Research of Cognitive Conceptual Schemes of Hierarchical Type Regularities Formation by Means of Statistical Method

Abstract

The statistical research of time reguliarities of the hierarchical type knowledge structure formation in large groups of students has been carried out. The idea of improvement of the effectiveness of learning through the usage of conceptual problems in constructing hierarchical type conceptual schemes is implemented. The original training program for teaching activities automatization and for experimental researches of this process as well, was developed. In the studying process the distribution of time spent by students to build conceptual hierarchies was analyzed. It is shown, that these distributions are well approximated by the sum of normal curves, which are shifted relatively to each other on the timeline. Every individual normal circuit presented a separate level of development of conceptual schemes. In every next attempt of task completion the experimental division changed its form. It is shown that the knowledge formation process of large groups of students can be represented by the original mechanism of «swapping» of areas of normal contours of long-term performance to the high-speed circuits of tasks performing. This mechanism explains the change in shape of the experimental distribution. A modified statistical method of moments was used for integrated assessments in the trends changing the shape of the contours distribution of time spent by students to build a conceptual hierarchy. The originality of the approach was that in contrast to the standard method of moments, it was proposed not to consider some integral characteristics, and their dependence on number of attempt. The transformation of the form of the experimental distribution over time depending on the attempt of task fulfillment, depending from the number of attempt: center of gravity, its distribution, asymmetry and sharpness of the top were analyzed. The mathematical approximation process of the changes in the position of the center of gravity distribution is proposed. It is shown that the trend of transforma­tion of the experimental distribution contour is the following.  The center of gravity as a distribution curve smoothly moves toward high-speed tasks, the dispersion decreases, the form of distribution is close to normal. The normal form of the experimental distribution indicates the completion of the structure of knowledge formation.