Rethinking Matrix Instruction: A Mixed-Methods Analysis of Students’ Problem-Solving Skills and Pedagogical Challenges

This study aims to analyze students’ problem-solving skills in the matrix topic and to identify instructional constraints that influence the learning process. A mixed-methods approach was employed: the quantitative phase involved an eight-session expository intervention (90 minutes per session) and an assessment consisting of 30 multiple-choice and 5 essay questions (scored 0–100), while the qualitative phase included open-ended interviews with the teacher responsible for matrix instruction. Quantitative findings revealed that most students remained at the basic mastery level, with an average score of 26.82 and a distribution dominated by the “Low” category. Only 3.88% of students reached the “Good” level, and a binomial test confirmed that this proportion was significantly lower than the reference threshold (p < 0.001), reinforcing the conclusion that student performance fell short of expected standards. These findings highlight the urgent need for early diagnosis of foundational algebra skills—such as row-column operations and linear equation manipulation—before introducing more complex matrix concepts. The qualitative analysis revealed that although the teacher still employed expository methods—lectures, question and answer, and open discussions—these strategies were insufficient for fostering deep problem-solving skills. Students often relied on mechanical procedures without conceptual understanding, struggled to connect algebraic notation to real-world contexts, and lost motivation when facing multi-step problems. The combined results suggest that instructional design should shift toward more contextual and concept-exploratory approaches. Strategic steps are recommended, including the adoption of structured problem-solving methods to improve learning outcomes in mathematics. Furthermore, curriculum development should allocate sufficient time and resources to matrix topics, provide professional development for teachers in designing innovative instruction, and ensure access to digital infrastructure that supports mathematical visualization.