Fractal Approach to the Development of Electronic Textbooks in Naturall Science Disciplines

Abstract

UDC 53.075 The methods of designing electronic textbooks (ETB) suggested in [1–3] are based on the logical-semantic representation of the discipline content. The electronic courses and ETB are constructed in accordance with the cognitology principles in the form of a semantic graph network or a network of overlapping frames. The semantic network involves a set of nodes and a set of links that form a spatial graph. Nodes represent the objects that denote categories, terms, phenomena, effects or processes. Links-attributes that represent the properties of objects or their definitions can also be introduced. Then the semantic network represents an object-property space. As a rule, a three-dimensional network is obtained, which should be reduced for practical use. From the rational viewpoint, this calls for a semantic structure with minimum redundancy. To this end, problems on the detection of a base set of uncorrelated clusters are solved by the methods of graph theory, average paths from the center of the graph to sets of nodes are evaluated, complexes or clusters of closely related nodes are identified, and some other parameters of the optimization procedure are determined. The training process is considered as going around the graph of a single semantic network, and the minimum path can be found for a finite time interval. From the viewpoint of the qualified teacher who has already prepared a course of lectures on the discipline and has published some traditional books and methodical instructions, the fractal approach to the ETB development is more comfortable. The point is that the practical use of complex semantic networks is reduced, voluntary or involuntary, to the construction of a one-dimensional network and a minimal graph being the key-note of all the subject matter of the discipline and found by the skilled teacher intuitively, heuristically, or using expert methods when he/she writes the textbook on the discipline. Starting from already available base of linear ordering of educational information in printed matter, it can be transformed into a linear-cyclic sequence [4] with modules surrounded by individual didactic elements grouped around central concepts and with linear-series route through these modules. In this case, the hypertext links are organized inside and between the modules, subjects, and didactic doses of information. The fractal model is the development of the linear-concentric model. First, a fractal image is used with allowance for the absence of clearly defined boundaries between disciplines (physical concepts are used in all technical disciplines, humanitarian disciplines use the mathematical apparatus, etc.). Second, fractal structures open no less complex connections of the elements when we penetrate deeper into them to examine closer their construction. Rephrasing the well-known Laplace statement about inexhaustible science, we can state that our knowledge of the nature is fractal as the nature itself. The method of presentation of our knowledge should be adequate, that is, fractal.