Semiosis formal construction of limit concepts: a study on students’ comprehensive triadic understanding

Abstract

This study applied Peirce’s triadic semiotic framework to map students’ representational transitions in constructing the formal definition of limit, an approach that has rarely been employed in limit research. Meanwhile, the prior studies documented students’ difficulties and instructional interventions, few explicate the internal semiotic mechanisms underlying the shift from visual intuition to the epsilon-delta formulation. Using a qualitative case study approach, this study examined students’ semiotic processes in formally constructing the concept of limit through written tests and interviews. The test was administered to 21 students for 120 minutes to assess their understanding of the limit concept, meanwhile interview with 2 students was conducted for 90 minutes for each student to explore their semiotic processes. The results indicated that the students constructed the limit concept in a formal manner through the sequential stages of representamen, object, and interpretant operating in a triadic and comprehensive. Multimodal representamens facilitate the transition toward the formal epsilon-delta conception; the object was construed as the function’s behavior near a point; and the interpretant emerges as a coherent formal understanding. Findings show that multimodal representamens facilitate students’ transition from intuition to rigorous epsilon-delta reasoning.