Reflective thinking process of students in completing mathematical problems based on mathematical reasoning ability

Abstract

This research aimed to describe the reflective thinking process of eighth-grade students of junior high schools in solving mathematical problems of circle material based on mathematical reasoning. It was a qualitative descriptive with a case study approach. There were 6 subjects selected by using purposive sampling technique based on mathematical reasoning levels. The methods used were test, interviews, and documentation techniques. The results showed that students with high mathematical reasoning level were able to fulfill all indicators of the reflective thinking process including identifying facts and questions, explaining the operations to be chosen, carrying out plans, and giving logical conclusions with indicators students wrote the correct final answers based on the order of the previous problem solving process; students with medium mathematical reasoning fulfilled two to three indicators of identifying facts and questions, explaining the operations to be chosen, carrying out a problem-solving plan; students with low mathematical reasoning fulfilled an indicator of identifying facts and questions; students tend to experience errors in the calculation aspects, lack of students’ prior knowledge, understanding, and mathematical attitude. It was concluded that there is a connection between problem solving and mathematical reasoning with reflective thinking ability of students. It have implications for teachers to condition mathematics learning by paying attention to students’ thinking skills.

Development of logical thinking of high school students through a problem-based approach to teaching mathematics

“…Instead, Bakhy et al [6] are convinced that the development of logical thinking is possible directly in mathematics lessons -by various methods of solving problems, such as the method of analogy, the method of analytical-synthetic reasoning, special cases, trial and error, heuristic method, incomplete induction method, method comparison, the method of proof from the opposite. Tisngati and Genarsih [7] argue that the ability to reason based on "if -then" rules is the basis for mathematical skills because, without conditional reasoning, scientific reasoning is based on hypotheses and their proof or refutation is impossible. The need for reflexive considerations arises in situations that go beyond everyday experience when the problem can not be solved only by the process of finding the necessary information in memory.…”