Unveiling the roots of students’ low comprehension of quadratic functions: A hermeneutic phenomenological study in a West Lombok junior high school, Indonesia

Abstract

Quadratic functions are a core topic in junior high school mathematics, yet many students continue to struggle to master this material. This study explored, in depth, the factors underlying the low comprehension of quadratic functions among eighth-grade students at a public junior high school in West Lombok Regency, Indonesia. A hermeneutic phenomenological design was used to capture students’ lived experiences and interpretations of their learning difficulties, complemented by thematic analysis to identify recurring patterns across responses. Data were collected through an open-ended questionnaire completed by ten purposively selected students and analyzed following Braun and Clarke’s six-phase thematic analysis, assisted by an artificial intelligence tool (ChatGPT) during initial coding and subsequently verified manually by the researchers. The analysis produced ten initial codes, condensed into five categories and, ultimately, four overarching themes: (1) difficulty in understanding basic concepts, (2) lack of participation in learning, (3) less effective teaching methods, and (4) low motivation to learn mathematics. These findings indicate that students’ struggles with quadratic functions stem not merely from the material’s cognitive complexity but from an interplay of cognitive, behavioral, pedagogical, and affective factors. By foregrounding students’ own voices rather than relying solely on achievement scores, this study offers a more holistic understanding of algebra learning difficulties. It recommends that teachers design more contextual, participatory, and enjoyable instructional strategies, supported by visual and concrete media, to strengthen students’ conceptual understanding of quadratic functions and to inform future intervention-based research.