Contextualized teaching strategies to improve the understanding of differential calculus among Architectural Engineering students.
Keywords:
Differential calculus, teaching strategies, contextualization, Architectural Engineering, higher educationAbstract
The teaching of differential calculus in engineering programs represents one of the main challenges in higher education, particularly in degrees such as Architectural Engineering, where students often perceive mathematical contents as abstract and weakly connected to their future professional practice. This situation is reflected in persistent conceptual difficulties, low levels of understanding, and high failure rates. The aim of this study is to analyze the implementation of contextualized teaching strategies to improve the understanding of differential calculus among students of the Architectural Engineering program. The research follows an applied and mixed-methods approach, focusing on the design and implementation of didactic activities that connect fundamental concepts of differential calculus with situations related to the architectural field, promoting geometric interpretation, the use of multiple representations, and conceptual reasoning. The methodology included the application of a diagnostic test and a final assessment, as well as observation of academic performance and analysis of learning products before and after the didactic intervention. The results show a significant improvement in students’ conceptual understanding of differential calculus, along with increased participation, motivation, and ability to establish connections among algebraic, graphical, and contextual representations. It is concluded that disciplinary contextualization of differential calculus constitutes an effective teaching alternative to strengthen meaningful learning in Architectural Engineering students, providing relevant empirical evidence for innovation in mathematics education at the higher education level.
Downloads
References
Abou-Hayt, I. (2025). Utilizar un contexto realista para motivar y enseñar a los estudiantes de ingeniería la regla de la cadena. Education Sciences, 15(4), 433. https://doi.org/10.3390/educsci15040433
Bedada, T. B., & Machaba, M. F. (2022). Investigation of students’ perception learning calculus with GeoGebra and cycle model. EURASIA Journal of Mathematics, Science and Technology Education, 18(11), Article em2175. https://doi.org/10.29333/ejmste/12443
Borba, M. C., Askar, P., Engelbrecht, J., Gadanidis, G., Llinares, S., & Aguilar, M. S. (2017). Digital technology in mathematics education: Research over the last decade. En G. Kaiser (Eds.), Proceedings of the 13th International Congress on Mathematical Education (pp. 221–233). Springer.
Borji, V., Alamolhodaei, H., & Radmehr, F. (2019). Correction on applying APOS-ACE theory to improve students’ graphical understanding of the derivative. EURASIA Journal of Mathematics, Science and Technology Education, 15(1), Article em1658. https://doi.org/10.29333/ejmste/99811
Bossé, M. J., Adu-Gyamfi, K., & Cheetham, M. R. (2011). Assessing the Difficulty of Mathematical Translations: Synthesizing the Literature and Novel Findings. nternational Electronic Journal of Mathematics Education, 6(3), 113–133. https://doi.org/10.29333/iejme/264
Cho, H., & Kwon, O. N. (2023). Undergraduate students’ understanding of the concept of derivatives in multivariable calculus. En M. Ayalon, B. Koichu, R. Leikin, L. Rubel, & M. Tabach (Eds.), Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 187–194). Psychology of Mathematics Education. https://snu.elsevierpure.com/en/publications/undergraduate-students-understanding-of-the-concept-of-derivative
Drijvers, P. (2019). Embodied instrumentation: Combining different views on the use of digital technology in mathematics education. Eleventh Congress of the European Society for Research in Mathematics Education (CERME 11). Utrecht, Netherlands.
