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On the relations between historical epistemology and students’ conceptual developments in mathematics

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Abstract

There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students’ conceptual developments in mathematics. We problematize this attempt to link the two fields on the basis of Grattan-Guinness’ distinction between “history” and “heritage”. We argue that when parallelism claims are made, history and heritage are often mixed up, which is problematic since historical mathematical definitions must be interpreted in its proper historical context and conceptual framework. Furthermore, we argue that cultural and local ideas vary at different time periods, influencing conceptual developments in different directions regardless of whether historical or individual developments are considered, and thus it may be problematic to uncritically assume a platonic perspective. Also, we have to take into consideration that an average student of today and great mathematicians of the past are at different cognitive levels.

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Notes

  1. “La tâche de l’éducateur est de faire reprasser l’esprit de l’enfant par où a passé celui de ses pères.”

  2. A well–known debate regarding this issue can be found in Unguru (1975) and Weil (1978).

  3. Discussions regarding modern interpretations of Greek mathematics can be found in Grattan-Guinness (2004a, b).

  4. “Functio quantitatis variabilis est expressio analytica quomodocunque composita ex illa quantitate variabili et numeris seu quantitatibus constantibus.”

  5. “Quae autem quantitates hoc modo ab aliis pendent, ut his mutatis etiam ipsae mutationes subeant, eae harum functiones appellari solent; quae denominatio latissime patet atque omnes modos, quibus una quantitas per alias determinari potest, in se complectitur. Si igitur x denotet quantitatem variabilem, omnes quantitates, quae utcunque ab x pendent seu per eam determinantur, eius functiones vocantur.”

  6. “On appelle quantités variables celles qui augmentent ou diminuent continuellement; & au contraire quanitités constantes celles qui demeurent les mêmes pendant que les autres changent.”

  7. This conclusion is similar to the conclusion of Viirman et al. (2010, p. 5) that we referred to above: “the definitions given by the students mostly resemble an 18th or 19th century view of functions”.

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Acknowledgements

We would like to thank the anonymous referees with the help of whom the manuscript has improved considerably.

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  1. Johanna Pejlare

    Present address: Department of Mathematical Sciences, University of Gothenburg and Chalmers University of Technology, Göteborg, Sweden

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  1. Department of Education, Uppsala University, Uppsala, Sweden

    Kajsa Bråting

  2. School of Education and Behavioural Sciences, University of Borås, Borås, Sweden

    Johanna Pejlare

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Bråting, K., Pejlare, J. On the relations between historical epistemology and students’ conceptual developments in mathematics. Educ Stud Math 89, 251–265 (2015). https://doi.org/10.1007/s10649-015-9600-8

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