The authors of this article actualize the problem of developing the abilities of children of senior preschool age in specially organized conditions. Through theoretical analysis, it was proved that tasks are units of search and research activities that contribute to the development of the subject's abilities and activate his search and research activities; the specifics of the development of intellectual and artistic abilities of preschool children were determined; the specifics of the organization of search and research activities, taking into account the features of the construction of the subject-developing environment were described. The main components that were required for any type of problem situations were identified: the need for a new mode of action, caused by the inability to solve an intellectual problem using known methods; unknown (in this case it is a method of cognitive actions), which must be found; the ability of the child (the level of development of abilities necessary for the search). Also, the effectiveness of the program for developing abilities of children at various stages of pre-school childhood was proved. The obtained results allow to assert, that the allocation by adults of the moment of finding the solution of the problem and the positive assessment of the overcoming of difficulties in the decision process contributed to an increase in the productivity of cognitive activity and, as a result, an increase in the level of abilities of preschool children.