Feudel, F., & Biehler, R. (2021). Students’ understanding of the derivative concept in the context of mathematics for economics. Journal für Mathematik-Didaktik, 42, 273–305. https://doi.org/10.1007/s13138-020-00174-z
Fuentealba, C., Badillo, E., Sánchez-Matamoros, G., & Cárcamo, A. (2019). The understanding of the derivative concept in higher education. EURASIA Journal of Mathematics, Science and Technology Education, 15(2), Article em1662. https://doi.org/10.29333/ejmste/100640
Galindo Illanes, M. K., & Breda, A. (2024). Proceso de instrucción de la derivada aplicado a estudiantes de Ingeniería Comercial en Chile. Uniciencia, 38(1), 303–325. https://doi.org/10.15359/ru.38-1.17
Hong, D. S., & Lee, J. K. (2024). Contrasting cases of college calculus instructors: Their preferences and potential pedagogy in teaching derivative graphs. International Journal of Mathematical Education in Science and Technology, 55(9), 2087–2106. https://doi.org/10.1080/0020739X.2022.2120838
Hurrell, D. P. (2021). Conceptual knowledge OR procedural knowledge OR conceptual knowledge AND procedural knowledge: Why the conjunction is important to teachers. Australian Journal of Teacher Education, 46(2). https://doi.org/10.14221/ajte.2021v46n2.4
Litteck, K., Rolfes, T., & Heinze, A. (2025). The structure of knowledge about the concept of derivative: A study investigating a process-object framework. International Journal of Mathematical Education in Science and Technology, 56(11), 2164–2184. https://doi.org/10.1080/0020739X.2024.2397990
Mkhatshwa, T. P. (2024). Best practices for teaching the concept of the derivative: Lessons from experienced calculus instructors. EURASIA Journal of Mathematics, Science and Technology Education, 20(4), Article em2426. https://doi.org/10.29333/ejmste/14380
Moru, E. K. (2020). An APOS analysis of university students’ understanding of derivatives: A Lesotho case study. African Journal of Research in Mathematics, Science and Technology Education, 24(2), 279–292. https://doi.org/10.1080/18117295.2020.1821500
Pinto, M., & Tall, D. (2002). Building formal mathematics on visual imagery: A case study and a theory. For the Learning of Mathematics, 22(1), 2–10. https://flm-journal.org/Articles/5DF87CDA4C761DF844802867C13B00.pdf
Quintero Covarrubias, G., Armenta Beltrán, M., & Plata Rocha, W. (2025). Cambio conceptual en la comprensión de la derivada en estudiantes universitarios. NTHE. Revista Electrónica del Consejo de Ciencia y Tecnología del Estado de Querétaro, 47, 13–22. https://doi.org/10.5281/zenodo.15231887
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2022). A new view about connections: The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 53(6), 1231–1256. https://doi.org/10.1080/0020739X.2020.1799254
Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., & García-García, J. (2021). Exploring university Mexican students’ quality of intra-mathematical connections when solving tasks about derivative concept. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), Article em2006. https://doi.org/10.29333/ejmste/11160
Ryberg, U. (2018). Generating different lesson designs and analyzing their effects: The impact of representations when discerning aspects of the derivative. The Journal of Mathematical Behavior, 51, 1–14. https://doi.org/10.1016/j.jmathb.2018.03.012
Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2(1), Article 16. https://doi.org/10.1186/s40594-015-0029-5
Straehler-Pohl, H., Bohlmann, N., & Pais, A. (Eds.). (2017). The disorder of mathematics education: Challenging the sociopolitical dimensions of research. Springer.
Trigueros, M., & Martínez-Planell, R. (2020). Understanding of the derivative concept in higher education. ZDM – Mathematics Education, 52(5), 839–853. https://doi.org/10.1007/s11858-020-01157-7
Trigueros, M., Badillo, E., Sánchez-Matamoros, G., & Hernández-Rebollar, L. A. (2024). Contributions to the characterization of the schema using APOS theory: Graphing with derivative. ZDM – Mathematics Education, 56, 1093–1108. https://doi.org/10.1007/s11858-024-01615-6
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Mailyn Medero-Ruíz, Abdiel Quiñones-Martínez
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish in Revista UGC agree to the following terms:
1. Copyright
Authors retain unrestricted copyright to their work. Authors grant the journal the right of first publication. To this end, they assign the journal non-exclusive exploitation rights (reproduction, distribution, public communication, and transformation). Authors may enter into additional agreements for the non-exclusive distribution of the version of the work published in the journal, provided that acknowledgment of its initial publication in this journal is given.
© The authors.
2. License
The articles are published in the journal under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0). The terms can be found at: https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en
This license allows:
- Sharing: Copying and redistributing the material in any medium or format.
- Adapting: Remixing, transforming, and building upon the material.
Under the following terms:
- Attribution: You must give appropriate credit, provide a link to the license, and indicate if any changes were made. You may do this in any reasonable manner, but not in any way that suggests the licensor endorses or sponsors your use.
- NonCommercial: You may not use the material for commercial purposes.
- ShareAlike: If you remix, transform, or build upon the material, you must distribute your creation under the same license as the original work.
There are no additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
