Exploring Students' Conceptual Images of Function and Their Properties: A Hermeneutic Phenomenological Study - Hana Auriel Sharon Siahaan; Muhammad Daut Siagian; Rikayanti (Jurnal Didactical Mathematics, 2026)
Understanding students' concept images of functions is fundamental to mathematics education because these images influence how learners interpret definitions, reason about function properties, and construct mathematical representations. Although previous studies have documented common misconceptions, relatively little is known about how students construct mathematical meaning through their lived learning experiences. Addressing this gap, this study explored students' concept images of functions using Ricoeur's hermeneutic phenomenology integrated with Tall and Vinner's concept image framework. A qualitative phenomenological design was employed, involving 30 Grade X secondary school students. Data were collected through written tasks focusing on function evaluation, function properties, and multiple representations, followed by semi-structured interviews with purposively selected participants. Data were analyzed through Ricoeur's hermeneutic process of naïve understanding, structural analysis, and appropriation to reveal the interpretive meanings underlying students' mathematical reasoning. The findings identified four major interpretive patterns: procedural, integrated, misconception, and representational concept images. While most students successfully performed routine procedures, many interpreted functions in terms of procedural routines, perceptual characteristics, and familiar examples rather than through formal structural definitions. Persistent misconceptions, including the conflation of codomain and range, domain-centered interpretations of surjectivity, and limited representational flexibility, reflected coherent interpretive structures rather than isolated conceptual errors. These findings extend Tall and Vinner's concept image theory by demonstrating that concept images are continuously reconstructed through the interpretation of mathematical experiences. The study suggests that function instruction should move beyond procedural fluency by engaging students with contrasting examples, multiple representations, reflective justification, and explicit connections between concept images and formal concept definitions to support meaningful conceptual development.