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Effects of using history as a tool to teach mathematics on students’ attitudes, anxiety, motivation and achievement in grade 11 classrooms

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Abstract

For decades, educators have advocated using history of mathematics in mathematics classrooms. Empirical research on the efficacy of this practice, however, is scarce. A quasi-experiment was used to investigate the effects of using history as a tool to teach mathematics on grade 11 students’ mathematics achievement. Effects in three affective domains (attitudes, anxiety, and motivation) were also measured. Four classes from a school in Singapore participated in this quasi-experiment. The experimental group (n = 51) and control group (n = 52) were each made up of two classes. Results indicated that using history as a tool to teach mathematics had a significant positive effect on students’ mathematics achievement, in an initial posttest and in two retention tests taken 4 months and 1 year, respectively, after the last intervention session. Significant positive effects were also found on two subscales within the affective domain variables (perceived value of mathematics and introjection, a type of extrinsic motivation), but only at a posttest administered midway through the study. These results suggest that using history in mathematics classrooms have both immediate short- and long-term effects on students’ achievement, but only short-term positive effects in the affective domains. These results were discussed using qualitative feedback obtained from the participants of this study.

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References

  • Akinsola, M. K., & Olowojaiye, F. B. (2008). Teacher instructional methods and student attitudes towards mathematics. International Electronic Journal of Mathematics Education, 3(1), 60–73.

    Google Scholar 

  • Arcavi, A., & Bruckheimer, M. (2000). Didactical uses of primary sources from the history of mathematics. Themes in Education, 1, 55–74.

    Google Scholar 

  • Arcavi, A., & Isoda, M. (2007). Learning to listen: From historical sources to classroom practice. Educational Studies in Mathematics, 66(2), 111–129.

  • Berlyne, D. E. (1965). Curiosity and education. In J. D. Krumboltz (Ed.), Learning and the educational process (pp. 67–89). Chicago: Rand McNally.

    Google Scholar 

  • Bidwell, J. K. (1993). Humanize your classroom with the history of mathematics. Mathematics Teacher, 86(6), 461–464.

    Google Scholar 

  • Black, M. (2001). Achilles and the tortoise. In W. C. Salmon (Ed.), Zeno’s Paradoxes (pp. 67–81). Indianapolis: Hackett Publishing.

    Google Scholar 

  • Bolzano, B. (1950). Paradoxes of the infinite. New Haven: Yale University Press.

    Google Scholar 

  • Burton, L. (1998). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37(2), 121–143.

  • Cajori, F. (1923). The history of notations of the calculus. Annals of Mathematics, 25(1), 1–46.

    Article  Google Scholar 

  • Calinger, R. (Ed.). (1996). Vita mathematica: Historical research and integration with teaching. Washington, DC: MAA.

  • Chamberlin, S. A. (2010). A review of instruments created to assess affect in mathematics. Journal of Mathematics Education, 3(1), 167–182.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Clark, K. M. (2012). History of mathematics: Illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educational Studies in Mathematics, 81, 67–84.

    Article  Google Scholar 

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale: Erlbaum.

    Google Scholar 

  • Coolidge, J. L. (1949). The story of the binomial theorem. The American Mathematical Monthly, 56(3), 147–157.

    Article  Google Scholar 

  • Crowe, M. J. (1994). A history of vector analysis: The evolution of the idea of a vectorial system. New York: Dover.

    Google Scholar 

  • Deci, E. L. (1972). Intrinsic motivation, extrinsic reinforcement, and inequity. Journal of Personality and Social Psychology, 22, 113–120.

    Article  Google Scholar 

  • Deci, E. L. (1975). Intrinsic motivation. New York: Plenum.

    Book  Google Scholar 

  • Dennis, D., & Addington, S. (2010). Mathematical Intentions. Retrieved March 23, 2013 from http://quadrivium.info/MathInt/Notes/NewtonBinomial.pdf.

  • Dittrich, A. B. (1973). An experiment in teaching the history of mathematics. Mathematics Teacher, 66(1), 35–37.

