Probabilistic Thinking Process in Probability Problem-Solving Prospective Mathematics Teacher with Field-Independent based on Polya's Three Stages

Background/purpose. This study investigates the probabilistic thinking process in solving probability problems by prospective mathematics teachers with a field-independent cognitive style. The objective is to explore how individuals with this cognitive style approach problem-solving based on the three stages of Polya’s framework: understanding the problem, devising a plan, and carrying out the plan. Materials/Methods. A descriptive qualitative approach with a case study design was employed. The participant was a female student enrolled in the Mathematics Education Program at the Universitas Sembilanbelas November Kolaka, identified as having a field-independent cognitive style through the Group Embedded Figures Test (GEFT). The research instruments included a probability problem-solving task constructed based on indicators of probabilistic thinking and Polya’s stages, along with semi-structured interview guidelines. Data were collected through task-based problem-solving and interviews, and were analyzed using data reduction, data display, and conclusion drawing. Results. The participant demonstrated a systematic probabilistic thinking process across all three stages. During the problem-understanding phase, she successfully identified known and unknown information and accurately interpreted mathematical symbols. In the planning phase, she applied deductive reasoning to develop appropriate strategies. In the execution phase, she implemented the procedures precisely and arrived at logical conclusions. Conclusion. The findings suggest that solving binomial distribution problems requires more than procedural knowledge; it also involves conceptual understanding, logical reasoning, and the capacity to manage uncertainty. Prospective mathematics teachers with a field-independent cognitive style exhibit strong potential in integrating structured probabilistic thinking with Polya’s problem-solving stages.