Reflective thinking

Creativity

Mathematics education

Psychoanalysis

Statistics

Social psychology

Data collection

Confusion

Archaeology

Thinking processes

Computer science

Convergent thinking

Creative thinking

Psychology

Triangulation

Mathematics

Lateral thinking

Critical thinking

Geometry

Statistical thinking

Plan (archaeology)

History

Journal for the Education of Gifted Young Scientists

Mathematics students with a reflective thinking tend to have self-confidence in solving mathematics easily. In recent years, however, there have not been the results of the researches that classify students’ reflective thinking for solving non-routine questions of Analytical Geometry questions, in particular. The present research paper reveals the new classification of the students’ reflective thinking for solving the problems. These are solving Analytical Geometry which can cause the students’ confusion to apply their reflective thinking. The classification of the study comprises four components. It employed a descriptive-qualitative approach. The amounts of the subjects were 21 out of 140 students who used their reflective thinking for solving questions. The data collection consisted of test, observation, and in-depth interview. The data validation employed a method triangulation technique. The results of the study show there are three classification of reflective thinking, namely: assumptive, virtual, and connective. The three classifications differ in the way they deal with confusion. Meanwhile, the three classifications have similarities. The students tended to use all of the reflective thinking components although there were a few indicators that were not realized maximally. These were making a plan before solving the problems, using an efficient way, and relating among concepts. The factor is students play an inactive role or low active in reflective thinking. Moreover, they think that the most important thing is answering the questions correctly and they do not understand the purposes of the problem. Therefore, the students need to get the treatments.

How are students’ reflective thinking for problem solving?