Exploring the Thinking Processes of Female Students in Solving Number Pattern Problems Based on Self-Directed Learning

Problem solving in mathematics requires integrating conceptual understanding, procedural knowledge, and logical reasoning. This qualitative exploratory case study investigates the intuitive and analytical thinking processes of two female students with contrasting levels of Self-Directed Learning (SDL) in solving number pattern problems. Data were collected through written problem-solving tasks and semi-structured interviews and analyzed descriptively. In this case study, the student with high SDL tends to use analytical thinking, including systematic data organization, strategic planning, and reflective evaluation, while the student with low SDL tends to rely on intuitive thinking, using rapid pattern recognition and prior experience without systematic verification. These findings suggest that SDL may support structured reasoning and reflective engagement in mathematics learning. Pedagogically, promoting SDL through guided problem-solving exercises and reflective tasks can help students develop more analytical approaches and enhance independent problem-solving skills.