Vologda Institute of Law and Economics of the Federal Penal Service of Russia implements the professional academic program “Psychology of Official Activities” for the training of prison psychologists. The Federal state educational standard of higher education establishes a competency-based approach to assessing the quality of training of future specialists. In the complex of competencies that a graduate should have, the competencies ensuring the ability of future specialists-psychologists to research activities hold a specific place. The paper analyzes the role of mathematical disciplines in the formation of these competencies and considers some problems of teaching disciplines “Mathematics” and “Mathematical methods in psychology” such as the low level of competence in mathematics of secondary school graduates entering the psychology programs of study; the insufficient formedness of a number of research skills of the underclassmen; the application of mathematical methods in psychology. In the course of the study, the authors carried out a survey of the first-year students of psychology faculty entered the university in 2016-2018 and studied their distribution according to the selected levels of the USE in mathematics and their ideas (before entering the university) about the role of mathematics in psychology. The paper specifies the main provisions that guide the authors in teaching mathematical disciplines to future prison psychologists. The authors carried out the analysis of the application of mathematical methods in the graduate qualification works in the specialty “Psychology of Official Activities” in 2017-2018. The graduate qualification works demonstrate a sufficient level of formedness of the competencies under consideration; however, the authors note a rather narrow range of mathematical methods applied in the students’ works. The authors proposed the directions for further development of mathematical and statistical methods.