The article presents the results of pedagogical researches aimed at solving the problem of designing methodological approaches in teaching mathematical disciplines to undergraduate students of pedagogical directions based on competence and integrative approaches, actualizing interdisciplinary connections of mathematics through the introduction of integrated programs, modular training, electronic information educational environment (EIEE) and the method of projects. The use of the project method is associated with the introduction of the system of case studies in mathematical disciplines into the educational process. The design of e-learning courses is implemented on the basis of the Learning Management System Moodle Platform and involves the use of textbooks that implement the concept of integration of education with the actualization of interdisciplinary connections (Numerical methods – computer studies; geometry – computer studies and modern means of assessing learning results). In the process of experimental work, some empirical research methods are used: observation, pedagogical experiment, conducting pedagogical measurements, experimental training in mathematical disciplines; methods of theoretical research: an analysis of scientific and pedagogical, psychological, philosophical literature and dissertation research, an analysis of university programs, textbooks and manuals on mathematical disciplines, an analysis of the organization of the process of teaching mathematical disciplines to undergraduate students of pedagogical directions. To test the hypothesis about the effectiveness of the methodological approaches used, the Wilcoxon-Mann-Whitney test was chosen. In order to identify the relationship between the level of development of students' professional competencies and the implemented methodological approaches, the dichotomous scale, the Pearson φ-correlation coefficient and the four-band contingency table are used. Based on the analysis of the results of the pedagogical experiment, the following conclusions were made: it is advisable to carry out the design of the process of teaching the mathematical disciplines to undergraduate students of pedagogical directions on the basis of competence and integrative approaches; effective formation of students' professional competence is possible by means of educational content of mathematical courses using ICT, electronic information educational environment, the project method, specially developed methodological support and the case-study system using psychological and sociological diagnostics to ensure an effective teamwork.