Lecture
Compactness and expandedness of knowledge consist in a person's ability, on the one hand, to express knowledge compactly, yet in such a way that it represents the visible result of condensing a certain body of knowledge, and, on the other hand, to unfold the sequence of steps leading to the compression, the folding, of that knowledge. [16, 31-32].
If a student cannot unfold a compactly expressed thought and fill it with concrete content, then that thought remains empty. At the same time, a lack of readiness for conscious unfolding makes compact presentation impossible. That is why tasks requiring the generalization of concrete material are important, ones that would make it possible to formulate this or that theoretical proposition in compressed form. Alongside these, tasks on unfolding knowledge and presenting a chain of reasoning are also necessary.
One of the general regularities of the learning process is that the assimilation of any new, complex knowledge or mode of activity must proceed as the assimilation of the individual elements of that knowledge, or of the operations that make up the action. Otherwise, assimilation either fails to occur or requires considerably more effort and time. The practical realization of this regularity therefore presupposes, on the one hand, unfolding concrete knowledge and breaking it down into individual elements during assimilation, and, on the other hand, compressing the already-assimilated elements in order to obtain generalized knowledge.
It follows from the foregoing that the compactness and expandedness of knowledge are closely related to its generality and concreteness, but they are not the same thing. The compactness of knowledge can be expressed in the fact that the student cites a concrete fact whose meaning reveals the content of both the concrete and the generalized knowledge that student possesses. Compactness of knowledge is a necessary quality, one that is achieved through the many-sided application of knowledge.
The compactness of knowledge lies in a person's ability to express knowledge compactly while at the same time making visible the process of condensing that knowledge. A student's inability to unfold compressed knowledge indicates that the knowledge is of low quality. The compactness of knowledge is related to its generality, while expandedness is related to its concreteness, but these two qualities are not identical.
Comments