ABOUT SOME AMBIGUOUS FRAGMENTS OF THE CONTENT OF TEACHING VECTOR ALGEBRA, COMPLEX NUMBERS AND ANALYTICAL GEOMETRY IN UNIVERSITIES

Fokin Roman Romanovich, Pavlenko Yuliya Vladimirovna

The article examines fragments of the content of teaching some sections of mathematics in universities with a view to their subsequent modification to improve their understanding by students. Ambiguous means fragments that can be improved in the above sense. Firstly, the authors present a simple example (the definition of a geometric vector taken from textbooks) of educational mathematical material that cannot be understood by a student in a logical-conceptual sense, but can only be understood in an associative-intuitive-visual sense. The reasons for this typical phenomenon are discussed further. Secondly, the article presents the ambiguous fragments of the vector algebra teaching content identified by the authors and their proposed changes. In addition to the above definition, these are also definitions of the equality of geometric vectors and the angle between vectors. Thirdly, a similar ambiguous fragment of complex numbers is presented. This is an algorithm for converting a number from an algebraic form to a trigonometric one. Fourth, a fragment from analytical geometry. This is the recalculation of the coordinates of a point from one coordinate system (Cartesian) to another (affine).

Keywords:content of education, universities, mathematics, vector, complex number, geometry, students, reasons for misunderstanding