History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers Article First Online: 11 November 2011 DOI :
10.1007/s10649-011-9361-y

Cite this article as: Clark, K.M. Educ Stud Math (2012) 81: 67. doi:10.1007/s10649-011-9361-y
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 Arcavi, A., & Isoda, M. (2007). Learning to listen: From historical sources to classroom practice.

Educational Studies in Mathematics, 66 (2), 111–129.

CrossRef Google Scholar 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 Google Scholar 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 Google Scholar 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.

Google Scholar Fauvel, J., & Gray, J. (1987).

The history of mathematics: A reader . Basingstoke: Macmillan Education.

Google Scholar Fauvel, J., & van Maanen, J. (Eds.). (2000).

History in mathematics education—The ICMI study . Dordrecht: Kluwer Academic.

Google Scholar Fried, M. N. (2001). Can mathematics education and history of mathematics coexist?

Science Education, 10 (4), 391–408.

CrossRef Google Scholar 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 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 Google Scholar Furinghetti, F. (2007). Teacher education through the history of mathematics.

Educational Studies in Mathematics, 66 (2), 131–143.

CrossRef Google Scholar 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 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 Google Scholar 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 Katz, V. J., & Michalowicz, K. D. (Eds.). (2005).

Historical modules for the teaching and learning mathematics . Washington, DC: Mathematical Association of America.

Google Scholar Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001).

Adding it up: Helping children learn mathematics . Washington, DC: National Academy Press.

Google Scholar 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 Liu, P.-H. (2003). Do teachers need to incorporate the history of mathematics in their teaching?

Mathematics Teacher, 96 (6), 416–421.

Google Scholar Moritz, R. E. (1914).

Memorabilia mathematica; or, the philomath’s quotation-book . New York: The Macmillan Company.

Google Scholar 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 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 .

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 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 Strauss, A., & Corbin, J. (1998).

Basics of qualitative research: Techniques and procedures for developing grounded theory . Thousand Oaks: Sage Publications.

Google Scholar © Springer Science+Business Media B.V. 2011

Authors and Affiliations 1. Florida State University Tallahassee USA