Abstract
Despite the wide interest in combining mathematics education and the history of mathematics, there are grave and fundamental problems in this effort. The main difficulty is that while one wants to see historical topics in the classroom or an historical approach in teaching, the commitment to teach the modern mathematics and modern mathematical techniques necessary in thepure and applied sciences forces one either to trivialize history or to distortit. In particular, this commitment forces one to adopt a “Whiggish” approach to the history of mathematics. Two possible resolutions of the difficulty are (1) “radical separation” – putting the history of mathematics on a separate track from the ordinary course of instruction, and (2) “radical accommodation” – turning the study of mathematics into the study of mathematical texts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arcavi, A., Bruckheimer, M. & Ben-Zvi, R.: 1982, ‘Maybe a Mathematics Teacher Can Profit from the Study of the History of Mathematics’, For the Learning of Mathematics 3, 30–37.
Avital, S.: 1995, ‘History of Mathematics Can Help Improve Instruction and Learning’, in F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz (eds.), Learn from the Masters, The Mathematical Association of America, Washington, DC, pp. 3–12.
Barwell, M.: 1913, ‘The Advisability of Including some Instruction in the School Course on the History of Mathematics’, The Mathematical Gazette 7, 72–79.
Bernoulli, J.: 1968, Opera Omnia, Vol. II. Georg Olms Verlagsbuchhandlung, Hildesheim.
Boyer, C. B.: 1985, A History of Mathematics, Princeton University Press, Princeton.
Brann, E. T. H.: 1979, Paradoxes of Education in a Republic, The University of Chicago Press, Chicago and London.
Brown, S. I.: 1993, ‘Towards a Pedagogy of Confusion’, in White, pp. 107–122.
Butterfield, H.: 1931/1951, The Whig Interpretation of History, Charles Scribner's Sons, New York.
Corry, L.: 1989, ‘Linearity and Reflexivity in the Growth of Mathematical Knowledge’, Science in Context 3(2), 409–440.
Dedekind, R.: 1901/1963, Essays on the Theory of Numbers, Dover Publications, Inc., New York.
Elkana, Y.: 1978, ‘Two-Tier-Thinking: Philosophical Realism and Historical Relativism’, Social Studies of Science 8, 309–326.
Elkana, Y.: 1981, ‘A Programmatic Attempt at an Anthropology of Knowledge’, in E. Mendelson and Y. Elkana (eds.), Science and Cultures. Sociology of the Sciences, Vol. 5, Reidel, Dordrecht.
Elton, G. R.: 1969, The Practice of History, The Fontanta Library, London and Glasgow (in association with Sydney University Press).
Euler, L.: 1922, Introductio in Analysin Infinitorum, in Opera Omnia, Ser. I, Vol. VII, Teubner Verlag, Leipzig and Berlin.
Fauvel, J.: 1991, ‘Using History in Mathematics Education’, For the Learning of Mathematics 11(2): 3–6.
Fauvel, J. & Gray, J.: 1987, The History of Mathematics: A Reader, The Open University, London.
Freudenthal, G.: 1996, ‘Pluralism or Relativism?’, Science in Context 9: 151–163.
Fried, M. N.: 1998, A New Look of the Geometric Character of Hellenistic Mathematics: The Case of Apollonius, unpublished Ph.D. dissertation, University of Tel-Aviv.
Garner, M.: 1996, ‘The Importance of History in Mathematics Teaching and Learning’, a paper presented at Interface’ 96, Atlanta.
Grattan-Guinness, I.: 1996, ‘Numbers, Magnitudes, Ratios, and Proportions in Euclid's Elements: How Did He Handle Them?’, Historia Mathematica 23, 355–375.
Heath, T. L.: 1926, The Thirteen Books of Euclid's Elements, Translated from the text of Heiberg with Introduction and Commentary, 3 vols, Cambridge University Press, Cambridge (repr., Dover Publications, Inc., New York, 1956).
Katz, V. J.: 1995, ‘Napier's Logarithms Adapted for Today's Classroom’, in F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz (eds.), Learn from the Masters, The Mathematical Association of America, Washington, DC, pp. 49–56.
Katz, V. J.: 1993, ‘Using the History of Calculus to Teach Calculus’, Science & Education 2, 243–249.
