Skip to main content
SpringerLink
Log in

Mathématique Moderne: A Pioneering Belgian Textbook Series Shaping the Modern Mathematics Reform of the 1960s

  • Chapter
  • First Online:
Rods, Sets and Arrows

Part of the book series: History of Mathematics Education ((HME))

Abstract

In 1963 the Belgian mathematician and mathematics educator Georges Papy published the first volume of his groundbreaking textbook series entitled Mathématique Moderne (in collaboration with Frédérique Papy-Lenger), intended for students from 12 to 18 and based on several years of classroom experimentation. It marked a revolution in the teaching of mathematics and in the art of textbook design. Papy reshaped the content of secondary school mathematics by basing it upon the unifying themes of sets, relations, and algebraic structures. Meanwhile, he proposed an innovative pedagogy using multi-coloured arrow graphs, playful drawings, and “visual proofs” by means of drawings of film strips. During the 1960s and early 1970s, translations of the volumes of Mathématique Moderne appeared in European and non-European languages and were reviewed in mathematics education journals of that time. Papy’s “MMs” influenced the national and international debates and became major guides for shaping the modern mathematics reform in several countries.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    However, there are areas of difference. For example, whereas Choquet deliberately assumed the distance on a line and the structure of the real numbers, Papy gradually developed these concepts.

References

  • Artin, E. (1957). Geometric algebra. New York, NY: Interscience Publishers.

    Google Scholar 

  • Baligand, V., Hamoir, C., & Noël, G. (1969). Étude des manuels de mathématique pour la première année de l’enseignement secondaire [Study of mathematics textbooks for the first year of secondary education]. Mathematica & Paedagogia, 37, 23–32.

    Google Scholar 

  • Behnke, H. (1970). La crise de l’enseignement mathématique [The crisis in mathematics education]. In Le passage du secondaire à l’université et les études mathématiques. Conférences et exposés du 2e séminaire organisée par la CIEM à Echternach (G.-D. de Luxembourg), mai 1969 [The transition from secondary school to university and mathematical studies. Conferences and lectures of the 2nd seminar organized by ICMI in Echternach (Grand Duchy of Luxembourg), May 1969] (pp. 7–24). Luxembourg, Luxembourg: CIEM /Service Central des Imprimés de l’État (en collaboration avec l’Institut Grand-Ducal Section des Sciences Naturelles, Physiques et Mathématiques).

    Google Scholar 

  • Bourbaki, N. (1939). Éléments de mathématique: Théorie des ensembles [Elements of mathematics: Set theory]. Paris, France: Hermann.

    Google Scholar 

  • Campedelli, L., & Giannarelli, R. (1972). Presentazione [Preface]. In G. Papy, La geometria piana nella matematica moderna [Plane geometry in modern mathematics] (pp. v–vii). Firenze, Italy: Le Monnier.

    Google Scholar 

  • CBPM. (1964a). Arlon 6. Brussels, Belgium: Author.

    Google Scholar 

  • CBPM. (1964b). Programme expérimental de mathématique pour les classes de 6e, 5e, 4e (12 à 15 ans) proposé par le Centre Belge de Pédagogie de la Mathématique en avril 1964 [Experimental curriculum for mathematics in the first, second and third year of secondary schools (12–15-year olds) proposed by the Belgian Centre for Mathematics Pedagogy in April 1964. In Arlon 6 (pp. 4–14). Brussels, Belgium: Author (also published in Mathematica & Paedagogia, 30, 1966, pp. 9–17).

    Google Scholar 

  • Choquet, G. (1961). Recherche d’une axiomatique commode pour le premier enseignement de la géométrie élémentaire (Les brochures de l’A.P.M.) [Search for a convenient axiomatic for the first teaching of elementary geometry (The brochures of A.P.M.)]. Paris, France: Association des Professeurs de Mathématiques de l’Enseignement Public.

    Google Scholar 

  • Choquet, G. (1964). L’enseignement de la géométrie [The teaching of geometry]. Paris, France: Hermann.

    Google Scholar 

  • Debbaut, P. (1966). Une approche géométrique des nombres réels [A geometric approach to real numbers]. In Les répercussions de la recherche mathématique sur l’enseignement. Textes originaux des conférences faites au séminaire organisée par la CIEM à Echternach (G.-D. de Luxembourg), été 1965 [The implications of mathematical research on teaching. Original texts of the conferences given at the seminar organized by ICMI in Echternach (Grand Duchy of Luxembourg), Summer 1965] (pp. 205–209). Luxembourg, Luxembourg: CIEM (en collaboration avec l’Institut Grand-Ducal Section des Sciences Naturelles, Physiques et Mathématiques).

