**1. Іntegration: genesis, essence and role in modern education Historical preconditions**

**1.2. Definitions and characteristics of integration**

Now there are dozens of definitions of the term "integration", the ideas of
integration actually penetrated into all areas of education. In 1993 at the session of
UNESCO the interpretation of knowledge integration as an organic relationship,
interpenetration which is determined by its result, i.e. the forming of a single
integrative world picture was made. *The definition of "integration" in its educative *
*context*, with strictly fixed sense and meaning is a necessary condition for the
development of the theoretical basis of integration.

The concept of "integration" is a category of general scientific sense: the same
functions it can perform also in educative systems. We did not want to create a strict
definition of the concept. Below we give *an expanded definition of integration*:

**integration** is*the process* (two-way process, systematic and structural)
interpenetration, consolidation, unification of knowledge; integrity incipience;

establishing connections between relatively independent earlier things, processes,
phenomena when these relationships are essential defining phenomena functioning
which are integrated; *combining* elements that is accompanied by complicated and

Educational integrology: methodology, theory…

strengthened connections among them, the interpenetration of the whole system
elements, transformation of some forms in others; *the historical stage* of knowledge
movement to the unity; *a specific form* of educational content unity; *interpenetration*
of information from one training course in the other one.

Basing on the mentioned above, we offer our interpretation of a narrower concept:

* integrative integration* is the interaction of elements (with given properties)
accompanied by the establishment, complexity and strengthening of significant
connections among these elements on the basis of sufficient cause as a result of which
the integrated object (the whole system) with qualitative new properties is formed, the
individual properties of the output elements are stored in the structure of it.

Various characteristics of integration are highlighted in a number of scientific and methodological developments (block10). We mention only some of them that are important in the educative aspect.

Today we have a variety of studies concerning **integration levels** selection.

Generalizing them and basing on our own developments on this problem, we note
that the selection of integration levels corresponds to division operation of the
concept in formal logic and requires a clear choosing of characteristic according to
which the division is made. In our opinion, the following features are advisable to
select: *the number of elements* that are integrated; the *degree of relationship* between
the elements of integration, nature of integration elements. Basing on such selection
of features, there are three options for the allocation of integration levels:

**Classification of the integration levels according to the number of integrated *** elements:* first level is microintegration (for a small number of elements), the second
level is mezointegration (with optimal number of elements), the third level is
macrointegration – with a significant number of items that require additional
clustering). During the integration we distinguish especially the integration level: if
there is a small number of items, there is a micro integration with weak symptoms of
the integration result. Similarly, at the level macrointegration the number of items is
too large and the newly integrative system can "collapse". Those extreme cases are
sometimes useful but for short educative purposes. Stable integrative system is
formed only according to optimal number of elements on the level of
mesointegration: this number should be large enough to provide a new quality due to
the integration and at the same time not too large to prevent the destructive processes
inside the integrated object. Such approach is based on the synergetic ideas
mentioned, in particular, in the works of Н. Haken [H. Haken, 1993]. We consider
such a visual analogy is useful: properties of chemical elements depend on the
number of protons in the atomic nuclei but with the very large number of protons
these nuclei become unstable as in the transuranic elements. However, each of the
elements is necessary if

*to use its properties correctly*. We would like to note that this division is

*natural*, not artificial, as the number of items is one of the essential features in determining the integration levels.

**Classification of the integration levels according to the degree of *** interconnection between elements: *the first level is the

*interdisciplinary connections*(minimal, apparent interrelations), the second level is

*systematic integration*(optimal essential interrelations that cause forming of integrative systems, in particular

Yuryi Kozlovskyi, Iryna Kozlovska

*integrative courses*), the third level is *metaintegration* (grouping items in subsystems
with strong relations and those subsystems into metasystem with the optimal relations
leading to the appearance of *metasubjects*). Here we give another analogy: the power
of interrelations between the particles of matter determines *the state* of matter. Due to
practical lack of interaction between particles, we have gaseous state: analog of
interdisciplinary connections because on their level integration elements can exist
quite independently and interact only for the tiny fraction of the time.

Interdisciplinary connections, relatively speaking, do not have their own "volume" or
their own "shape" and interactions can only be used occasionally. Here we have *most *
*degrees of freedom, the greatest mobility but, at the same time, and the smallest *
*ammount of the interaction. *

Systematic integration is similar to the matter being in the liquid state, when it's
shape is not saved yet but volume is stable. In this case certain reguliarities appear in
integration using, *the degrees of freedom reduced but the results of integration using *
*increase*. Variation of integrative courses, integrative learning systems or integrative
teaching problems is entirely on this integration level that is often optimal for
educational systems. On the level of metaintegration weak relations between large
blocks of knowledge and at the same time strong relations inside these blocks there is
a solid body according to the distant order in the arrangement of particles. The shape
and volume in each block are defined as in model of solid state allowing *to use the *
*advantages of previous levels at the same time*: to place the integrated blocks inside
the metasubjects freely (as for interdisciplinary relations) and at the same time to
provide sufficient power of the interaction inwside the blocks in order to systematize
knowledge.

This division into levels is natural too because the degree of interaction between elements influences on the integration result significantly. Besides, we have important analogs as of metasubjects as well as systematic objects in the "grand"

science. For example, a number of sciences, particularly physics or biology can be interpreted as metasubject, metascience that consists of a number of disciplines:

physics and mechanics, thermodynamics, optics etc. and biology with botany, zoology, cytology etc. Pelations between subjects (blocks) are not very strong but inside those disciplines systematic knowledge integration dominates. Such sciences can be called metascientific disciplines. We note that not all sciences are the following: for example, historical sciences are built according to other principles.

Among metascientific disciplines (and, accordingly, educational metasubjects) can be distinguished two main types: natural and artificial ones. To the natural ones that were formed according to the basic idea of metascience relate physics, mathematics or biology. The artificial metasciences appear to meet specific needs at certain stage of development and are developed in so-called hybrid sciences.

* Classification of the integration levels according to the nature of elements:* the
first level is

*corpuscular*integration (the elements have clear boundaries or values and interact as particles), the second level is

*the integration of the wave*(the elements do not have clear boundaries and interact according to the principle of waves). We would like to note that the principle of systematic quantization is fundamental in the theory of "compression" of educational information basing on which such theories

Educational integrology: methodology, theory…

are developed as the theory of generalized semantic generalization, theory of
consolidation of educative units, the concept of knowledge engineering etc.** **