Klein, J.: 1965, ‘On Liberal Education’, Lecture delivered March 25, 1965, at the Colloquium held at St. Mary's College, California.
Klein, J.: 1968, Greek Mathematical Thought and the Origin of Algebra, trans. by E. Brann (from ‘Die griechische Logistik und die Entstehung der Algebra’ in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik (Abteilung B: Studien), Vol. 3 (fasc. 1, 1934), pp. 18–105 and Vol. 3 (fasc. 2, 1936), pp. 122–235), The MIT Press, Cambridge, MA.
Kleiner, I.: 1993, ‘Functions: Historical and Pedagogical Aspects’, Science & Education 2, 183–209.
Kooper, A.: 1996, ‘The Historical Development of Mathematics — Its Integration into the Teaching of the Subject in the Upper Grades by Means of Independent Readings by Students' (in Hebrew), Aleh 18, 27–31.
Kragh, H.: 1987, An Introduction to the Historiography of Science, Cambridge University Press, Cambridge.
Lindberg, D. C.: 1992, The Beginnings of Western Science, The University of Chicago Press, Chicago.
National Council of Teachers of Mathematics: 1989, Historical Topics for the Mathematics Classroom, NCTM, Reston, VA.
Ness, H.: 1993, ‘Mathematics; an Integral Part of Our Culture’, in A. M. White (ed.), Essays in Humanistic Mathematics, The Mathematical Association of America, Washington, DC, pp. 49–52.
Neugebauer, O.: 1933, ‘Apollonius-Studien’, Quellen und Studien zur Geschichte der Mathematik. Abteilung B: Studien Band 2, 215–253.
Ricky, V. F.: 1995, ‘My Favorite Ways of Using History in Teaching Calculus’, in F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz (eds.), Learn from the Masters, The Mathematical Association of America, Washington, DC, pp. 123–134.
Sarton, G.: 1957, Six Wings: Men of Science in the Renaissance, Indiana University Press, Bloomington.
Sfard, A.: 1995, ‘The Development of Algebra: Confronting Historical and Psychological Perspectives’, Journal of Mathematics Behavior 14, 15–39.
Swetz, F. J.: 1995, ‘Using Problems from the History of Mathematics in Classroom Instruction’, in F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz (eds.), Learn from the Masters, The Mathematical Association of America, Washington, DC, pp. 25–38.
Swetz, F., Fauvel, J., Bekken, O., Johansson, B. & Katz, V.: 1995, Learn from the Masters, The Mathematical Association of America, Washington, D.C.
Thomaidis, Y.: 1993, ‘Aspects of Negative Numbers in the Early 17th Century: An Approach for Didactic Reasons’, Science & Education 2, 69–86.
Tymoczko, T.: 1993, ‘Humanistic and Utilitarian Aspects of Mathematics’, in A. M. White (ed.), Essays in HumanisticMathematics, The Mathematical Association of America, Washington, DC, pp. 11–14.
Unguru, S.: 1975, ‘On the Need to Rewrite the History of Greek Mathematics’, Archive for History of Exact Sciences 15, 67–114.
Unguru, S.: 1979, ‘History of Ancient Mathematics: Some Reflections of the State of the Art’, Isis 70, 555–565.
Unguru, S. & Fried, M. N.: 1996, ‘On the Synthetic-Geometric Character of Apollonius's Conica’, Mathesis 12, 148–223.
Van der Waerden, B. L.: 1963, Science Awakening, John Wiley & Sons, New York.
Van der Waerden, B. L.: 1976, ‘Defence of a ‘shocking’ Point of View’, Archive for History of Exact Sciences 15, 199–210.
White, A. M., ed.: 1993, Essays in Humanistic Mathematics, The Mathematical Association of America, Washington, D.C.
Youschkevitch, A. P.: 1976, ‘The Concept of Function up to the Middle of the 19th Century’, Archive for History of Exact Sciences 16, 37–88.
Zeuthen, H. G.: 1886, Die Lehre von den Kegelschnitten im Altertum, Kopenhagen (repr., Georg Olms Verlagsbuchhandlung, Hildesheim, 1966).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fried, M.N. Can Mathematics Education and History of Mathematics Coexist?. Science & Education 10, 391–408 (2001). https://doi.org/10.1023/A:1011205014608
Issue Date:
DOI: https://doi.org/10.1023/A:1011205014608