Abstract:

Teacher training, and in particular the training of mathematics teachers, is an open question without a relevant answer. This problem has been studied by experts in mathematics and mathematics education like Hilbert, Klein, Freudenthal, Kilpatrick, Schoenfeld, Dewey and other classics in their scientific areas. The social and technological progress, globalization, current educational paradigms and several other factors bring new elements and aspects in teacher education to meet the latest conditions and requirements. In addition, the non-traditional environment caused by the COVID-19 crisis, in which the educators are, catalyzes the processes of analyzing, rethinking, updating, and adapting the training of mathematics teachers. One significant and as if overwhelming problem is a lack of real connection with the learning environment and all arising negative consequences. This leads to the sought of alternatives to at least partial compensation of this lack.

We, as university teachers, set ourselves a task not only to find alternatives but also to find ones that are not palliative and have a horizon for application and development even after the crisis. We see such opportunity in the early involvement of students in research work on specific problem concerning psychological, cognitive, and didactical aspects of the mathematics education. Through the study of these problems, the students would become acquainted, albeit theoretically, with the complicated and complex nature of teaching, and especially the teaching of mathematics. It is said in the methodical literature that even the students that show a low results in learning, are interested in such challenges. They realize their own significance, a self-affirmation of their personality occurs and they show desire to unravel the issue on their own, building their own conclusions and expressing their own opinions. Scientists from Russia, Europe and America write about the necessity and benefit from research activities for students that are preparing for teachers.

The realization of such research activity is carried out through the topic “Psychological, cognitive and didactical barriers to the gaining of mathematical knowledge (by the students)”. The research plan and activities of the students are within the elective course “Cognitive processes in mathematics” of the bachelor's program “Mathematics and Informatics” at the Faculty of Mathematics and Informatics of Sofia University “St. Kliment Ohridski”. The reason for such research is the fact that to understand the difficulties that many students have with comprehension of mathematics, we need to determine the cognitive functioning, laying in the base of the diversity of the mathematical processes. Which are the cognitive models that are necessary to provide access to mathematical objects? Are these models common to all cognitive processes or on the contrary some of them are only specific to mathematical processes? The content of the course, which addresses these issues, is adapted to the circumstances. Thus, students are not overburdened and receive the appropriate credits.

The toolkit that students have to develop is set and includes:
- A questionnaire for self-monitoring, self-organization and self-assessment, i.e. self-reflection of their personal difficulties as learners;
- A questionnaire for feedback with students to identify the difficulties they encounter, i.e. reflection;
- An analytical text (essay) as a product of the research.

Keywords:

Students’ research, learning barriers, cognition, didactics, psychology, teaching experience, higher education.