Оценка дидактической сложности доказательства теорем школьного курса геометрии

Abstract

In the study of geometry, the student’s assimilation of the reasonings carried out in the theorems proofs has great importance. The diffi culty of understanding reasonings depends on the number of logical links, terms diversity and semantic complexity of mathematical statements. The article proposes the method for determining the didactic complexity of the theorems proofs and the results of its application. The essence of the method consists in “measuring” the amount of semantic information in theorem formulation, picture, reasonings and multiplication of the received volume with the diversity indicator of the terms used. For this, the theorem statement, the picture and the actual proof should be presented in text form, and the resulting file should be analyzed using a special computer program which calculates the number of diff erent terms in this text, takes into account their complexity, and fi nds the diversity indicator. The expert estimates complexity of terms by counting the words included in its defi nition and by the method of paired comparisons. An assessment of 12 frequently used theorems was carried out; this allowed them to be ordered by complexity. For each theorem the proof volume, the total amount of semantic information in it, the terms diversity indicator, the logical reasoning number, the information folding coeffi cient and the didactic complexity were determined.