Abstract
Historical texts tell us much about how mathematical concepts and techniques were conceived and evolved. But they can also tell us even more. Usually, their contents embody a pedagogy, specific organizational forms and methods used for teaching mathematics. This article isolates and examines several particular pedagogical techniques: the use of an instructional discourse; a logical sequencing of mathematical problems and exercises and employment of visual aids, evident in historical works. It concludes that much of present day mathematical pedagogy evolved from distant historical antecedents.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ang, T.S.: 1977, ‘Chinese computation with counting rods’,Papers on Chinese Studies, University of Malaya1, 97–109.
Archibald, R.C.: 1950, ‘The first translation of Euclid's Elements into English and its source’,The American Mathematical Monthly 57, 443–452.
Billingsley, H.M.: 1570,The Elements of Geometrie of the Most Auncient Philosopher Euclide o Megara, John Day, London.
Burton, D.M.: 1988,The History of Mathematics, Wm. C. Brown Publishers, Dubuque, IA.
Caratini, R.: 1957, ‘Quadrature du cercle et quadrature des lunules en Mesopotamie’,Revue d'assyriologie et d'archeologie orientale 51, 11–20.
Chace, A.B.: 1967,The Rind Mathematical Papyrus, National Council of Mathematics, Reston, VA.
Easton, J.B.: 1964, ‘A Tudor Euclid’,Scripta Mathematica 27, 339–355.
Freydberg, B.: 1993, ‘Geometry, insight and ignorance in Plato's Meno’,Mathematical Connections 2, 33–39.
Gadd, C.J.: 1922, ‘Forms and colours’,Revue d'assyriologie et d'archeologie orientale 19, 149–159.
Gillon, B.S.: 1976, ‘Introduction, translation and discussion of Chao Chum-Ch'ing's Notes to the Diagrams of Short Legs and Long Legs of Squares and Circles’,Historia Mathematica 4, 253–93.
Howson, G.: 1982,A History of Mathematics Education in England, Cambridge University Press, Cambridge.
Johnson, F. and Larkey, S.: 1935, ‘Robert Recorde's mathematical teaching and the anti-Aristotelian movement’,The Huntington Library Bulletin 7 59–87.
Kaplan, E.: 1960,Robert Recorde (c 1510–1558): Studies in the Life and Works of a Tudor Scientist. Ph.D. dissertation, New York University.
Lam, L.Y. and Ang, T.S.: 1992,Tracing the Conception of Arithmetic and Algebra in Ancient China: Fleeting Footsteps, World Scientific, Singapore.
Lieske, G.S.: 1985, ‘Right triangles II’,Mathematics Teacher 78, 498–499.
Needham, J.: 1954,Science and Civilization in China vol. 3, Cambridge University Press, Cambridge.
Neugebauer, O.: 1973,Mathematische Keilschrift-Texte, Springer, Berlin.
Ritter, J.: 1989, ‘Prime numbers’,UNESCO Courier, 12–17.
Saggs, H.W.: 1960, ‘A Babylonian geometrical text’,Revue d'assyriologie et d'archeologie orientale 54, 131–145.
Siu, M.K.: 1993, ‘Proof and pedagogy in ancient China: Examples from Liu Hui's commentary on Jiu Zhang Suan Shu’,Educational Studies in Mathematics 24, 345–357.
Smith, D.E.: 1958,History of Mathematics vol. II, Dover Publications, New York.
Swetz, F.J.: 1993, ‘Right triangle concepts in ancient China: From application to theory,History of Science 31, 421–439.
Swetz, F.J.: 1992,The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China, The Pennsylvania State University Press, University Park, PA.
Swetz, F.J. and Kao, T.I.: 1977,Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China, The Pennsylvania State University Press, University Park, PA.
Van der Waerden, B.L.: 1983,Geometry and Algebra in Ancient Civilizations, Springer, New York.
Van Egmond, W.: 1976,The Commercial Revolution and the Beginnings of Western Mathematics in Renaissance Florence 1300–1500. Ph.D. dissertation, Department of History and Philosophy of Science, Indiana University.
Vogel, K.: 1968,Neun Bucher arithmetischer Technik, F. Vieweg and Son, Braunschweig.
Warmington, E. and Rouse, P.G.: 1961,Great Dialogues of Plato, The New American Library, New York.
Watson, F.: 1909,The Beginnings of the Teaching of Modern Subjects in England, Pitman and Son Ltd., London.
Wilkenfeld, M.: 1985, ‘Right triangle relationships’,Mathematics Teacher 78, 12.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Swetz, F. To know and to teach: Mathematical pedagogy from a historical context. Educ Stud Math 29, 73–88 (1995). https://doi.org/10.1007/BF01273901
Issue Date:
DOI: https://doi.org/10.1007/BF01273901