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Relevance (context) of the article. The analysis of the sources shows the effect of the P. Ya. Galperin’s theory of step-by-step development of intellectual activity. Relevance of the study is evident both at the level of fundamental general psychological mechanisms of intellectual processes, and at the level of educational technology development. P. Ya. Galperin’s theory has found its usage in developing methods for correctional and educational work in teaching children with disabilities.

The purpose of this paper is to show relevance of P. Ya. Galperin’s theory implementation, when developing methods in correctional education to form intellectual activity in preschoolers with intellectual disabilities.

Description of the research. The thesis reveals gradual development of intellectual activity in preschoolers with intellectual disabilities. There is an author’s method of forming intellectual activity in preschool children with intellectual disabilities. This method is presented on the example of actions of assigning the subject to the standard of form and direct quantitative counting. It is used in preparing children for school. This study is implemented in the educational field Intellectual Development. It is possible to use this method in the future to ensure preschool education of children with intellectual disabilities.

Findings. The research studied formation of a perceptive ability to match a particular object’s properties with the set standards of form and the ability to make direct quantitative calculations when using the method based on P. Ya. Galperin’s theory. The study revealed that, though the tasks at each stage of learning were getting more and more complicated, the intellectual activity acquirement was progressing. This is shown through preschoolers with intellectual impairments being more independent from an adult’s help and being able to shift to a more ‘reduced’ action according to P. Ya. Galperin. The distinguished gradual development of intellectual activity (first shifting from conceiving the task to acquiring the intellectual action in the tangible and physical way, second shifting to handling the observed objects without motor actions involved, finally shifting to prospective planning of the action) has proven to be effective when assisting a child in forming various intellectual actions, such as objective figure modeling, objects size-ranking, comparison, qualitative division, etc.

Conclusion. The method of forming intellectual skills in preschoolers with intellectual disabilities, built on the principle of gradual development of intellectual activity can be widely used in correctional, developmental and educational work. This study is possible to go beyond the actual intellectual development and be used in other educational areas of preschool education of this group of children.

The article gives an overview of improving the methodology for developing elementary mathematical representations in preschool pedagogy and in preschool special education concerning the formation of mass perception. The authors describe the history methodology development in preschool education including the task for forming such measuring skills in children as an orientation in the mass of objects. Theoretical review made it possible to elucidate the under-development of the methodology for forming elementary mathematical representations in preschool children with intellectual disabilities. The article reveals the content of the methodology for corrective and pedagogical work on the formation of a mathematical function like understanding the mass of objects in preschool children with intellectual disabilities (mental retardation). It is based on the theory of the stage-by-stage formation of mental actions by P. Ya. Galperin. The methodology presupposes eight stages, each of which uses its own set of methods and techniques of training and a set of illustrative and handout material. The authors offer fragments of tasks on the formation of this understanding in preschool children with intellectual disabilities in the mass of objects at each stage of education. The methodology is implemented within the framework of the educational field “Cognitive Development” in classes on the formation of elementary mathematical representations. The introduction of the methodology in correctional and educational process of special (correctional) preschools in Ufa showed its effectiveness.

The article presents diagnostic and corrective methods designed for study and correction of sensory-perceptual activity of preschool children with intellectual disabilities. Sensory-perceptual activity is considered as a basis for further cognitive development of children in this group. The diagnostic method of its study involves differential criteria for fulfilling experimental tasks by three groups of preschool children – normally developing children, children with developmental delay and children with mental retardation. The corrective method aimed at forming such sensory-perceptual processes, as the ability to relate the properties of subjects to predetermined reference forms and the ability to model planar shapes of subjects is based on the gradual formation of mental actions theory developed by P.Y. Galperin. Both the diagnostic and corrective methods are based on L.A. Venger’s approach to the study of sensory-perceptive activity of preschool children.

The article presents methods of construction teaching of preschool children (6–8 years) with intellectual disabilities (mental retardation). Construction is one of the most accessible activities for preschoolers with intellectual disabilities. The technique is based on the theory of the gradual formation of mental actions by P.Ya. Galperin and involves the formation of mental activity in the planar and volumetric construction, which, in turn, include the formation of skills to build figures and to make scene construction. The main directions of correctional and pedagogical work are teaching flatness and volume, object and scene construction. The article provides a detailed description of the methods of teaching the volumetric construction using the example of two construction skills – the ability to construct three-dimensional figures and skills to build volumetric scenes.