Analysis of Mathematics Student Teachers’ Conceptions of the Limit of a Function: An Autoethnographic Perspective
Keywords:
calculus; conceptions; limit concept; operational conceptions; structural conceptions
Abstract
The limit concept is often regarded as the foundation for Calculus. This study explores the First-year Mathematics student teachers’ conceptions of the limit of a function. This study was carried out in one of the public universities in Limpopo Province, South Africa. We used an autoethnographic design to describe and interpret three student teachers’ conceptions about the limit of a function concept. The test was used as a data collection instrument. The test was based on the limit concept, covering the intuitive definition of a limit, the application of the intuitive definition of a limit using a table of values, the graphical determination of a limit, and the algebraic determination of a limit. The thematic analysis procedure was used to analyse student teachers’ test scripts. Three student teachers’ test scripts were qualitatively analysed. The findings of the study revealed that students have underdeveloped conceptions of the intuitive definition of the limit concept. The findings also revealed that students show some conceptions of the limit concepts, particularly on the algebraic representations, as compared to other forms of representations, such as numerical and graphical.
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References
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Beynon, K. A., & Zollman, A. (2015). Lacking a formal concept of limit: Advanced non-mathematics students’ personal concept definitions. Investigations in Mathematics Learning, 8(1), 47-62. https://doi.org/10.1080/24727466.2015.11790347.
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Brown, A, (2004). “Learners’ Conceptions of the Limit in Calculus” Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada.
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Elia, A., Gagatsis, A., Panaoura, A., Zachariades, T., & Zoulinaki, F. (2009). Geometric and Algebraic approaches in the concept of limit and the impact of the Didactic Contract. International Journal of Science and Mathematics Education, 7(4), 765–790. https://doi.org/10.1007/s10763-009-9149-z.
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Fernández-Plaza, J.A., Simpson, A. (2016). Three concepts or one? Students’ understanding of basic limit concepts. Educ Stud Math 93, 315–332. https://doi.org/10.1007/s10649-016-9707-6.
Hutkemri, E. Z. (2014). Impact of using GeoGebra on students’ conceptual and procedural knowledge of limit function. Mediterranean Journal of Social Sciences, 5(23), 873. https://doi.org/10.5901/mjss.2014.v5n23p873.
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Juter, K. (2007). Students’ conceptions of limits, high achievers versus low achievers. The Montana Mathematics Enthusiast, 4(1), 53–65. https://www.diva-portal.org/smash/get/diva2:207620/FULLTEXT01.pdf.
Kado, K. (2021). Impact of GeoGebra on the Students’ Conceptual: Understanding of Limit of a Function in Bhutan. International Journal of Asian Education, 2(4), 539-548. https://doi.org/10.46966/ijae.v2i4.140.
Kim, D. J., Kang, H., & Lee, H. J. (2015). Two Different Epistemologies about Limit Concepts. International Education Studies, 8(3), 138-145. http://dx.doi.org/10.5539/ies.v8n3p138.
Machaba, F. M. (2017). Grade 9 learners’ structural and operational conceptions of the equal sign: a case study of a Secondary School in Soshanguve. Eurasia journal of mathematics, science and technology education, 13(11), 7243-7255. https://doi.org/10.12973/ejmste/78017.
Przenioslo, M. (2004). Images of the limit of function formed in the course of mathematical studies at the university. Educational Studies in Mathematics, 55(1), 103-132. https://doi.org/10.1023/B:EDUC.0000017667.70982.05.
Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University). Available from ProQuest dissertations and theses. (UMI 3683397).
Salas, S. L., Hille, E., & Etgen, G. J. (2021). Calculus: One and several variables. Hoboken, New Jersey: John Wiley & Sons. https://books.google.co.za/books?id=R-1ZEAAAQBAJ.
Sebsibe, A. S. (2019). Overcoming difficulties in learning calculus concepts: The case of grade 12 students (Doctoral dissertation, University of South Africa). http://hdl.handle.net/10500/26225.
Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), em0574. https://doi.org/10.29333/iejme/6294.