    Google Scholar 

  • Debefve, S. (1972, May 9). Le vaisseau de la réforme de la mathématique s’est embourbé [The ship of the reform of mathematics is stranded]. Le Soir, p. 7.

    Google Scholar 

  • De Bock, D., Janssens, D., & Verschaffel, L. (2004). Wiskundeonderwijs in Vlaanderen: van modern naar realistisch? [Mathematics education in Flanders: from modern to realistic?]. In M. D’hoker & M. Depaepe (Eds.), Op eigen vleugels: Liber amicorum prof. dr. An Hermans [On its own wings: liber amicorum prof. dr. An Hermans] (pp. 157–169). Antwerp, Belgium-Apeldoorn, The Netherlands: Garant.

    Google Scholar 

  • De Bock, D., & Vanpaemel, G. (2015). Modern mathematics at the 1959 OEEC Seminar at Royaumont. In K. Bjarnadóttir, F. Furinghetti, J. Prytz, & G. Schubring (Eds.), “Dig where you stand” 3. Proceedings of the Third International Conference on the History of Mathematics Education (pp. 151–168). Uppsala, Sweden: Uppsala University, Department of Education.

    Google Scholar 

  • De Bock, D., & Zwaneveld, B. (2019). From Royaumont to Lyon: Applications and modelling during the sixties. In G. A. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense making. Cham, Switzerland: Springer.

    Google Scholar 

  • Dieudonné, J. (1964). Algèbre linéaire et géométrie élémentaire [Linear algebra and elementary geometry]. Paris, France: Hermann.

    Google Scholar 

  • Fehr, H. F. (1968). Introduction. In G. Papy, Modern mathematics 1 (pp. v–viii). London, United Kingdom: Collier/New York, NY: Macmillan.

    Google Scholar 

  • Félix, L. (1986). Aperçu historique (1950–1984) sur la Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques (CIEAEM). 2ième édition revue et augmentée [Historical overview (1950–1984) on the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM). 2nd revised and expanded edition]. Bordeaux, France: l’IREM de Bordeaux. Retrieved December 31, 2017, from http://math.unipa.it/~grim/cieaem_files/CIEAEM_histoire_FLucienne_ 1985.pdf.

  • Fielker, D. (1961). Developments in the teaching of mathematics. Report of the Easter Conference, London, 1961. Mathematics Teaching, 16, 32–52.

    Google Scholar 

  • Freudenthal, H. (1991). Revisiting mathematics education. China Lectures. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Furinghetti, F., Menghini, M., Arzarello, F., & Giacardi, L. (2008). ICMI Renaissance: The emergence of new issues in mathematics education. In M. Menghini, F. Furinghetti, L. Giacardi, & F. Arzarello (Eds.), The first century of the International Commission on Mathematical Instruction (1908–2008). Reflecting and shaping the world of mathematics education (pp. 131–147). Rome, Italy: Istituto della Enciclopedia Italiana.

    Google Scholar 

  • Holvoet, R. (1992). Professor Georges Papy, his life and work, up to now. Bulletin de la Société Mathématique de Belgique (Série A), 44(2), 113–120.

    Google Scholar 

  • Howson, G. (2013). The development of mathematics textbooks: Historical reflections from a personal perspective. ZDM Mathematics Education, 45, 647–658.

    Article  Google Scholar 

  • Kilpatrick, J. (2012). The new math as an international phenomenon. ZDM Mathematics Education, 44, 563–571.

    Article  Google Scholar 

  • Krooshof, G. (1967). Moderniseren—Nieuwbouw of verbouw? [Modernising – New construction or renovation?]. Euclides, 42(7), 193–203.

    Google Scholar 

  • Matthys, J.-C. (2011). Hommage à Georges Papy [Tribute to Georges Papy]. Losanges, 15, 3–6.

    Google Scholar 

  • Ministerie van Nationale Opvoeding. (1969). Leerplan wiskunde voor het tweede jaar van het rijksmiddelbaar onderwijs van de lagere graad [Mathematics program for the second year of the secondary schools of the state of the lower grade]. Brussels, Belgium: Author (published in Mathematica & Paedagogia, 39, 1969, pp. 39–45).

    Google Scholar 

  • Nationaal Verbond van het Katholiek Middelbaar Onderwijs. (1969). Leerplan wiskunde voor de vijfde van de humaniora [Mathematics program for the second year of general secondary education]. Brussels, Belgium: Author (published in Mathematica & Paedagogia, 39, 1969, pp. 31–38).

    Google Scholar 

  • Niss, M. (2008). Perspectives on the balance between applications and modelling and ‘pure’ mathematics in the teaching and learning of mathematics. In M. Menghini, F. Furinghetti, L. Giacardi, & F. Arzarello (Eds.), The first century of the International Commission on Mathematical Instruction (1908–2008). Reflecting and shaping the world of mathematics education (pp. 69–84). Rome, Italy: Istituto della Enciclopedia Italiana.

