Introduction

Abstract

The task of the school is not only to convey to the pupils information in various fields, but also to develop in them the ability of correctly carrying out cognitive operations. These two tasks, which in practice are being carried out parallelly, have been termed, respectively, the material and the formal goal of teaching. But to be able to train his pupils in a correct performance of cognitive operations the teacher must himself provide the standard of correct thinking. This, however, does not suffice: the pupils must carry out the operations themselves, and the teacher must see to it that they do that properly. Hence, if a pupil, when proving a theorem, or explaining a phenomenon, or defining a concept, commits an error, the teacher must draw his attention to the fact. But it does not suffice if he tells the pupil that he committed an error; he also ought to point out where the error is and in what it consist. The practical ability to think correctly, which every teacher should have, will alone suffice for him to notice that the pupil made an error; it will probably also suffice for him to explain to the pupil where the error is. But it need not necessarily suffice for him to be able to tell in what that error consists and what its nature is. To be able to do so he must know those concepts and terms which make it possible to discuss cognitive operations and their types, properties, etc.