Students' conceptual understanding of limit of functions reviewed from mathematical beliefs

Conceptual understanding is a student’s cognitive structure characterised by the ability to transform and explain concepts in solving problems. Many students were unable to explain the concepts and the relationships between concepts in solving the limit of functions. This study aimed to explore students' conceptual understanding of the limit of functions in terms of mathematical beliefs. The subjects were 30 mathematics education students at Syiah Kuala University who had taken calculus courses for advanced real analyses. Data were collected using questionnaires, tests, and interviews. Data processing was carried out by reducing data, presenting, analysing, and drawing conclusions. The results of the study showed that students with strong mathematical beliefs demonstrated a more complete and integrated conceptual understanding of the limits of functions, as they could connect concepts, procedures, and graphical representations. In contrast, students with medium and low mathematical beliefs tended to focus only on procedural knowledge, often failing to explain underlying concepts or make meaningful connections between concepts and problem-solving steps. Based on the results, calculus lecturers need to build a strong conception of the material on the real number system and real functions so that the concept of the limit of functions is easily understood and memorised.