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An empirical study of using history as a ‘goal’

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Abstract

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.

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Notes

  1. These studies are by the following authors: Demattè and Furinghetti (1999), Demattè (2007), Isaacs, Ram, and Richards (2000), Greenwald (2005), Kjeldsen and Blomhøj (2009), and Jankvist (2008b, e, 2009b, c, d, e).

  2. The new regulation of 2006 was somewhat modified in 2007. The word “demonstrate” in Danish has a dual meaning; it may be used both as the word “prove” and as the word “display.” Thus, students may only need to display knowledge.

  3. The supplemental curriculum can then become part of the local, final oral examination together with selected parts of the core curriculum. The core curriculum itself is also tested on a national written examination.

  4. Actually, these are what, in metric spaces, are normally referred to as closed balls, since they contain both the inside and the boundary, but I shall follow the convention in coding theory and call them spheres.

  5. A similar text, 100 pages long, was prepared for the second module: Jankvist (2008d).

  6. In order to get them accustomed to doing and writing these essays, the module also included a number of smaller introductory essay assignments (see Jankvist, 2009e).

  7. This correct observation does not go into the hand-in answer, here it mistakenly says that Shannon was the one to generalize the (7,4)-code.

  8. Foul language was removed by the Editor-in-Chief. For the full transcription see Jankvist (2009e, pp. 342–343).

  9. Another difference is that Sfard states that a commognitive conflict is practically indispensable for meta-level learning (meta-level learning not having anything to do with meta-issues in this case), something which cannot be claimed for the discursive conflict described above.

  10. In particular, two papers are in preparation: Anchoring students’ meta-perspective discussions of history in mathematics and Changing students’ images of mathematics as a discipline.

References

  • 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).

  • 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 

  • 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.

  • 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 

  • Epple, M. (2000). Genisis, Ideen, Institutionen, mathmatische Werkstätten: Formen der Mathematikgeschichte—Ein metahistorischer Essay. Mathematische Semesterberichte, 47, 131–163.

    Article  Google Scholar 

  • Fréchet, M. (1906). Sur quelques points du calcul fonctionnel. Rend. Circolo Mat., 74, 1–74.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Golay, M. J. E. (1949). Notes on digital coding. Proceedings of the IRE, 37, 657.

    Google Scholar 

  • Grassmann, H. (1844). Die lineale Ausdehnungslehre. Leipzig: Otto Wigand.

    Google Scholar 

  • 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 

  • Hamming, R. W. (1950). Error detecting and error correcting codes. Bell System Technical Journal, 29, 147–160.

    Google Scholar 

  • 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 

  • Hardy, G. H. (1992). A mathematician’s apology (Canto ed.). Cambridge: Cambridge University Press (foreword by C. P. Snow).

    Google Scholar 

  • Hersh, R. (1997). What is mathematics really? Oxford: Oxford University Press.

    Google Scholar 

  • 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 

  • 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 

  • 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).

  • 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 

  • 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.)

  • 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).

  • Jankvist, U. T. (2008e). A teaching module on the history of public-key cryptography and RSA. BSHM Bulletin, 23(3), 157–168.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jankvist, U. T. (2009b). History of modern applied mathematics in mathematics education. For the Learning of Mathematics, 29(1), 8–13.

    Google Scholar 

  • Jankvist, U. T. (2009c). On empirical research in the field of using history in mathematics education. ReLIME, 12(1), 67–101.

    Google Scholar 

  • 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).

  • 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. http://milne.ruc.dk/ImfufaTekster/

  • 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.

    Article  Google Scholar 

  • 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).

  • Rheinberger, H.-J. (1997). Toward a history of epistemic things: Synthesizing proteins in the test tube. Stanford: Stanford University Press.

    Google Scholar 

  • Sfard, A. (2008a). Learning mathematics as developing a discourse. PowerPoint slides from regular lecture at ICME 11, Monterrey, Mexico.

  • Sfard, A. (2008b). Thinking as communicating. New York: Cambridge University Press.

    Book  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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).

  • 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.

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  1. Department of Mathematics and Computer Science, Southern University of Denmark, Campusvej 55, 5230, Odense M, Denmark

    Uffe Thomas Jankvist

  2. IMADA, Odense, Denmark

    Uffe Thomas Jankvist

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Jankvist, U.T. An empirical study of using history as a ‘goal’. Educ Stud Math 74, 53–74 (2010). https://doi.org/10.1007/s10649-009-9227-8

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