Hierarchy of Students’ Reflective Thinking Levels in Mathematical Problem Solving

Resumo

Background: Reflective thinking plays an essential role in problem solving. However, the hierarchy of students’ reflective thinking levels when solving problems is not yet known. Objectives: The study aims to determine the hierarchy levels of students’ reflective thinking in solving mathematical problems. Design: This type of research was qualitative and employed an explorative approach. Setting and Participants: This research examined 104 reflective thinkers from Java, Sumatra, and Sulawesi. Data collection and analysis: We used analytical geometry instrument tests, observation sheets, and interview guidelines to refine the data. The instruments underwent a review process by validators experts in mathematics education research, qualitative research, and mathematical thinking skills research. We used the think-aloud method to capture the data, which were recorded through an audiovisual recording tool. The data were analysed through three stages: preliminary analysis, open coding, and axial coding. Results: The analysis reveals that reflective thinking has four levels: in-depth understanding, relating concepts, making errors and willingness to correct them, and being convinced of answers. to elevate it to a higher level. Conclusions: The research concluded four hierarchy levels of reflective thinking. Further research can focus on defragmenting students’ reflective thinking during problem solving in an attempt to improve such thinking. Moreover, determining the steps to defragment students’ reflective thinking at each level is necessary.