Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study

Thembinkosi Peter Mkhatshwa

doi:10.29333/ejmste/13575

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Thembinkosi Peter Mkhatshwa ¹ ^*

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¹ Department of Mathematical and Physical Sciences, Miami University, Middletown, OH, USA^* Corresponding Author

Abstract

This study investigated opportunities to learn about optimization problems provided by undergraduate calculus textbooks. To accomplish this, we analyzed examples and practice problems from two calculus textbooks widely used in the teaching of calculus in the United States. Findings of this study indicate that a majority of the problems in both textbooks lack realistic and essential contexts, have matching or missing information, and require a low cognitive demand to solve. Setting up objective functions is either not necessary or it is straightforward for most problems in the two textbooks. In addition, both textbooks provide ample opportunities to interpret critical numbers and extrema in context. Overall, findings of this study suggest the existence of a relationship between known students’ difficulties with solving optimization problems and the opportunities to learn about optimization problems provided by calculus textbooks. Implications for several stakeholders, including calculus textbook authors and calculus instructors are discussed.

Keywords

opportunity to learn
textbook research
textbook analysis
calculus
optimization problems

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2023, Volume 19, Issue 10, Article No: em2335

https://doi.org/10.29333/ejmste/13575

Publication date: 01 Oct 2023

Online publication date: 11 Aug 2023

Article Views: 722

Article Downloads: 468

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How to cite this article

APA

Mkhatshwa, T. P. (2023). Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study. Eurasia Journal of Mathematics, Science and Technology Education, 19(10), em2335. https://doi.org/10.29333/ejmste/13575

Vancouver

Mkhatshwa TP. Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study. EURASIA J Math Sci Tech Ed. 2023;19(10):em2335. https://doi.org/10.29333/ejmste/13575

AMA

Mkhatshwa TP. Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study. EURASIA J Math Sci Tech Ed. 2023;19(10), em2335. https://doi.org/10.29333/ejmste/13575

Chicago

Mkhatshwa, Thembinkosi Peter. "Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study". Eurasia Journal of Mathematics, Science and Technology Education 2023 19 no. 10 (2023): em2335. https://doi.org/10.29333/ejmste/13575

Harvard

Mkhatshwa, T. P. (2023). Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study. Eurasia Journal of Mathematics, Science and Technology Education, 19(10), em2335. https://doi.org/10.29333/ejmste/13575

MLA

Mkhatshwa, Thembinkosi Peter "Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study". Eurasia Journal of Mathematics, Science and Technology Education, vol. 19, no. 10, 2023, em2335. https://doi.org/10.29333/ejmste/13575