The aim of the article. The article reveals the question of determination of methodological basis of forming of professional readiness of the future mathematics teachers to the use of the tools of computer visualization of mathematical knowledge. Research methods: theoretical (analysis and systematization of philosophical, pedagogical and psychological literature, works of the local and foreign authors, legal documents, teaching materials) and empirical (research and compilation of the national and international teaching experience, observation, introspection) with the help of which effective approaches to teacher training in mathematics are defined. Results. Methodological bases of formation of professional readiness of mathematics teachers to use TCVMK reflect the relationship and interaction of different approaches of general scientific and specifically-scientific methodology in the context of formation of professional readiness of the mathematics teachers for the use of mathematical knowledge computer visualizationtools. Among the existing approaches to preparing teachers of mathematics in the context of formation of their professional readiness to use mathematical knowledge computer visualization tools the author has identified systems approach, activity approach, competence approach, integrated approach and acmeological approach. Conclusions. The systems approach ensures the integrity of the educational process which is characterized by hierarchy and continuity; using of integrated approach promotes the emergence of a new quality of knowledge of informatics and mathematic and technological skills; competence approach is important from the standpoint of practice learning; activity approach ensures activity skills; acmeological approach provides further reflection of our activity and professional activities of colleagues with orientation on individual self-improvement and self-development. The perspectives of further research. The further researches will be directed at defining principles of forming the professional readiness to use computer visualization tools of mathematical knowledge.