ON RIGOROUS AND PLAUSIBLE REASONING IN THE STUDY OF VECTORS AND MATRICES IN UNIVERSITY MATHEMATICS

Fokin Roman Romanovich, Ershova Elena Viktorovna

The article considers, firstly, the author's classification of reasonings used in mathematics. These reasonings are divided by the authors into rigorous (both in the sense of Euclid and Aristotle, and in the sense of Hilbert) and plausible (in the sense of Poya). Secondly, the article examines the main problems of studying mathematics by modern students. The first problem is related to the departure of modern higher education from the academic teaching style that had developed by the beginning of the 20th century. The second problem is related to a significant increase in the proportion of right-brainers among students of all professional fields over the past 30-40 years. Thirdly, various mathematical definitions of the terms "vector" and "matrix" are considered, and the innovations in the style of studying mathematics proposed in the article are described using the example of studying vectors and matrices. The teacher is offered methods for organizing two channels of perception of mathematical educational material: for right-hemisphere and for left-hemisphere students.

Keywords:mathematics, vector, matrix, learning style, problems, students, right hemisphere, left hemisphere, plausible reasoning