Abstract
In the early 1950s, Caleb Gattegno, who held doctorates in both mathematics and psychology, took the initiative to organize regular meetings of internationally renowned psychologists, mathematicians, and mathematics teachers, and the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) was born. During the 1950s, Belgians including Frédérique Lenger, Louis Jeronnez, and Willy Servais played a prominent role within CIEAEM. The work of CIEAEM also had a major influence on Belgian mathematics education. Much attention was given to the study and stimulation of students’ learning processes by concrete models and other new teaching aids, among them geoboards, mathematical films, electrical circuits, and the Cuisenaire rods. A confrontation with Bourbaki’s mathematical structures and their assumed relation with the basic structures of early mathematical thinking, as revealed by Jean Piaget, led to a call to experiment with some elements of modern mathematics at the secondary school level.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Although Choquet and Lichnerowicz were not “members” of Bourbaki, they were strongly imbued with their ideas.
- 2.
Piaget’s chapter in Piaget et al. (1955) was the summary of the presentation he had made at the conference in La Rochette (1952), as mentioned in a footnote to that chapter. From the book’s preface, we know that Piaget wrote his chapter after reading the other ones.
References
Association Cuisenaire Belgique. (1989). Compte-rendus des conférences de l’Association Cuisenaire Belgique [Reports of the conferences of the Belgian Cuisenaire Association]. Mathématique et Pédagogie, 74, 35–38.
Atiyah, M. (2007). [Review of the books Bourbaki, a secret society of mathematicians and The artist and the mathematician]. Notices of the AMS, 54(9), 1150–1152.
Bernet, T., & Jaquet, F. (1998). La CIEAEM au travers de ses 50 premières rencontres [The CIEAEM through its first 50 meetings]. Neuchâtel, Switzerland: CIEAEM.
Bkouche, R. (1997). Epistémologie, histoire et enseignement des mathématiques [Epistemology, history and teaching of mathematics]. For the Learning of Mathematics, 17(1), 34–42.
Bourbaki, N. (1939). Éléments de mathématique: Théorie des ensembles [Elements of mathematics: Set theory]. Paris, France: Hermann.
Bourbaki, N. (1948). L’architecture des mathématiques [The architecture of mathematics]. In F. Le Lionnais (Ed.), Les grands courants de la pensée mathématique [Major trends in mathematical thinking] (pp. 35–47). Paris, France: Cahiers du Sud.
Brown, L., Hewitt, D., & Tahta, D. (Eds.) (2010). A Gattegno anthology: Selected articles by Caleb Gattegno reprinted from Mathematics Teaching. Derby, United Kingdom: ATM.
Castelnuovo, E. (1998). Commission international pour l’étude et l’amélioration de l’enseignement des mathématiques (CIEAEM) [International commission for the study and improvement of mathematics teaching (CIEAEM)]. In Les liens entre la pratique de la classe et la recherche en didactique des mathématiques. Actes de la CIEAEM 50 [Relationships between classroom practice and research in mathematics education. Proceedings of the CIEAEM 50] (pp. 463–465). Neuchâtel, Switzerland: CIEAEM.
CIEAEM. (2000). 50 years of CIEAEM: Where we are and where we go? “Manifesto 2000 for the Year of Mathematics.” Retrieved December 31, 2017, from http://www.cieaem.org/?q=system/files/cieaem-manifest2000-e.pdf.
Corry, L. (1992). Nicolas Bourbaki and the concept of mathematical structure. Synthese, 92(3), 315–348.
Cuisenaire, G. (1952). Les nombres en couleurs. Nouveau procédé de calcul par la méthode active, applicable à tous les degrés de l’école primaire [Numbers in colour. New method of calculation by the active method, applicable to all grades of primary school]. Tamines, Belgium: Duculot-Roulin.
Cuisenaire, G., & Gattegno, C. (1954). Numbers in colour: A new method of teaching arithmetic in primary schools. London, United Kingdom: Heinemann.
Deans, J. F. (1972). Structural apparatus. In L. R. Chapman (Ed.), The process of learning mathematics (pp. 254–270). Oxford, United Kingdom: Pergamon Press.
de Lange, J. (1987). Mathematics, insight and meaning. Utrecht, The Netherlands: OW&OC.
