Proof-Based Guided Inquiry: A Strategy for Improving Algebraic Thinking Skills in Linear Algebra Learning

Algebraic thinking skills play an important role in mastering mathematical concepts and problem-solving; however, Linear Algebra learning still faces difficulties, particularly in understanding proofs. Therefore, a proof-based Guided Inquiry strategy is needed to help students develop deeper algebraic thinking skills. This study aims to describe the implementation of the proof-based Guided Inquiry strategy, analyze the improvement and achievement of students’ algebraic thinking skills between classes using this strategy and those using conventional learning, and describe students’ responses to Linear Algebra learning through this approach. The research employed a mixed-method approach with a quasi-experimental design using a non-equivalent control group. The subjects were two classes of mathematics education students, each acting as an experimental and control class. The instruments consisted of pre- and post-tests of algebraic thinking skills, implementation observation sheets, and student response questionnaires. Quantitative data were analyzed using N-Gain and mean difference tests, while qualitative data were obtained from observations and student responses. The results showed that the implementation of learning achieved an average score of 92% (very good category). N-Gain analysis revealed that the experimental class achieved a moderate improvement (0.401), higher than the control class (0.246, low category). Moreover, student responses were positive, with an average percentage of 84.8%. These findings indicate that integrating inquiry exploration with mathematical proof effectively enhances students’ algebraic thinking skills and the quality of Linear Algebra learning.