The relevance of the research is due to the fact that the study of further mathematics in an engineering university provides the level of general education and general cultural development of students, and educational background in special disciplines for the subsequent professional tasks solution. At the same time, there are significant difficulties in mastering the "Further Mathematics" course by students. In this regard, this work is aimed at solving the problem of improving the process of teaching further mathematics in an engineering university using a combination of project based learning and case study (project-case technology). It contributes to developing professional competencies of students of architectural and engineering specialties through the use of solving practice-oriented problems, which brings them closer to real future professional activities. The leading methods in the problem study were: entrance subject testing of the training level in mathematical; pedagogical observation during lessons where project based learning and case study were used; questionnaires upon completion of the "Further Mathematics" course, aimed at identifying both the level of mathematical maturity and the level of ability to conduct research activities necessary to solve non-standard professional tasks. Methods of mathematical statistics were used to process the experimental data. The main results of the study consist in highlighting the features of the combination of project based learning and case study when mastering the "Further Mathematics" course by students, future architect engineers. The significance of the obtained results lies in the fact that the proposed organization of the educational process can be implemented in various engineering specialties, considering a selection of specific professional case tasks.
The modern transformation of all spheres of life is associated with rapid technological and digital development. The educational sphere, focusing on external demands, systematically introduces technological and digital solutions into the processes of pedagogical systems functioning, focusing on the expansion of the educational space, on increasing the availability of educational services. In order to create a comfortable and effective digital environment in universities, it is important to take into account not only the level of development of digital competencies of students and teachers, but also their basic needs and requirements in this area. We set a goal to identify the most successful digital solutions used at this stage in university education from the students’ perspective and to consider the factors inhibiting these processes. To solve the problems, we used methods of theoretical analysis and empirical processing of research data. The main method was a survey of students using the questionnaires “Digital learning environment and online learning format” and “Quality of digital educational resources and organizational aspects of e-learning” developed by the authors. More than a thousand students from Russian universities took part in the survey. The results of the survey showed what means of communication in online learning are considered by students to be the most effective, what means of increasing productivity and what means of organization and support in online learning are most useful to them. The platforms and learning systems were considered in detail to understand the important characteristics of these services for students. The analysis highlighted the main areas in the digital transformation of the educational environment, which should be targeted for their development and improvement.
In the teaching community, there is an ongoing discussion about the difference between visual and analytical thinking and the issues of psychological-pedagogical argumentation of the concept of visual teaching mathematics. Following the discussion, this paper is aimed to identify visual images understanding. The research objective is to identify the role of images in the formation of mathematical concepts (using an example of the concept of function). The novelty of the work is that an image is considered not as a result but as a condition for mathematical concept understanding. The authors used theoretical and experimental methods of study (the analysis of psychological and pedagogical sources, testing, and survey). To achieve the goal, special examinational questions were developed. The authors identified the role of influence of using images and concepts initially existing in the student’s mind on the efficiency of understanding the essence of a mathematical concept. The study revealed that students who have the skills of both visual and analytical thinking demonstrate the best results of understanding mathematical concepts. The research shows that visual and analytical types of thinking not always comply with each other, therefore, methodologically verified teaching mathematical concepts and relations should be proportionally balanced. The prevalence of any type of thinking by the students is individual. The essential prerequisite for successful application of visual teaching methods is to take into account the initial images, ideas, and associations of students in teaching. Visualization is an important method of learning mathematics; however, understanding mathematical concepts does not suppose isomorphism between understanding of a concept and its image.
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