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Problem-solving is an action that requires a thinking process to solve a mathematical problem. Reflective thinking is a mental activity that begins with confusion and repeatedly evaluation for problem-solving. The confusion is a doubt experience or mistakes conducted by individuals in determining a solution for problem-solving. The reflective thinkers categorized into productive, connective, and clarification. It distinguishes how problem-solvers overcome confusion. This study reveals the pattern-change and characteristics of analytical geometry problem-solving. The research urgency focuses on identifying characteristics of students’ reflective thinking pattern-change as well as contributing theories in determining indicators of reflective thinking. Research stages include administering analytical geometry problems to students that are solved by think-aloud techniques, making observations on observation and answer sheets, conducting interviews, reducing data, coding processes, analysing data, and concluding. The data include students’ answer sheets, think-aloud transcripts, observation sheets, and interview transcripts. Researchers administered the analytical geometry problems to mathematics education students in some universities in Indonesia. Based on data analysis and discussion, the study successfully concluded that the pattern-changes found are complete, incomplete, consistent, and inconsistent. Further research may focus on the development of an infused learning model in defragmenting students’ reflective thinking.

Students’ reflective thinking pattern changes and characteristics of problem solving