University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus

Eddie Aparicio-Landa; Landy Sosa-Moguel; Gerardo García-Almeida; Eric Avila-Vales

doi:10.29333/ejmste/16002

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Eddie Aparicio-Landa ¹ , Landy Sosa-Moguel ¹ ^* , Gerardo García-Almeida ¹ , Eric Avila-Vales ¹

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¹ Facultad de Matemáticas, Universidad Autónoma de Yucatán, Mérida, MEXICO^* Corresponding Author

Abstract

Understanding the fundamental theorem of calculus (FTC) is complex for university students. In this paper, an alternative approach to the FTC that relies on the use of the calculation of average values of a continuous function for a certain interval is shown. Likewise, researchers present the reflections of twelve advanced university mathematics students on solving five tasks with this approach, as well as the reflections of two professors of calculus and mathematical analysis about the alternative approach and the resolutions given by the students. Students’ reflections reveal that they found the approach to FTC generally appropriate, because it helped them mobilize their knowledge of calculus and supported their understanding of the theorem. The professors expressed in their reflections that the approach is pedagogically viable, and they seemed it a way of strengthening the students’ conceptual knowledge in calculus.

Keywords

reflections
average
fundamental theorem of calculus
university students
professors

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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, Volume 21, Issue 3, March 2025, Article No: em2593

https://doi.org/10.29333/ejmste/16002

Publication date: 01 Mar 2025

Online publication date: 19 Feb 2025

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Article Downloads: 42

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How to cite this article

APA

Aparicio-Landa, E., Sosa-Moguel, L., García-Almeida, G., & Avila-Vales, E. (2025). University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus. Eurasia Journal of Mathematics, Science and Technology Education, 21(3), em2593. https://doi.org/10.29333/ejmste/16002

Vancouver

Aparicio-Landa E, Sosa-Moguel L, García-Almeida G, Avila-Vales E. University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus. EURASIA J Math Sci Tech Ed. 2025;21(3):em2593. https://doi.org/10.29333/ejmste/16002

AMA

Aparicio-Landa E, Sosa-Moguel L, García-Almeida G, Avila-Vales E. University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus. EURASIA J Math Sci Tech Ed. 2025;21(3), em2593. https://doi.org/10.29333/ejmste/16002

Chicago

Aparicio-Landa, Eddie, Landy Sosa-Moguel, Gerardo García-Almeida, and Eric Avila-Vales. "University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 3 (2025): em2593. https://doi.org/10.29333/ejmste/16002

Harvard

Aparicio-Landa, E., Sosa-Moguel, L., García-Almeida, G., and Avila-Vales, E. (2025). University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus. Eurasia Journal of Mathematics, Science and Technology Education, 21(3), em2593. https://doi.org/10.29333/ejmste/16002

MLA

Aparicio-Landa, Eddie et al. "University students and professors’ reflections on an averages-based approach to the fundamental theorem of calculus". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 3, 2025, em2593. https://doi.org/10.29333/ejmste/16002