    Google Scholar 

  • Noël, G. (1971). Étude des manuels de mathématique pour la première année de l’enseignement secondaire II [Study of mathematics textbooks for the first year of secondary education II]. Mathematica & Paedagogia, 47, 67–80.

    Google Scholar 

  • OECD. (1964). Mathematics to-day – A guide for teachers. Paris, France: Author.

    Google Scholar 

  • OEEC. (1961a). New thinking in school mathematics. Paris, France: Author.

    Google Scholar 

  • OEEC. (1961b). Synopses for modern secondary school mathematics. Paris, France: Author.

    Google Scholar 

  • Papy, F. (1969). Minicomputer. Educational Studies in Mathematics, 2(2–3), 333–345.

    Article  Google Scholar 

  • Papy, G. (1960). Premiers éléments de mathématique moderne [First elements of modern mathematics]. Brussels, Belgium: Author.

    Google Scholar 

  • Papy, G. (1961). Suggestions pour un nouveau programme de mathématique dans la classe de sixième [Suggestions for a new mathematics program in the sixth class]. Mathematica & Paedagogia, 20, 20–29.

    Google Scholar 

  • Papy, G. (1962a). Géométrie affine plane et nombres réels [Affine plane geometry and real numbers]. Brussels, Belgium: Presses Universitaires de Bruxelles.

    Google Scholar 

  • Papy, G. (1962b). L’enseignement de la mathématique dans le tronc commun [The teaching of mathematics in the common core]. Mathematica & Paedagogia, 23, 47–60.

    Google Scholar 

  • Papy, G. (1962–1963). Die ersten Elemente der modernen Mathematik (Schriftenreihe zur Mathematik, Hefte 10-11) [First elements of modern mathematics (Series on mathematics, booklets 10-11)]. Frankfurt-Hamburg, Germany: Otto Salle Verlag.

    Google Scholar 

  • Papy, G. (1963). Mathématique moderne 1 [Modern mathematics 1]. Brussels, Belgium-Paris, France: Didier.

    Google Scholar 

  • Papy, G. (1964). Methods and techniques of explaining new mathematical concepts in the lower forms of secondary schools. In H. F. Fehr (Ed.), Mathematics to-day – A guide for teachers (pp. 99–147). Paris, France: OECD.

    Google Scholar 

  • Papy, G. (1965). Mathématique moderne 2. Nombres réels et vectoriel plan [Modern mathematics 2. Real numbers and the vector plane]. Brussels, Belgium-Montréal, Canada-Paris, France: Didier.

    Google Scholar 

  • Papy, G. (1966a). Arlon 8. Premières leçons d’analyse mathématique par Frédérique [Arlon 8. First lessons in mathematical analysis by Frédérique]. Brussels, Belgium: CBPM.

    Google Scholar 

  • Papy, G. (1966b). Mathématique moderne 5. Arithmétique [Modern mathematics 5. Arithmetic]. Brussels, Belgium-Montréal, Canada-Paris, France: Didier.

    Google Scholar 

  • Papy, G. (1967a). Arlon 9. Nouvelles leçons d’analyse mathématique par Frédérique [Arlon 9. New lessons in mathematical analysis by Frédérique]. Brussels, Belgium: CBPM.

    Google Scholar 

  • Papy, G. (1967b). Mathématique moderne 3. Voici Euclide [Modern mathematics 3. Euclid now]. Brussels, Belgium-Montréal, Canada-Paris, France: Didier.

    Google Scholar 

  • Papy, G. (1967c). Mathématique moderne 6. Géométrie plane [Modern mathematics 6. Plane geometry]. Brussels, Belgium-Montréal, Canada-Paris, France: Didier/Brussels, Belgium: Labor.

    Google Scholar 

  • Papy, G. (1968a). Influence de la recherche mathématique dans l’enseignement scolaire [Influence of mathematical research on school education]. In G. Papy (in collaboration with P. R. Burgraeve, R. Holvoet, F. Papy, & A. Terfve) (Ed.), Arlon 10 (pp. 1–12). Brussels, Belgium: CBPM (also published in Progrès, 15, 1968, pp. 43–49).

    Google Scholar 

  • Papy, G. (1968b). Le premier enseignement de l’analyse [The first teaching of analysis]. Brussels, Belgium: Presses Universitaires de Bruxelles.

    Google Scholar 

  • Papy, G. (1970). Minimath 1. Brussels, Belgium-Montréal, Canada-Paris, France: Didier.

    Google Scholar 

  • Papy, G. (1974). Minimath 2. Brussels, Belgium-Montréal, Canada-Paris, France: Didier.

