TEACHING STUDENTS TO PROVE MATHEMATICAL STATEMENTS (TEACHERS’ VISION)

Introduction. Students' mastering in the art of proof is one of the most important educational results of mathematics teaching. That's why it's important to reveal mathematics teachers' vision on a problem of teaching the proofs of mathematical facts in secondary school. A survey of math teachers was organized to this purpose. Purpose. The purpose of the survey was: 1) to identify the value attitude of teachers towards the methodological work in teaching students the proofs of the theorems in the course of planimetry; 2) to distinguish whether the teachers use all stages of work with the theorem (work with the formulation of the theorem, the search for a method of its proof, the proof of the theorem itself and the consolidation of the proof), what teaching techniques do they use in this activity; 3) to determine what difficulties, according to teachers, prevail among students in the process of teaching the theorems proofs in the course of geometry in the secondary school. Methods. Empirical methods: diagnostic (conversations, questionnaires, testing, interviews), observational methods (observation). Theoretical analyses of psychological and pedagogical literature on the problem were used as well. Results. It is found that an insufficient motivation to study the proofs of the theorems becomes the first impediment for students to learn math statement's proof. The findings show that do not organize pupil's research by performing measurements, construction, generalizations of observations in order to bring up assumptions about the properties of geometric figures for further proof or refutation. It was stated that in the teachers' opinion, operation with the theorem's formulation is an important, didactically meaningful stage of the process of making sense about the theorem itself. However, it is a matter of concern that only about half of the survey participants make the methodologically competently use of it when teaching students. Therefore, the ability to identify indicated or implied submitted data in hypothesis of theorem isn't formed at a sufficient level among the most of the students. Students encounter complications in presenting the corresponding arguments in the substantiation chains, since the condition, the explanatory part and the requirement of the theorem are not explicitly revealed. Originality. The provided investigation showed that there are significant challenges, gaps, and weaknesses in the practice of teaching reasoning-and-proving in the secondary school. Conclusion. Although teachers are aware of the importance of teaching students reasoning-and-proving, this work is often carried out unsystematically. Teachers don't take into account the laws of the process of learning, the laws of the construction and functioning of the didactic cycle. This leads to considerable difficulties for students in mastering the methods of non-contradictory arguments.