Journal of Research in Science, Mathematics and Technology Education

An APOS Analysis of Undergraduate Mathematics Students’ Understanding of the Limit of a Function Concept: A Case of a University in Zimbabwe

Edmore Mangwende 1 * ,
Aneshkumar Maharaj 2
1 University of Zimbabwe, Department of Mathematics and Computational Sciences, Harare, Zimbabwe2 University of KwaZulu Natal* Corresponding Author
Download PDF
Journal of Research in Science, Mathematics and Technology Education, Volume 9, Issue 3, September 2026, pp. 1-15
OPEN ACCESS VIEWS: 4 DOWNLOADS: 2 Publication date: 15 Sep 2026
ABSTRACT
Despite the foundational importance of limits in calculus, many students struggle to move beyond procedural knowledge. This study analyzed fifty-one first-year mathematics students using the APOS-ACE framework to identify specific cognitive barriers. Results show that after standard instruction, more than half of the students could not reach the "Object" level of understanding. These findings suggest that traditional lecture formats may be insufficient; instead, the researchers advocate for a more dynamic instructional approach incorporating peer collaboration and diverse visual activities to facilitate the construction of complex mental schemas.
KEYWORDS
APOS-ACE, limit of a function, mathematics student, mental structure.
CITATION (APA)
Mangwende, E., & Maharaj, A. (2026). An APOS Analysis of Undergraduate Mathematics Students’ Understanding of the Limit of a Function Concept: A Case of a University in Zimbabwe. Journal of Research in Science, Mathematics and Technology Education, 9(3), 1-15.
REFERENCES
  1. Arnon, I., Cottrill, J. Dubinsky, E., Oktac, A., Roa, S., Trigueros, M., & Weller, K. (2014), APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, Springer, NY, Heidelberg, Dondrecht: London. https://doi.org/10.1007/978-1-4614-7966-6
  2. Asiala, M., Brown, A., DeVeris, D.J., Dubunisky, E., Mathews, D. & Thomas, K. (1996). A Framework for Research and Curriculum Development in Undergraduate Mathematics Education. ·Retrieved from https://www.researchgate.net/publication/2784058
  3. Cetin, I. (2009). Students’ understanding of limit concept: An APOS perspective. Phd Thesis. Middle East Technical University. Retrieved from https://etd.lib.metu.edu.tr/upload/12611259/index.pdf
  4. Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: Beginning with a coordinated process scheme. Journal of Mathematical Behavior, 15, 167–192. https://doi.org/10.1016/S0732-3123(96)90015-2
  5. Denbel, D.G. (2014). Students’ misconceptions of the limit concept in a first Calculus Course. Journal of Education and Practice, 5(34). https://www.iite.org.journals/index-php/jep/article
  6. Dubinsky, E. (1984). The Cognitive effect of computer experiences on learning abstract mathematical concepts. Korkeakoulujen Ark-Vutiset, 2:41-47.
  7. Fernández, E. (2004). The students’ take on the epsilon-delta definition of a limit. Primus, 14(1), 43–54. https://doi.org/10.1080/10511970408984076
  8. Juter, K. (2005). Limits of functions. How do students handle them? Pythagorus, 61, 11-20. https://www.doi.org/10.4102/pythagoras.voi61.117.
  9. Liang, S. (2016). Teaching the concept of limit by using conceptual conflict strategy and Desmos graphing calculator. International Journal of Research in Education and Science (IJRES), 2(1), 35-48. https://www.doi.org/10.21890/ijres.62743.
  10. Maharaj, A. (2010). Am APOS Analysis of students’ understanding of the concept of a limit of a function. Pythagoras, 71. https://doi.org/10.4102/pythagoras.v0i71.6.
  11. Mukuka, A. & Tatira, B. (2024). Unpacking pre-service teachers’ conceptualization of logarithms differentiation through the APOS theory. Eurasian Journal of Mathematics, Science and Technology Education, 20(12), 1-13. https://www.10.29333/ejmste/15655.
  12. Ndagijimana, J.B., Munyaruhengeri, J.P.A., & Hukizimana, T. (2024). Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan Secondary Schools. International Journal of Education and Practice, 19(2), 467-482. https://doi.org/10.194488/61.v1212.3719.
  13. Oktac, A., Trigueros, M., & Romo, A. (2019). APOS theory: Connecting research and teaching. FLM Publishing association. For the Learning of Mathematics, 39(1), 33-37. https://www.jstro.org/stable/26742010.
  14. Sebsibe, A.S. & Feza, N.N. (2020). Assessment of students’ conceptual knowledge in limit of functions. International electronic journal of mathematics education. 15(2). https://www.doi.org/10.29333/iejme/6294.
  15. Swinyard, C., & Larsen, S. (2012). Coming to understand the formal definition of limit: Insights gained from engaging students in reinvention. Journal for Research in Mathematics Education, 43(4), 465-493. https://www.doi.org.10.5951/jresematheduc.43.4.0465.
  16. Trigueros, M., Badillo, E., Sanchez-Matamaros, G., & Hernandez-Rebollar, L.A. (2024). Contributions in the characterization of the schema using APOS theory: Graphing with derivatives. ZDM- Mathematics Education, 56, 1093-1108. https://www.doi.org.10.1007/s11858-024-016156.
  17. Weller, K., Arnon, I. & Dubunisky, E. (2009). Pre-service teachers’ understanding of the relation between a fraction or an integer and its decimal expansion. Canadian Journal of Science, Mathematics and technology education, 9, 5-28. https://www.doi.org/10.1080/14026150902817381.
  18. Weller, K., Arnon, I., & Dubinsky, E. (2011). Pre-service teachers’ understanding of the relation between a fraction or integer and its decimal expansion: Strength and stability of belief. Canadian Journal of Science, Mathematics, and Technology Education, 11(2), 129–159. https://doi.org/10.1080/14926156.2011.570612
LICENSE
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.