Junior High School Students’ Misconceptions and Problem-Solving Strategies in Relations and Functions

Mathematical misconceptions can hinder students’ problem-solving abilities, particularly in relations and functions, which involve multiple representations. Previous research has generally examined misconceptions and problem-solving abilities separately, leaving the relationship between them insufficiently understood. This study aimed to identify misconceptions and mathematical difficulties and analyze the problem-solving strategies of eighth-grade students at SMP Negeri 2 Parepare in relations and functions by integrating the Certainty of Response Index (CRI) with an analysis based on Polya’s problem-solving stages. A qualitative approach with a descriptive-narrative design was employed. Twenty-eight students completed a CRI-based diagnostic test, after which six students were purposively selected based on their test scores, with two students representing each of the high-, medium-, and low-score categories. These six participants completed a written test consisting of non-routine, open-ended problems structured around Polya’s stages. Five of them subsequently participated in semi-structured interviews to clarify aspects of their responses at stages requiring further investigation. Data were analyzed using the Miles and Huberman model. Trustworthiness was established through source triangulation, involving comparisons across participants, and methodological triangulation, involving comparisons among CRI results, written responses, and interviews. The findings revealed conceptual difficulties in distinguishing between the codomain and range and understanding the conditions that define a function, representational errors involving the use of set labels in ordered pairs, and procedural difficulties in applying formulas to tabulated data. At the understanding-the-problem stage, students generally identified the domain correctly but were less accurate in identifying the range. At the devising-a-plan stage, some students made notational errors. At the carrying-out-the-plan stage, difficulties were procedural. At the looking-back stage, most students checked only whether pairings existed without verifying their uniqueness. These findings highlight the importance of strengthening conceptual understanding, using multiple representations, and fostering the habit of checking solutions in mathematics instruction.