A Study of Mathematical Conceptual Understanding of Limits of Functions in Indeterminate Forms Based on the APOS Theory among Undergraduate Students at the Faculty of Science and Technology, Princess of Naradhiwas University
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Abstract
This study aimed to examine levels of mathematical conceptual understanding of limits of functions in indeterminate forms and to analyze characteristics of conceptual understanding in terms of content, procedural, and relational aspects among undergraduate students in the Faculty of Science and Technology, Princess of Naradhiwas University. The study was grounded in the APOS framework proposed by Dubinsky (1991) and the conceptual understanding framework of Kilpatrick et al. (2001). The research instruments comprised a 30-item Mathematical Conceptual Understanding Test and five task-based performance tasks, complemented by task-based in-depth interviews. The participants were 40 first- and second-year undergraduate students selected through purposive selection, and six target students from high, medium, and low achievement groups were selected to provide in-depth qualitative data. The results indicated a mean total score of 19.50 out of 30 (65.00%), which was classified as a good level. According to the APOS framework, most students were classified at the Action and Process levels, reflecting a tendency to rely on substitution and procedural execution rather than structural analysis of expressions. Findings from task-based performances and interviews further showed that students at the Action and Process levels demonstrated conceptual understanding of content, procedures, and relationships mainly through substitution, formula use, or familiar methods, whereas students at the Object and Schema levels were able to analyze the structure of expressions, justify solution methods, and coherently connect the concepts of limits, continuity, and derivatives in accordance with the underlying mathematical structure. Overall, the findings suggest that integrating the APOS framework with components of mathematical conceptual understanding provides a systematic account of students’ thinking and reasoning about limits of functions in indeterminate forms.
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หากผู้เสนอบทความมีความจำเป็นเร่งด่วนในการตีพิมพ์โปรดส่งลงตีพิมพ์ในวารสารฉบับอื่นแทน โดยกองบรรณาธิการจะไม่รับบทความหากผู้เสนอบทความไม่ปฏิบัติตามเงื่อนไขและขั้นตอนที่กำหนดอย่างเคร่งครัด ข้อมูลของเนื้อหาในบทความถือเป็นลิขสิทธิ์ของ Journal of Inclusive and Innovative Education คณะศึกษาศาสตร์ มหาวิทยาลัยเชียงใหม่
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