Reflective Abilities of Students: Ways and Means of Development While Studying Geometry

Abstract

A reflective ability as an ability to comprehend one’s experience, knowledge, evaluations is a psychological condition of thinking activity. But in researches, reflection is mainly considered as an indicator of a high level of thinking, creativity, the ability to analyze, types of reflection are not distinguished. For teaching mathematics, the development of intellectual reflection is especially important. In our study, the problem of the development of intellectual reflection is identified as an independent one. As a means of its development, we proposed geometric "many-valued" problems in which a situation of choice is organized. Three levels of development of reflective abilities in teaching geometry, in accordance with certain types of reflection are distinguished. The purpose of the study is to find out whether the level of development of students' reflection will change if "many-valued" problems are used in geometry. Is there a correlation of the manifestation of reflection on the geometric content and the content of another object? The experiment involved 375 students. The Pearson criterion was used in processing the results. The inclusion of "many-valued" problems in teaching geometry showed an increase in the level of formation of reflective skills of students and the transfer of these skills to another subject.

Developing Professional Creativity of Teachers Based on Problem Based Learning (PBL)

“…It is based on a survey applied to a sample of 1,024 teacher educators from 14 higher education institutions that offer initial teacher education programs. The results show that most teacher educators have a doctoral degree and a permanent position, but they also face some challenges regarding their research activities, such as lack of time, funding, and institutional support [4][5][6][7][8]. Currently, obstacles affecting the professional development of teachers in professional educational institutions are still considered urgent problems.…”