VIETA'S THEOREM: MATHEMATICAL AND ETHNOMATHEMATICAL ASPECT
DOI:
https://doi.org/10.31110/fmo2024.v39i4-03Keywords:
polynomial, roots of a polynomial, Vieta's Theorem, parameter, division with remainder, condition for the existence of polynomial roots, progression, prime numbersAbstract
Formulation of the problem. The main task of a modern school is to develop pupils' natural abilities and talents, build competitiveness and skills for their socialization, develop critical thinking, and create conditions to ensure their harmonious development. Therefore, the problem arises in shaping students with a comprehensive system of theoretical knowledge and practical skills across various disciplines, enabling them to apply acquired knowledge to address contemporary life issues. However, school textbooks do not sufficiently consider students' knowledge of related subjects and modern life. The article aims to integrate a problem series of "Vieta's Theorem" and create complex exercises of different levels.
Materials and methods. The research uses theoretical methods, including analyzing mathematics curricula and educational programs in pedagogical specialties with mathematical components and the content of contemporary school textbooks. Furthermore, combining personal and advanced pedagogical experiences regarding the integrated tasks application in the educational processes of both schools and higher education institutions. Empirical methods included observations during mathematics classes in high schools and extracurricular activities, and observations during mathematics sessions in pedagogical specialties at HEIs.
Results. The authors examined a problem series based on Vieta's Theorem, providing an overview of typical issues encountered in school mathematics courses and mathematics courses within pedagogical specialties at HEIs. Examples of tasks incorporating local geography were proposed to guide teachers in considering historical-geographical local themes or the profile of mathematics study when creating similar tasks. The use of Vieta's Theorem in geometry and other branches of algebra, including tasks with practical content, was demonstrated. High-level questions suitable for extracurricular scientific research or project work with students were presented.
Conclusions. The creation of a series of math problems with varying integrated tasks will serve as invaluable experience for beginner math teachers, including those in classes of different specializations, and for STEM students.
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