Fleksibilitas Representasional Mahasiswa dalam Memahami Kekontinuan dan Keterdiferensialan Fungsi

Abstract

Understanding continuity and differentiability requires students to coordinate the same mathematical meaning across symbolic and visual representations. However, procedural success in one representation does not necessarily indicate consistent conceptual understanding in another. This study aimed to describe students’ representational flexibility in understanding continuity and differentiability, identify emerging misconceptions, and examine the relationship between symbolic and visual understanding. A descriptive design combining quantitative descriptive analysis and qualitative thematic analysis was employed. Eighty-three undergraduate mathematics education students completed six diagnostic tasks comprising three algebraic and three visual tasks. Semi-structured interviews were conducted with selected participants representing variations in written-response patterns. The findings showed that the proportion of correct responses was higher for algebraic representations (25.7%) than for visual representations (22.1%), whereas blank responses were more frequent in visual tasks (34.1%) than in algebraic tasks (29.7%). Aggregate-score analysis revealed four cross-representational patterns: decreasing performance (45%), consistently incorrect performance (30%), consistently correct performance (15%), and increasing performance (10%). Thematic analysis identified five reasoning patterns: contextually appropriate reasoning, formal understanding, formal-perceptual reasoning, intuitive visual reasoning, and conceptual confusion. The most prominent misconceptions involved treating graph smoothness as sufficient evidence of differentiability and conflating continuity with differentiability. These findings indicate that students’ difficulties are related not only to procedural knowledge but also to their ability to maintain conceptual consistency across representations. Calculus instruction should therefore explicitly engage students in converting, comparing, and justifying symbolic and visual representations to strengthen representational flexibility.