STRUCTURED MATHEMATICAL THINKING: EVALUATING POLYA’S PROBLEM-SOLVING APPROACH IN EXPONENT MULTIPLICATION AND DIVISION

Abstract

This study examines the effectiveness of Polya’s four-step problem-solving approach in strengthening students’ structured mathematical thinking when learning multiplication and division of exponents. Although exponent operations are fundamental in algebra, many Grade 7 students continue to experience difficulties in interpreting problem structures, applying exponent rules, and verifying their solutions. This research employed a quasi-experimental one-group pretest-posttest design involving 32 students at a junior secondary school. The instructional intervention applied Polya’s four phases: understanding the problem, devising a plan, carrying out the plan, and looking back. These phases were integrated into guided teaching activities and structured practice tasks. Data were collected through a ten-item test, an analytic scoring rubric, and an error analysis framework. The findings reveal a statistically significant improvement in students’ posttest performance when compared with the predetermined sixty percent competency benchmark. This indicates meaningful progress in both procedural fluency and structural reasoning. The error analysis also shows that students initially struggled with misinterpreting the structure of exponent expressions, inconsistent use of exponent laws, and limited monitoring of their own work. After the instructional intervention, most students demonstrated clearer reasoning patterns, more accurate translation of problem structures, and greater consistency in checking their answers. These results confirm that Polya’s four-step approach can support students in developing structured mathematical thinking by helping them express problem meaning, plan appropriate solution steps, and reflect on accuracy.