Studying the Concept of а Group in the Professional Study of Mathematics in General Secondary Education Institutions
DOI:
https://doi.org/10.63437/3083-6425-2026-2(101)-09Keywords:
critical thinking, logic of learning mathematics, group, action of group on set, clarity of examplesAbstract
The study of mathematics at school is traditionally associated with the development of logical thinking. In fact, the goal of strictly logically consistent study of mathematics is not proclaimed in the curricula. And with the content proposed in the current curricula, it is not achieved and cannot be achieved. The lack of strict formulations and the ability to deduce the properties of objects from them forces students to adapt to the teaching methodology, in which only what the teacher draws attention to is proven. The problem is not only that some knowledge is not obtained, and skills and abilities are not developed. The worst thing is that the ability to think critically is suppressed by the need to adapt to such a logically inconsistent study of mathematics and a misconception about mathematics in the modern sense has been created.
The paper presents an overview of the beginnings of group theory, adapted for work with students. Simple but meaningful examples of studying the structure of a permutation group are given, including using a computer experiment. Thus, the prerequisites for an inductive method of teaching the beginnings of group theory, including integrated with information technologies, are created. It is formulated with statements that are sometimes overlooked when studying higher algebra in higher education institutions and which can be used in constructing effective algorithms. For example, when solving some problems of Olympiad in Informatics. The paper explains which elements of the theory it is convenient to motivate for studying by the need to solve certain algorithmic problems.
The presented results can be used in specialized mathematics teaching in schools, in extracurricular work, to prepare students for intellectual competitions, and in advanced training courses.
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