The article deals with the competence approach in education, the ways of forming methodological competence as a component of professional competence of future teachers of mathematics to implement competency approach at school. The analysis of contemporary psychological and educational literature on the professional competence of future teachers of mathematics is made. It is found out that the problem of formation of the methodological competence of future teachers of mathematics to work with pupils hasn’t been a subject of separate research yet. During the study of the problems and solutions of the tasks in the process of research the author used a series of theoretical (the analysis of psycho-pedagogical and scientific-methodological literature on the research problem) and empirical (generalization of pedagogical experience, observation of training activities, questionnaires, interviews) methods that complement each other. The article defines pedagogical conditions of such component of the methodological competence of future teachers of mathematics as a willingness to work with mathematical mistakes of the students. The requirements for such readiness are highlighted. The author hypothesizes about the feasibility of introducing into the curriculum of pedagogical education courses, whose primary goal is to study the organization of preventive methods which the teachers can use to overcome students’ common mistakes in the study of various sections and topics in mathematics. The role and tasks of teaching exercises that include common mistakes of students in mathematics; conditions of the skills of the future mathematics teachers to guide students through mental activity of compliance psycho-pedagogical patterns and direct this activity to prevent errors; means of forming of methodological competence to work with mathematical mistakes of students at lectures, practical laboratory courses on methods of teaching mathematics and during pedagogical practice are characterized. The conclusion is made about the need to prepare future teachers of mathematics to effective science-based methodology for organizing and carrying out the work on prevention, detection and elimination of students’ mistakes, which is one of the problem areas in the preparation of teachers of mathematics.