Brief characteristics
The logical and system approaches to the solution of delimited problem leads to the need to find three metalanguages. Metalanguage J1, its metalingual terms (network graphs) constitute the models of logical structure of target concept or knowledge. Metalanguage J2, its metalingual terms (network graphs) constitute the models of logical structure of developing target concept or knowledge. Metalanguage J3, its metalingual terms (network graphs) constitute the models of arranged logical structure of developing target concept or knowledge. The metalanguage J3 is again associated with the methods of network analysis. The Thomas method belongs among semifinished methods in the field of metalanguage J3. The Thomas matrix as arranged logical structure of developing target concept or knowledge represents the form of network graph.
This matrix is possible to call by matrix model of cognitive structure.
Within the framework of creation of matrix model of cognitive structure is first of all necessary to delimit the survey of by linear way concurring elements of matrix main diagonal with brief description of their contents. The elements of main diagonal form a definition line of matrix and they are often called by subject matter units. The delimitation of definition line of matrix is starting from linear arrangement of the analytical synthetic model of cognitive structure. Often it is possible to take the important segments of definition line as the partial conclusions dk of analytical synthetic model as partial conceptual knowledge systems (ASM - Fig.1). These segments is afterwards possible to complete by the found essences ck, eventually by the partial problems bk (ASM - Fig. 1)). The projection of definition line, for example, into creation of textbook, should be to enable to carry out the intellectual reconstruction “e” of problem solved in the cooperation of addressees of education with teacher.
For example, the definition line of matrix contains 21 elements (21 subject matter units). The individual subject matter units will be marked by numbers from 1 to 21 and they will be to occupy the main diagonal of matrix. Afterwards it is possible the matrix model of investigated cognitive structure to represent by Fig. 1.
The construction of matrix model of cognitive structure with 21 subject matter units will be in the following described. Resulted matrix will be squared with 21 matrix rows and matrix columns. The numeral succession of sequential numbers will be written down into main diagonal – definition line. The being relations (associations and discriminations) among 21 elements of definition line (among 21 subject matter units) will be afterwards set out into matrix (associations will be marked by =, discriminations by +).
In the course of developing the same conceptual knowledge system on the basis of collective elements or in the course of direct sequence in light of the arrangement into definition line, the elements (subject matter units) are associated. In the course of developing the same conceptual knowledge system on the basis of diversity, the relation of discrimination will be among the elements of definition line (among the subject matter units).
Fig. 1. Matrix Model of Cognitive Structure with 21 Subject Matter Units
The matrix element given by i-th row and j-th column bears the usual incication aij. Element aij remains without indication in that case – none of delimited relations (neither relation of association, nor relation of discrimination) is between elements aii and ajj of definition line. In the course of matrix filling first of all the elements a11 and a22 of definition line will be overlooked. The relation between them is being, the element a12 will be marked = or +. Gradually, in this way, all the elements aij for i greater than j will be explored. Thus the elements above definition line will be marked or unmarked. The verification of analysis correctness of relations between the elements of definition line is given by the execution of this analysis in contrary order – first of all the relation of elements a21 and a20 will be determined, afterwards a21 and a19 etc. Thus the elements aij for j greater than I will be marked or unmarked. The both halves of filled matrix are axially symmetrical according to definition line the analysis of relations among elements of definition line was carried out correctly.
The matrix capable to interpreting should have to signalize all the elements aij for j=i+1 (so called ideal matrix). Such groups of elements are important which, in spite of structure to definition line, are absented from it in the various directions. It is showing to the close associations among corresponding elements of definition line – the definition line elements of such group contribute to delimitation of the same conceptual knowledge system. Mistaken construction of matrix (caused, for example, by replacement of definition line elements sequence) shows itself by disturbance of matrix ideality.
In the course of matrix modeling cognitive structure the main diagonal of matrix (definition line) with 21 matrix elements was taken into account. The matrix contained 5 conceptual knowledge systems. The resulting matrix can be elaborated into a compages of qualification and quantification micro-matrices – these micro-matrices can be treated in light of methods structuring transfer of physical knowledge as acceptable method for forming some variant forms of curriculum.
The method is well decribed in ZASKODNY, P. Methods of structuring of variant forms of curriculum. In monograph: Educational and didactic communication, Vol. 1 - Methods. Bratislava: Didaktis, 2007, pp. 85 - 103. ISBN 987-80-89160-56-3. more>>
Main references
ZASKODNY, P. Methods of structuring of variant forms of curriculum. In monograph: Educational and didactic communication, Vol. 1 - Methods. Bratislava: Didaktis, 2007, pp. 85 - 103. ISBN 987-80-89160-56-3. more>>
ZASKODNY, Premysl. Curricular Process of Physics (with Survey of Principles of Theoretical Physics). Ostrava : Algoritmus, 2009. (Czech version, English version in print) more>>