    Google Scholar 

  • Ernest, P. (1994). History, mathematics and education. In P. Ernest (Ed.), Constructing mathematical knowledge: Epistemology and mathematics education (pp. 237–239). Washington, DC: Falmer.

    Google Scholar 

  • Evans, J. (2001). Adults’ mathematical thinking and emotions: A study of numerate practices. New York: Routledge.

    Google Scholar 

  • Fairchild, A. J., Horst, S. J., Finney, S. J., & Barron, K. E. (2005). Evaluating existing and new validity evidence for the academic motivation scale. Contemporary Educational Psychology, 30, 331–358.

    Article  Google Scholar 

  • Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3–6.

    Google Scholar 

  • Fauvel, J., & van Maanen, J. (Eds.). (2002). History in mathematics education: The ICMI study. Dordrecht: Kluwer.

    Google Scholar 

  • Fennema, E., & Sherman, J. A. (1976). Fennema-sherman mathematics attitudes scales: Instruments designed to measure attitudes toward the learning of mathematics by males and females. Journal for Research in Mathematics Education, 7(5), 324–326.

    Article  Google Scholar 

  • Fowler, D. (1991). Perils and pitfalls of history. For the Learning of Mathematics, 11(2), 15–16.

    Google Scholar 

  • Freudenthal, H. (1991). Revisiting mathematics education: The China lectures. Dordrecht: Kluwer.

    Google Scholar 

  • Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science and Education, 10(4), 391–408.

    Article  Google Scholar 

  • Fried, M. N. (2014). History of mathematics and mathematics education. In M. Matthews (Ed.), History, philosophy and science teaching handbook (Vol. I, pp. 669–705). New York: Springer.

    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.

    Article  Google Scholar 

  • Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131–143.

    Article  Google Scholar 

  • Ginsburg, D., Groose, B., Taylor, J., Vernescu, B. (2015). James Gregory’s infinite series for arctan. In The history of the calculus and the development of computer algebra systems. Retrieved March 22, 2013, from http://www.math.wpi.edu/IQP/BVCalcHist/calc3.html#_Toc407004361.

  • Ginsburg, D., Groose, B., Taylor, J., Vernescu, B. (2015). History of the integral from the 17th century. In The history of the calculus and the development of computer algebra systems. Retrieved March 22, 2013, from http://www.math.wpi.edu/IQP/BVCalcHist/calc1.html#_Toc407004348.

  • Gjertsen, D. (1986). The Newton handbook. New York: Routledge & Kegan Paul.

    Google Scholar 

  • Gottfried, A. E. (1982). Relationships between academic intrinsic motivation and anxiety in children and young adolescents. Journal of School Psychology, 20(3), 205–215.

    Article  Google Scholar 

  • Green, T. F. (1971). The activities of teaching. New York: McGraw Hill Book Company.

    Google Scholar 

  • Grouzet, M. E., Otis, N., & Pelletier, L. G. (2006). Longitudinal cross-gender factorial invariance of the academic motivation scale. Structural Equation Modeling, 13(1), 73–98.

    Article  Google Scholar 

  • Gulikers, I., & Blom, K. (2001). ‘A historical angle’, a survey of recent literature on the use and value of history in geometrical education. Educational Studies in Mathematics, 47(2), 223–258.

    Article  Google Scholar 

  • Hayamizu, T. (1997). Between intrinsic and extrinsic motivation: Examination of reasons for academic study based on the theory of internalization. Japanese Psychological Research, 39(2), 98–108.

    Article  Google Scholar 

  • Higdem, R. L. (1959). The method of Archimedes and the method of exhaustion. Grand Forks: University of North Dakota.

    Google Scholar 

  • Ho, W. K. (2008). Using history of mathematics in the teaching and learning of mathematics in Singapore. Paper presented at the 1st RICE, Singapore: Raffles Junior College.

  • Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Dynnikov, C., Furinghetti, F., et al. (2000). The use of original sources in the mathematics classroom. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education—the 10th ICMI study (pp. 291–328). Boston: Kluwer.

  • 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.

    Article  Google Scholar 

  • Jankvist, U. T. (2011). Anchoring students’ metaperspective discussions of history in mathematics. Journal for Research in Mathematics Education, 42(4), 346–385.

    Google Scholar 

  • Jankvist, U. T. (2012). A first attempt to identify and classify empirical studies on history in mathematics education. In B. Sriraman (Ed.), Crossroads in the history of mathematics and mathematics education (TMME Monographs 12 (pp. 295–332). Charlotte: Information Age Publishing.

    Google Scholar 

  • Katz, V. J. (1993). Using the history of calculus to teach calculus. Science & Education, 2, 243–249.

    Article  Google Scholar 

  • Katz, J. V. (1995). Ides of calculus in Islam and India. Mathematics Magazine, 68(3), 163–174.

    Article  Google Scholar 

  • Katz, V. J. (1998). History of mathematics: An introduction. Boston: Addison-Wesley.

    Google Scholar 

  • Kjeldsen, T. H., & Blomhøj, M. (2012). Beyond motivation: History as a method for learning meta-discursive rules in mathematics. Educational Studies in Mathematics, 80(3), 327–349.

    Article  Google Scholar 

  • Klima, V. W. (2011). A different sort of calculus debate. In D. Jardine & A. Shell-Gellasch (Eds.), Mathematical time capsules (pp. 139–148). Washington, DC: Mathematical Association of America.

    Chapter  Google Scholar 

  • Lim, S. Y., & Chapman, E. (2013a). Adapting the academic motivation scale for use in pre-tertiary mathematics classrooms. Mathematics Education Research Journal. Advance online publication. doi:10.1007/s13394-014-0140-9.

  • Lim, S. Y., & Chapman, E. (2013b). An investigation of the Fennema-Sherman mathematics anxiety subscale. Measurement and Evaluation in Counseling and Development, 46(1), 26–37. doi:10.1177/0748175612459198.

    Article  Google Scholar 

  • Lim, S. Y., & Chapman, E. (2013c). Development of a short form of the attitudes toward mathematics inventory. Educational Studies in Mathematics, 82(1), 145–164. doi:10.1007/s10649-012-9414-x.

  • Lit, C. K., Siu, M. K., & Wong, N. Y. (2001). The use of history in the teaching of mathematics: Theory, practice, and evaluation of effectiveness. Educational Journal, 29(1), 17–31.

  • Ma, X., & Xu, J. M. (2004). The causal ordering of mathematics anxiety and mathematics achievement: A longitudinal panel analysis. Journal of Adolescence, 27(2), 165–179.

  • MacDonnell, J. F. (2015). The mathematician’s quest for superlatives from geometrical and calculus considerations. Retrieved March 21, 2013, from http://www.faculty.fairfield.edu/jmac/ther/superlatives.htm.

  • McBride, J. C., & Rollins, J. H. (1977). The effects of history of mathematics on attitudes towards mathematics of college algebra students. Journal for Research in Mathematics Education, 8, 57–61.

    Article  Google Scholar 

  • Montelle, C. (2011). A ‘Symbolic’ history of the derivative. In D. Jardine & A. Shell-Gellasch (Eds.), Mathematical time capsules (pp. 151–158). Washington, DC: Mathematical Association of America.

    Chapter  Google Scholar 

  • Ng, W. L. (2006). Effects of an ancient Chinese mathematics enrichment programme on secondary school students achievements in mathematics. International Journal of Science and Mathematical Education, 4, 485–511.

    Article  Google Scholar 

  • O’Connor, J. J., & Robertson, E. F. (1998, June). Niels Henrik Abel. Retrieved from http://www-history.mcs.st-and.ac.uk/Biographies/Abel.html.

  • Perkins, P. (1991). Using history to enrich mathematics lessons in a girls’ school. For the Learning of Mathematics, 11(2), 9–10.

    Google Scholar 

  • Perry, A. B. (2011). Connections between Newton, Leibniz, and calculus I. In D. Jardine & A. Shell-Gellasch (Eds.), Mathematical time capsules (pp. 133–137). Washington, DC: Mathematical Association of America.

    Chapter  Google Scholar 

  • Ponza, M. V. (1998). A role for the history of mathematics in the teaching and learning of mathematics: An Argentinean experience. Mathematics in School, 27(4), 10–13.

  • Radford, L., & Puig, L. (2007). Syntax and meaning as sensuous, visual, historical forms of algebraic thinking. Educational Studies in Mathematics, 66(2), 145–164.

    Article  Google Scholar 

  • Rice, A. (2011). The harmonic series: A primer. In D. Jardine & A. Shell-Gellasch (Eds.), Mathematical time capsules (pp. 269–276). Washington, DC: Mathematical Association of America.

  • Rogers, R. (2011). Leibniz’s calculus (real retro calc.). In D. Jardine & A. Shell-Gellasch (Eds.), Mathematical time capsules (pp. 159–167). Washington, DC: Mathematical Association of America.

    Chapter  Google Scholar 

  • Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic Motivations: Classic definitions and new directions. Contemporary Educational Psychology, 25, 54–67.

  • Ryan, R. M., & Connell, J. P. (1989). Perceived locus of causality and internalization: Examining reasons for acting in two domains. Journal of Personality and Social Psychology, 57(5), 749–761.

    Article  Google Scholar 

  • Sandifer, E. (2003). Euler’s solution of the basel problem – the longer story. Retrieved March 23, 2013, from http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/NYU%20Basel%20Problem%20Paper.PDF.

  • Siegel, M., & Borasi, R. (1994). Demystifying mathematics education through inquiry. In P. Ernest (Ed.), Constructing mathematical knowledge: Epistemology and mathematics education (pp. 201–214). Washington, DC: Falmer.

    Google Scholar 

  • Siu, M. K. (1997). The ABCD of using history of mathematics in the (undergraduate) classroom. Bulletin of the Hong Kong Mathematical Society, 1(1), 143–154.

    Google Scholar 

  • Spaulding, C. L. (1992). Motivation in the classroom. New York: McGraw-Hill.

    Google Scholar 

  • Strachan, L. (2009). A slice of pi. London: Constable & Robinson Ltd.

    Google Scholar 

  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Journal Educational Studies in Mathematics, 12(2), 151–169.

    Article  Google Scholar 

  • Tapia, M., & Marsh, G. E., II. (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly, 8(2), 16–21.

    Google Scholar 

  • Turnbull, H. W. (Ed.). (1959). The correspondence of Isaac Newton (Vol. 1, p. 416). Cambridge: Cambridge University Press.

    Google Scholar 

  • University of British Columbia (2015). Overview of calculus from a historical perspective. Retrieved March 22, 2013 from http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/integration/history.html.

  • Vallerand, R. J., Pelletier, L. G., Blais, M. R., Brière, N. M., Senécal, C., & Vallières, E. F. (1992). The academic motivation scale: A measure of intrinsic, extrinsic, and amotivation in education. Educational and Psychological Measurement, 52, 1003–1017.

  • Wang, J., Hagger, M., & Liu, W. C. (2009). A cross-cultural validiation of perceived locus of causality scale in physical education context. Research Quarterly for Exercise and Sport, 80(2), 313–325.

    Article  Google Scholar 

  • Wilson, P. S., & Chauvot, J. B. (2000). Who? How? What? A strategy for using history to teach mathematics. Mathematics Teacher, 93(8), 642–645.

    Google Scholar 

  • Zakaria, E., & Nordin, N. M. (2008). The effects of mathematics anxiety on matriculation students as related to motivation and achievement. Eurasia Journal of Mathematics Science and Technology Education, 4(1), 27–30.

    Google Scholar 

  • Zan, R., & Martino, P. D. (2007). Attitudes towards mathematics: overcoming positive/negative dichotomy. The Montana Mathematics Enthusiasts Monograph, 3, 157–168.

    Google Scholar 

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Lim, S., Chapman, E. Effects of using history as a tool to teach mathematics on students’ attitudes, anxiety, motivation and achievement in grade 11 classrooms. Educ Stud Math 90, 189–212 (2015). https://doi.org/10.1007/s10649-015-9620-4

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