MATHEMATICAL MODELING AS A SCIENTIFIC BASIS FOR DEVELOPING ANALYTICAL THINKING IN ACADEMIC LYCEUM STUDENTS
Keywords:
Mathematical modeling, analytical thinking, academic lyceum, function, optimization, probability, formalization, problem solving, mathematical literacy, STEM education.Abstract
This article investigates mathematical modeling as a scientifically grounded and pedagogically productive basis for developing analytical thinking in academic lyceum students. The study proceeds from the idea that mathematics education should not be limited to the memorization of formulas, the reproduction of standard algorithms, or the mechanical performance of symbolic transformations. In contemporary education, especially in academically oriented secondary institutions, mathematics must function as a method of inquiry that teaches students to identify a problem, distinguish essential variables, formulate assumptions, construct formal relations, transform a model, evaluate the result, and interpret conclusions in relation to the original situation. The article uses theoretical analysis, structural-functional modeling, comparative didactic interpretation, and methodological synthesis. It examines functions, equations, inequalities, optimization, probability, statistics, matrices, vectors, and graph-based representations as key mathematical instruments through which modeling competence can be formed. The results show that mathematical modeling develops analytical thinking through abstraction, formalization, structuralization, optimization, algorithmic reasoning, and reflective interpretation. The discussion emphasizes that modeling should not be treated as a decorative supplement to mathematics lessons but as a methodological core connecting algebra, geometry, calculus, probability, discrete mathematics, and STEM-oriented reasoning. The article concludes that systematic use of modeling tasks in academic lyceums can strengthen mathematical literacy, scientific worldview, independent problem solving, and readiness for higher education in technical, economic, engineering, and natural science fields.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
