COMPETENCY-BASED APPROACH TO TEACHING STUDENTS OF TECHNICAL SPECIALTIES IN THE EDUCATIONAL COMPONENT «ALGEBRA AND GEOMETRY»

Abstract

Summary. Problem. The current stage of development of higher technical education in Ukraine is characterized by intensive modernization, caused by dynamic changes in the labor market and increasing requirements for the quality of training of specialists. This is especially relevant for future specialists in the field of statistics and data analysis, where mathematical training is the foundation of professional activity. There is an urgent need to bridge the gap between the abstract nature of fundamental mathematical disciplines and their practical application in real engineering and statistical problems. The competency-based approach is considered as a key methodology that allows shifting the emphasis from the simple accumulation of knowledge to the formation of the ability to act effectively in professional situations, to develop critical thinking and adaptability.

The purpose of the study is to theoretically substantiate and reveal practical aspects of implementing a competency-based approach in the learning process of applicants for technical specialties (in particular, the specialty "Statistics") during the mastery of the educational component "Algebra and Geometry", as well as to demonstrate the effectiveness of integrating mathematical methods with professionally oriented tasks.

Research methods. To solve the tasks set, a set of methods was used: theoretical analysis, systematization and generalization of scientific and methodological literature to determine the structure of mathematical competencies; empirical methods, including pedagogical observation of the educational process, analysis of the products of applicants' activities and conducting an interview to assess the level of motivation and assimilation of the material.

Main results of the study. The article details the content of the competency-based approach through the development of a system of applied tasks, where objects of linear algebra and analytic geometry act as tools for statistical analysis. A methodology is proposed in which matrices are studied as forms of representation of multidimensional data, and operations on them are studied as methods of normalization and sample processing. It is established that the use of vector models and Euclidean distance allows applicants to understand the concepts of clustering and proximity of objects more deeply. The feasibility of the geometric interpretation of statistical indicators is proven, where the correlation coefficient is considered as the cosine of the angle between the observation vectors. Special attention is paid to preparing for the principal component analysis (PCA) method through the study of eigenvalues and vectors. The need to use software tools (Excel, R, Python, MATLAB, GeoGebra) for the visualization of complex models is justified.

The scientific novelty lies in the development of an integrated learning model that combines fundamental mathematical training with contextual learning. For the first time, a system of professional and applied tasks for the course "Algebra and Geometry" has been proposed, in which mathematical concepts are directly transformed into statistical categories (a straight line as a regression model, eigenvectors as directions of maximum dispersion, etc.). Interdisciplinary interaction has been substantiated, which ensures the continuity of the formation of professional competencies.

Author's conclusions and specific suggestions. The implementation of a competency-based approach contributes to increasing the competitiveness of future specialists by forming in them not only knowledge, but also ways of thinking. It is proposed to introduce project forms of work into the educational process, in particular mini-projects on the visualization of real datasets, which allows applicants to independently go from an abstract model to a practical interpretation of the results. It is recommended to diversify assessment methods, giving priority to practical cases and research tasks