works by R. D’Enfert, P. Kahn and H. Gispert quoted above).

  4. Bibliographie de la France, supplément « rentrée des classes » , Cercle de la Librairie (1958–1961).

  5. The hyphen is not used systematically.

  6. “Observational science” refer to the syllabus for cours complémentaires, while “natural science” refers to collèges and lycées (see below for the differences regarding those types of schools), but the contents were roughly similar to each other. The official instructions are presented in the following texts: Arrêté du 25 septembre 1957, Bulletin Officiel de l’Education Nationale [BOEN] n° 35, 3 octobre 1957, pp. 2939-2941; Circulaire du 20 octobre 1957, BOEN n° 42, 21 novembre 1957, p. 3429; Arrêté du 10 octobre 1958, BOEN n° 38, 23 octobre 1958, pp. 3061–65.

  7. See above footnote 3.

  8. A third—technical—order also accommodated some children in technical schools. It concerned a minority of students.

  9. The lycées were created in 1802 in order to form the future national elite: they were located in big cities and were maintained by the State. Some of these schools resulted of the transformation of older establishments, called collèges, which existed in the Old Regime. Not all collèges were transformed into lycées and cities could, at the beginning of the nineteenth Century, chose to maintain these establishments. Some delivered the same kind of instruction as lycées, others delivered shorter training, but all depended on the secondary order of instruction. The lycées remained the most prestigious establishments. At the end of the 1950 s, both structures still existed (even though their number, the way they were maintained, and the teaching they offered had changed), and the difference of reputation remained. For the history of lycées, see Caspard et al. (2005).

  10. See above Fig. 1.

  11. Modern streams also included the study of foreign living languages, and did not require the study of Latin.

  12. Created in 1802, the Inspection générale had had until 1968 clear missions: its members inspected classrooms, presided over juries of teachers’ recruitment and had a real pedagogical authority. Over time, the corporation had grown up and had become more and more organized according to school subjects. Since 1968, its missions have profoundly changed (Rioux 2002).

  13. At the time, the names “primaire” and “secondaire” were officially replaced by “premier degré” and “second degré”.

  14. Such a change most of the time took place for the books issued in 1961 which results in series including textbooks for the first years of cours complémentaires (issued up to 1960 and including one, two or three books according to the rhythm of publication) and then textbooks for the last years of collèges d’enseignement général. Only the publisher Belin reissued (only in 1963) a textbook for the sixième form following “the united syllabus of 1960”.

  15. It is important to note that even so these pupils might have received the same books in mathematics as pupils accommodated in long streams.

  16. In order to lighten the phrasing, I use from now on “physics textbooks” instead of “physics-chemistry textbooks”: late 1950 s textbooks usually included separated sections devoted to physics and chemistry. The series published by Masson under the name of Maxime Joyal featured separated books for physics and for chemistry and was, as such, an exception, but it strengthened the disciplinary division (Delattre and Boué 1961a, b, c, d).

  17. Following the official syllabi, textbooks for Classes de fin d’études were slightly different: distinct textbooks existed for mathematics on the one hand, and for “applied sciences” on the other hand (which included notions in natural sciences). However, they maintained a sharp boundary between mathematics and other sciences. In another period, one textbook series which included mathematics textbooks within other science textbooks had been published: entitled the “Collection scientifique”, it had been edited by Albert Châtelet and published by Baillière in the 1930 s.

  18. These figures are given for information purpose only. They should not be considered as irrevocable ones: they depend on my choices to focus on children accommodated in cours complémentaires and short streams of collèges and lycées in the late 1950s, on the sources used to identify the textbooks series (the supplement “Rentrée des classes” of the Bibliographie de la France published by the Cercle de la Librairie for the years 1958–1961) and on the categories used by the publishers’ catalogues to organize the textbooks production according to their audience.

  19. See above, footnote 16.

  20. André Godier’s carrier path is actually remarkable as it calls into question the apparently strict separation between primary and secondary orders of instruction in the interwar years. Indeed, Godier started his teacher training as many other primary schools teachers in an école normale (Saint-Lô from 1917 to 1920). He then pursued his training during an additional fourth year, and after his national service, he taught in a primary school and passed the examination in mathematics that allowed him to teach in écoles normales. Afterwards, he was appointed to the école normale de Saint-Lô. In parallel to his teaching, he studied at the university and succeeded in a bachelor’s degree in science, with a specialization in physics in 1933, which he completed with a “diplôme d’études supérieures” in physical sciences in 1934. He thus entered university after a primary order training and received training both in mathematics and in physics. These details come from his carrier records, archived under F1728308 in the French national archives.

