The article deals with the theoretical analysis of the traditional approaches to electrodynamics teaching. The authors pay attention to the contradictions arising in the process of combined application of Biot-Savart and Coulomb`s laws. The thesis of some limitation of the traditional presentation of the course of electrodynamics is substantiated. In this connection the necessity of updating methodology of electrodynamics teaching is determined. As an innovative approach to solving this problem, it is proposed to analyze and address the existing contradictions of electrodynamics teaching using a specially developed (copyright) methodology - the methodology of the development of students` critical thinking (MDCT). Using specific examples, the content of each of the stages of the proposed methodology, which can be used in the study of electrodynamics in secondary and higher school, is characterized