Investigation of Arithmetical Skill

Abstract

The investigation of arithmetical skill comprises part of the basic program for studying disturbances of higher mental processes in the presence of local brain lesions, for it may shed light on certain important aspects of these disturbances. The reason for this is that arithmetical operations are based on spatial relationships that, in the early stages of mathematical development, were expressed in three-dimensional form in surveying and mensuration. Mathematics only gradually acquired the character of abstract, symbolic processes; despite this fact, however, it maintained its genetic connection with these spatial operations. These special features are evident during the analysis of the psychological processes underlying the ideal of number and arithmetical operations and may easily be studied by examining their formation in childhood. The work of Piaget (1950), Ingel’der (1960), Gal’perin (1959), Talyzina (1957), Davydov (1957), Nepomnyashchaya (1956), and others has shed new light on the stages through which the preschool child passes in developing number concepts, starting with material operations with objects arranged in space, passing through a phase of actions “materialized” with the hand and gaze, and ending with the formation of tabular calculation, the basis of the true concept of number and of the mental activities fundamental to fully developed arithmetical operations.