Educational Studies in Mathematics

, Volume 74, Issue 1, pp 53–74 | Cite as

An empirical study of using history as a ‘goal’

  • Uffe Thomas Jankvist


This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented in a Danish upper secondary class in order to study the students’ capabilities at engaging in meta-issue discussions and reflections on mathematics and its history. Based on videos of the implementation, students’ hand-in essay assignments, questionnaires, and follow-up interviews, the conditions, sense, and extent to which the students are able to perform such discussions and reflections are analyzed using a described theoretical framework.


Using history in mathematics education History as a goal Meta-issue discussions, reflections, and discourses Commognition Historical teaching modules Error-correcting codes 


  1. Berlekamp, E. R. (1974). Introduction. In E. R. Berlekamp (Ed.), Key papers in the development of coding theory (pp. 1–6, 67–69, 107–108, 157–158, 233–237). New York: IEEE (introductory comments).Google Scholar
  2. Davis, C. (1994). Where did twentieth-century mathematics go wrong? In S. Chikara, S. Mitsuo, & J. W. Dauben (Eds.), The intersection of history and mathematics. Science networks (Historical studies) (No. 15, pp. 129–142). Basel: Birkhäuser.Google Scholar
  3. Demattè, A. (2007). A questionnaire for discussing the ‘strong’ role of the history of mathematics in the classroom. In F. Furinghetti, S. Kaijser, & C. Tzanakis (Eds.), Proceedings HPM2004 & ESU4 (Revised ed., pp. 218–228). Uppsala Universitet.Google Scholar
  4. Demattè, A., & Furinghetti, F. (1999). An exploratory study on students’ beliefs about mathematics as a socio-cultural process. In G. Philippou (Ed.), Eighth European workshop: Research on mathematical beliefs—MAVI-8 proceedings (pp. 38–47). Nicosia: University of Cyprus.Google Scholar
  5. Epple, M. (2000). Genisis, Ideen, Institutionen, mathmatische Werkstätten: Formen der Mathematikgeschichte—Ein metahistorischer Essay. Mathematische Semesterberichte, 47, 131–163.CrossRefGoogle Scholar
  6. Fréchet, M. (1906). Sur quelques points du calcul fonctionnel. Rend. Circolo Mat., 74, 1–74.CrossRefGoogle Scholar
  7. Fried, M. N. (2001). Can mathematics education and history of mahtematics coexist? Science & Education, 10, 391–408.CrossRefGoogle Scholar
  8. Golay, M. J. E. (1949). Notes on digital coding. Proceedings of the IRE, 37, 657.Google Scholar
  9. Grassmann, H. (1844). Die lineale Ausdehnungslehre. Leipzig: Otto Wigand.Google Scholar
  10. Greenwald, S. J. (2005). Incorporating the mathematics achievements of women and minority mathematicians into classrooms. In A. Shell-Gellasch, & D. Jardine (Eds.), From calculus to computers—Using the last 200 years of mathematics history in the classroom. MAA Notes (No. 68, pp. 183–200). Washington: The Mathematical Association of America.Google Scholar
  11. Hamming, R. W. (1950). Error detecting and error correcting codes. Bell System Technical Journal, 29, 147–160.Google Scholar
  12. Hansen, V. L. (2008). The dual nature of mathematics. In M. Niss (Ed.), ICME-10 proceedings & regular lectures (pp. 1–11). Copenhagen: ICME-10. Regular Lecture.Google Scholar
  13. Hardy, G. H. (1992). A mathematician’s apology (Canto ed.). Cambridge: Cambridge University Press (foreword by C. P. Snow).Google Scholar
  14. Hersh, R. (1997). What is mathematics really? Oxford: Oxford University Press.Google Scholar
  15. Isaacs, I., Ram, V. M., & Richards, A. (2000). A historical approach to developing the cultural significance of mathematics among first year preservice primary school teachers. In V. Katz (Ed.), Using history to teach mathematics—An international perspective. MAA Notes (No. 51, pp. 123–128). Washington: The Mathematical Association of America.Google Scholar
  16. Jahnke, H. N. (2000). The use of original sources in the mathematics classroom. In: J. Fauvel, & J. van Maanen (Eds.), History in mathematics education. The ICMI study (Chapter 9, pp. 291–328). Dordrecht: Kluwer Academic.Google Scholar
  17. Jankvist, U. T. (2008a). Den matematikhistoriske dimension i undervisning—Gymnasialt set. MONA, 4(1), 24–45 (English translation of title: The dimension of the history of mathematics in teaching—The case of upper secondary level).Google Scholar
