The article is composed of two parts: discussion of psychological criteria of the computer competence in schoolchildren, and conditions of efficient development of it. Three types of competence are named in the first part: a) daily life, b) professional, c) related to the computer as an intellectual tool; for schoolchildren the third one is most important. Further a system of intellectual abilities required for efficient application of the computer for a wide scope of problems is considered. The second part deals with the so-called problem instruction which is stated to be the basic condition for the proper development of the computer competence. Principles of organization of the instruction of this type are outlined, as well as some issues of individualized approach to instruction, and of control and optimization of children's functional states during learning.