Abstract
The 1960s were characterized by a wide range of activities aimed at assisting the actual implementation of modern mathematics into the classroom: experimentation with different target groups, related to the development of new curricula, and large-scale programs of teacher re-education. After a first experiment, Georges Papy, a professor of algebra, was consulted, his task being to promote the quality of the experimental actions. Papy engaged himself completely and soon became the architect and undisputed leader of the modern mathematics reform in Belgium. He designed and carried out audacious experiments, developed new programs and teaching materials, and engaged mathematics teachers through large-scale in-service education programs. Papy’s actions were coordinated by the newly founded Belgian Centre for Mathematics Pedagogy, of which he became the chairman. A very different approach to the modernization of the teaching of mathematics was advocated by Paul Libois whose collaborators conducted their own experiments at the École Decroly.
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Notes
- 1.
A set with exactly one element.
- 2.
In French “la mathématique,” singular, refers to the unified (modern) mathematics, in contrast to “les mathématiques,” plural, referring to (traditional) mathematics as an umbrella term for several subdisciplines with little or no interrelationships.
- 3.
There may occur some confusion regarding references to publications by Frédérique Lenger and Georges Papy, wife and husband from October 1, 1960. From the 1960s, Georges typically signed his publications as “Papy,” while Frédérique, after marriage, used her husband’s surname (and signed “Frédérique Papy”) or signed with only her first name “Frédérique.” The lists of publications from both authors can be found at http://www.rkennes.be/
References
There may occur some confusion regarding references to publications by Frédérique Lenger and Georges Papy, wife and husband from October 1, 1960. From the 1960s, Georges typically signed his publications as “Papy,” while Frédérique, after marriage, used her husband’s surname (and signed “Frédérique Papy”) or signed with only her first name “Frédérique.” The lists of publications from both authors can be found at http://www.rkennes.be/
Anonymous. (2012, January 5). Georges Papy: A mathematics educator for the ages. Retrieved July 16, 2016, from https://www.eimacs.com/blog/2012/01/georges-papy-mathematics-educator-gifted-math-curriculum/.
Avant-propos. (1960). Avant-propos de la rédaction. Bulletin de la Société Mathématique de Belgique, 12(3), 105–106.
Bernet, T., & Jaquet, F. (1998). La CIEAEM au travers de ses 50 premières rencontres [The CIEAEM through its first 50 meetings]. Neuchâtel, Switzerland: CIEAEM.
Bourbaki, N. (1939). Éléments de mathématique: Théorie des ensembles [Elements of mathematics: Set theory]. Paris, France: Hermann.
Braunfeld, P. (1973). The role of algebra in a modern K-12 curriculum (including a description of the CSMP algebra program). International Journal of Mathematical Education in Science and Technology, 4(2), 175–185.
Castelnuovo, E. (1965). Belgique: Mathématique d’avant-garde [Belgium: Pioneering mathematics] (French translation of Castelnuovo, Emma (1965). Matematica d’avanguardia. Riforma della Scuola, 11, 3–19). Retrieved October 15, 2016, from http://www.science.unitn.it/~fontanar/EMMA/riforma_scuola_maggio_1965.pdf.
Castelnuovo, E. (1997). Federigo Enriques et Guido Castelnuovo [Federigo Enriques and Guido Castelnuovo] (French translation by S. Trompler of Castelnuovo, E. (1997). Federigo Enriques e Guido Castelnuovo. Bollettino dell’Unione Matematica Italiana, 7(11-A), 227–235). Retrieved December 17, 2017, from http://dev.ulb.ac.be/urem/Frederigo-Enriques-e-Guido.
CBPM. (1964a). Arlon 6. Brussels, Belgium: Author.
CBPM. (1964b). Programme de mathématique pour les écoles normales moyennes (section mathématique) proposé par le Centre Belge de Pédagogie de la Mathématique et adopté à titre expérimental par le Ministère de l’Éducation Nationale et de la Culture depuis l’année scolaire 1963–1964 [Mathematics curriculum for teaching colleges (mathematics section) proposed by the Belgian Centre for Mathematics Pedagogy and adopted on an experimental basis by the Ministry of National Education and Culture]. In Arlon 6 (pp. 25–42). Brussels, Belgium: Author.
