Implementation of the principle of practical orientation in the study of mathematics by university students (using the topic “Vectors” as an example)

This article explores the implementation of a practical focus in a mathematics course, using the topic “Vectors” as an example. It substantiates the need to overcome the traditional approach limited to physical interpretations of vectors, and proposes a method for shifting the emphasis to the use of vectors and their manipulation in modern IT applications. A key example is the operation of marketplace recommender systems, where vector representations of data and the dot product operation form the mathematical basis for calculating the semantic similarity of objects. The article describes in detail a lesson fragment using case study technology, in which students, acting as data analysts, independently create vector models of products and users, calculate the cosine similarity measure, and generate personalized recommendations. The method includes clear stages of work: from immersion in a problematic situation to presentation of results and reflection. Particular attention is paid to the development of meta-subject competencies–communication skills, critical thinking, and functional mathematical literacy. During the case study, students master the principles of vector data representation and methods for assessing semantic similarity, which develops an understanding of the practical value of mathematical knowledge. The author presents the results of a three-year pilot study of the methodology at a pedagogical and technical university on a sample of 65 students. Statistical data demonstrate high student engagement: 83% of students participated actively in class, 78.4% of mathematical calculations were correct, and 61.5 % of students demonstrated sustained interest throughout the lesson. The methodology proved most effective for students majoring in Business Informatics, where 85.7 % of respondents successfully completed the tasks. The results confirm the effectiveness of the proposed approach for developing practice-oriented competencies in the context of the digital transformation of education and can be used in teaching mathematics in schools and universities.