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.
Similar content being viewed by others
References
Ališauskas, A., Janušaitienė, O., Arefjeva, M., & Daukšytė-Koncevičienė, L. (2017). MATEMATIKA. Vadovėlis 6 klasei, 1 dalis (ATRASK). Šviesa, Vilnius.
Bailey, D.H., Hoard, M.K., Nugent, L., & Geary, D.C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447–455. https://doi.org/10.1016/j.jecp.2012.06.004
Bal, M. (2009) Narratology: introduction to the theory of narrative, (3rd edn.) Toronto: University of Toronto Press.
Bal, M. (2017) Narratology: introduction to the theory of narrative, (4th edn.) Toronto: University of Toronto Press.
Daschmann, E.C., Goetz, T., & Stupnisky, R.H. (2011). Testing the predictors of boredom at school: development and validation of the precursors to boredom scales. British Journal of Educational Psychology, 81(3), 421–440. https://doi.org/10.1348/000709910X526038
Devlin, K. (2008a). It ain’t no repeated addition. Devlin’s Angle. Retrieved January 30, 2023, from https://www.maa.org/external_archive/devlin/devlin_06_08.html.
Devlin, K. (2008b). It’s still not repeated addition. Devlin’s Angle. Retrieved January 30, 2023, from https://www.maa.org/external_archive/devlin/devlin_0708_08.html.
Devlin, K. (2008c). Multiplication and those Pesky British spellings. Devlin’s Angle. Retrieved January 30, 2023, from https://www.maa.org/external_archive/devlin/devlin_09_08.html.
Devlin, K. (2011). What exactly is multiplication? Devlin’s angle. Retrieved January 30, 2023, from https://www.maa.org/external_archive/devlin/devlin_01_11.html.
Dietiker, L. (2013). Mathematical texts as narrative: rethinking curriculum. For the Learning of Mathematics, 33(3), 14–19.
Dietiker, L. (2015). Mathematical story: a metaphor for mathematics curriculum. Educational Studies in Mathematics, 90(3), 285–302. https://doi.org/10.1007/s10649-015-9627-x
Dietiker, L. (2016). The role of sequence in the experience of mathematical beauty. Journal of Humanistic Mathematics, 6 (1), 152–173. https://doi.org/10.5642/JHUMMATH.201601.10
Dietiker, L., & Richman, A.S. (2021). How textbooks can promote inquiry: using a narrative framework to investigate the design of mathematical content in a lesson. Journal for Research in Mathematics Education, 52(3), 301–331. https://doi.org/10.5951/jresematheduc-2020-0318
Dietiker, L., Singh, R., Riling, M., & Nieves, H.I. (2020). What makes a mathematics lesson interesting to students? In Mathematics education across cultures: proceedings of the 42nd meeting of the North American chapter of the international group for the psychology of mathematics education, PME-NA. https://doi.org/10.51272/pmena.42.2020-49 (pp. 391–399). Mexico.
Gerofsky, S. (1996). A linguistic and narrative view of word problems in mathematics education. For the Learning of Mathematics, 16(2), 36–45.
Intienė, K., Knyvienė, J. G., Meškauskaitė, V., Stundžienė, Z., & Vanagas, V. (2015) Matematika Tau plius. 6 klasė. 1 dalis. Vilnius: TEV.
OECD. (2016) Opportunity to learn and students’ attitudes towards mathematics. Paris: Technical report, OECD.
Richman, A.S., Dietiker, L., & Riling, M. (2019). The plot thickens: the aesthetic dimensions of a captivating mathematics lesson. The Journal of Mathematical Behavior, 54, 100671. https://doi.org/10.1016/j.jmathb.2018.08.005.
Rosenblatt, L.M. (1988) Writing and Reading: the Transactional Theory. (Technical Report No 416). University of Illinois at Urbana-Champaign: Reading Research and Education Center.
Ryan, L.E., & Dietiker, L. (2018). Using plot twists to engage learners. Teaching Children Mathematics, 24(5), 316–323. https://doi.org/10.5951/teacchilmath.24.5.0316
Ryan, M.-L. (2009). Cheap plot tricks, plot holes, and narrative design. Narrative, 17(1), 56–75. https://doi.org/10.1353/nar.0.0016
Simon, S., Singh, R., & Dietiker, L (2021). THAT’S CRAZY: an exploration of student exclamations in high school mathematics lessons. In Proceedings of the Psychology of Mathematics Education - North American Chapter.
Sinclair, N. (2001). The aesthetic “is” relevant. For the Learning of Mathematics, 21(1), 25–32.
Sinclair, N. (2005). Chorus, colour, and contrariness in school mathematics. THEN: Journal, 1(1).
Sinclair, N. (2011). Aesthetic considerations in mathematics. Journal of Humanistic Mathematics, 1(1), 2–32. https://doi.org/10.5642/jhummath.201101.03
Tall, D. (2013) How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge: Cambridge University Press.
Tymoczko, T. (1993). Value judgments in mathematics: can we treat mathematics as an art? In essays in humanistic mathematics, MAA Notes (pp. 67–77). MAA Press.
Weinberg, A., & Wiesner, E. (2011). Understanding mathematics textbooks through reader-oriented theory. Educational Studies in Mathematics, 76 (1), 49–63. https://doi.org/10.1007/s10649-010-9264-3
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
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
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-023-10216-1