E-learning as a mean of forming students’ mathematical competence in a research-oriented educational process

Abstract

The article is devoted to the substantiation of approaches to the effective use of advantages and minimization of disadvantages and losses of e‑learning as a mean of forming mathematical competence of students in the conditions of research-oriented educational process. As a result of the ascertaining experiment, e-learning has certain disadvantages besides its obvious advantages (adaptability, possibility of individualization, absence of geographical barriers, ensuring social equality, unlimited number of listeners, etc.). However, the nature of these drawbacks lies not as much in the plane of opportunity itself as in the ability to use them effectively. On the example of the e-learning course (ELC) “Mathematical Analysis” (Calculus) of Borys Grinchenko Kyiv University, which is developed on the basis of the Moodle platform, didactic and methodical approaches to content preparation and organization of activities in the ELC in mathematics are offered. Given the specifics of mathematics as a discipline, the possibility of using ELCs to support the traditional learning process with full-time learning is revealed, introducing a partially mixed (combined) model. It is emphasized that effective formation of mathematical competence of students by means of e-learning is possible only in the conditions of research-oriented educational environment with active and concerned participation of students and partnership interaction. The prospect of further research in the analysis of e-learning opportunities for the formation of students’ mathematical competence, in particular, research and investigation tools, and the development of recommendations for the advanced training programs of teachers of mathematical disciplines of universities are outlined.

Research on visualization in probability problem solving

“…In other words, it is a process of forming an image and using it to understand and finally to solve a problem. This has the immediate effect not only of visual or spatial perception but also of an intuitive understanding of a problem (Astafieva et al, 2022). This is also confirmed by previous research, and in fact, visualization contributes significantly to enhancing students' creativity (Cioca & Nerișanu, 2020).…”

“…For instance, it is easier for a student to obtain information from a pie chart to answer a variety of questions than to read or listen to a long text. The advantages of this method are in the faster understanding of the exercise, its less tedious presentation, and the speed of its solution (Astafieva et al, 2022).…”

Organization of Independent Work of Students in LMS Moodle Using a Metacognitive Approach (on the Example of Physical and Mathematical Disciplines)

“…All material should be divided into small logically complete blocks, and the presentation of the material (proof of the theorem, for example) should take place in the form of an imaginary dialogue (the author / lecturer asks a question and answers himself), so that the student has the feeling that he is thinking out loud. For more information about the virtual lecture, see [12].…”