Félix, L. (1985). Aperçu historique (1950–1984) sur la Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques (CIEAEM). [Historical overview (1950–1984) on the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM)]. Bordeaux, France: l’IREM de Bordeaux.
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.
Félix, L. (2005). Réflexions d’une agrégée de mathématiques au XXe siècle [Reflections of certified mathematics teacher in the 20th century]. Paris, France: l’Harmattan.
Fennema, E. H. (1972). Models and mathematics. The Arithmetic Teacher, 19(8), 635–640.
Festraets-Hamoir, C. (2001). Cuisenaire. In Nouvelle biographie nationale [New national biography] (Vol. 6, pp. 93–94). Brussels, Belgium: Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique.
Fletcher, T. J. (1954–1955). Un nouveau langage mathématique [A new mathematical language]. Mathematica & Paedagogia, 4, 28–32.
Fletcher, T. J. (1958). Les problèmes du film mathématique [The problems of the mathematical film]. In C. Gattegno, W. Servais, E. Castelnuovo, J. L. Nicolet, T. J. Fletcher, L. Motard, L. Campedelli, A. Biguenet, J. W. Peskett, & P. Puig Adam, Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics] (pp. 81–99). Neuchâtel, Switzerland: Delachaux et Niestlé.
Fletcher, T. J. (1966). L’apprentissage de la mathématique aujourd’hui [The learning of mathematics today]. Paris, France: OCDL.
Fletcher, T. J. (Director). (n.d.). The cardioid [Film]. United Kingdom: Polytechnic Films Limited. Retrieved December 31, 2017, from https://www.atm.org.uk/Trevor-Fletcher-Films.
Fletcher, T. J., & Birtwistle, C. (1961). A problem in visual presentation. Mathematics Teaching, 16, 7–12.
Fletcher, T. J., & Harris, I. (1956). Mathematical filmstrips and films. Mathematics Teaching, 3, 30–36.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: Reidel.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: Reidel.
Freudenthal, H. (1991). Revisiting mathematics education. China Lectures. Dordrecht, The Netherlands: Kluwer.
Furinghetti, F. (2008). The emergence of women on the international stage of mathematics education. ZDM Mathematics Education, 40, 529–543.
Furinghetti, F., & Giacardi, L. (2008). The first century of the International Commission on Mathematical Instruction (1908–2008). The history of ICMI. Torino, Italy: Dipartimento di Matematica dell’Università. Retrieved December 31, 2017, from http://www.icmihistory.unito.it/.
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.
Gattegno, C. (1951). Remarques sur les structures mentales [Notes on mental structures]. Enfance, 4(3), 239–250.
Gattegno, C. (1952). A note on the teaching of mathematics. The Journal of General Education, 6(4), 260–267.
Gattegno, C. (1953). Numbers in colour. Bulletin of the Association for Teaching Aids in Mathematics, 2.
Gattegno, C. (1954a). Les nombres en couleurs de Cuisenaire [Numbers in colour by Cuisenaire]. Moniteur des Instituteurs et des Institutrices Primaires, 72(11), 162–163.
Gattegno, C. (1954b). The Gattegno geoboards. Bulletin of the Association for Teaching Aids in Mathematics, 3.
Gattegno, C. (1954–1955). Les nombres en couleurs de Georges Cuisenaire [Numbers in colour by Georges Cuisenaire]. Mathematica & Paedagogia, 4, 17–22.
Gattegno, C. (1955–1956). Remarques théoriques sur le matériel Cuisenaire [Theoretical remarks on the Cuisenaire material]. Mathematica & Paedagogia, 9, 30–36.
Gattegno, C. (1956). New developments in arithmetic teaching in Britain: Introducing the concept of “set.” The Arithmetic Teacher, 3(3), 85–89.
Gattegno, C. (1958a). La perception et l’action comme bases de la pensée mathématique [Perception and action as bases of mathematical thinking]. In C. Gattegno, W. Servais, E. Castelnuovo, J. L. Nicolet, T. J. Fletcher, L. Motard, L. Campedelli, A. Biguenet, J. W. Peskett, & P. Puig Adam, Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics] (pp. 13–21). Neuchâtel, Switzerland: Delachaux et Niestlé.
Gattegno, C. (1958b). L’enseignement par le film mathématique [Teaching by the mathematical film]. In C. Gattegno, W. Servais, E. Castelnuovo, J. L. Nicolet, T. J. Fletcher, L. Motard, L. Campedelli, A. Biguenet, J. W. Peskett, & P. Puig Adam, Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics] (pp. 105–117). Neuchâtel, Switzerland: Delachaux et Niestlé.
Gattegno, C. (1958c) Les matériels multivalents [Multivalent materials]. In C. Gattegno, W. Servais, E. Castelnuovo, J. L. Nicolet, T. J. Fletcher, L. Motard, L. Campedelli, A. Biguenet, J. W. Peskett, & P. Puig Adam, Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics] (pp. 191–201). Neuchâtel, Switzerland: Delachaux et Niestlé.
Gattegno, C. (1960a). L’emploi du géoplan individuel dans l’enseignement de la géométrie [The use of the individual geoboard in the teaching of geometry]. Mathematica & Paedagogia, 19, 17–31.
Gattegno, C. (1960b). Modern mathematics with numbers in colour. Reading, United Kingdom: Educational Explorers.
Gattegno, C. (1963). Teaching foreign languages in schools: The silent way. Reading, United Kingdom: Educational Explorers.
Gattegno, C. (1971). Geoboard geometry [Guide for teachers]. New York, NY: Educational Solutions Worldwide Inc.
Gattegno, C. (1987). Parts and wholes. Mathematics Teaching, 119, 26–27.
Gattegno, C. (1988). Reflections on forty years of work on mathematics teaching. For the Learning of Mathematics, 8(3), 41–42.
Gattegno, C. (2007). The method of Jean Louis Nicolet. Mathematics Teaching, 205, 42–43.
Gattegno, C., & Fletcher, T. (1968). Obituary – Jean Louis Nicolet. Mathematics Teaching, 38, 16–17.
Gattegno, C., Servais, W., Castelnuovo, E., Nicolet, J. L., Fletcher, T. J., Motard, L., Campedelli, L., Biguenet, A., Peskett, J. W., & Puig Adam, P. (1958). Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics]. Neuchâtel, Switzerland: Delachaux et Niestlé.
Germain, P. (1955–1956). Les grandes machines mathématiques [Large mathematical machines]. Mathematica & Paedagogia, 7, 52–62.
Goutard, M. (1964). Mathematics and children. Reading, United Kingdom: Educational Explorers.
Goutard, M. (1965). Cet enchantement si particulier [This magic so special]. Les Nombres en Couleurs. Bulletin Cuisenaire, 17-18, 2–6.
Grosjean, C. C. (1964). Beschrijving van een eenvoudige electronische rekenmachine: de IBM 610 [Description of a simple electronic calculator: The IBM 610]. Mathematica & Paedagogia, 25, 15–34.
Howard, C. F. (1957). British teachers’ reactions to the Cuisenaire-Gattegno materials: The color-rod approach to arithmetic. The Arithmetic Teacher, 4(5), 191–195.
Jacquemart, E. (1946). Les mathématiques et le cinéma d’enseignement [Mathematics and the educational cinema]. Bulletin de l’Association des Professeurs de Mathématiques de l’Enseignement Public, 112, 53–54.
Jeronnez, L. (1954–1955). Sur les nombres en couleurs [About the numbers in colour]. Mathematica & Paedagogia, 6, 39.
Jeronnez, L. (1966a). Les nombres en couleurs à l’heure de la mathématique moderne [Numbers in colour at the time of modern mathematics]. In Journées d’études 45: Nombres en couleurs [Pedagogical days 45: Numbers in colour] (pp. 15–27). Brussels, Belgium: Ministère de l’éducation nationale et de la culture, Organisation des études, Méthodes, stages de formation et de perfectionnement du personnel et matériel didactique.
Jeronnez, L. (1966b). Mathématique moderne et réglettes Cuisenaire [Modern mathematics and Cuisenaire rods]. Les Nombres en Couleurs. Bulletin Cuisenaire, 24, 1–5.
Jeronnez, L. (1968). Mathématique moderne à l’école primaire et les réglettes Cuisenaire [Modern mathematics in the primary school and Cuisenaire rods]. Brussels, Belgium: Calozet.
Jeronnez, L. (1976). Hommage à Georges Cuisenaire [Tribute to Georges Cuisenaire]. Mathématique et Pédagogie, 6, 75–81.
Jeronnez, L., & Lejeune, I. (1970). À la découverte de la mathématique et les réglettes Cuisenaire [Discovering mathematics and the Cuisenaire rods]. Brussels, Belgium: Calozet.
Jeronnez, L., & Lejeune, I. (1972a). L’expérience de Waterloo d’un enseignement moderne de la mathématique à l’école primaire [The Waterloo experiment on a modern teaching of mathematics at the primary school]. Mathematica & Paedagogia, 53-54, 69–80.
Jeronnez, L., & Lejeune, I. (1972b). Les réglettes Cuisenaire et la mathématique moderne [The Cuisenaire rods and modern mathematics]. Math-École, 50-51, 30–38.
Lenger, F. (1954–1955). VIIIe rencontre internationale des professeurs de mathématiques [8th international meeting of teachers of mathematics]. Mathematica & Paedagogia, 6, 86–88.
Menghini, M., Furinghetti, F., Giacardi, L., & Arzarello, F. (Eds.) (2008). The first century of the International Commission on Mathematical Instruction (1908–2008). Reflecting and shaping the world of mathematics education. Rome, Italy: Istituto della Enciclopedia Italiana.
Michaut, P. (1948). The educational cinema in France. Sight and Sound, 17(67), 146–148.
Motard, L. (1958). Les techniques du dessin animé mathématique [The techniques of the mathematical animated movie]. In C. Gattegno, W. Servais, E. Castelnuovo, J. L. Nicolet, T. J. Fletcher, L. Motard, L. Campedelli, A. Biguenet, J. W. Peskett, & P. Puig Adam, Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics] (pp. 101–103). Neuchâtel, Switzerland: Delachaux et Niestlé.
Natalis, E. (1954). Matériel de calcul. Didactique et psychologie [Material for calculation. Didactics and psychology]. Moniteur des Instituteurs et des Institutrices Primaires, 78(7), 97–111.
Nicolet, J.-L. (1954–1955). Réflexions sur l’intuition en mathématiques [Reflections on intuition in mathematics]. Mathematica & Paedagogia, 4, 22–28.
Nicolet, J. -L. (1958). Intuition mathématique et dessins animés [Mathematical intuition and animated movie]. In C. Gattegno, W. Servais, E. Castelnuovo, J. L. Nicolet, T. J. Fletcher, L. Motard, L. Campedelli, A. Biguenet, J. W. Peskett, & P. Puig Adam, Le matériel pour l’enseignement des mathématiques [Materials for the teaching of mathematics] (pp. 63–80). Neuchâtel, Switzerland: Delachaux et Niestlé.
Noël, G. (2018). Regards sur Caleb Gattegno [Views on Caleb Gattegno]. Losanges, 41, 68–69.
Noël, G. (in preparation). 1945–1960: Quinze années d’enseignement des mathématiques en Belgique [1945–1960: Fifteen years of mathematics teaching in Belgium] [Booklet]. Mons, Belgium: SBPMef.
Noël, G., & Midavaine, R. (2011). Revoir les films de J.-L. Nicolet [Reviewing the films of J.-L. Nicolet]. Losanges, 13, 41–48.
Papy, F. (1968). 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.
Piaget, J. (1955). Les structures mathématiques et les structures opératoires de l’intelligence [The mathematical structures and the operational structures of intelligence]. In J. Piaget, E. W. Beth, J. Dieudonné, A. Lichnerowicz, G. Choquet, & C. Gattegno, L’enseignement des mathématiques [The teaching of mathematics] (pp. 11–33). Neuchâtel, Switzerland: Delachaux et Niestlé.
Piaget, J., Beth, E. W., Dieudonné, J., Lichnerowicz, A., Choquet, G., & Gattegno, C. (1955). L’enseignement des mathématiques [The teaching of mathematics]. Neuchâtel, Switzerland: Delachaux et Niestlé.
Powell, A. B. (2007). Caleb Gattegno (1911–1988): A famous mathematics educator from Africa? Revista Brasileira de História da Matemática, Especial n° 1–Festschrift Ubiratan D’Ambrosio, 199–209.
