On the Methodology of Teaching Higher Algebra to Future Mathematics Teachers

Identificator

EDN: MQQOYD ; УДК: 37.016:511:378

Authors

Vechtomov Evgeniy Mikhailovich, Doctor of Physics and Mathematics, professor, Chief Researcher of the Institute of Exact Sciences аnd Information Technologies, Pitirim Sorokin Syktyvkar State University. Russia, Syktyvkar. E-mail: vecht@mail.ru

Journal

HERALD OF VYATKA STATE UNIVERSITY №4 (158), 2025

Section

PEDAGOGICAL SCIENCES

Pages

43-53

Abstract

The article examines and analyzes methodological questions and questions of teaching method in the instruction of higher algebra within the system of training mathematics teachers. In today's world, the questions of teaching mathematics at university and in secondary school are more relevant than ever. For Russia, high-quality mathematical education is the foundation of its sovereignty. The aim of our work is to draw the attention of university mathematics lecturers and of students of mathematical specialties to the most important didactic and methodological principles and propositions in the study of higher algebra, which ensure an understanding of algebraic material. The article discusses the principles of completeness, of integrity, and of the substantive connections of the higher algebra course with other mathematical courses. Within the didactics of university algebra, the structural and problem-based approaches, the principle of harmony, the axiomatic method, and the fundamental ideas of isomorphism, coordinatization, and factorization are singled out. The role of the introductory algebra course is noted as a kind of "bridge" between the school algebra course and the university course of higher algebra. Such continuity will also have a beneficial effect on the successful solution of problems in elementary algebra, which is so important for the mathematics teacher. The problem-based and structural approaches to teaching students higher algebra are regarded as particularly significant. The importance of developing cycles of interrelated problems and exercises for each topic of the course is emphasized. In solving each specific mathematical problem, one must strive to identify the abstract structure hidden within it and to use the information about this structure to solve the problem. This, in turn, requires a knowledge of the fundamental mathematical structures, their properties, and their basic models. At the end of the article, examples of educational-research and scholarly-research problems are analyzed that illustrate the structural approach and the significance of basic logical and mathematical ideas and methods. The implementation of these propositions, taken together, is the path to the understanding and high-quality assimilation of algebraic knowledge. The significance and necessity of algebraic education in the training of the modern mathematics teacher are substantiated.

Keywords

higher algebra course methodology and didactics of the course algebraic training of mathematics teachers

Recieved

30.04.2026

Published

08.10.2026

References

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