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In constructive teaching besides this on the structures of knowledge are performed logical
operations of thinking. These operations allow students to integrate structures of knowledge
into groups to clarify their interrelationship and relationship, classify, enrich, or replace
them with other structures. A student, performing thinking activities of such operations on
the structures of knowledge adequately builds the structure of his/her thinking and logical
structure of his/her knowledge. Logical operations on the structures of knowledge are
performed by commands or setting of a student.
1.
The operation of classification
With the assistance of this operation, students acquire intellectual skills of the partition of
the set into subsets according to certain criteria.
2.
The operation of seriation
Performing the logical operation of seriation on structures of knowledge, students form
intellectual skills of grouping structures of knowledge according to their combining criteria
or for only one criterion.
3.
The operation of substitution
By this operation structures are replaced by others (for example, in mathematics, numbers
replaced by letters (6 +7) = (a + b); replacement of signs 5 x 5 = 5 2 , etc.). This is very basic
logical operation on the structures of knowledge and intellectually important skill that
qualitatively transforms knowledge. This operation destroys the vertical structure of
knowledge and develops in students the ability to arrange them into thinking in a
horizontal structure [6].
4.
The operation of enrichment
In carrying out this operation on the structures of knowledge, students who have
knowledge enriched their knowledge with new structures of knowledge and turn it into
new knowledge. The operation of enrichment, as the operation of substitution, generates
future knowledge from the acquired knowledge.
5.
Multiplicative operations
This operation is used simultaneously on multiple structures of knowledge that have
common relations or communications (example: in a linguistic knowledge it is the change of
some parts of speech - on cases, by the numbers.
Principle 5. Mental models of students
According to psychology of intelligence by Piaget, a child from birth to 8 years old goes
through a pre logical operations; from 8 to 12 years, the stage of concrete operations, and
from 12 to the end of youth stage of formal operations. Each stage of development
corresponds to its settings, its commands. Under pre logical operations stage students
typically argue based on their life experiences, and try as much as possible to extend it with
such tasks that are set for them. In the bowels of pre logical operations students in a logical
setting ask teacher questions generated by the makings of concrete operations, which are
expanded, enriched, balanced and smoothly go to transition to the stage of concrete
operations. In the frequent repetition of the same commands, units of the structures of
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