Puig Adam, P. (1956–1957). Les mathématiques et le concret [Mathematics and the concrete]. Mathematica & Paedagogia, 12, 62–65.
Puig Adam, P. (1957–1958). L’aire des polygones au géoplan [The area of polygons in the geoboard]. Mathematica & Paedagogia, 15, 44–47.
Puig Adam, P. (1958). El material didáctico matemático actual [Current mathematical teaching material]. Madrid, Spain: Ministerio de Educación Nacional.
Rogers, L. (2008). Imagining the cardioid. Mathematics Teaching, 206, 43–45.
Roller, S. (1964). Georges Cuisenaire, notre ami, bonne année! [Georges Cuisenaire, our friend, happy new year!]. Les Nombres en Couleurs. Bulletin Cuisenaire, 11, 1–3.
Roller, S. (1966). Allocution prononcée à l’Athénée d’Ixelles le samedi 5 juin 1965 [Address given at the Athénée d’Ixelles on Saturday June 5, 1965]. Les Nombres en Couleurs. Bulletin Cuisenaire, 21, 1–3.
Rollin, J. (1971). L’heure Cuisenaire [The Cuisenaire clock]. Brussels, Belgium: Calozet.
Savary, N. (1965). Georges Cuisenaire a l’honneur [Georges Cuisenaire has the honor]. Les Nombres en Couleurs. Bulletin Cuisenaire, 19, 1–7.
Servais, W. (1955–1956). Modèles. Objects concrets et symboles [Models. Concrete objects and symbols]. Mathematica & Paedagogia, 8, 33–44.
Servais, W. (1956). Modèles logiques [Logical models]. In Ministère de l’Instruction Publique/Ministerie van Openbaar Onderwijs, Documentation/Documentatie: Het onderwijs in de wiskunde met de hulp van modellen/Les modèles dans l’enseignement mathématique. Cahier n° 5 [Documentation: Models in the teaching of mathematics. Booklet n° 5] (pp. 92–99). Brussels, Belgium: Ministère de l’Instruction Publique/Ministerie van Openbaar Onderwijs.
Servais, W. (1959). Les nombres en couleurs [Numbers in colour]. Mathematica & Paedagogia, 17, 51–64.
Servais, W. (1969a). L’importance du matériel concret dans l’enseignement mathématique [The significance of concrete materials in the teaching of mathematics]. Bulletin de l’A.M.Q., 72–77.
Servais, W. (1969b). Logique et enseignement mathématique [Logic and mathematics teaching]. Educational Studies in Mathematics, 2(2-3), 160–179.
Servais, W. (1970). The significance of concrete materials in the teaching of mathematics. In Association of Teachers of Mathematics, Mathematical reflections. Contributions to mathematical thought and teaching, written in the memory of A. G. Sillitto (pp. 203–208). Cambridge, United Kingdom: University Press.
Shannon, C. E. (1938). A symbolic analysis of relay and switching circuits. Transactions of the American Institute of Electrical Engineers, 57, 713–723.
Van der Waerden, B. L. (1930). Moderne algebra [Modern algebra]. Berlin, Germany: Springer.
Vanhamme, W. (1954–1955). Le “Géoplan” [The “geoboard”]. Mathematica & Paedagogia, 6, 43–44.
Vanhamme, W. (1956). Les géoplans [Geoboards]. In Ministère de l’Instruction Publique/Ministerie van Openbaar Onderwijs, Documentation/Documentatie: Het onderwijs in de wiskunde met de hulp van modellen/Les modèles dans l’enseignement mathématique. Cahier n° 5 [Documentation: Models in the teaching of mathematics. Booklet n° 5] (pp. 38–41). Brussels, Belgium: Ministère de l’Instruction Publique/Ministerie van Openbaar Onderwijs.
Warbecq, A. (2000). Hommage à Willy Servais: Willy Servais et la CIEAEM [Tribute to Willy Servais: Willy Servais and the CIEAEM]. Mathématique et Pédagogie, 126, 9–10.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
De Bock, D., Vanpaemel, G. (2019). Revival of International Collaboration in Mathematics Education During the 1950s. In: Rods, Sets and Arrows. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-20599-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-20599-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20598-0
Online ISBN: 978-3-030-20599-7
eBook Packages: EducationEducation (R0)