Description language of educational content structure: Possibilities of modern mathematics

Abstract

In modern conditions of intensive growth and differentiation of scientific knowledge, continuing reforms of educational systems, the pedagogical society is constantly facing the problem of justification of the content of education and its structuring. One of the tasks referring to this problem is a task of development of the description language of the educational content structure. Research objective consists of justification of the possibility of use of fractal geometry statements for the description of the educational content structure. As a main research method we have chosen a theoretic methodological analysis of scientific works concerning a development of an educational content theory and describing empirically stated defining peculiarities of its structure. Comparison of the description language of the educational content structure accepted in pedagogy and the description methods of structure of objects researched by the fractal geometry. The hypothesis about fractal nature of the educational content structure has been formed and proved immediately by means of the empiric material: the content structure of education and its "through" branches has a mosaic nature consisting of elements with different qualities (for example, mathematic, scientific and humanitarian disciplines or: basic, vocational and polytechnic education. The mosaic elements create a multistage system and are characterized by essentially divergent proportions. With the increasing of density or weight (with respect to "size") of elements of bearers of some properties we can state that the element of a larger proportion consisting of smaller elements expresses mainly the given property (so it plays a key role). The general picture looks like a mosaic board consisting of elements made themselves as mosaic pictures. This procedure occurs again on several levels. This description presents properly an idea of a multifractal formed by means of overlapping fractals, because the iteration procedure of creation of geometrical fractals looks on every step as a mosaic picture. The article may be useful for educationists researching the questions concerning the educational content and its structure and also for practitioners selecting the training documentation while developing different levels of educational programs. © 2019 by the authors; licensee Modestum Ltd., UK.