For the teaching of arithmetic the creation of consistent habits is of great importance. But it is impossible to reduce the teaching of arithmetic in elementary schools to a mechanical creation of arithmetical habits only, as some pedagogues have done during the period of the school reform in the former republic especially through the globular method of the beginning of teaching arithmetic.
The training of arithmetical habits should not involve any conscious elements, explanations, etc. This is said to be of no use and even makes the process of training more difficult. A reformist conception of the teaching of arithmetic has been criticized by contemporary progressive teachers. It signified a deviation from our progressive methodical tradition.
Survivals of this conception appear sometimes even nowadays in the teaching of arithmetic when mechanical methods of training and insuitable means of instruction are used.
The present progressive praxis which is built on the basis of marxist pedagogy and psychology proves that the process of the creation of arithmetical habits can be conscious if it is connected with the explanation of rules and their motivation. The knowledge of rules and understanding of the logical relations on the basis of which the habits have been formed guarantees that by accidental failure of the habits it is possible to renew them easily.
Against the rejection of the importance which is attributed to the explanation of rules and generalisation by the formation of habits speak the generalisations which are axquired by the pupils themselves through training. These elemental generalisations often come about unconsciously from the part of the pupils and without any interference of the teacher. But "proper rules" formed in this way are not always right. Should the pupils axquire rightly the most suitable carrying out of the rules of arithmetic the teacher has to lead them with his aim in view. The creation of arithmetical habits has to get out of thoroughly acquired knowledge, of analogy, and a knowledge of the relations of the single rules of arithmetic, etc.
Under the guidance of the teacher the pupils comprehend quite easily the relations and rules among the single rules of arithmetic. The understanding of these relations is important for the comprehension of the logical structure of mathematics. It is also possible to make practical use of it by means of tests examining the exactitude of the comuptations etc. Besides this it makes the understanding of these relations and rules of the teaching of arithmetic interesting.