Dubovyk V. Methodology of teaching linear algebra to students of pedagogical universities using information and communication technologies

The gradual renewal of the system of higher pedagogical education in Ukraine reorients the paradigm of training students of pedagogical universities from the school of assimilation of knowledge of higher education seekers to the school of creative search. This requires preliminary development and implementation in pedagogical institutions of higher education, particularly in the process of training future teachers of mathematics, of effective forms, methods and means of teaching. One of the ways to solve this problem is the introduction of information and communication technologies for learning, in particular, during the learning of linear algebra. The object of research is the process of mathematical training of students in pedagogical universities. The subject of the study is the method of learning linear algebra using ICT. The purpose of the research is to develop, theoretically substantiate and experimentally verify the methodology of teaching linear algebra to students of pedagogical universities using information and communication technologies. In accordance with the purpose of the study, the following tasks were outlined: 1. To find out the state of development of the problem in psychological-pedagogical, scientific-methodological literature and in the practice of teaching linear algebra in pedagogical universities. 2. To reveal the essence, classification and peculiarities of the use of information and communication technologies of education during the training of future teachers. 3. To develop a method of teaching linear algebra to students of pedagogical universities using information and communication technologies, aimed at forming subject competence in them. 4. To experimentally verify the effectiveness of the introduced method of using information and communication technologies during the teaching of linear algebra by students of pedagogical universities. The scientific novelty of the research results is that: for the first time: a method of teaching linear algebra for students of pedagogical universities using ICT was developed, theoretically substantiated and experimentally tested, which involves the purposeful formation of subject competence in linear algebra of students of higher education; a model of learning linear algebra for students of pedagogical universities using ICT was built; clarified: the essence of the concepts «information and communication technologies of learning», «electronic educational quest-guide», «microclimate of the system (teacher, students, teaching aids (ICT))» «subject competence in linear algebra»; classification of information and communication technologies, which are appropriate to use during learning linear algebra; characterized: components of subject competence in linear algebra (motivational, cognitive, operational and activity); determined: criteria (motivational-value, substantive, operational-activity) and levels of formation of subject competence according to each of the criteria: beginner (awareness), intermediate (reproduction), advanced (application); improved: the system of organizing classroom and extracurricular educational activities of students in linear algebra based on the introduction of information and communication technologies; educational and methodological support for teaching linear algebra; the theory and methodology of learning linear algebra for students of pedagogical universities have gained further development. The practical significance of the research results is: the training of future teachers of the educational and methodological complex of the educational discipline «Linear Algebra»; distance course «Linear Algebra» in the information and educational environment «Moodle» developed and implemented; a number of information and communication technologies into the educational process of learning linear algebra: during lectures using online resource «Timeline» («Linear Algebra Course Structure», «History of Linear Algebra»), tag clouds, software tools for visualizing educational material ( GeoGebra, Gran 1), mental maps, etc.; in practical classes of computer and mobile programs, online services MAPLE, Mathematica, GeoGebra, Linear Algebra (Darshan University), matrixcalc, Microsoft Excel.