Features of structure of mathematical abilities of high school students, learning information profile

The modern educational practice of the school system is aimed at creating conditions for the development of each child based on its individual characteristics. In this regard, studies to determine the qualitative uniqueness of the structure of mathematical abilities of students depending on the profile of training are of a particular interest. The aim of our study was to identify the structural features of the mathematical abilities of advanced high-school students studying computers. We relied on the structure of V.A. Krutetskiy consisting of four components: obtaining mathematical information (perceptual component); processing mathematical information (procedural component); storage mathematical information (mnemonic component); mathematical orientation of the mind (general synthetic component). The following hypothesis was proposed: the use of information technology affects the positive trend in the development of all components of mathematical abilities, and especially on general synthetic component due to the harmonious combination of two sub-components: verbal-logical and visual-figurative. We used a modified technique, which is a shortened version of tasks classification of V.A. Krutetskiy. The tasks consisted of nine batteries of problems whose solution was assessed by a dichotomous scale, and then the result was expressed as a percentage by a number of correctly solved tasks in the series. A study conducted on a sample of 140 students from different grades (from 5th to 11th) with advanced curriculum in Mathematics, showed that all four structural components of mathematical abilities tend to increase with the age of students, the most even development takes place only after the 7th grade. There is a qualitative leap for the period of students training in grades 6 and 7. Analysis of the results of the comparison of mathematical abilities in schoolchildren programmers and non-programmers (from the grade with advanced curriculum in Mathematics) showed that general synthetic and procedural components at programmers are more developed. Programmers better perform tasks that can be solved by relying on visual representations and schemes, general mathematical and heuristic tasks. This allows us to conclude that students programmers are characterized by a high level of flexibility of thought and desire for elegance of solving problems, they represent better arithmetic reasoning and show a good level of generalization of a mathematical material. The study confirmed the hypothesis and assumptions, and provided a basis for the continuation of further study of the mathematical abilities structure.

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