<![CDATA[Third-semester electrical engineering students taking linear algebra had an average pretest of 54.2, indicating poor conceptual mastery of critical thinking skills (CTS). They struggled with variable analysis, mathematical inferences, and logical engineering problem solutions. This report suggests an innovative learning model that bridges mathematical theory and engineering applications. This study examines whether Problem-Based Learning (PBL) improves students' CTS and explains the qualitative mechanisms. This study employs an explanatory sequential mixed-methods approach. To measure CTS pre- and post-test scores using Facione indicators (interpretation, analysis, evaluation, inference, and explanation), 42 electrical engineering students were tested. In the second stage (quantitative), the researchers explained the quantitative results through observation of the learning process, in-depth interviews, and document analysis. The findings indicate the CTS score increased 31.2% from 54.2 to 71.1. The paired t-test (T (41) = 8.72; p < 0.001) confirmed statistical significance, while the Cohen’s d Effect Size value of 1.39 indicated significant practical impact. 10 The Inference (44%) and Analysis (38%) indicators increased most. The qualitative results indicated that PBL forced students to think investigatively instead of procedurally. High group activity also improved students' explanation and evaluation skills (p = 0.006) by encouraging coherent arguments. With PBL, electrical engineering students' CTS, especially higher order thinking skills like analysis and inference, improved greatly. Positive group dynamics and changes in students' learning experiences, which PBL promotes to develop critical thinking and engineering-relevant problem-solving skills, supported this effectiveness.]]>
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