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Dialogues on Dialogues: The Use of Classical Dialogues in Mathematics Teacher Education

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Scripting Approaches in Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

We illustrate how the classical dialogues – Galileo’s Dialogue on Infinity from Dialogues Concerning Two New Sciences, Plato’s Meno, and Lakatos’ Proofs and Refutations – can be used in teacher education. By re-capturing our conversation, we demonstrate the use of the classical dialogues to revisit mathematical notions, such as infinity, or to highlight meta-mathematical issues, such as definitions and proofs. We share several scripting assignments used with teachers and several student-written scripts produced in response to such assignments. We elaborate on the benefits of bringing classical dialogues for discussion in classes of mathematics teachers. These include, but are not limited to, enculturation by exposure to historical context, reinforcement of mathematical ideas and concepts, introduction to subsequent readings and assignments, and extended variety of tasks for the use in mathematics teacher education.

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Notes

  1. 1.

    https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

  2. 2.

    http://oll.libertyfund.org/titles/galilei-dialogues -concerning-two-new-sciences

    This text is in the public domain

  3. 3.

    https://en.wikipedia.org/wiki/Two_New_Sciences

  4. 4.

    https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

  5. 5.

    http://mathworld.wolfram.com/HilbertHotel.html

    https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

  6. 6.

    https://en.wikipedia.org/wiki/Ross%E2%80%93Littlewood_paradox

  7. 7.

    See Mamolo and Zazkis (2008) .

  8. 8.

    See Mamolo and Zazkis (2008, p.176) .

  9. 9.

    See Mamolo and Zazkis (2008, p.179) .

  10. 10.

    See Zazkis and Mamolo (2009)

  11. 11.

    See, for example, Tsamir and Tirosh (1999 ), Fischbein (2001 ), Fischbein, Tirosh, and Hess (1979).

  12. 12.

    The dialogue excerpts in this section are from http://oll.libertyfund.org/titles/galilei-dialogues -concerning-two-new-sciences

    This text is in the public domain

  13. 13.

    This term is borrowed from Harel (2008) who posits repeated reasoning as one of the foundational principles of mathematics learning.

  14. 14.

    http://classics.mit.edu/Plato/meno.html

  15. 15.

    Cited from http://classics.mit.edu/Plato/meno.html

  16. 16.

    For instance, see Sfard (1998) .

  17. 17.

    The classical dialogue excerpts in this section are from http://classics.mit.edu/Plato /meno.html

  18. 18.

    See De Bock , Verschaffel and Janssens (1998) .

  19. 19.

    The intended papers are De Bock, Verschaffel, and Janssens (1998) and van Dooren et al. (2003) .

  20. 20.

    See Stavy and Tirosh (2000) .

  21. 21.

    See Leron and Hazzan (1997) .

  22. 22.

    See Zazkis and Chernoff (2008) .

  23. 23.

    This is by Definition 2, Book VII given in Euclid’s Elements.

  24. 24.

    See Jahnke et al. (2000) .

  25. 25.

    See Bishop (1976) , later revisited by Rowland and Zazkis (2013) .

  26. 26.

    See Zazkis and Leikin (2008) .

  27. 27.

    See Koichu (2012) .

  28. 28.

    The term “proof-generated definition” is borrowed from Ouvrier-Buffet’s (2006) discussion of Lakatos.

  29. 29.

    See Pimm, Beisiegel, and Meglis (2008) .

  30. 30.

    See Kontorovich and Zazkis (2016) .

  31. 31.

    See, for example, Usiskin (2008) .

  32. 32.

    See Koichu and Zazkis (2013) .

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Author information

Authors and Affiliations

  1. Simon Fraser University, Burnaby, BC, Canada

    Rina Zazkis

  2. Weizmann Institute of Science, Rehovot, Israel

    Boris Koichu

Authors
  1. Rina Zazkis
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  2. Boris Koichu
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Correspondence to Rina Zazkis .

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Editors and Affiliations

  1. Simon Fraser University, Burnaby, British Columbia, Canada

    Rina Zazkis

  2. University of Michigan, Ann Arbor, Michigan, USA

    Patricio Herbst

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Zazkis, R., Koichu, B. (2018). Dialogues on Dialogues: The Use of Classical Dialogues in Mathematics Teacher Education. In: Zazkis, R., Herbst, P. (eds) Scripting Approaches in Mathematics Education . Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-62692-5_16

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  • DOI: https://doi.org/10.1007/978-3-319-62692-5_16

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