One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of oral and written calculation in elementary school. From the authors' point of view all these difficulties are located much deeper: at the basis of their formation. In the traditional system of teaching elementary school children, they are caused by the contradictions resulting from a sensory approach to mental skills formation. Having appeared initially from the sensory perception of a child working with objects an denoted by a symbolic word, calculation methods with objects are often transferred directly into abstract word-logical forms, which do not demonstrate to students their essential meaning. One of the perspective directions in overcoming the drawbacks of a sensory approach to the formation of calculation skills is an "activity" approach to the mastering of these concepts.