  21. This was, for instance, the case of André Godier wrote science and mathematics textbooks for elementary forms (Godier et al. 1958, a, b), and only wrote physics textbooks for later forms (Godier et al. 1960, 1961a, b, c).

  22. See Fig. 2.

  23. For another example, see Fig. 3.

  24. The “collection Paul Dubreil” published by Vuibert included four books, aimed at lycées and collèges d’enseignement général. Its editor was the mathematician Paul Dubreil who was then professor at the Faculty of Sciences in Paris. He had been appointed to the chair of arithmetic and number theory in 1954. All the textbooks of the series had their own authors. The analysis of the books contents does not suffice to know the part Paul Dubreil took in their edition. In each textbook, Paul Dubreil signed the foreword in which he highlighted the approach chosen by the authors to introduce their subject.

  25. The Cours J. Marvillet published by the Librairie Armand Colin included five books. The first two books, for the sixième and cinquième forms of all types of schools, were entitled “initiation aux mathématiques” (first editions respectively issued in 1958 and 1959). The next three books (one for the quatrième form of all types of schools, one for the troisième form of cours complémentaires and another one for the troisième form of lycées and collèges) were entitled “mathématiques” (first editions respectively issued in 1960 and 1961 for both troisième books).

  26. See Fig. 4 for an example.

  27. See also Fig. 5.

  28. See Fig. 6.

  29. The presence of astronomy within mathematics can be seen as legacy of a nineteenth century consensus between mathematicians and physicists (Atten 1996).

  30. Roland Maillard was a former student of the École Normale Supérieure (Ulm) which trained elite teachers of the secondary order of instruction. In the late 1950s, he had joined the Inspection générale after a successful carrier as mathematics teacher in lycées. He had authored many textbooks for the publishing house Hachette before obtaining a textbooks series named after him. For this series, he remained an author and was helped by two mathematics teachers in Parisian lycées, Raymond Cahen and Eugène Caralp.

  31. I comment on the pedagogy of “practical works” in Sect. 2.2.

  32. In France, geography has traditionally been linked with history at school. However it was also considered as a subject connected to sciences, especially physics and geology; see (Hulin 2007, pp. 49–62).

  33. The name itself suggested an origin within physics, see above footnote 2.

  34. Bourbaki is the name given to a group that young French mathematicians created in the 1930 s with the aim of reorganizing mathematics according to the central notion of structure. Bourbaki would have an important influence on the development of mathematics and (though rather indirectly) mathematics teaching after World War II.

  35. The Cours J. Marvillet was named after its editor and author Joseph Marvillet, agrégé of Mathematics and teacher in the lycée of Strasbourg. Other authors contributed to this series, among which some were also agrégés of mathematics (Lucette Chopard-Lallier or Robert Girard), but some were not: Pierre-Marie Fournier was head of a cours complémentaire and Alphonse Adam was inspector of primary instruction. The latter thus belonged to the primary order of instruction (and so was, to a certain extent, Robert Girard as he had been trained as a primary school teacher before passing the Agrégation and joining the secondary order of instruction).

  36. Among the titles mentioned in this paper, the Monge & Guincham and Lebossé & Hémery series included distinct textbooks for cours complémentaires on the one hand and for collèges and lycées on the other hand from the quatrième form onwards. By contrast, the Cours R. Maillard and the Collection Paul Dubreil were addressed to all children. The Cours J. Marvillet stood in between as it fragmented the audiences in the troisième form only.

  37. The idea was also explicitly stated in chapters dealing with measurements and measuring devices.

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Acknowledgments

I wish to thank Laure Pellet and Laura Dang for the information they gave me regarding primary instruction pupils and their teachers, Ricardo Karam for his comments on an earlier version of this paper, and the anonymous referees whose remarks and suggestions helped to improve it. I am also grateful to Michael Matthews for his patience in waiting for this paper. I also wish to thank the publishing houses which kindly permitted the reproduction of the images illustrating the paper.

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    Catherine Radtka

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Radtka, C. Negotiating the Boundaries Between Mathematics and Physics. Sci & Educ 24, 725–748 (2015). https://doi.org/10.1007/s11191-015-9760-z

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