CBPM. (1966). Projet de programme pour la classe expérimentale de troisième scientifique [Draft curriculum for the fourth year of secondary school in the scientific streams]. Mathematica & Paedagogia, 30, 27–31.
Colmant, P. (1991). L’occasion de rencontrer nos collègues [The occasion to meet our colleagues]. In Un présent du passé, un passé du présent. Fascicule à Georges Papy à l’occasion de ses 70 ans [A presence of the past, a past of the present. Fascicle to Georges Papy on the occasion of his 70 years] (p. 13). Arlon, Belgium: SBPMef.
Colot, L. (1969). Lettre d’un professeur de mathématique à un collègue [Letter of a mathematics teacher to a colleague]. Mathematica & Paedagogia, 38, 34–40.
Comprehensive School Mathematics Program. (1978). CSMP in action. St. Louis, US: CEMREL Inc. (French translation published in Nico, 23, 1979, pp. 4–98).
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.
De Bock, D., & Vanpaemel, G. (2018). Early experiments with modern mathematics in Belgium. Advanced mathematics taught from childhood? In F. Furinghetti & A. Karp (Eds.), Researching the history of mathematics education: An international overview (pp. 61–77). Cham, Switzerland: Springer.
De Bruyn, K. (2012). Georges Papy, 4 November 1920 – 11 November 2011 [Georges Papy, November 4, 1920 – November 11, 2011]. Wiskunde & Onderwijs, 38(150), 138–142.
De Latil, P. (1960). Sensationnelles expériences en Belgique: Les “Mathématiques modernes” enseignées dès l’enfance [Sensational experiments in Belgium: “Modern Mathematics” taught from childhood]. Sciences et Avenir, 164, 539–544. 553.
Denée, M. (1969). Minicomputer à l’école primaire [Minicomputer in primary school]. Nico, 3, 36–38.
Dieudonné, J. (1992). Les travaux mathématiques de Georges Papy [The mathematical works of Georges Papy]. Bulletin de la Société Mathématique de Belgique (Série A), 44(2), 149–151.
Fielker, D. (1961). Developments in the teaching of mathematics. Report of the Easter Conference, London, 1961. Mathematics Teaching, 16, 32–52.
Frédérique. (1970). Les enfants et la mathématique 1 [Children and mathematics 1]. Brussels, Belgium-Montréal, Canada-Paris, France: Marcel Didier.
Frédérique. (1971). Les enfants et la mathématique 2 [Children and mathematics 2]. Brussels, Belgium-Montréal, Canada-Paris, France: Marcel Didier.
Frédérique. (1972). Les enfants et la mathématique 3 [Children and mathematics 3]. Brussels, Belgium-Montréal, Canada-Paris, France: Marcel Didier.
Frédérique. (1976). Les enfants et la mathématique 4 [Children and mathematics 4]. Brussels, Belgium-Montréal, Canada-Paris, France: Marcel Didier.
Furinghetti, F., & Menghini, M. (2014). The role of concrete materials in Emma Castelnuovo’s view of mathematics teaching. Educational Studies in Mathematics, 87, 1–6.
Goffree, F. (1985). Ik was wiskundeleraar [I was a mathematics teacher]. Enschede, The Netherlands: Stichting voor de Leerplanontwikkeling.
Gotovitch, J. (1991). Les multiples résistances universitaires [Multiple academic resistance]. In A. Despy-Meyer, A. Dierkens, & F. Scheelings (Eds.), 25 Novembre 1941. L’Université Libre de Bruxelles ferme ses portes [November 25, 1941. The Free University of Brussels closes its doors] (pp. 153–165). Brussels, Belgium: Archives de l’ULB.
Groupe International de Recherche en Pédagogie de la Mathématique [International Group for the Study of the Pedagogy of Mathematics]. (1971). Nico, 10, 3–11.
Holvoet, R. (1968). De werkgroepen van het Centrum [The working groups of the Centre]. In G. Papy (in collaboration with P. R. Burgraeve, R. Holvoet, F. Papy, & A. Terfve) (Eds.), Arlon 10 (pp. 90–111). Brussels, Belgium: CBPM.
Holvoet, R. (1971). Over de opbouw van de methode-Papy [About the structure of the method Papy]. In J. H. Wansink (Ed.), Didactische oriëntatie voor wiskundeleraren II. Tweede druk [Didactical orientation for mathematics teachers II. 2nd edition] (pp. 405–449). Groningen, The Netherlands: Wolters-Noordhoff.
