In order to teach on the basis of the genetic approach, one should undertake an analysis consisting of the following two stages: (1) a genetic elaboration of the subject matter and (2) an analysis of the arrangement of the material, including a consideration of various ways of representing it and its effect on students. The genetic elaboration of subject matter consists of the analysis of the subject from four points of view: historical, logical, psychological, and socio-cultural. Also important is the epistemological analysis of the subject. This paper describes the design of the system of study of the concepts of Euclidean ring and equivalence relation.