The Future of Education

Mastering logical proofs in primary school is a prerequisite for the development of mathematical thinking in students. They are an important alternative route for the utilization of under-used mental capacities of students. Particularly valuable in this field is the use of indirect apagogical proof.

The aim of this publication is to present our research on the theoretical foundations of the indirect apagogical proof and the methodological possibilities for studying this topic in primary mathematics education. This study is also aimed at both discovering and presenting some possibilities, offered by the primary mathematics curriculum in Bulgaria, for propaedeutic training in using the apagogical proof.

The theoretical aspects of this work reveal the complex logical structure of the proof in question.

The developed methodology determines how training of primary school students is done through a system of principles, methods and means of training.

As a result of the training, after the implementation of the developed technological option for training in this field, we expect students to have mastered the knowledge and skills to solve problems by applying the indirect apagogical proof, in accordance with their age and perceptive abilities.

The mathematical ideas and methods, which are used in solving this class of problems, and the described technology contribute to organizing the process of solving them. The variety of forms of training in mathematics provide a good opportunity to enable an educational environment for the realization of the created methodological system. The system of problems is a technological option for training and can be adapted and modified by keeping its structure and varying it with different practical and mathematical tasks.