Problems of studying the direct consequences of the axioms of planimetry in a general school

Рудик, Олександр Борисович (2026) Problems of studying the direct consequences of the axioms of planimetry in a general school Наукові записки. Серія: Педагогічні науки (223). pp. 405-410. ISSN 2415-7988

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Abstract

The article describes the problems of the existence of a barrier to high-quality general secondary education in the field of geometry. It is about studying the direct consequences of the axioms of planimetry and its influence on the correct perception of the mathematics course. They concern the development of critical thinking at the time most favorable for the development of the ability to concentrate and think critically when studying the basics of planimetry. The study of mathematics (especially geometry) at school is traditionally associated with the development of logical thinking. 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 they prove only what the teacher or the author of the textbook draws attention to. Excessive appeal to clarity in the absence of appropriate comments from the teacher leads to the inability to notice the need to substantiate reasoning based on axioms and already established facts. The problem is not only that some knowledge is not obtained, but skills and abilities are not developed. This complicates the correct ordering of educational material by the student in the future, when he will encounter a violation of the logic of the presentation when he needs to have logically ordered knowledge as a specialist. Another problem is the inconsistency of terminology. And it is not only about different formulations in different textbooks. Some textbook authors use the concept of a figure that they do not define. And those who present it as a set of points do so imperfectly from the point of view of formal logic. Sometimes the definition of a concept in a school textbook can have several significantly different interpretations in terms of content. As a result, there is a habituation to inattentive perception of verbal formulations, substitution of their content at the level of figurative thinking without appropriate correction at the verbal level. The purpose of the work is to investigate the possibility of presenting a comprehensive description of overcoming the described problems, acceptable for novice teachers and students of general secondary education. It seems promising to study the problem of logically consistent presentation to students of at least the basics of the theory of integers and rational numbers in the specialized study of mathematics, similar in purpose.

Item Type:	Article
Uncontrolled Keywords:	logic of learning mathematics; critical thinking; axioms; immediate consequences; clarity; levels of mastery of mathematical theory
Subjects:	Статті у базах даних > Index Copernicus Статті у періодичних виданнях > Фахові (входять до переліку фахових, затверджений МОН)
Divisions:	Інститут післядипломної освіти > Кафедра природничо-математичної освіти і технологій
Depositing User:	доцент Олександр Борисович Рудик
Date Deposited:	17 Jun 2026 10:33
Last Modified:	17 Jun 2026 10:33
URI:	https://elibrary.kubg.edu.ua/id/eprint/57895

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