The specific aspects of designing computer-based tutors for future engineers in numerical methods studying

Introduction: the paper considers the topical problem of teaching students - future engineers - by computational methods of mathematics. The focus is on developing students necessary professional competencies. Competencies are described in accordance with the Russian Federal State Educational Standard and the international standard by the European Association for Engineering Education SEFI. In order for students to thoroughly study the subject and have a strong professional competence, it is proposed to use a computer-based tutor. The aim of this research is to develop the special methodology of creating the computer-based tutors for teaching mathematical and engineering disciplines to students of technical specialties within the framework of a competence-oriented approach, to compare the effectiveness of classical teaching computational methods by using manual calculations, and training with the involvement of computer-based tutors. The advantages of computer-based tutors were proved in this paper. Materials and Methods: the basis of the research was methods of system analysis and descriptive and analytical methods, primarily experimental. To identify advantages of the proposed approach the methods of empirical research were used (observation and comparison). To prove the efficiency, classical methods of measurement were used. Results: based on the competence approach, a methodology of creating a computer tutor has been developed. It covers most the professional competencies that need to be studied. Also, students are guaranteed to receive the necessary competencies in the right sequence. The research showed that the use of specially designed software, such as Computer-based tutors, in the process of mathematical methods studying connected with the computational procedures allows us to achieve: on the one hand, deep digestion by students (as in using manual calculations), on the other hand to accelerate learning process and increase students motivation. As a result of pedagogical experiment on the use the computer-based tutors the progress in studies has been recorded: the percentage of positive ratings increased from 65 to 88 %. Also, the motivation of students to study mathematics was increased by 12 percent on average. Discussion and Conclusions: the methodology of creation and use of computer-based tutors has high practical significance and allows increasing the effectiveness of teaching mathematics within the competence approach for students of technical specialties. The use of the interactive computer-based tutors focused on mastering professional competencies, is effective for studying mathematical and engineering disciplines by students of technical universities. In particular, a positive effect has been achieved with the introduction of computer-based tutors in the educational process of Kazan National Research Technical University named after A. N. Tupolev-KAI, Kazan, Russia (the University is aimed at training engineers-designers for aerospace industry), Saarland Technical University, Saarbrucken, Germany (the University is focused on training IT engineers), and a number of other Russian and foreign technical universities.