Sebsibe, A. S., Dorra, B. T., & Beressa, B. W. (2019). Students’ difficulties and misconceptions of the function concept. International Journal of Research, Granthaalayah, 7(8), 181-196. https://doi.org/10.29121/granthaalayah.v7.i8.2019.656.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36. https://www.jstor.org/stable/3482237.
Sulastri, R., Suryadi, D., Prabawanto, S., Cahya, E., Siagian, M. D., & Tamur, M. (2021). Prospective mathematics teachers’ concept image on the limit of a function. In Journal of Physics: Conference Series (Vol. 1882, No. 1, p. 012068). IOP Publishing. https://doi.org/10.1088/1742-6596/1882/1/012068.
Taylor-Powell, E., & Renner, M. (2003). Analyzing qualitative data. Programme Development & Evaluation, University of Wisconsin-Extension Cooperative Extension, 1-10.
Tossavainen, A., & Helenius, O. (2024). Student Teachers' Conceptions of Fractions: A Framework for the Analysis of Different Aspects of Fractions. Mathematics Teacher Education and Development, 26(1), 4.1 -20. : https://mted.merga.net.au/index.php/mted/article/view/889
Adams, T. E., Ellis, C., & Jones, S. H. (2017). Autoethnography. The international encyclopedia of communication research methods, 1-11. https://doi.org/10.1002/9781118901731.iecrm0011.
Adhikari, K. P. (2021). Difficulties and misconceptions of students in learning limit. Interdisciplinary Research in Education, 5(1-2), 15-26. https://doi.org/10.3126/ire.v5i1-2.34731.
Ahmed, S. K. (2024). The pillars of trustworthiness in qualitative research. Journal of Medicine, Surgery, and Public Health, 2, 100051. https://doi.org/10.1016/j.glmedi.2024.100051.
Assagaf, S. F., & Arwadi, F. (2021). Students’ Understanding on Formal Definition of Limit. In Journal of Physics: Conference Series, 1752 (1), p. 012082. IOP Publishing. doi:10.1088/1742-6596/1752/1/012082.
Bansilal, S., & Mkhwanazi, T. W. (2022). Pre-service student teachers’ conceptions of the notion of limit. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2020.1864488.
Baye, M. G., Ayele, M. A., & Wondimuneh, T. E. (2021). Implementing GeoGebra integrated with multi-teaching approaches guided by the APOS theory to enhance students’ conceptual understanding of limit in Ethiopian Universities. Heliyon, 7(5). https://doi.org/10.1016/j.heliyon.2021.e07012.
Beynon, K. A., & Zollman, A. (2015). Lacking a formal concept of limit: Advanced non-mathematics students’ personal concept definitions. Investigations in Mathematics Learning, 8(1), 47-62. https://doi.org/10.1080/24727466.2015.11790347.
Bezuidenhout, J. (2001). Limits and continuity: Some conceptions of first-year students. International journal of mathematical education in science and technology, 32(4), 487-500. https://doi.org/10.1080/00207390010022590
Bressoud, D., Ghedamsi, I., Martinez-Luaces, V., & Törner, G. (2016). Teaching and learning of calculus. Springer Nature. https://doi.org/10.1007/978-3-319-32975-8_1.
Brown, A, (2004). “Learners’ Conceptions of the Limit in Calculus” Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada.
Creswell, J. W. (2014). Qualitative, quantitative and mixed methods approach. Thousand Oaks, CA: Sage.
Denbel, D. G. (2014). Students’ misconceptions of the limit concept in a first calculus course. Journal of Education and Practice, 5(34), 24-40. https://core.ac.uk/download/pdf/234636567.pdf.
Duru, A. (2011). Pre-Service Teachers' Perception about the Concept of Limit. Kuram ve Uygulamada Egitim Bilimleri, 11(3), 1710-1715. Retrieved from https://www.proquest.com/scholarly-journals/pre-service-teachersperception-about-concept/docview/884455138/se-2.
Elia, A., Gagatsis, A., Panaoura, A., Zachariades, T., & Zoulinaki, F. (2009). Geometric and Algebraic approaches in the concept of limit and the impact of the Didactic Contract. International Journal of Science and Mathematics Education, 7(4), 765–790. https://doi.org/10.1007/s10763-009-9149-z.
