The Effectiveness of Cramer’s Rule on the System of Linear Equations (LES) of 2-Loop Electrical Circuits in Improving Mathematical Thinking Ability and Learning Outcomes

Mathematical thinking skills are high-level thinking competencies needed in the 21st century. Many physics problems are expressed in various forms of mathematical equations that require mathematical thinking skills. The low level of mathematical thinking has an impact on physics learning outcomes. Cramer’s rule is more attractive to students when solving the Linear Equation System (LES) than the substitution method or other methods. So this study aims to examine the effectiveness of Cramer’s rule on the system of linear equations of 2-loop electrical circuits as an alternative solution to problem solving. The research was conducted in the odd semester of 2024/2025 with research subjects as many as 44 students and 30 high school students in Jember using Pre-Experimental Design and One Group Pretest-Posttest form. The results showed the improvement of college students’ mathematical thinking skills in the high category for indicators of specializing (72.7%), generalizing (95.5%), and conjecturing (86.4%) while the convincing indicator was in the medium category (65.9%). The improvement of college student learning outcomes (79%) and high school students (81%) in the high category with a very positive response or 82.14%. So Cramer’s rule is effective in improving mathematical thinking skills and learning outcomes.