History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers
 Kathleen Michelle Clark
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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.
Inside
Within this Article
 Introduction
 Rationale
 Relevant literature
 Conceptual framework
 Description of the context
 Data analysis
 Discussion
 References
 References
Other actions
 Arcavi, A., & Isoda, M. (2007). Learning to listen: From historical sources to classroom practice. Educational Studies in Mathematics, 66(2), 111–129. CrossRef
 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. CrossRef
 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.
 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. CrossRef
 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.
 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.
 Conference Board for the Mathematical Sciences. (2001). The mathematical education of teachers: Vol. 11. Issues in mathematics education. Providence, RI: American Mathematical Society.
 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. Basingstoke: Macmillan Education.
 Fauvel, J., & van Maanen, J. (Eds.). (2000). History in mathematics education—The ICMI study. Dordrecht: Kluwer Academic.
 Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science Education, 10(4), 391–408. CrossRef
 Furinghetti, F. (1997). History of mathematics, mathematics education, school practice: Case studies linking different domains. For the Learning of Mathematics, 17(1), 55–61.
 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. CrossRef
 Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131–143. CrossRef
 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.
 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.
 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. CrossRef
 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.
 Katz, V. J., & Michalowicz, K. D. (Eds.). (2005). Historical modules for the teaching and learning mathematics. Washington, DC: Mathematical Association of America.
 Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
 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, CERME7. Poland: Rzeszów.
 Liu, P.H. (2003). Do teachers need to incorporate the history of mathematics in their teaching? Mathematics Teacher, 96(6), 416–421.
 Moritz, R. E. (1914). Memorabilia mathematica; or, the philomath’s quotationbook. New York: The Macmillan Company.
 National Council for the Accreditation of Teacher Education. (2003). NCATE/NCTM Program standards: Programs for initial preparation of mathematics teachers. Washington, DC: Author.
 O’Connor, J., & Robertson, E. F. (1999). AlKhwarizmi biography. Retrieved on February 1, 2011 from http://wwwhistory.mcs.stand.ac.uk/Biographies/AlKhwarizmi.html.
 Pimm, D. (1983). Why the history and philosophy of mathematics should not be rated x. For the Learning of Mathematics, 3(1), 12–15.
 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.
 Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks: Sage Publications.
 Title
 History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers
 Journal

Educational Studies in Mathematics
Volume 81, Issue 1 , pp 6784
 Cover Date
 20120901
 DOI
 10.1007/s106490119361y
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 History of mathematics
 AlKhwarizmi
 Mathematical knowledge for teaching
 Algebra
 Quadratic equations
 Completing the square
 Mathematics teacher preparation
 Industry Sectors
 Authors

 Kathleen Michelle Clark ^{(1)}
 Author Affiliations

 1. Florida State University, Tallahassee, FL, USA