  18. Jankvist, U. T. (2008b). Evaluating a teaching module on the early history of error correcting codes. In M. Kourkoulos, & C. Tzanakis (Eds.), Proceedings 5th international colloquium on the didactics of mathematics (Vol. II, pp. 447–460). Rethymnon: The University of Crete.Google Scholar
  19. Jankvist, U. T. (2008c). Kodningsteoriens tidlige historie—Et undervisningsforløb til gymnasiet. Tekster fra IMFUFA (No. 459). Roskilde: IMFUFA. (English translation of title: The early history of error correcting codes—A teaching module for upper secondary school.)Google Scholar
  20. Jankvist, U. T. (2008d). RSA og den heri anvendte matematiks historie—Et undervisningsforløb til gymnasiet. Tekster fra IMFUFA (No. 460). Roskilde: IMFUFA (English translation of title: RSA and the history of the applied mathematics in the algorithm—A teaching module for upper secondary school).Google Scholar
  21. Jankvist, U. T. (2008e). A teaching module on the history of public-key cryptography and RSA. BSHM Bulletin, 23(3), 157–168.CrossRefGoogle Scholar
  22. Jankvist, U. T. (2009a). A categorization of the ‘whys’ and ‘hows’ of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235–261.CrossRefGoogle Scholar
  23. Jankvist, U. T. (2009b). History of modern applied mathematics in mathematics education. For the Learning of Mathematics, 29(1), 8–13.Google Scholar
  24. Jankvist, U. T. (2009c). On empirical research in the field of using history in mathematics education. ReLIME, 12(1), 67–101.Google Scholar
  25. Jankvist, U. T. (2009d). Students’ beliefs about the evolution and development of mathematics. In: Proceedings from the CERME6 working group 15. CERME (pp. 1–10). (Preprint).Google Scholar
  26. Jankvist, U. T. (2009e). Using history as a ‘goal’ in mathematics education. Ph.D. thesis, IMFUFA, Roskilde University, Roskilde. Number 464 in Tekster fra IMFUFA.
  27. Kjeldsen, T. H., & Blomhøj, M. (2009). Integrating history and philosophy in mathematics education at university level through problem-oriented project work. ZDM Mathematics Education, 41, 87–103.CrossRefGoogle Scholar
  28. Niss, M., & Jensen, T. H. (Eds.). (2002). Kompetencer og matematiklæring—Ideer og inspiration til udvikling af matematikundervisning i Danmark. Undervisningsministeriet. Uddannelsesstyrelsens temahæfteserie nr. 18 (English translation of title: Competencies and learning of mathematics—Ideas and inspiration for the development of mathematics education in Denmark).Google Scholar
  29. Rheinberger, H.-J. (1997). Toward a history of epistemic things: Synthesizing proteins in the test tube. Stanford: Stanford University Press.Google Scholar
  30. Sfard, A. (2008a). Learning mathematics as developing a discourse. PowerPoint slides from regular lecture at ICME 11, Monterrey, Mexico.Google Scholar
  31. Sfard, A. (2008b). Thinking as communicating. New York: Cambridge University Press.CrossRefGoogle Scholar
  32. Shannon, C. E. (1948). A mathematical theory of communication I, II. In: D. Slepian (Ed.), Key papers in the development of information theory (pp. 5–18; 19–29). New York: IEEE Press.Google Scholar
  33. Siu, F.-K., & Siu, M.-K. (1979). History of mathematics and its relation to mathematical education. International Journal of Mathematical Education in Science and Technology, 10(4), 561–567.CrossRefGoogle Scholar
  34. Thompson, T. M. (1983). From error-correcting codes through sphere packings to simple groups, No. 21 in The Carus Mathematical Monographs. The Mathematical Association of America.Google Scholar
  35. Undervisningsministeriet. (2007). Vejledning: Matematik A, Matematik B, Matematik C. Bilag 35, 36, 37 (English translation of title: Ministerial order of 2007—Mathematics levels A, B, and C).Google Scholar
  36. van Gulik-Gulikers, I. (2005). Meetkunde opnieuw uitgevonden—Een studie naar de waarde en de toepassing van de geschiedenis van de meetkunde in het wiskundeonderwijs. Ph.D. thesis, Rijksuniversiteit Groningen, Groningen.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceSouthern University of DenmarkOdense MDenmark
  2. 2.IMADAOdenseDenmark

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