Educational Studies in Mathematics

, Volume 81, Issue 1, pp 67–84 | Cite as

History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers

Article

Abstract

The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.

Keywords

History of mathematics Al-Khwarizmi Mathematical knowledge for teaching Algebra Quadratic equations Completing the square Mathematics teacher preparation 

References

  1. Arcavi, A., & Isoda, M. (2007). Learning to listen: From historical sources to classroom practice. Educational Studies in Mathematics, 66(2), 111–129.CrossRefGoogle Scholar
  2. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  3. Boero, P., & Guala, E. (2008). Development of mathematical knowledge and beliefs of teachers: The role of cultural analysis of the content to be taught. In P. Sullivan and T. Wood (Eds.), The international handbook of mathematics teacher education, Volume 1: Knowledge and beliefs in mathematics teaching and teaching development (pp. 223–244). Rotterdam, the Netherlands: Sense.Google Scholar
  4. Charalambous, C. Y., Panaoura, A., & Phillippou, G. (2009). Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: Insights from evaluating a teacher education program. Educational Studies in Mathematics, 71(2), 161–180.CrossRefGoogle Scholar
  5. Clark, K. M. (2008a). Heeding the call: History of mathematics and the preparation of secondary mathematics teachers. In F. Arbaugh & P. M. Taylor (Eds.), Inquiry into mathematics teacher education: Association of mathematics teacher educators (AMTE) monograph series, Volume 5 (pp. 85–95). San Diego: AMTE.Google Scholar
  6. Clark, K. (2008b). Reflection and revision: First experiences with a “using history” course. In E. Barbin, N. Stehlikova, & C. Tzanakis (Eds.), History and epistemology in mathematics education: Proceedings of the fifth European summer university (pp. 343–351). Prague: Vydavatelsky Press.Google Scholar
  7. Conference Board for the Mathematical Sciences. (2001). The mathematical education of teachers: Vol. 11. Issues in mathematics education. Providence, RI: American Mathematical Society.Google Scholar
  8. Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3–6.Google Scholar
  9. Fauvel, J., & Gray, J. (1987). The history of mathematics: A reader. Basingstoke: Macmillan Education.Google Scholar
  10. Fauvel, J., & van Maanen, J. (Eds.). (2000). History in mathematics education—The ICMI study. Dordrecht: Kluwer Academic.Google Scholar
  11. Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science Education, 10(4), 391–408.CrossRefGoogle Scholar
  12. Furinghetti, F. (1997). History of mathematics, mathematics education, school practice: Case studies linking different domains. For the Learning of Mathematics, 17(1), 55–61.Google Scholar
  13. Furinghetti, F. (2000). The history of mathematics as a coupling link between secondary and university teaching. International Journal of Mathematical Education in Science and Technology, 31(1), 43–51.CrossRefGoogle Scholar
  14. Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131–143.CrossRefGoogle Scholar
  15. Heiede, T. (1996). History of mathematics and the teacher. In R. Calinger (Ed.), Vita mathematica: Historical research and integration with teaching (pp. 231–243). Washington, DC: Mathematical Association of America.Google Scholar
  16. Hoepfl, M. C. (1997). Choosing qualitative research: A primer of technology education researchers. Journal of Technology Education, 9(1). Retrieved January 6, 2010 from http://scholar.lib.vt.edu/ejournals/JTE/v9n1/hoepfl.html.
  17. Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in teaching mathematics education. Educational Studies in Mathematics, 71(3), 235–261.CrossRefGoogle Scholar
  18. Katz, V. J. (1997). Some ideas on the use of history in the teaching of mathematics. For the Learning of Mathematics, 17(1), 62–63.Google Scholar
  19. Katz, V. J., & Michalowicz, K. D. (Eds.). (2005). Historical modules for the teaching and learning mathematics. Washington, DC: Mathematical Association of America.Google Scholar
  20. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.Google Scholar
  21. Kjeldsen, T. H. (2001). Uses of history in mathematics education: Development of learning strategies and historical awareness. Paper presented at Working Group 12: History in Mathematics Education, CERME-7. Poland: Rzeszów.Google Scholar
  22. Liu, P.-H. (2003). Do teachers need to incorporate the history of mathematics in their teaching? Mathematics Teacher, 96(6), 416–421.Google Scholar
  23. Moritz, R. E. (1914). Memorabilia mathematica; or, the philomath’s quotation-book. New York: The Macmillan Company.Google Scholar
  24. National Council for the Accreditation of Teacher Education. (2003). NCATE/NCTM Program standards: Programs for initial preparation of mathematics teachers. Washington, DC: Author.Google Scholar
  25. O’Connor, J., & Robertson, E. F. (1999). Al-Khwarizmi biography. Retrieved on February 1, 2011 from http://www-history.mcs.st-and.ac.uk/Biographies/Al-Khwarizmi.html.
  26. Pimm, D. (1983). Why the history and philosophy of mathematics should not be rated x. For the Learning of Mathematics, 3(1), 12–15.Google Scholar
  27. Siu, M.-K. (2000). The ABCD of using history of mathematics in the (undergraduate) classroom. In V. Katz (Ed.), Using history to teach mathematics: An international perspective (pp. 3–9). Washington, DC: Mathematical Association of America.Google Scholar
  28. Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks: Sage Publications.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Florida State UniversityTallahasseeUSA

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