The article is devoted to the problem of development of I-conception of a personality of young schoolchildren under the conditions of transition to second generation FGOS./FSES (Federal State Educational Standards) In the course of empirical research the author finds out the much lower level of self-esteem and self-consciousness of young schoolchildren who study using the new standards than of those who study using the previous program. The author thinks this fact may be explained in two ways: on the one hand I-conception structure of the children whose studying is based on new FGOS/FSES is similar to I-conception of fifth/sixth graders. On the other hand, low self-esteem may be explained by some peculiarities of the attitudes of the teachers working with these children towards their pupils.