Development of students' mathematical skills is associated with quality teaching, which means that mathematics teachers should be able to successfully solve mathematical, teaching, and professional problems. The article aims to describe the assessment system of mathematics school teachers' professional competence, which helps identify gaps in their training and design tailor-made retraining courses. 2,359 mathematics teachers from 13 regions of Russia participated in the research on 05-29 September 2017. Foremost, we conducted a survey and collected data about their teacher category and teacher expertise. Next, we provided a preliminary diagnostic test to enable the participants to self-assess their subject matter and teaching competencies. After that, they completed a three-part diagnostic test to assess their abilities to solve mathematical, teaching, and professional problems. Finally, the participants conducted video lessons. The three-part diagnostic test and video lessons allowed determining the professional competence level for every mathematics teacher. 24% participants showed level I of professional competence, 44% -- level II, 9% -- level III; 23% participants did not pass the basic level of professional competence. The results show that the mathematics teachers have difficulties in solving mathematical, teaching, or professional problems so tailor-made retraining courses are required. The developed assessment system underlies designing the courses.