Stage-Specific Patterns in Students’ Statistical Problem Solving: A Qualitative Analysis Through Pólya’s Framework

Abstract

This study examined Grade VIII students’ mathematical problem-solving performance in statistical tasks through Pólya’s four problem-solving stages: understanding the problem, devising a plan, carrying out the plan, and looking back. A qualitative descriptive design was employed to examine students’ written responses across these stages. The participants were 30 eighth-grade students from MTsN 4 Bogor who completed an open-ended mathematical problem-solving test. Based on their overall scores, six students representing high-, moderate-, and low-achievement categories were purposively selected for qualitative analysis. The analysis focused on the evidence of students’ problem interpretation, planning, procedural execution, and post-solution evaluation in their written work. The findings showed that students’ performance was uneven across the four stages. Students differed in how explicitly they identified relevant information and documented their solution plans, while procedural execution varied in accuracy and consistency. The clearest difficulty occurred in the looking-back stage, as the responses examined did not provide explicit written evidence of verification or evaluation of the obtained results. Stage-specific performance also did not consistently correspond to overall achievement classification: students with lower overall scores demonstrated competence in particular stages, while a student with the highest overall score did not explicitly demonstrate verification in the response examined. These findings indicate that overall achievement scores do not fully represent the characteristics of students’ problem-solving processes. Examining written work across Pólya’s stages can therefore provide a more differentiated account of students’ statistical problem solving, particularly by making stage-specific strengths and difficulties visible