Polya’s Stages in Students’ Mathematical Problem Solving of Linear Programming Word Problems: A Qualitative Study

Abstract

This study aims to identify senior high school students’ mathematical problem-solving abilities in solving linear programming word problems based on Polya’s problem-solving stages. This research employed a descriptive qualitative approach. The participants consisted of six Grade XI Social Science students from SMA Muhammadiyah 1 Pontianak, selected based on high Mathematical Prior Ability (MPA). The MPA classification was determined from students’ average daily scores, final semester examination results in linear programming, and recommendations from the mathematics teacher among 34 students. Data were collected through problem-solving tests and semi-structured interviews. The instruments were developed based on Polya’s four problem-solving stages: (1) understanding the problem, (2) devising a plan, (3) carrying out the plan, and (4) looking back. Data analysis followed the procedures of data reduction, data display, conclusion drawing, and technique triangulation to ensure data validity. The findings reveal variations in students’ problem-solving performance across Polya’s stages. In the understanding stage, students demonstrated very good performance, as they were able to identify known and required information systematically. In the planning stage, students showed fairly good performance by constructing tables, defining variables, and forming mathematical models, although their work lacked systematic structure. In the execution stage, students performed poorly, as they encountered difficulties in determining coordinate points, graphing feasible regions, identifying corner points, and calculating optimal values. In the checking stage, students also showed very poor performance, indicated by their inability to re-examine procedures and draw accurate conclusions.