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Cheap plot tricks and plot holes in mathematical stories

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Abstract

Good stories, literary or mathematical, have the ability to keep the reader engaged and wanting for more. However, poorly designed stories may also elicit a negative aesthetic reaction and thereby reduce engagement. By drawing on literary theory and Dietiker’s (For the Learning of Mathematics 33(3):14–19, 2013; Educational Studies in Mathematics 90(3):285–302, 2015) theoretical framework of mathematical stories, this essay conceptualises two aspects of mathematical stories that are likely to be perceived by the readers as aesthetic deficiencies: mathematical cheap plot tricks and mathematical plot holes. Additionally, examples of them are proposed from various areas of mathematics curriculum and some ideas of how they can be avoided, so as not to hinder engagement, are offered.

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Notes

  1. See Devlin (2008a, 2008b, 2008c, 2011) for a discussion on this topic.

  2. For the remainder of the reading, I will only reference the line number and will omit the reference to Fig. 1.

  3. This list was inspired by Tall (2013, ch. 4).

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Acknowledgements

I would like to express sincere thanks to the considerate and thorough anonymous reviewers; also to Ieva Kilė, Tomas Šiaulys, Linas Tranas, Nijolė Keršytė, Leslie Dietiker and my wonderful wife Jogilė whose support allowed me to write this paper.

Funding

This work was supported by the Research Council of Lithuania, grant no. S-DNR-20-7.

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Correspondence to Vytautas Miežys.

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Miežys, V. Cheap plot tricks and plot holes in mathematical stories. Educ Stud Math 113, 271–285 (2023). https://doi.org/10.1007/s10649-023-10216-1

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