The False Promises of Application-Driven Learning: Mathematical Thinking in Today’s Rapidly Evolving Technology Landscape

Rajtmajer, Sarah

doi:10.1007/978-3-031-61290-9_2

Sarah Rajtmajer²

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Abstract

Undergraduate curricula in informatics programs typically include several courses in mathematics. In my time teaching mathematics in IST, I have noticed continual and increasing calls from colleagues and administrators to prove to students the relevance of these courses through application-driven lesson plans and preferential treatment of topics with well-understood connection to today’s technologies. This chapter offers a counterpoint to these calls. I suggest that the treatment of foundational mathematical concepts as a means to well-defined and highly circumscribed ends perpetuates math anxiety and undermines flexibility of mathematical reasoning critical to highly dynamic IST careers. The examples I provide center around a course on discrete mathematics. However, the message is general.

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Notes

1.
Here is the Millennium Prize Problem as webpage: https://www.claymath.org/millennium-problems/

References

Agrawal, M., Kayal, N., & Saxena, N. (2004). PRIMES is in P. Annals of Mathematics, 781–793.
Google Scholar
Ascher, M. (1990) A river-crossing problem in cross-cultural perspective. Mathematics Magazine, 63(1), 26–29.
Article MathSciNet Google Scholar
Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181–185. https://doi.org/10.1111/1467-8721.00196
Article Google Scholar
Bogomolny, A. (2024). Retrieved from https://www.cut-the-knot.org/
Cubitt, T., Perez-Garcia, D. & Wolf, M. (2015) Undecidability of the spectral gap. Nature, 528, 207–211.
Article Google Scholar
Dowker, A., Sarkar, A., & Looi, C. Y. (2016). Mathematics anxiety: What have we learned in 60 years?. Frontiers in Psychology, 7, 508.
Article Google Scholar
Dweck, C. (2016). What having a “growth mindset” actually means. Harvard Business Review, 13(2), 2–5.
Google Scholar
Gill, R. (2010). Monty hall problem. International Encyclopaedia of Statistical Science, 858–863.
Google Scholar
Gonthier, G. (2008) Formal proof–the four-color theorem. Notices of the AMS 55(11), 1382–1393.
MathSciNet Google Scholar
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
Google Scholar
Hofstadter, D. R. (1999). Gödel, Escher, Bach: an eternal golden braid. Basic Books.
Google Scholar
Mendick, H. (2005). A beautiful myth? The gendering of being/doing ‘good at maths’. Gender and Education, 17(2), 203–219.
Article Google Scholar
Middleton, J. A., & Spanias, P. A. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30(1), 65–88.
Article Google Scholar
NIST Announces First Four Quantum-Resistant Cryptographic Algorithms. (2022). Retrieved from https://www.nist.gov/news-events/news/2022/07/nist-announces-first-four-quantum-resistant-cryptographic-algorithms
Nosek, B. A., Banaji, M. R., & Greenwald, A. G. (2002). Math = male, me = female, therefore math me. Journal of Personality and Social Psychology, 83(1), 44–59.
Article Google Scholar
O’connor, K. (2017). How to grade for learning: Linking grades to standards. Corwin Press.
Google Scholar
(2022). Retrieved from https://www.claymath.org/millennium-problems/
Ribenboim, P. (1979) 13 lectures on Fermat’s last theorem. Springer Science & Business Media.
Google Scholar
Tobias, S. (1993). Overcoming math anxiety. WW Norton & Company.
Google Scholar
Wiles, A. (1995). Modular elliptic curves and Fermat’s last theorem. Annals of Mathematics, 141(3), 443–551.
Article MathSciNet Google Scholar
Yu, X., Zhou, H., Sheng, P., Ren, B., Wang, Y., Wang, H., & Zhou, X. (2024). Math anxiety is more closely associated with math performance in female students than in male students. Current Psychology: A Journal for Diverse Perspectives on Diverse Psychological Issues, 43(2), 1381–1394. https://doi.org/10.1007/s12144-023-04349-y
Article Google Scholar

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College of Information Sciences and Technology, The Pennsylvania State University, University Park, PA, USA
Sarah Rajtmajer

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Sarah Rajtmajer
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Correspondence to Sarah Rajtmajer .

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College of Information Sciences and Technology, University Park, Pennsylvania State University, Pennsylvania, PA, USA
John M. Carroll

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Rajtmajer, S. (2024). The False Promises of Application-Driven Learning: Mathematical Thinking in Today’s Rapidly Evolving Technology Landscape. In: Carroll, J.M. (eds) Innovative Practices in Teaching Information Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-61290-9_2

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DOI: https://doi.org/10.1007/978-3-031-61290-9_2
Published: 11 June 2024
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-61289-3
Online ISBN: 978-3-031-61290-9
eBook Packages: Computer ScienceComputer Science (R0)

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