From words to matrices: uncovering students' errors in solving contextual matrix algebra problems

Abstract

Contextual problems in matrix algebra require students not only to perform matrix operations but also to construct mathematical models and interpret results meaningfully. However, many students encounter difficulties when translating real-world situations into matrix representations. This study aims to identify the types of errors students make when solving contextual matrix algebra problems and to explore the underlying factors contributing to these errors. Employing a qualitative descriptive design, the study involved sixteen Mathematics Education students who had completed a Matrix Algebra course. Data were collected through contextual matrix algebra tests and semi-structured interviews. Data were analyzed using methodological triangulation. The results revealed four categories of errors: conceptual, mathematical modeling, procedural, and interpretation. Mathematical modeling errors emerged as the most dominant category, particularly in constructing matrix representations and determining the appropriate order of matrix operations. Conceptual errors were associated with misconceptions about matrix structures and operations, whereas procedural errors involved calculation inaccuracies. Interpretation errors occurred when students failed to connect mathematical results to the problem's context. These findings indicate that students’ difficulties extend beyond computational skills and are closely related to their ability to understand, model, and interpret contextual situations mathematically. Therefore, instructional practices should emphasize contextual problem-solving and mathematical modeling to foster deeper conceptual understanding and higher-order thinking skills in learning matrix algebra.