    Google Scholar 

  • Papy, G. (1976). Het onderwijs in de wiskunde [Mathematics education]. Nico, 21, 3–46.

    Google Scholar 

  • Papy, G. (n.d.). Mathématique moderne 4 [Modern mathematics 4]. Retrieved November 10, 2017, from http://www.rkennes.be/Articles%20de%20Papy/MM4/MM4-presentation. htm.

  • Revuz, A. (1965). Pour l’enseignement de la géométrie, la route est tracée [For the teaching of geometry, the road is drawn]. Mathematica & Paedagogia, 28, 74–77.

    Google Scholar 

  • Servais, W. (1975). Continental traditions and reforms. International Journal of Mathematical Education in Science and Technology, 6(1), 37–58.

    Article  Google Scholar 

  • Solvang, R. (1972). [Review of Vols. 1 and 2 of Moderne matematik [Modern mathematics], by G. Papy]. Nordisk Matematisk Tidskrift, 20(4), 145–147.

    Google Scholar 

  • Tammadge, A. R. (1969). [Review of Modern Mathematics Volume 1 by G. Papy]. The Mathematical Gazette, 53(386), 425–426.

    Article  Google Scholar 

  • Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics education. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute Cd-rom for ICME9. Utrecht, The Netherlands: Utrecht University. Retrieved November 10, 2017, from http://www.staff.science.uu.nl/~ heuve108/download-rme/vdHeuvel-2000_rme-guided-tour.pdf.

  • Van der Plassche, R. (1964). Désormais, avec le prof révolutionnaire, les maths s’apprennent en souriant [Now, with the revolutionary professor, maths are learned with a smile]. Paris Match, 786, BX–BXI.

    Google Scholar 

  • Vázquez, M. S. (2008). El Centre Belge de Pédagogie de la Mathématique (1958–1973): Nota histórica [The Belgian Centre for Mathematics Pedagogy (1958–1973): Historical note]. Revista Diálogo Educacional, 8(25), 633–645.

    Article  Google Scholar 

  • Vredenduin, P. J. G. (1964). Een opzienbarend boek [A remarkable book]. Euclides, 39(8), 237–247.

    Google Scholar 

  • Vredenduin, P. J. G. (1966). Papy, Mathématique moderne II [Papy, Modern mathematics II]. Euclides, 42(3), 90–94.

    Google Scholar 

  • Vredenduin, P. J. G. (1967a). Het experiment Papy [The experiment Papy]. Euclides, 42(6), 167–172.

    Google Scholar 

  • Vredenduin, P. J. G. (1967b). Papy, Mathématique moderne 5 [Papy, Modern mathematics 5]. Euclides, 42(6), 161–166.

    Google Scholar 

  • Vredenduin, P. J. G. (1967c). Papy, Mathématique moderne 6 [Papy, Modern mathematics 6]. Euclides, 43(4), 124–135.

    Google Scholar 

  • Vredenduin, P. J. G. (1968). Papy, Mathématique moderne 3 [Papy, Modern mathematics 3]. Euclides, 44(1), 14–19.

    Google Scholar 

  • Walusinski, G. (1963). La réforme est en acte [The reform is in act]. Bulletin de l’Association des Professeurs de Mathématiques de l’Enseignement Public, 233, 121–126.

    Google Scholar 

  • Walusinski, G. (1966). Continuité et avenir d’une réforme [Continuity and future of a reform]. Bulletin de l’Association des Professeurs de Mathématiques de l’Enseignement Public, 253, 456–457.

    Google Scholar 

  • Warrinnier, A. (1984). Balans van de hervorming van het wiskundeonderwijs en opties voor de toekomst [Balance of the reform of mathematics education and options for the future]. Bulletin de la Société Mathématique de Belgique (Série A), 36(2), 166–173.

    Google Scholar 

  • Zwaneveld, B., & De Bock, D. (2019). Views on usefulness and applications during the sixties. In K. Bjarnadóttir, F. Furinghetti, J. Krüger, J. Prytz, G. Schubring, & H. J. Smid (Eds.), “Dig where you stand” 5. Proceedings of the Fifth International Conference on the History of Mathematics Education (pp. 387–399). Utrecht, the Netherlands: Freudenthal Institute.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. KU Leuven, Brussels, Belgium

    Dirk De Bock & Geert Vanpaemel

Authors
  1. Dirk De Bock
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Geert Vanpaemel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

De Bock, D., Vanpaemel, G. (2019). Mathématique Moderne: A Pioneering Belgian Textbook Series Shaping the Modern Mathematics Reform of the 1960s. In: Rods, Sets and Arrows. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-20599-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-20599-7_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-20598-0

  • Online ISBN: 978-3-030-20599-7

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation