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History of Teaching Geometry

Abstract

Since the beginning of the transmission of geometric knowledge, two aspects of geometry have been present: the abstract “speculative” and the practical. These two aspects correspond to an essential dialectic in geometry teaching, between a deductive/rational science and a practical/intuitive one. In the nineteenth and twentieth centuries, the stress on the second aspect led to experimental geometry. After the work of Descartes, another tension concerned the solution of problems: between “pure” methods and methods coming from algebra or analysis. Attempts to find a new language for school geometry reached their apex when geometry was substituted by linear algebra in the 1960s.

Keywords

  • Nineteenth Century
  • Descriptive Geometry
  • Conic Section
  • Analytic Geometry
  • School Geometry

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 23.1

Notes

  1. 1.

    This and subsequent translations are by the authors unless indicated otherwise.

References

  • Amiot, A. 1857. Éléments de Géométrie, 5th ed. Paris: Dezobry, Magdeleine et Cie.

    Google Scholar 

  • Arnauld, Antoine. 1667. Nouveaux éléments de géométrie. Paris: Savreux.

    Google Scholar 

  • Ausejo, Elena. 2010. The introduction of “modern mathematics” in secondary education in Spain (1954–1970). International Journal for the History of Mathematics Education 5(2): 1–14.

    Google Scholar 

  • Auvinet, Jérôme. 2013. Charles-Ange Laisant. Itinéraires et engagements d’un mathématicien de la troisième République. Paris: Hermann.

    Google Scholar 

  • Barbin, Evelyne. 1991. Les ‘eléments de géométrie’ de Clairaut: une géométrie problématisée. Repères IREM 4: 119–133.

    Google Scholar 

  • Barbin, Evelyne. 2007. On the argument of simplicity in elements and schoolbooks of geometry. Educational Studies in Mathematics 66(2): 225–242.

    CrossRef  Google Scholar 

  • Barbin, Evelyne. 2009a. The notion of magnitude in teaching: The new elements of Arnauld and his inheritance. International Journal for the History of Mathematics Education 4(2): 1–18.

    Google Scholar 

  • Barbin, Evelyne. 2009b. L’association créatrice de l’analyse et de la géométrie selon Gabriel Lamé. In Gabriel Lamé. Les pérégrinations d’un ingénieur du XIXe siècle, ed. Evelyne Barbin, 101–111. Paris: Sabix, École Polytechnique.

    Google Scholar 

  • Barbin, Evelyne. 2010. Evolving geometric proofs in the 17th century: From icons to symbols. In Explanation and proof in mathematics: Philosophical and educational perspectives, ed. Gila Hanna, Niels Jahnke, and Helmut Pulte, 237–252. New York: Springer.

    CrossRef  Google Scholar 

  • Barbin, Evelyne. 2012. Teaching of conics in 19th and 20th centuries: on the conditions of changing (1854–1997). In Dig where you stand. Proceedings of the Second International on the History of Mathematics Education, eds. Kristin Bjarnadottir, Fulvia Furinghetti, José-M. Matos, and Gert Schubring, 44–59. Lisbon: Universidade Nova.

    Google Scholar 

  • Barbin, Evelyne, Marta Menghini, and Amirouche Moktefi. 2013. Les dernières batailles d’Euclide: sur l’usage des Eléments pour l’enseignement de la géométrie au XIXe siècle. in Les ouvrages de mathématiques entre recherche, enseignement et culture, eds. Evelyne Barbin and Marc Moyon, 57–68. Limoges: PUR.

    Google Scholar 

  • Belhoste, Bruno. 1995. Les sciences dans l’enseignement secondaire français t.1: 1789–1914. Paris: INRP/Economica.

    Google Scholar 

  • Bender, Peter. 1982. Abbildungsgeometrie in der didaktischen Diskussion. Zentralblatt für Didaktik der Mathematik 14: 9–24.

    Google Scholar 

  • Biot, Jean-Baptiste. 1805. Essai de géométrie analytique. Paris: Bachelier.

    Google Scholar 

  • Birkhoff, George David, and Ralph Beatley. 1941. Basic geometry. New York: Chelsea Publishing.

    MATH  Google Scholar 

  • Bkouche, Rudolf. 2003. La géometrie dans les premières années de la revue L’Enseignement Mathématique. In One hundred years of L’Enseignement Mathématique, ed. Daniel Coray, Fulvia Furinghetti, Hélène Gispert, Bernard Hodgson, and Gert Schubring, 95–112. Monographie 39, Geneva: L’Enseignement Mathématique.

    Google Scholar 

  • Bkouche, Rudolf. 2007. Les démonstrations du postulat des parallèles. In Histoire et enseignement des mathématiques. Rigueurs, erreurs, raisonnements, ed. Evelyne Barbin and Dominique Bénard, 29–62. Lyon: INRP.

    Google Scholar 

  • Borel, Émile. 1905. Geometrie: premier et second cycles. Paris: Librarie Armand Colin.

    Google Scholar 

  • Bretschneider, Carl Anton. 1844. Lehrgebäude der niederen Geometrie: für den Unterricht an Gymnasien und höheren Realschulen. Jena: F. Fromann.

    Google Scholar 

  • Casey, John. 1885. A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples. Dublin/London: Hodges, Figgis, & Co/Longmans, Green & Co.

    Google Scholar 

  • Castelnuovo, Emma. 1946. Un metodo attivo nell’insegnamento della geometria intuitiva. Periodico di Matematiche, IV 24:129–140. Castelnuovo, Emma. 1963. La didattica della matematica. Firenze: La Nuova Italia.

    Google Scholar 

  • Choquet, Gustave. 1964. L’Enseignement de la Geometrie. Paris: Hermann.

    MATH  Google Scholar 

  • Clairaut, Alexis. 1741. Elémens de géométrie. Paris: David.

    Google Scholar 

  • Coolidge, Julian Lowell. 1916. A treatise on the circle and sphere. Oxford: Clarendon press.

    MATH  Google Scholar 

  • Cremona, Luigi. 1873. Elementi di geometria projettiva: ad uso degli Istituti tecnici del Regno d’Italia. Roma: Paravia.

    Google Scholar 

  • Crozet, Pascal. 2009. Les sciences modernes en Egypte. Transfert et appropriation, 1805–1902. Paris: Geuthner.

    Google Scholar 

  • De Dainville, François. 1954. L’enseignement des mathématiques dans les collèges jésuites de France du XVIe au XVIIIe siècle. Revue d’histoire des sciences VII: 109–123. PUF, 6–21.

    Google Scholar 

  • De Moor, Ed.W.A. 1995. Vormleer-an innovation that failed. Paedagogica Historica XXXI(1): 103–113. new series.

    CrossRef  Google Scholar 

  • De Paolis, Riccardo. 1884. Elementi di geometria. Torino: Loescher.

    Google Scholar 

  • Desboves, M. 1875. Questions de géométrie élémentaire. Méthodes et solutions, 2nd ed. Paris: Delagrave.

    Google Scholar 

  • Descartes, René. 1637. La Géométrie. In Discours de la méthode, 376–493. Leyde: Jan Maire.

    Google Scholar 

  • Djebbar, Ahmed. 2001. Une histoire de la science arabe. Paris: Points Seuil.

    Google Scholar 

  • Dorier, Jean-Luc. 2000. On the teaching of linear algebra. Dordrecht: Kluwer Academic.

    MATH  Google Scholar 

  • Dufailly, Jules. 1874. Géométrie. Paris: Delagrave.

    Google Scholar 

  • Fehr, Henri. 1911. Compte rendu du congrès de Milan. l’Enseignement Mathématique 13: 437–511.

    Google Scholar 

  • Frattini, Giovanni. 1901. Geometria intuitiva per uso delle scuole complementari e del ginnasio inferiore. Torino: G. B. Paravia.

    Google Scholar 

  • Freudenthal, Hans. 1973. What groups mean in mathematics and what they should mean in mathematical education. In Developments in mathematical education proceedings of ICME-2, Exeter 1972, ed. Geoffrey Howson, 101–114. Cambridge: University Press.

    Google Scholar 

  • Furinghetti, Fulvia, Marta Menghini, Livia Giacardi, and Ferdinando Arzarello. 2008. ICMI renaissance: The emergence of new issues in mathematics education. In The first century of the international commission on mathematical instruction. Reflecting and shaping the world of mathematics education, 131–147. Roma: Istituto della Enciclopedia Italiana.

    Google Scholar 

  • Gabriel-Marie (F.G. -M.), Frère. 1920. Exercices de géométrie comprenant l’exposé des méthodes géométriques et 2000 questions résolues, 6th ed. Tours/Paris: Mame/de Gigoro.

    Google Scholar 

  • Gispert, Hélène. 2009. Two mathematics reforms in the context of twentieth century France: Similarities and differences. International journal for the history of Mathematics Education 4(1): 43–49.

    Google Scholar 

  • Godfrey, Charles, and Arthur W. Siddons. 1903. Elementary geometry: Practical and theoretical. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Grattan-Guinness, Ivor. 2005. The ecole polytechnique, 1794–1850: Differences over educational purpose and teaching practice. American Mathematical Monthly 112: 235–250.

    CrossRef  MathSciNet  Google Scholar 

  • Günther, Siegmund. 1900. Le développement historique de l’enseignement mathématique en Allemagne. L’Enseignement Mathématique 2: 237–265.

    MATH  Google Scholar 

  • Halsted, George B. 1904. Rational geometry: A text book for the science of space. New York: Wiley.

    Google Scholar 

  • Hayward, James. 1829. Elements of geometry upon the inductive method to which is added an introduction to descriptive geometry. Cambridge/Philadelphia: Hiliard and Brown/Uriah Hunt.

    Google Scholar 

  • Henrici, Julius, and Peter Treutlein. 1881–1883. Lehrbuch der Elementar Geometrie, vol. 3. Leipzig: B. G. Teubner.

    Google Scholar 

  • Hon, Giora, and Bernard Goldstein. 2005. Legendre’s revolution (1794): The definition of symmetry in solid geometry. Archives for History of Exact Sciences 59(2): 107–155.

    CrossRef  MATH  MathSciNet  Google Scholar 

  • Houel, Jules. 1867. Essai critique sur les principes fondamentaux de la géométrie élémentaire. Paris: Gauthier-Villars.

    Google Scholar 

  • Howson, Geoffrey. 1982. A history of mathematics education in England. New York: Cambridge University Press.

    CrossRef  MATH  Google Scholar 

  • Howson, Geoffrey. 2003. Geometry: 1950–70. In One hundred years of L’Enseignement Mathématique, ed. Daniel Coray, Fulvia Furinghetti, Hélène Gispert, Bernard Hodgson, and Gert Schubring, 115–131. Monographie vol. 39. Geneva: L’Enseignement Mathématique.

    Google Scholar 

  • Howson, Geoffrey, Christine Keitel, and Jeremy Kilpatrick. 1981. Curriculum development in mathematics. Cambridge: Cambridge University Press.

    CrossRef  Google Scholar 

  • Kaestner, Abraham Gotthelf. 1710. Anfangsgründe der Arithmetik, Geometrie, ebenen und sphärischen Trigonometrie und Perspective. Göttingen: Vandenhoek & Ruprecht Johann Achille.

    Google Scholar 

  • Kastanis, Iason, and Nikos Kastanis. 2006. The transmission in Greek education 1800–1840, from individual initiatives to institutionalization. Paedagogica Historica XVII(4–5): 515–534.

    CrossRef  Google Scholar 

  • Klein, Felix. 1909. Elementarmathematik vom höheren Standpunkte aus, Teil II: Geometrie. Leipzig: Teubner.

    MATH  Google Scholar 

  • Klein, Felix, and Rudolf Schimmack. 1907. Vorträge über den mathematischen Unterricht an den höheren Schulen. Leipzig: B. G. Teubner.

    MATH  Google Scholar 

  • Lacroix, Sylvestre-François. 1798. Traité élémentaire de trigonométrie rectiligne et sphérique et d’application de l’algèbre à la géométrie. Paris: Duprat.

    Google Scholar 

  • Lacroix, Silvestre-François. 1799. Éléments de géométrie, à l’usage de l’École Centrale des Quatre-Nations. Paris: Duprat.

    Google Scholar 

  • Laisant, Charles-Ange. 1907. La Mathématique, 2nd ed. Paris: Gauthier-Villars.

    MATH  Google Scholar 

  • Lamé, Gabriel. 1818. Examen des différentes méthodes pour résoudre les problèmes de géométrie. Paris: Bachelier.

    MATH  Google Scholar 

  • Lamy, Bernard. 1685. Éléments de géométrie ou de la mesure du corps. Paris: Pralard.

    Google Scholar 

  • Lamy, Jérôme. 2006. Le problème des longitudes en mer dans les traités d’hydrographie des jésuites aux XVIIe et XVIIIe siècles. Histoire et mesure XXI(2): 95–120.

    CrossRef  Google Scholar 

  • Lazzeri, Giulio, and Anselmo Bassani. 1891. Elementi di geometria. Livorno: Giusti.

    Google Scholar 

  • Lebossé, Camille, and Corentin Hémery. 1962. Arithmétique, algèbre et géométrie Classe de quatrième. Paris: Nathan.

    Google Scholar 

  • Legendre, Adrien-Marie. 1794. Éléments de géométrie. Paris: Firmin Dodot.

    Google Scholar 

  • Legendre, Adrien-Marie. 1823. Éléments de géométrie. Paris: Firmin Didot.

    Google Scholar 

  • Menghini, Marta. 1996. The Euclidean method in geometry teaching. In History of mathematics and education: Ideas and experiences, ed. H. Niels Jahnke, H. Norbert Knoche, and Michael Otte, 195–212. Göttingen: Vanderhoeck & Ruprecht.

    Google Scholar 

  • Menghini, Marta. 2006. The role of projective geometry in Italian education and institutions at the end of the 19th century. International Journal for the History of Mathematics Education 1: 35–55.

    Google Scholar 

  • Méray, Charles. 1874. Nouveaux éléments de geometrie. Paris: F. Savy.

    Google Scholar 

  • Méray, Charles. 1903. Nouveaux éléments de géométrie. Dijon: Jobard.

    Google Scholar 

  • Milliet Dechalles, Claude François. 1682. Les Elements d’Euclide. Paris: Estienne Michallet.

    Google Scholar 

  • Mocnik, Franz [Ritter von]. 1846. Lehrbuch der Geometrie. Wien: Schulbücher-Verschl.-Admin.

    Google Scholar 

  • Moktefi, Amirouche. 2011. Geometry: The Euclid debate. In Mathematics in Victorian Britain, ed. Raymond Flood, Adrian Rice, and Robin Wilson, 320–336. Oxford: Oxford University Press.

    Google Scholar 

  • Monge, Gaspard. 1799. Géométrie descriptive; leçons données aux Ecoles normales. Paris: Baudouin.

    Google Scholar 

  • Montessori, Maria. 1934. Psico Geometría: el estudio de la geometría basado en la psicología infantil. Barcelona: Araluce.

    Google Scholar 

  • Moore, Eliakim Hastings. 1903. On the foundations of mathematics, 402–424. IX: Bulletin of the American Mathematical Society.

    Google Scholar 

  • Moyon, Marc. 2008. La géométrie pratique en Europe en relation avec la tradition arabe, l’exemple du mesurage et du découpage: Contribution à l’étude des mathématiques médiévales. Lille. Thesis of the University of Lille I.

    Google Scholar 

  • OECE. 1961. Mathématiques nouvelles. Paris: OECE. (English ed.): OECE. 1961. New thinking in school mathematics. Paris: OECE.

    Google Scholar 

  • OECE. 1962. Un programme moderne de mathématiques pour l’enseignement secondaire. Paris: OECE. (English ed.): OECE. 1962. Synopses for modern secondary school mathematics. Paris: OEEC.

    Google Scholar 

  • Pardies, Ignace-Gaston. 1671. Élémens de géométrie. Paris: Mabre-Cramoisy.

    Google Scholar 

  • Paul, Matthias. 1980. Gaspard Monges “Geometrie Descriptive” und die Ecole Polytechnique, Materialien und Studien Band, vol. 17. Bielefeld: Institut für Didaktik der Mathematik.

    Google Scholar 

  • Pepe, Luigi. 2004. Insegnamenti matematici e libri elementari nella prima metà dell’ Ottocento: modelli francesi ed esperienze italiane. Pisa: Domus Galileiana.

    Google Scholar 

  • Perry, John. 1901. The teaching of mathematics. Nature 63: 317–320.

    Google Scholar 

  • Petersen, Julius. 1879. Methods and Theories for the Solution of Geometrical Constructions Applied to 410 Problems. Trans. S. Haagensen. Copenhagen: Host.

    Google Scholar 

  • Piaget, Jean, and Barbara Inhelder. 1956. The child’s conception of space. London: Routledge/Kegan Paul.

    Google Scholar 

  • Playfair, John. 1795. Elements of geometry: Containing the first six books of Euclid, with two books on the geometry of solids. Edinburgh/London: Bell & Bradfute/G. G. & J. Robinson.

    Google Scholar 

  • Pomeroy, Ralf. 1836. The engineer’s Practical Elements. Philadelphia: Hogan & Thompson.

    Google Scholar 

  • Rickey, Frederick, and Amy Shell-Gellash. 2004. 201 years of mathematics at West-Point. In West Point: Two centuries and beyond, ed. Lance Betros. Abilene: McWhiney Foundation Press.

    Google Scholar 

  • Roguet, Charles. 1854. Leçons de géométrie analytiques à deux ou trios dimensions. Paris: Carilian-Gœury et Dalmont.

    Google Scholar 

  • Romano, Antonella. 2006. Teaching mathematics in Jesuit schools. In The Jesuits II: Cultures, sciences and the arts, 1540–1773, eds. John Maley, et al., 355–370. Toronto: University of Toronto Press.

    Google Scholar 

  • Romera-Lebret, Pauline. 2009. Teaching new geometrical methods with an ancient figure in the nineteenth and twentieth centuries: The new triangle geometry in textbooks in Europe and USA (1888–1952). In Dig where you stand, ed. Kristin Bjarnadottir, Fulvia Furinghetti, and Gert Schubring, 167–180. Reykjavik: University of Iceland.

    Google Scholar 

  • Rouché, Eugene, and Charles de Comberousse. 1883. Traité de Géométrie plane; conforme aux programmes officiels renfermant un tres grand nombre d’exercices et plusieurs appendices consacres a l’exposition des principales methodes de la geometrie moderne. Paris: Gauthier-Villars.

    Google Scholar 

  • Salmon, George. 1855. A treatise on conic sections: Containing an account of some of the most important modern algebraic and geometric methods, Revised and enlarged, vol. 3. London: Longman.

    Google Scholar 

  • Sannia, Achille, and Enrico D’Ovidio. 1869. Elementi di Geometria. Napoli: Pellerano.

    Google Scholar 

  • Schellbach, Karl Heinrich. 1843. Die Kegelschnitte, für den Gebrauch an Gymnasien und Realschulen. Berlin: Simion.

    Google Scholar 

  • Schimmack, Rudolf. 1911. Die Entwicklung der mathematischen Unterrichts-Reform in Deutschland. Leipzig/Berlin: B.G. Teubner.

    Google Scholar 

  • Schönbeck, Jürgen. 1994. Der mathematikdidaktiker Peter Treutlein. In Der Wandel in Lehren und Lernen von Mathematik und Naturwissenschaften, Bd. 1, eds. Jürgen Schönbeck, Klaus Volkert, and Horst Struve, 50–72. Weinheim: Deutscher Studien Verlag.

    Google Scholar 

  • Schubring, Gert. 1987. On the methodology of analysing historical textbooks: Lacroix as textbook author. For the learning of mathematics 7: 41–51.

    Google Scholar 

  • Schubring, Gert. 1989. Pure and applied mathematics in divergent institutional settings in Germany: The role and impact of Felix Klein. In The history of modern mathematics, vol. II, eds. David Rowe and John McCleary, 171–220. London/San Diego: Academic.

    Google Scholar 

  • Schubring, Gert. 2007. La diffusion internationale de la géométrie de Legendre: différentes visions des mathématiques: Raisons – Comparaisons – Éducations. La Revue française d’éducation comparée 2: 31–54.

    Google Scholar 

  • Sime, Mary. 1973. Implications of the work of Piaget in the training of students to teach primary mathematics. In Developments in mathematical education (Proceedings of ICME-2, Exeter 1972), ed. Geoffrey Howson, 272–282. Cambridge: Cambridge University Press.

    Google Scholar 

  • Simon, Max. 1906. Über die Entwicklung der Elementar-Geometrie im XIX Jahrhundert. Leipzig: Teubner.

    Google Scholar 

  • Simons, Lao. 1931. The influence of French mathematicians at the end of the eighteen century upon the teaching of mathematics in American colleges. Isis 15(1): 104–123.

    CrossRef  MATH  Google Scholar 

  • Siu Man Keung. 2009. Mathematics education in East Asia from antiquity to modern times. In Dig where you stand, ed. Kristin Bjarnadottir, Fulvia Furinghetti, and Gert Schubring, 197–208. Reykjavik: University of Iceland.

    Google Scholar 

  • Smith, David Eugene. 1912. Intuition and experiment in mathematical teaching in the secondary schools. L’Enseignement Mathématique 14: 507–534.

    Google Scholar 

  • Smith, David Eugene. 1913. The teaching of elementary mathematics. New York: Macmillan.

    Google Scholar 

  • Struve, Horst. 1984. Zur diskussion um die abbildungsgeometrie. Zentralblatt für Didaktik der Mathematik 2: 69–74.

    Google Scholar 

  • Sturm, Christopher. 1699. Mathesis Juvenilis. Nürnberg: apud J. Hoffmanni & E. Streckii viduas.

    Google Scholar 

  • Tacquet, André. 1654. Elementa geometriae planae ac solidae quibus accedunt selecta ex Archimede theoremata. Antwerp: apud Iacobum Meursium.

    Google Scholar 

  • The Nuffield Mathematics Project. 1967. Shape and size. London: John Murray Publishers.

    Google Scholar 

  • Thibault, M. 1844. Éléments de géométrie, par Eugène Catalan, répétiteur à l’École Polytechnique. Nouvelles annales de mathématiques 3: 378–387.

    Google Scholar 

  • Treutlein, Peter. 1907. Mathematische aufgaben aus den reifeprüfungen der badischen mittelschulen (gymnasien, realgymnasien, oberrealschulen). Leipzig/Berlin: Teubner.

    MATH  Google Scholar 

  • Treutlein, Peter. 1911. Der geometrische anschauungsunterricht als unterstufe eines zweistufigen geometrischen unterrichts an unseren höheren schulen. Leipzig: B. G. Teubner.

    Google Scholar 

  • van Hiele, Pierre, and Dina van Hiele-Geldof. 1958. A method of initiation into geometry at secondary schools. In Report on methods of initiation into geometry, ed. Hans Freudenthal, 67–80. Groningen: J. B. Wolters.

    Google Scholar 

  • Veronese, Giuseppe. 1897. Elementi di geometria: ad uso dei licei e degli istituti tecnici; trattati con la collaborazione del prof. Paolo Gazzaniga. Verona: Fratelli Drucker.

    Google Scholar 

  • Walker Stamper, Alva. 1909. A history of the teaching of elementary geometry, with reference to present-day problems. New York: Columbia University.

    Google Scholar 

  • Wilson, James Maurice. 1868. Euclide come testo di geometria elementare. Giornale di matematiche VI: 361–368.

    Google Scholar 

  • Young, John Radford. 1827. Elements of geometry with notes. London: Souter.

    Google Scholar 

  • Young, Jacob W.A. 1920. The teaching of mathematics in the elementary and the secondary school. New York: Green.

    Google Scholar 

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Barbin, E., Menghini, M. (2014). History of Teaching Geometry. In: Karp, A., Schubring, G. (eds) Handbook on the History of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9155-2_23

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