Construction of reflective thinking: A field independent student in numerical problems

In educational settings, reflective thinking is often overlooked, with an excessive emphasis on final answers, resulting in students needing more ability to evaluate and reconstruct their problem-solving processes. The ability for reflective thinking is required by students in solving problems, including numerical problems. This study uses a qualitative approach to focus on field-independent students' numerical problem-solving processes. The data collection technique begins by administering the Group Embedded Figures Test (GEFT), a valid and reliable numeracy problem instrument, and conducting in-depth interviews. Two students with similar initial mathematical abilities and field-independent cognitive styles were selected as research subjects. Findings reveal that these students face challenges such as lengthy problem descriptions and a lack of confidence but gradually develop strategies, emphasizing repeated problem analysis, concept interconnections, and error awareness. Researcher-provided scaffolding facilitates critical reflection, enabling the construction of new ideas. These results have practical implications for teachers, suggesting the need to design lessons that cater to diverse cognitive styles, providing more complex problems to field-independent students to enhance their problem-solving skills.