The article highlights and theoretically substantiates the problem of methodical support for introducing innovations in preschool education institutions. Such basic research concepts as methodical support, innovations, innovative technologies, and stages of innovations (diagnostic, consultative-educational, corrective-developmental) are revealed. An important methodical aspect of the introduction of innovations is the readiness of the preschool teacher for innovative activities, who must be motivated to participate in innovative activities, be able to self-assess their capabilities, be a creative person, a teacher-researcher, and be able to reflect. The article discloses modern innovative technologies, the main goal of the methodical work of the state preschool education institution. Preschool education is the first link in the formation and development of a child as an individual. That is why preschool education is the foundation of the educational system of the country and has great socio-economic importance, which is determined by the need for comprehensive implementation of the development program for preschool children. Presented forms of methodical support (consulting, seminars, workshops, coaching, master classes, «round tables», pedagogical readings, business games -these forms of methodical support reach a new stage with the use of ICT. Such platforms as Zoom, Google Meet, Skype, etc. allow one to organize an informative methodical event not only individually for one teacher but also for a group of educators who need help in solving pedagogical problems in online conference mode). In the activities of preschool educators, their initiative and ingenuity, creative approach and desire to develop and implement changes, interesting ideas aimed at the educational process and their practical implementation, as well as the conditions which the head of the preschool educational institution creates for his employees to carry out innovative activities.

The urgency of the topic is due to the need to study the methodological foundations of the development of acquaintance with the number of young children using play activities. The game is essential for the formation of basic mathematical concepts at the initial stage of development of a child of this age. In the article we reveal the problem of development of acquaintance with the number of young children through play activities, we present several features of perception and reflection of sets by young children.The functions of assistance to preschool teachers and young children in mastering the number in the process of play activities are determined. It is in play activities that the child acquires new knowledge, skills, abilities, develops, and improves their abilities. The essence of the concept of «set» is clarified and several features regarding the perception and reflection of sets by young children are identified.There are proposed methods and techniques of work in the process of acquainting young children with the number, such as: visual (showing illustrations and actions with objects); verbal (conversations, use of verbal artistic image); game (game situations, game exercises, songs).The authors identify the following functions of assistance to preschool teachers and young children in learning the number: the implementation of the principle of clarity; adaptation of abstract mathematical concepts in a form accessible to children; assistance to preschool children in mastering the methods of action necessary for the emergence of basic mathematical concepts; promoting the accumulation in children of the experience of sensory perception of properties, relationships, connections and dependencies, its constant expansion and enrichment.The main types of innovative technologies used in preschool educational establishments for the mathematical development of young children to increase interest in educational activities and promote better learning of new material are proposed.

A comprehensive scientific analysis of the problem of the motivation of the professional development of preschool teachers as a tool for improving the quality of preschool education was done. The results of an empirical study of the professional priorities of the future preschool teacher are presented. It was concluded that the formation of motivation for the professional development of preschool teachers is a complex process that depends on many components of activity at all stages of its implementation. The professional priorities of studentsfuture preschool teachers, which will contribute to the formation of their professional selfdevelopment, their awareness of the importance of their own professional activities, and the value of building a professional career.

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Комунальний заклад вищої освіти Київської обласної ради «Білоцерківський гуманітарно-педагогічний коледж», м. Біла Церква, Україна;Комунальний навчальний заклад Київської обласної ради «Київський обласний інститут післядипломної освіти педагогічних кадрів», м. Біла Церква, Україна;Київський університет імені Бориса Грінченка, м. Київ, Україна