The development of literate speech of students, including mathematics, as one of the areas of communicative component of learning outcomes, is a requirement of higher education standards. The authors have analysed the educational standards for the content of the requirements to the general education of a graduate related to the development of literate speech, as well as the works of domestic and foreign teachers-researchers on the development of mathematical literacy. The literature review and the authors’ own experience of teaching mathematics to engineering students at technical University showed that the ability of students to use logically correct, reasoned and clear oral and written speech is developed insufficiently to apply the mathematical apparatus in their educational and professional activities. The authors have identified the criteria of competent speech and theoretical and methodological conditions of the educational process which enable the ensure the organizational and methodological support of educational process aimed at the development of competent mathematical speech of students. The main applied methods of teaching are advanced self-directed work of students, lecture-discussion, mutual dictation, interchange of tasks, interchange of themes, study of the text fragments, repetition training-game, etc. The effectiveness of educational activities is achieved through the use of active and interactive forms of teaching. The prepared organizational and methodological support of teaching, the systemic educational work allow students to improve their speech skills and skills of active use of mathematical language as a universal language of science, to develop logical, algorithmic and mathematical thinking, the ability to apply methods of mathematical analysis and modeling, theoretical and experimental research in solving professional problems.