Science & Education

, Volume 10, Issue 4, pp 391–408 | Cite as

Can Mathematics Education and History of Mathematics Coexist?

  • Michael N. Fried

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.

Mathematics education history of mathematics Whiggism sedimentation two-tiered thinking humanistic mathematics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.Google Scholar
  2. 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.Google Scholar
  3. Barwell, M.: 1913, ‘The Advisability of Including some Instruction in the School Course on the History of Mathematics’, The Mathematical Gazette 7, 72–79.Google Scholar
  4. Bernoulli, J.: 1968, Opera Omnia, Vol. II. Georg Olms Verlagsbuchhandlung, Hildesheim.Google Scholar
  5. Boyer, C. B.: 1985, A History of Mathematics, Princeton University Press, Princeton.Google Scholar
  6. Brann, E. T. H.: 1979, Paradoxes of Education in a Republic, The University of Chicago Press, Chicago and London.Google Scholar
  7. Brown, S. I.: 1993, ‘Towards a Pedagogy of Confusion’, in White, pp. 107–122.Google Scholar
  8. Butterfield, H.: 1931/1951, The Whig Interpretation of History, Charles Scribner's Sons, New York.Google Scholar
  9. Corry, L.: 1989, ‘Linearity and Reflexivity in the Growth of Mathematical Knowledge’, Science in Context 3(2), 409–440.Google Scholar
  10. Dedekind, R.: 1901/1963, Essays on the Theory of Numbers, Dover Publications, Inc., New York.Google Scholar
  11. Elkana, Y.: 1978, ‘Two-Tier-Thinking: Philosophical Realism and Historical Relativism’, Social Studies of Science 8, 309–326.Google Scholar
  12. 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.Google Scholar
  13. Elton, G. R.: 1969, The Practice of History, The Fontanta Library, London and Glasgow (in association with Sydney University Press).Google Scholar
  14. Euler, L.: 1922, Introductio in Analysin Infinitorum, in Opera Omnia, Ser. I, Vol. VII, Teubner Verlag, Leipzig and Berlin.Google Scholar
  15. Fauvel, J.: 1991, ‘Using History in Mathematics Education’, For the Learning of Mathematics 11(2): 3–6.Google Scholar
  16. Fauvel, J. & Gray, J.: 1987, The History of Mathematics: A Reader, The Open University, London.Google Scholar
  17. Freudenthal, G.: 1996, ‘Pluralism or Relativism?’, Science in Context 9: 151–163.Google Scholar
  18. 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.Google Scholar
  19. Garner, M.: 1996, ‘The Importance of History in Mathematics Teaching and Learning’, a paper presented at Interface’ 96, Atlanta.Google Scholar
  20. Grattan-Guinness, I.: 1996, ‘Numbers, Magnitudes, Ratios, and Proportions in Euclid's Elements: How Did He Handle Them?’, Historia Mathematica 23, 355–375.Google Scholar
  21. 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).Google Scholar
  22. 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.Google Scholar
  23. Katz, V. J.: 1993, ‘Using the History of Calculus to Teach Calculus’, Science & Education 2, 243–249.Google Scholar
  24. Klein, J.: 1965, ‘On Liberal Education’, Lecture delivered March 25, 1965, at the Colloquium held at St. Mary's College, California.Google Scholar
  25. 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.Google Scholar
  26. Kleiner, I.: 1993, ‘Functions: Historical and Pedagogical Aspects’, Science & Education 2, 183–209.Google Scholar
  27. 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.Google Scholar
  28. Kragh, H.: 1987, An Introduction to the Historiography of Science, Cambridge University Press, Cambridge.Google Scholar
  29. Lindberg, D. C.: 1992, The Beginnings of Western Science, The University of Chicago Press, Chicago.Google Scholar
  30. National Council of Teachers of Mathematics: 1989, Historical Topics for the Mathematics Classroom, NCTM, Reston, VA.Google Scholar
  31. 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.Google Scholar
  32. Neugebauer, O.: 1933, ‘Apollonius-Studien’, Quellen und Studien zur Geschichte der Mathematik. Abteilung B: Studien Band 2, 215–253.Google Scholar
  33. 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.Google Scholar
  34. Sarton, G.: 1957, Six Wings: Men of Science in the Renaissance, Indiana University Press, Bloomington.Google Scholar
  35. Sfard, A.: 1995, ‘The Development of Algebra: Confronting Historical and Psychological Perspectives’, Journal of Mathematics Behavior 14, 15–39.Google Scholar
  36. 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.Google Scholar
  37. Swetz, F., Fauvel, J., Bekken, O., Johansson, B. & Katz, V.: 1995, Learn from the Masters, The Mathematical Association of America, Washington, D.C.Google Scholar
  38. Thomaidis, Y.: 1993, ‘Aspects of Negative Numbers in the Early 17th Century: An Approach for Didactic Reasons’, Science & Education 2, 69–86.Google Scholar
  39. 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.Google Scholar
  40. Unguru, S.: 1975, ‘On the Need to Rewrite the History of Greek Mathematics’, Archive for History of Exact Sciences 15, 67–114.Google Scholar
  41. Unguru, S.: 1979, ‘History of Ancient Mathematics: Some Reflections of the State of the Art’, Isis 70, 555–565.Google Scholar
  42. Unguru, S. & Fried, M. N.: 1996, ‘On the Synthetic-Geometric Character of Apollonius's Conica’, Mathesis 12, 148–223.Google Scholar
  43. Van der Waerden, B. L.: 1963, Science Awakening, John Wiley & Sons, New York.Google Scholar
  44. Van der Waerden, B. L.: 1976, ‘Defence of a ‘shocking’ Point of View’, Archive for History of Exact Sciences 15, 199–210.Google Scholar
  45. White, A. M., ed.: 1993, Essays in Humanistic Mathematics, The Mathematical Association of America, Washington, D.C.Google Scholar
  46. 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.Google Scholar
  47. Zeuthen, H. G.: 1886, Die Lehre von den Kegelschnitten im Altertum, Kopenhagen (repr., Georg Olms Verlagsbuchhandlung, Hildesheim, 1966).Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Michael N. Fried
    • 1
  1. 1.The Center for Science and Technology EducationBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations