A qualitative study of students’ semiotic ability in calculus problem representation: A visual thinking perspective

Abstract

Amid limited attention to the interplay between visual thinking and semiotic processes in calculus learning, this study aims to describe students’ semiotic ability to represent calculus problems at different levels of visual thinking. This study employed a descriptive qualitative case study design to explore students’ semiotic abilities in representing calculus problems at different levels of visual thinking. The subjects were selected through purposive sampling from fourth-semester Mathematics Education students. Data were collected through written tests and semi-structured interviews, then analyzed using Peirce’s Triadic semiotic framework. The findings indicate that students with high visual thinking ability can construct deep conceptual interpretants, particularly in understanding derivatives as dynamic processes and as geometric transitions from secant lines to tangent lines; however, they have difficulty articulating this understanding through written visual representations. Students with moderate visual thinking ability demonstrate partial comprehension of semiotic components and can integrate them only with reflective scaffolding. In contrast, students with low visual thinking ability fail across all semiotic aspects and therefore tend to rely on mechanistic procedures without a strong conceptual foundation. These results suggest a strong positive relationship between visual thinking and semiotic ability and underscore the urgency of integrating multimodal, visually oriented approaches into calculus instruction to foster comprehensive conceptual understanding.