Формування професійних компетентностей студентів технічних спеціальностей засобами прикладних задач з вищої математики

Abstract

The article substantiates the role of applied problems as an effective means of ensuring the professional orientation of higher mathematics teaching in technical education institutions. It is argued that the integration of fundamental mathematical training with practice-oriented tasks enables the alignment of theoretical knowledge with future professional activity, enhances students` motivation, and contributes to the development of key professional competencies. An analysis of scholarly approaches to the professionalization of mathematical training confirms the relevance of applied and professionally oriented problems, interdisciplinary integration, mathematical modeling, and digital learning technologies. The essence of an applied problem is clarified as a tool for connecting abstract mathematical constructs with real engineering, industrial, and economic processes. Its main characteristics are identified as contextuality, modeling focus, goal orientation, and interdisciplinarity. The educational functions. Their impact on the formation of analytical and critical thinking, modeling skills, argumentation, reflection, and informed decision-making is demonstrated. A typology of applied problems in the higher mathematics course is proposed, encompassing process modeling, optimization, analytical, interdisciplinary, research-based, project-based, and digital problems. Methodological principles for their implementation are substantiated, including visualization, gradual increase in complexity, knowledge integration, problem orientation, and systematic incorporation into all forms of the educational process. Examples of professionally oriented applications of applied problems in lectures and practical classes for engineering students are provided. It is concluded that the effectiveness of applied problems depends on a methodologically sound ion of con tent, the use of digital tools, the organization of teamwork and project-based learning, and the implementation of formative assessment based on multi-component criteria. Applied problems are therefore considered an essential instrument for modernizing technical education and ensuring high-quality professional training of future specialists.