Understanding How Students Solve Statistical Problems Through Polya’s Problem-Solving Stages: A Preliminary Study

Abstract

Mathematical problem-solving ability is an essential competency in statistics learning because students must not only perform calculations but also interpret problems, develop strategies, implement procedures, and evaluate solutions. This preliminary study aimed to profile undergraduate students’ mathematical problem-solving abilities based on Polya’s four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. A qualitative descriptive approach was employed with 48 undergraduate students enrolled in a Statistics course. Data were collected through non-routine statistical problem-solving tests and semi-structured interviews with selected participants. The data were analyzed through reduction, categorization, interpretation, and triangulation of written responses and interview data. The findings showed three levels of problem-solving ability: high (26 students; 54.17%), moderate (14 students; 29.17%), and low (8 students; 16.6%). Most students performed relatively well in understanding problems and carrying out solution procedures. However, difficulties were evident in devising appropriate strategies and, particularly, in the looking-back stage. Many students stopped after obtaining numerical answers and showed limited verification, interpretation, and evaluation of their solutions. These findings indicate that statistics problem-solving involves interconnected cognitive and metacognitive processes. Integrating Polya’s stages into instruction may strengthen students’ statistical reasoning and higher-order thinking skills.