Results of research on the acquisition of counting skills in children is presented. The material, originally published in the Soviet Journal "Questions of Psychology," was deemed an important document that should be translated and made accessible to English readers. The question of how basic, extended processes are "abbreviated" when they become part of new, more complex ones is addressed. The subjects of this study were children between the ages of four and seven attending day care centers. All children studied were presented with a series of addition tasks. Data from the investigation provide a basis for a general outline of the way the mathematical operation of addition is internalized, and a psychological explanation is offered. More research is called for so that more detailed explanations of the origin of mental actions may be developed. (MP).