Exploring student’s mathematical reasoning in solving probability problems based on Polya's theory

Abstract

Mathematical reasoning is a fundamental competency in mathematics learning, particularly in solving probability word problems that require systematic and logical thinking. One widely used framework to support problem solving is Polya’s problem-solving theory, which consists of four stages: understanding the problem, devising a plan, carrying out the plan, and reviewing the solution. This study aims to analyze students’ mathematical reasoning abilities in solving probability word problems based on Polya’s steps. Polya’s theory is employed as an analytical framework to examine how students reason through probability tasks. The study adopted a qualitative descriptive approach involving tenth-grade students at a vocational high school in Jambi City. Data were collected through probability word problem tests, interviews, and classroom observations. The findings indicate that students’ mathematical reasoning abilities vary across the stages of Polya’s problem-solving process. At the understanding stage, most students were able to identify relevant information, although some experienced difficulties with probability terminology. During the planning stage, only a small number of students could formulate systematic solution strategies. In the execution stage, many students performed basic calculations correctly, but errors emerged when applying formulas to more complex problems. The reviewing stage was the least practiced, resulting in many undetected errors. These results suggest that while students possess basic problem-solving skills, they require further guidance to develop systematic and reflective reasoning. Therefore, reinforcing each stage of Polya’s problem-solving process is essential for improving students’ mathematical reasoning in solving probability word problems.