Analysis of students’ mathematical reflective thinking on problem based learning (PBL) based from learning styles

Reflective thinking is one of the high-level thinking skills that learners must possess. This study aimed to determine the effectiveness of Problem Based Learning (PBL) model and to describe the students' reflective mathematical thinking ability for each type of learning styles (visual, auditory, and kinesthetic). This research used a mixed method. The research class was taken with cluster random sampling. The subjects of this study were 6 students of class in one of junior high school in Purworejo which were selected by purposive sampling by selecting 2 students from each type of learning style. The data collection by using tests, questionnaires, and interviews. The results showed (1) PBL was effective in achieving students’ reflective mathematical thinking ability; (2) mathematical reflective thinking ability of visual subject was unable to draw the analogy of the problems and the visual subject was unable to identify relevant data. The auditory subject was unable to explain correctly the concept used in drawing sketches and unable to understand and identify the concepts. In addition, the auditory subject was less able to identify relevant data. Whether the kinesthetic subject made a mistake in drawing the analogy but he was unable to mention the problems that existed and could not identify the relevant data. In addition, the kinesthetic subject was less able in doing proof by using the concept involved in the proof of argument