Lecture
According to I.Ya. Lerner, every piece of knowledge, explicitly or implicitly, carries within it the possibility of its application. [16, 23]
The more ways a person knows to apply a given piece of knowledge, and consequently the more situations of application, the more operational that knowledge is.
Operativeness - a quality characterized by the number of situations in which a student can knowingly apply a given piece of knowledge, or by the number of ways in which he can apply that knowledge. [16, 24]
It is possible to reveal the operativeness of knowledge (that is, the readiness to apply it) because the content of education includes skills and habits that represent ways of applying knowledge.
As noted above, the very concept of «application of knowledge» is ambiguous. Two types of application of knowledge can be distinguished:
When speaking of the operativeness of knowledge, one means the application of knowledge in familiar situations. In the creative application of knowledge, the student discovers new ways of acting, or new combinations of already known ones, which contributes to enriching the operativeness of his knowledge. But the creative application of knowledge itself, the search for ways to use it, is linked to another quality - the flexibility of knowledge.
Flexibility of a person's knowledge is manifested in a person's readiness to independently find a way of applying knowledge when the situation changes, or to find various ways within one and the same situation. [16, 27]
The faster a student finds a new way of applying previously acquired knowledge, the more flexible his knowledge is. Another indicator of the flexibility of a person's knowledge is the ability to propose independently discovered ways of applying it to one and the same situation.
The difference between flexibility and operativeness is that operativeness characterizes precise knowledge of the ways of application for specific cases and the ability to realize them in typical situations, whereas flexibility presupposes the ability to find the knowledge about a mode of action needed at a given moment, to transform it for a specific case, and the ability to create a new method or combine already known ones into a new method.
Thus, flexibility always presupposes operativeness and relies on it, but operativeness does not necessarily reflect flexibility.
The defining methods for achieving operativeness of knowledge are the explanatory-illustrative and reproductive methods, whereas flexibility of knowledge requires the use of research-based and heuristic methods.
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