Fostering Mathematical Minds: A Problem-Based Approach to Conquering Linear Equations
Keywords:
Problem-Based Learning (PBL), Logical-Mathematical Intelligence, Learning Material Development, 4D ModelAbstract
For many students, higher-level math feels like an insurmountable wall. We started this research to find a better way to teach one of those challenging topics: Systems of Linear Equations in Three Variables (SPLTV). Our goal was to develop learning materials that didn't just teach formulas, but actively nurtured students' own logical-mathematical intelligence. Using a four-stage development model (Define, Design, Develop, Disseminate), we created a complete learning package based on the Problem-Based Learning (PBL) model for Grade X vocational students. This package included everything from teaching modules and student worksheets to learning videos and tests. To see if it worked, we gathered feedback from experts, observed the materials in action, and measured student growth with pre- and post-tests. The results were incredibly positive. Experts gave the materials a strong "Valid" rating (with scores like 3.79 and 3.82 out of 4). In the classroom, the materials proved highly practical and easy to use. Most importantly, the students thrived. We saw an 84.6% class-wide learning completion rate, and a comparison with a control group showed a statistically significant improvement (p < 0.05) in their logical thinking skills. This study shows that with the right approach, we can move beyond rote memorization and create tools that empower students to think like true problem-solvers.
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