NUMERIC STRUCTURE SKILLS DEVELOPMENT VIA COMPUTER SIMULATORS

The necessity for development of skills to work with numeric structures is justified both by the requirements of state exams and by the data obtained concerning cognitive science on interconnection between capacity for mental calculation with the development of higher mental functions (the recursive thinking, in particular). The idea has been formed and the necessity of development of working memory simulators on base of target content, particularly numeric structures is proved. Their use for personality development makes it possible not only to improve the working memory capacity, but to implement the method of interval repetitions, and to workout perfectly the skills of working with numeric structures. The simulators are available at the website ‘working-memory.ru’. There are twelve simulators published. Three skills of working with numeric structures are directly developed: “Mental Calculation”, “Trigonometric circle”, “Reduction formulas”. The simulator “Mental Calculation” has been online since 2008, the launch of the project. The trainers “Trigonometric circle” and “Reduction formulas” were published in August the 1, 2016. Empirical data of the influence of working memory training on solving problem using its resources are analyzed. The empirical data are about two hundred thousand records of the results of the working memory exercises by different users of the working-memory.ru website in the period of 2008 - 2016. The main conclusions are (1) there are large individual differences in the ability to perform exercises on working memory in people about the same age; (2) long-term and systematic training of the working memory makes it possible both to maintain its operation and to extend its physiological limits. The increase in working memory performance in young adults of 16-20 engaging in training is ahead the average statistical growth of the working memory capacity within a period of three-four years. If the training duration is from a month to a year, the rate of multiplying two-digit numbers in mind increases to about two times. If the training duration is from two to four years, the rate of the exercise increases to three times. An explanation for the patterns observed of the rate of the working memory exercises depending on the total training duration is given. Noticeable growth of the rate in the first stage can be considered by improving strategy of working memory resources use. This stage takes about a week. Then when the strategy has been trained, the rate growth becomes slow and depends on improving working memory itself. The use of information technologies in education in such a way allows us to hope to resolve “the two sigma problem” in future.

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