SYSTEM OF APPLIED MATHEMATICAL PROBLEMS: CRITERIA FOR DEVELOPMENT AND FEATURES OF SOLUTION - Shvets, Vasyl; Prus, Alla (Physical and Mathematical Education, 2026)
Formulation of the problem. The State Standards of Basic Secondary Education (Ministry of Education and Science of Ukraine [MES], 2020) and Specialized Secondary Education (MES, 2024) define mandatory learning outcomes for students based on a competence-based approach, namely, the key competences (eleven in total). One of them is mathematical competence. These requirements as learning outcomes must be achieved during the study of every school subject, including mathematics. One of the most effective means of forming key competences in mathematics lessons is applied problems—problems that exist beyond mathematics but are solved using mathematical knowledge. They are commonly classified into real problems, which exist in practice, and imaginary (quasi-applied) problems, which arise in people’s imagination and may need to be solved in the future. Therefore, such problems are included in school mathematics textbooks, teaching aids, problem books, and didactic materials. These are special problems that differ from purely mathematical ones in their purpose, methods of solution, and the culture of mathematical communication. They help students develop skills in mathematical modelling, awareness, and the ability to apply mathematical knowledge in everyday life, in studying related subjects, and in acquiring professional knowledge in further education. A few isolated tasks cannot ensure the formation of the declared competences; therefore, systems of applied problems must be developed that correspond both to the content of mathematical training and to students’ age-related abilities and interests. To design such systems, clear selection criteria are required. This article addresses this issue and proposes a set of criteria for developing sets of applied mathematical problems to foster students’ key competences.Materials and methods. To develop the criteria for selecting applied mathematical problems, theoretical methods (analysis of regulatory documents, scientific papers, reference and teaching literature on mathematics education; synthesis and generalization of results), and empirical methods (teacher surveys, study of best teaching practices, analysis of students’ written work and test performance) were used.Results. The outcome is a system of criteria for constructing sets of applied mathematical problems, along with methodological recommendations for their solution.Conclusions. A system of applied mathematical problems is an effective means of forming key competencies among school students. Such problem sets should be an integral component of the task material in every topic of the school mathematics curriculum. Their solution makes a significant contribution to the development of students’ key competences.
Keywords: education standard; key competences; applied mathematical problems; criteria for designing problem systems; mathematical modelling; features of solving applied problems