The article analyzes the views of domestic and foreign scholars on the basic concepts of educational innovation, which include the concept of innovation, innovation process, innovation capabilities. During innovations in pedagogy we mean new (or improved) product pedagogical implemented in the educational process and promotes its development. in the context of innovation in mathematical education innovation process should be considered as a set of procedures and tools that allow pedagogical innovation digested educational company and effectively used in practice on a scientific basis. Innovative capacity is understood as the capacity of the teacher, which is defined as a set of cultural and creative individual teacher characteristics, expressing willingness to improve teaching activities and the availability of internal tools and techniques that provide this alert. To most essential characteristics of innovation processes that must be considered in the preparation of future mathematics teachers for innovative teaching activities include advisable stages (awareness forecasting of social needs, finding ways and means of conceptual solution to the problem, the birth of a new idea, of a new concept of innovation, invention, innovation implementation , spreading innovation saturation in a competitive industry, recession irradiation innovation) and patterns of flow (irreversible destabilization of pedagogical innovation environment; the final of the innovation process; stereotyping pedagogical innovations; loop, repayment of pedagogical innovations). In order to fruitful innovation in mathematics education should be organized targeted training of future and current teachers of mathematics to innovative educational activities. It should not only inform students (teachers) in teaching methodology courses and (or) the basic concepts of pedagogy pedagogical innovation, flow patterns and stages of innovation processes, but they form a conscious commitment to creative overcome these potential difficulties inherently accompany the work of teachers of mathematics-oriented production, analysis and innovation in their daily work, to promote their innovative potential. The prospect of future research is to clarify the concept and components of readiness of the future teachers of mathematics to innovative teaching.