The purpose of this article is to develop the content and methods, as well as the analysis of the approbation of the program of the academic discipline "History and methodology of mathematics" for graduate students of the Master's program of mathematical program tracks. The leading method in the study of this problem was the method of modeling the work program of the academic discipline "History and methodology of mathematics", as well as the selection and structuring of the system of classes of different types, which allowed us to generate a logically constructed course. The structural model of the curriculum "History and methodology of mathematics" has been developed and presented; the selection and structuring of this course has been carried out, which combines such meaningful lines interwoven with time and history as: 1) history of mathematics, 2) history of mathematical education, 3) philosophy of mathematics, 4) methodology of mathematics; the types of classes on selected topics have been offered; the examples of the successful implementation of creative ideas are given which can be adopted and taken as a basis by other academic researchers. The competent teaching of the academic discipline "History and methodology of mathematics", based on the developed work program with the application of the proposed forms of classes, broadens the scientific horizons of graduate students of mathematical and pedagogical program tracks and allows them to focus on educational, scientific and methodological types of the future professional activity. The materials of the article can be useful for graduate students of mathematical program tracks for teaching university teachers of mathematics.