A challenge for the school mathematics methodology is a selection of textbooks, which would correspond to the new social needs as well as the goals that it sets to the mathematical education. The importance issue is the problem of the content integrity, especially in connection with the transition of a school to the new term of learning. Its provision includes the development of the requirements for the content of school mathematics and the ways to implement them in textbooks. The common

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... ical and methodological requirements to the educational texts selection, a system of exercises and the methodological apparatus of textbooks in mathematics, in particular, the formation of a positive self-concept of pupil's personality, the sustained motivation for learning, enrichment of not only mathematical, but also the general cultural potential of a pupil, scientific nature and availability of the educational texts, the continuity of its two functions, namely, a compensatory and a prognostic ones, priority of the developing function of training, practice-oriented focus of the educational material, the correspondence of the content to the age and the cognitive characteristics of pupils, etc. are offered. It is proved that the implementation of the proposed requirements contributes to the formation of mathematical core competencies. These requirements may also be referred in the development of the state educational standards and curriculums for mathematics.