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Integrating history and philosophy in mathematics education at university level through problem-oriented project work

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Abstract

Through the last three decades several hundred problem-oriented student-directed projects concerning meta-aspects of mathematics and science have been performed in the 2-year interdisciplinary introductory science programme at Roskilde University. Three selected reports from this cohort of project reports are used to investigate and present empirical evidence for learning potentials of integrating history and philosophy in mathematics education. The three projects are: (1) a history project about the use of mathematics in biology that exhibits different epistemic cultures in mathematics and biology. (2) An educational project about the difficulties of learning mathematics that connects to the philosophy of mathematics. (3) A history of mathematics project that connects to the sociology of multiple discoveries. It is analyzed and discussed in what sense students gain first hand experiences with and learn about meta-aspects of mathematics and their mathematical foundation through the problem-oriented student-directed project work.

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Notes

  1. For literature on using history in mathematics education, see, e.g. Fauvel (1991a, 1991b), Fauvel & van Maanen (2000) and Katz (2000). For discussions about difficulties of incorporating history of mathematics in mathematics teaching, see Fried (2001, 2007).

  2. The practise of this student-directed problem-oriented project-organised study programme is introduced and discussed in the paper by Blomhøj and Kjeldsen (2009) in this issue of ZDM.

  3. The problem-oriented project work also constitutes half of the study time in the master’s programmes. Its significance for the master’s education in mathematics is treated by Niss (2001).

  4. Each project work is assessed through an oral examination that takes its point of departure within the project report. The students’ performance is individually evaluated by an external examinator, who has been chosen from the national list of mathematics examinators that are used at mathematics examinations at all universities in Denmark.

  5. Our translation and paraphrasing.

  6. The following paraphrase from the students’ project report also appears in the paper by Kjeldsen (2007).

  7. The students’ wording is a bit unclear here, r′ and r′ + Δr′ denotes the radius of the circles that form the cylinders.

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Acknowledgments

We wish to thank three anonymous referees for critique, helpful comments and suggestions on an earlier version of this paper.

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Authors and Affiliations

  1. IMFUFA, Department of Science, Systems and Models, Roskilde University, Roskilde, Denmark

    Tinne Hoff Kjeldsen & Morten Blomhøj

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  1. Tinne Hoff Kjeldsen
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  2. Morten Blomhøj
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Correspondence to Tinne Hoff Kjeldsen.

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Kjeldsen, T.H., Blomhøj, M. Integrating history and philosophy in mathematics education at university level through problem-oriented project work. ZDM Mathematics Education 41, 87–103 (2009). https://doi.org/10.1007/s11858-008-0101-4

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