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.
Hotyat, F. (1960). Le 8ème colloque de pédagogie expérimentale de langue française, Morlanwelz, Belgique, avril 1960 [The 8th French language colloquium on experimental psychology, Morlanwelz, Belgium, April 1960]. International Review of Education/Internationale Zeitschrift für Erziehungswissenschaft/Revue Internationale de l’Éducation, 6(3), 353–354.
Hotyat, F. (1961). L’enseignement des mathématiques au niveau secondaire. Les recherches dans les pays européens de langue française [Mathematics teaching at the secondary level. Researches in the French-speaking European countries]. International Review of Education/Internationale Zeitschrift für Erziehungswissenschaft/Revue Internationale de l’Éducation, 7(2), 235–247.
Janne, H. (1964). Une journée décisive [A decisive day]. Mathematica & Paedagogia, 26, 7–12.
Janne, H. (1965). Programme optionnel de mathématique [Optional program of mathematics] (ministerial circular). Brussels, Belgium: Ministère de l’Éducation Nationale et de la Culture.
Larock, V. (1962). Vernieuwing van het onderwijs in de wiskunde [Renewal of the teaching of mathematics] (ministerial circular). Brussels, Belgium: Ministerie van Nationale Opvoeding en Cultuur.
Lenger, F., & Lepropre, M. (1958–1959). Le programme B des écoles normales gardiennes [The program B of the schools for future kindergarten teachers]. Mathematica & Paedagogia, 16, 70–75.
Lenger, F., & Lepropre, M. (1959). Initiation aux mathématiques fondamentales dans une classe de première normale gardienne [Initiation to fundamental mathematics in a first year class of training of kindergarten teachers]. In Journées d’études 8: L’initiation aux mathématiques—Problèmes psycho-pédagogiques [Pedagogical days 8: Initiation in mathematics—Psycho-pedagogical problems] (pp. 17–24). Brussels, Belgium: Ministère de l’Enseignement Public, Secrétariat Général de la Réforme de L’enseignement Moyen et Normal.
Le programme B des écoles normales gardiennes [The future kindergarten teachers’ program B]. (1958–1959). Mathematica & Paedagogia, 16, 70–75.
Libois, L. (1962). Introduction [Introduction]. In Journées d’études 22: Mathématiques. Programme O.E.C.E. Journées pédagogiques internationales tenues à l’École Decroly 9–12 avril 1962 (pp. 5–10). Brussels, Belgium: Ministère de L’éducation Nationale et de la Culture, Secrétariat Général de la Réforme de l’Enseignement Moyen et Normal.
Libois, L. (1971). Mathematics in the Decroly School. Educational Studies in Mathematics, 4(2), 182–186.
Libois, P. (1955–1956). L’Enseignement de la géométrie et la réalité [The teaching of geometry and reality]. Mathematica & Paedagogia, 7, 30–34.
Matthys, J.-C. (2011). Hommage à Georges Papy [Tribute to Georges Papy]. Losanges, 15, 3–6.
Mawhin, J. (2004). Cinquante ans de mathématiques en Belgique: un survol [Fifty years of mathematics in Belgium: An overview]. Mathématique et Pédagogie, 145, 3–22.
Menghini, M. (2015). Emma Castelnuovo’s commitment to creating a new generation of mathematics teachers. 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. 263–278). Uppsala, Sweden: Uppsala University, Department of Education.
Ministerie van Nationale Opvoeding en Cultuur, Secretariaat Generaal voor de Hervorming van het Middelbaar Onderwijs. (1960). Internationale perfectionerings-cursussen voor doctoren en licentiaten in de wiskunde. Eerste jaar (Brussel, 25–31 augustus 1960) [International recycling and improvement courses for masters and doctors in mathematics. First year (Brussels, August, 25–31, 1960)]. Brussels, Belgium: Author.
Ministerie van Nationale Opvoeding en Cultuur, Secretariaat Generaal voor de Hervorming van het Middelbaar Onderwijs. (1961). Internationale perfectionerings-cursussen voor doctoren en licentiaten in de wiskunde. Tweede jaar (Brussel, 24–30 augustus 1961) [International recycling and improvement courses for masters and doctors in mathematics. Second year (Brussels, August, 24–30, 1961)]. Brussels, Belgium: Author.
