Journal of higher education curriculum studies

Journal of higher education curriculum studies

The Relationship of Concept Image and Concept Definition of the Limit of a Function with the Mathematical Motivation of Student Teachers at Farhangian University of Tehran

Document Type : Research Paper

Authors
1 Department of Mathematics Education, Farhangian University, P.O. Box 889-14665, Tehran, Iran.
2 Master's student, Shahid Beheshti University of Education, Tehran, Iran.
10.22034/hecs.2026.555034.2037
Abstract
The concept of limit is a transition point to advanced mathematical thinking and one of the most difficult concepts for learners. The present study aimed to determine the relationship between conceptual image and conceptual definition of the limit of a function and student-teachers' mathematics motivation. The research method was quantitative, of a descriptive-correlational type. The statistical population consisted of all 54 first-semester mathematics education students of Shahid Beheshti and Shahid Sharafat campuses of Farhangian University of Tehran, who were studied by census method. The instrument was a researcher-made twenty-item questionnaire on a Likert scale, whose structure was examined through exploratory factor analysis. The findings showed that there is no significant relationship between conceptual image and mathematics motivation, nor between conceptual definition and mathematics motivation; however, the two cognitive constructs are strongly correlated with each other, and men's mathematics motivation is significantly higher than women's. Also, students attributed the highest effect on the formation of their image of limit to teaching method and activity design. The results indicate that cognitive coherence and motivation are two relatively independent constructs, and the teacher education curriculum should target both separately.
Keywords
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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.
Bakhshalizadeh, Sh., Reyhani, E., & Nazari, K. (2013). The effect of a visualization-based teaching approach on high-school students' understanding of the limit concept and their spatial ability. Advances in Cognitive Sciences, 15(1), 27–42. [in Persian]
Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced mathematical thinking (pp. 153–166). Kluwer Academic Publishers.
Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: Beginning with a coordinated process schema. The Journal of Mathematical Behavior, 15(2), 167–192.
Davis, R. B., & Vinner, S. (1986). The notion of limit: Some seemingly unavoidable misconception stages. The Journal of Mathematical Behavior, 5(3), 281–303.
Denbel, D. G. (2014). Students' misconceptions of the limit concept in a first calculus course. Journal of Education and Practice, 5(34), 24–41.
Elia, I., 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.
Ferrini-Mundy, J., & Graham, K. (1994). Research in calculus learning: Understanding of limits, derivatives and integrals. In J. Kaput & E. Dubinsky (Eds.), Research issues in undergraduate mathematics learning (pp. 31–45). Mathematical Association of America.
Firoozshahi, F., & Yaftian, N. (2025). Exploring factors affecting students' mathematical performance: A meta-synthesis study. New Educational Approaches, 20(1), 21–54. [in Persian]
 
 
Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82(3), 439–453.
Jordaan, T. (2005). Misconceptions of the limit concept in a mathematics course for engineering students [Unpublished master's dissertation]. University of South Africa.
Juter, K. (2005). Limits of functions: How do students handle them? Pythagoras, 61, 11–20.
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, 2(1), 35–48.
Murphy, P. K., & Alexander, P. A. (2000). A motivated exploration of motivation terminology. Contemporary Educational Psychology, 25(1), 3–53.
Molkhasi, A. (2020). The whys of the limit concept and its applications. Pooyesh in Basic Sciences Education, 2, 1–9. [in Persian]
Nemati, Z. (2009). Factors affecting students' interest in mathematics. [in Persian]
Reyhani, E., Sharifi, M., & Soltani, A. (2017). Misconceptions of final-year secondary school students about the limit concept. Education, 32(4), 41–66. [in Persian]
Susiswo, Parameswari, P., Utami Putri, O. R., Lanya, H., Utami, A. D., & Murniasih, T. R. (2023). The growth of students' function limit concepts understanding in solving controversial problems based on Pirie–Kieren's theory. Jurnal Teori dan Aplikasi Matematika, 7(4), 1204–1220.
Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31(3), 258–276.
Sarmad, Z., Bazargan, A., & Hejazi, E. (2020). Research methods in behavioral sciences. Tehran: Agah. [in Persian]
Shahvarani, A., Gooya, Z., & Javadi, M. (2009). Concept image and concept definition. Mathematics Education Growth, No. 98. [in Persian]
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.
Um, E. K., Corter, J. E., & Tatsuoka, K. K. (2005). Motivation, autonomy support, and mathematics performance: A structural equation analysis. Teachers College, Columbia University.
Zeinivand, F. (2015). Conceptual explanation of mathematical thinking: What, why and how. Higher Education Curriculum Studies, 6(12), 153–172. [in Persian]