Examining Students’ Conceptual Understanding in Solving Contextual Problems on Linear Equations in One Variable: A Cross-Case Qualitative Analysis

Rispa Rispa; Siti Suprihatiningsih

doi:10.31949/dm.v8i2.18106

Authors

Rispa Rispa Universitas Katolik Santo Agustinus Hippo, Indonesia
Siti Suprihatiningsih Universitas Katolik Santo Agustinus Hippo, Indonesia

DOI:

https://doi.org/10.31949/dm.v8i2.18106

Abstract

Mathematical conceptual understanding plays a crucial role in enabling students to establish meaningful relationships among mathematical ideas and apply knowledge flexibly in problem-solving situations. However, many students continue to rely on procedural approaches without developing deeper conceptual reasoning, particularly when solving contextual mathematical problems. Existing studies have mainly focused on achievement outcomes or isolated dimensions of conceptual understanding, providing limited insight into how students demonstrate conceptual understanding across multiple indicators within contextual problem-solving situations. Therefore, this study aimed to analyze students’ conceptual understanding in solving contextual problems related to linear equations in one variable across different levels of ability. This study employed a descriptive qualitative research design involving 30 eighth-grade students at SMP Negeri 1 Jelimpo, West Kalimantan, Indonesia. Data were collected through written tests and semi-structured interviews. Participants representing high-, medium-, and low-level conceptual understanding were selected using purposive sampling techniques. Data were analyzed through data reduction, data display, and conclusion drawing using triangulation procedures. The findings revealed that students’ conceptual understanding demonstrated progressive differences in cognitive organization rather than merely differences in procedural performance. High-level students exhibited integrated conceptual structures, medium-level students demonstrated transitional characteristics, and low-level students showed fragmented understanding characterized by symbolic dependence and procedural imitation. Furthermore, conceptual understanding indicators functioned as interconnected dimensions in which difficulties in one indicator influenced performance in other dimensions. The findings highlight the importance of instructional practices emphasizing conceptual exploration, multiple representations, contextual learning, and structured scaffolding

Keywords:

Conceptual understanding, Contextual problems, Linear equations in one variable, Mathematical representation, Qualitative analysis

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