Ministerie van Nationale Opvoeding en Cultuur, Secretariaat Generaal voor de Hervorming van het Middelbaar Onderwijs. (1962). Internationale post-universitaire cursussen voor doctoren en licentiaten in de wiskunde. Derde jaar (Brussel, 24–30 augustus 1962) [International post-university courses for masters and doctors in mathematics. Third year (Brussels, August, 24–30, 1962)]. Brussels, Belgium: Author.
Ministerie van Nationale Opvoeding en Nederlandse Cultuur/Ministère de l’Éducation Nationale et de la Culture Française. (1978). International post-university courses: Mathematics. List of university professors and object of their lectures. Brussels, Belgium: Author.
Nachtergaele, J. (1964). XVIIème rencontre international de professeurs de mathématiques [XVIIth international meeting of teachers of mathematics]. Mathematica & Paedagogia, 25, 82–86.
Noël, G. (1993). La réforme des maths moderne en Belgique [The reform of modern mathematics in Belgium]. Mathématique et Pédagogie, 91, 55–73.
OEEC. (1961a). New thinking in school mathematics. Paris, France: OEEC.
OEEC. (1961b). Synopses for modern secondary school mathematics. Paris, France: OEEC.
Papy, F. (1968a). Une expérience pédagogique de dix ans en Belgique [A pedagogical experiment of ten years in Belgium]. In G. Papy (in collaboration with P. R. Burgraeve, R. Holvoet, F. Papy, & A. Terfve) (Ed.), Arlon 10 (pp. 25–89). Brussels, Belgium: CBPM.
Papy, F. (1968b). Sur le premier enseignement de la mathématique et une méthodologie de la formation continue des enseignants [On the first teaching of mathematics and a methodology for in-service teacher education]. Unpublished doctoral dissertation, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium.
Papy, F. (1969). Minicomputer. Educational Studies in Mathematics, 2(2–3), 333–345.
Papy, F. (1970a). L’expérience Belge à l’école primaire [The Belgian experiment in primary school]. In A. Revuz (Ed.), New trends in mathematics teaching—Tendances nouvelles de l’enseignement des mathématiques, Vol. II (pp. 95–111). Paris, France: UNESCO.
Papy, F. (1970b). Papy’s minicomputer. Mathematics Teaching, 50, 40–45.
Papy, F. (1971). Initiation à la notion de groupe [Initiation to the notion of group]. Mathematica & Paedagogia, 48–49, 160–179.
Papy, G. (1959). Aperçu général de la théorie des ensembles. Quelques notions essentielles de topologie [General outline of set theory. Some basic notions of topology] (Report of Arlon 1, July 4–6, 1959). Brussels, Belgium: Presses Universitaires de Bruxelles.
Papy, G. (1960). Premiers éléments de mathématique moderne [First elements of modern mathematics]. Brussels, Belgium: Author.
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.
Papy, G. (1962). L’enseignement de la mathématique dans le tronc commun [The teaching of mathematics in the common core]. Mathematica & Paedagogia, 23, 47–60.
Papy, G. (1965). Arlon 7. Vectoriel Euclidien plan [Arlon 7. Euclidean vector plan]. Brussels, Belgium: CBPM.
Papy, G. (1966a). Arlon 8. Premières leçons d’analyse mathématique par Frédérique [Arlon 8. First lessons in mathematical analysis by Frédérique]. Brussels, Belgium: CBPM.
Papy, G. (1966b). La géométrie dans l’enseignement moderne de la mathématique [Geometry in modern teaching of mathematics]. In International Congress of Mathematicians. Abstracts of Reports on Invitation (Vol. 3, pp. 82–89). Moscow, Russia: IMU (also published in L’Enseignement Mathématique, 12(3), 1966, pp. 225–233, and in Mathematica & Paedagogia, 30, 1966, pp. 32–39).
Papy, G. (1967a). Arlon 9. Nouvelles leçons d’analyse mathématique par Frédérique [Arlon 9. New lessons in mathematical analysis by Frédérique]. Brussels, Belgium: CBPM.
