To the methods of the axiom, theorem, definition and proving by means of contradiction concepts presentation in the course of geometry in the 6th form

Abstract

The new syllabi of mathematics recently accepted in our secondary schools, rightly determine the relationship between the inductive and deductive ways of introducing the geometrical material. At the eight-year school the inductive method will prevail: at the same time the school children will be acquainted with the logical structure of the course of geometry and will be prepared for the conscious assimilation of the deductive method much earlier and deeper if compared with the present syllabi. Already in the 6th form the concepts of mathematical statements (axiom, theorem and definition) will be introduced, the school children will be acquainted with the structure of the theorem, with four kinds of simple theorems and the relationship between them, and with proving by means of contradiction. The introduction of the material must be acceptable and appropriate for the schoolchildren's age. It is rather a difficult task for the teacher that requires high qualifications and sound knowledge of theory. The aim of the article is to help the teachers of mathematics with the presentation of this material. The material is put in the manner of conversation. That will be detailed notes of the lessons. The conversation is planned for more than one lesson, of course, and for this reason the material must be distributed with the selection of the most important parts for the given lesson. Four topics are dealt with in the above article, namely: l. The concepts of axioms, theorems and definitions; 2. The structure of theorems; 3. The kinds of simple theorems; 4. The ways of proving theorems by means of contradiction.