The preparation of future primary school teachers includes the analysis of textbooks and teaching aids in mathematics. The first domestic printed textbook on mathematics in Russia — “Arithmetic” by L.F. Magnitsky. The article describes the educational potential of this book as a source of methodological and mathematical knowledge, and as a means of stimulating professional self-development of students. The contents of a professionally oriented project aimed at introducing this book and its creator are disclosed.

The article analyses modern trends in the university graduates’ training based on a practice-oriented approach, which is interpreted as training focused on the specifics of solving pedagogical problems that arise in real practice. The world experience of practice-oriented educational practice aimed at the formation of a creative, thinking teacher is analysed. The author’s three-segment practice-oriented model of teacher training has been developed. The structural components of the model and the links between them are described: principles of model building (practice-oriented orientation, principles of flexibility, validity, compliance and integrativity); system-forming subjects (professional community, university and school); blocks (target, factorial, theoretical-methodological, content-technological, effective). The peculiarity of the visual image of the constructed model (fractal) is that each separate segment of the system retains the properties of the entire system, which means that at each level, target guidelines are preserved and the basic requirements for the preparation process are consistent with each other.

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The pedagogical problem of the formation of the ability to learn as a set of universal skills in conjunction with objective actions is considered in the article based on the performance of olympiad mathematical tasks by younger schoolchildren. The requirements for the development and formulation of olympiad tasks, with the help of which a set of pedagogical activities are implemented, contributing to the development of the ability to learn by children of primary school age. The types of Olympiad tasks offered by the authors are connected with the main thematic sections of the initial course of mathematics.