Papy, G. (1967b). Préface [Preface]. In G. Papy (in collaboration with J. Agusti, F. Darge, P. Debbaut, K. De Munter, I. Dumrauf, L. Konguetsof, & M. Mius d’Entremont) (Ed.), Arlon 9. Nouvelles leçons d’analyse mathématique par Frédérique [Arlon 9. New lessons in mathematical analysis by Frédérique] (pp. 1–37). Brussels, Belgium: CBPM.
Papy, G. (1968a). Arlon 10. Brussels, Belgium: CBPM.
Papy, G. (1968b). Minicomputer (in collaboration with Frédérique). Brussels, Belgium: IVAC.
Papy, G. (1975). Heureux vingtième anniversaire, minicomputer [Happy 20th birthday, minicomputer]. Nico, 19, 3–37.
Papy, G., & Holvoet, R. (1968). Centre Belge de Pédagogie de la Mathématique à Bruxelles: Statuts [Belgian Centre for Mathematics Pedagogy in Brussels: Articles]. In G. Papy (in collaboration with P. R. Burgraeve, R. Holvoet, F. Papy, & A. Terfve) (Ed.), Arlon 10 (pp. 133–135) (Reprint from Act 2472 published in the annexes of the Moniteur Belge of June 8, 1961). Brussels, Belgium: CBPM.
Randour, C. (2003). Frédérique et Papy, créateurs d’images mathématiques [Frédérique et Papy, creators of mathematical images]. Lecture given at the 29th annual congress of the Société Belge des Professeurs de Mathématique d’expression française, Forest, Belgium. Retrieved July 6, 2018, from http://www.rkennes.be/papy.ppt.htm.
Servais, W. (1959). Fundamental concepts and their development in the school curriculum: Thoughts on the teaching of algebra in secondary schools. Paris, France: OEEC (OSTP) (typewritten text, not paginated). Personal Archives Willy Servais, Morlanwelz, Belgium.
Smet, R., & Vannecke, A. (2002). Historiek van het technisch en beroepsonderwijs 1830–1990 [History of technical and vocational education 1830–1990]. Antwerp, Belgium-Apeldoorn, The Netherlands: Garant.
Stievenart, P. (1968). La guerre des math aura-t-elle lieu? [Will the math war take place?]. Special, 153, 16–19.
Terfve, A. (1968). En suivant les cours du Centre… [By following the courses of the Centre…]. In G. Papy (in collaboration with P. R. Burgraeve, R. Holvoet, F. Papy, & A. Terfve) (Ed.), Arlon 10 (pp. 13–22). Brussels, Belgium: CBPM.
Trompler, S. (2009). Libois professeur [Libois professor]. Unpublished paper based on a lecture given at “Une journée sur Paul Libois,” Brussels, Belgium.
Un groupe de professeurs américains. (1970). Frédérique dans une classe américaine [Frédérique in an American class]. Nico, 7, 63–70.
Van Arsdel, J., & Lasky, J. (1972). A two-dimensional abacus–the Papy minicomputer. The Arithmetic Teacher, 19, 445–451.
Vanhamme, J. (1991). Papy, un esprit ouvert [Papy, an open mind]. In Un présent du passé, un passé du présent. Fascicule à Georges Papy à l’occasion de ses 70 ans [A presence of the past, a past of the present. Fascicle to Georges Papy on the occasion of his 70 years] (pp. 72–73). Arlon, Belgium: SBPMef.
Van Praag, P. (2016). Papy. In Nouvelle biographie nationale [New national biography] (Vol. 13, pp. 262–263). Brussels, Belgium: Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique.
Van Praag, P. (n.d.). Georges Papy. Texte long [Georges Papy. Long text]. Retrieved November 10, 2017, from http://www.rkennes.be/Articles%20de%20Papy/Papy-notice%20longue-finale.pdf.
Warbecq, A. (1991). Nostalgie … regrets [Nostalgia … regrets]. In Un présent du passé, un passé du présent. Fascicule à Georges Papy à l’occasion de ses 70 ans [A presence of the past, a past of the present. Fascicle to Georges Papy on the occasion of his 70 years] (pp. 80–83). Arlon, Belgium: SBPMef.
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De Bock, D., Vanpaemel, G. (2019). Preparing for the Introduction of Modern Mathematics into the Classroom: Experimentation and Teacher Training. In: Rods, Sets and Arrows. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-20599-7_5
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