Fernández, C., Moreno, M., & Sánchez-Matamoros, G. (2024). Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development. ZDM–Mathematics Education, 1-15. https://doi.org/10.1007/s11858-024-01573-z.
Fernández-Plaza, J.A., Simpson, A. (2016). Three concepts or one? Students’ understanding of basic limit concepts. Educ Stud Math 93, 315–332. https://doi.org/10.1007/s10649-016-9707-6.
Hutkemri, E. Z. (2014). Impact of using GeoGebra on students’ conceptual and procedural knowledge of limit function. Mediterranean Journal of Social Sciences, 5(23), 873. https://doi.org/10.5901/mjss.2014.v5n23p873.
Jameson, G., Machaba, M. F., & Matabane, M. E. (2023). An Exploration of Grade 12 Learners' Misconceptions on Solving Calculus Problem: A Case of Limits. Research in Social Sciences and Technology, 8(4), 94-124. https://doi.org/10.46303/ressat.2023.34
Juter, K. (2007). Students’ conceptions of limits, high achievers versus low achievers. The Montana Mathematics Enthusiast, 4(1), 53–65. https://www.diva-portal.org/smash/get/diva2:207620/FULLTEXT01.pdf.
Kado, K. (2021). Impact of GeoGebra on the Students’ Conceptual: Understanding of Limit of a Function in Bhutan. International Journal of Asian Education, 2(4), 539-548. https://doi.org/10.46966/ijae.v2i4.140.
Kim, D. J., Kang, H., & Lee, H. J. (2015). Two Different Epistemologies about Limit Concepts. International Education Studies, 8(3), 138-145. http://dx.doi.org/10.5539/ies.v8n3p138.
Machaba, F. M. (2017). Grade 9 learners’ structural and operational conceptions of the equal sign: a case study of a Secondary School in Soshanguve. Eurasia journal of mathematics, science and technology education, 13(11), 7243-7255. https://doi.org/10.12973/ejmste/78017.
Przenioslo, M. (2004). Images of the limit of function formed in the course of mathematical studies at the university. Educational Studies in Mathematics, 55(1), 103-132. https://doi.org/10.1023/B:EDUC.0000017667.70982.05.
Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University). Available from ProQuest dissertations and theses. (UMI 3683397).
Salas, S. L., Hille, E., & Etgen, G. J. (2021). Calculus: One and several variables. Hoboken, New Jersey: John Wiley & Sons. https://books.google.co.za/books?id=R-1ZEAAAQBAJ.
Sebsibe, A. S. (2019). Overcoming difficulties in learning calculus concepts: The case of grade 12 students (Doctoral dissertation, University of South Africa). http://hdl.handle.net/10500/26225.
Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), em0574. https://doi.org/10.29333/iejme/6294.
Sebsibe, A. S., Dorra, B. T., & Beressa, B. W. (2019). Students’ difficulties and misconceptions of the function concept. International Journal of Research, Granthaalayah, 7(8), 181-196. https://doi.org/10.29121/granthaalayah.v7.i8.2019.656.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36. https://www.jstor.org/stable/3482237.
Sulastri, R., Suryadi, D., Prabawanto, S., Cahya, E., Siagian, M. D., & Tamur, M. (2021). Prospective mathematics teachers’ concept image on the limit of a function. In Journal of Physics: Conference Series (Vol. 1882, No. 1, p. 012068). IOP Publishing. https://doi.org/10.1088/1742-6596/1882/1/012068.
Taylor-Powell, E., & Renner, M. (2003). Analyzing qualitative data. Programme Development & Evaluation, University of Wisconsin-Extension Cooperative Extension, 1-10.
Tossavainen, A., & Helenius, O. (2024). Student Teachers' Conceptions of Fractions: A Framework for the Analysis of Different Aspects of Fractions. Mathematics Teacher Education and Development, 26(1), 4.1 -20. : https://mted.merga.net.au/index.php/mted/article/view/889
Published
2026-07-29
How to Cite
Mabotja, K., & Muthelo, D. (2026). Analysis of Mathematics Student Teachers’ Conceptions of the Limit of a Function: An Autoethnographic Perspective. Studies in Learning and Teaching, 7(2). https://doi.org/10.46627/silet.v7i2.833
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Articles
