Formation of maths teachers’ readiness for teaching how to solve proof tasks in stereometry

The article examines maths teachers' readiness to teach high school students how to solve proof tasks in stereometry. It is shown that the teacher's readiness to carry out the relevant activity can be divided into three components: mathematical, organizational and methodological, illustrative and technological. They include the teacher's personal ability to solve proof tasks in stereometry, to organize his or her students' work at the lesson when performing proof tasks in stereometry, to apply digital technology for illustrations in stereometric problems. Measurements and observations demonstrate the fact that there is only a small percentage of teachers who are ideally able to solve proof tasks of medium complexity; this percentage is the same as among the participants of external independent assessment in mathematics (it does not exceed 3%). A major group of issues that are more than 50% problematic for teachers working in high school is identified: they include proof tasks related to skew lines, the perpendicularity of planes, the interplanar angle, the distance of a point from a line, the distance of a point from a plane, between skew lines, loci in space, (cross) sections. It has been shown that teachers' poor skills in solving proof tasks cause the inability to identify students' mistakes and deficiencies in criteria-based assessment of solving a geometric problem with a detailed answer. Particular approaches to the development of teachers' readiness for teaching how to solve proof tasks in stereometry are proposed. At the advanced training courses they include diagnostics and teachers' self-analysis of the effectiveness of solving proof tasks, a system of lectures and practical workshops related to the logical structure of geometry course, delivering combined mathematical and methodological trainings, performing problem solving practicum and mini-projects with the use of modern educational digital technologies, forming individual plans of self-education. The dynamics of maths teachers' success in performing proof tasks in stereometry has been analyzed. It is shown that there is a tendency for increasing the number of maths teachers who can cope with solving proof tasks at the end of the advanced training courses (comparing with the beginning) providing that the proposed approaches were used.