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METHODOLOGICAL ASPECTS OF ADAPTIVE PHYSICS TEACHING // Pedagogical Review. 2015. Issue 3 (9). P. 62-68

Methods of adaptive teaching high school students and first-year students of non-technical areas to physics that experience steady objective difficulties in the learning of this discip line are offered. The reasons for the objective difficulties are lack of motivation, lack of working memory and undeveloped associative thinking. Accordingly, the methodology is founded on the principle of minimum load on working memory and heuristic conversation as method to provide the understanding of the material, spaced repetitions as a means of consolidation of long-term memory and humanistic approach to the assessment of student achievement as a tool for positive motivation. The “2 Sigma Problem” urgency is emphasized, because it is only for individual learning that the method of heuristic conversation to achieve the understanding of physics and the control of spaced repetition can be realized to the full extent.

Keywords: teaching physics, working memory, heuristic conversation, spaced repetition, motivation

METHODOLOGICAL ASPECTS OF TEACHING MATHEMATICS TO INCAPABLE STUDENTS // Pedagogical Review. 2020. Issue 1 (29). P. 37-45

Differences in the mathematical abilities of different students are manifested in the fact that the same practice and exercises for students with different abilities give different results. For a capable student, these exercises lead to the mastery of mathematical knowledge and skills, for an incapable student do not. The reason for the inability to mathematics is the lack of working memory. There are two main approaches to solve the problem of teaching mathematics to incapable students: (1) training working memory and (2) reducing the load on working memory in the educational process. The results of the first approach are ambiguous: training working memory leads to an improvement in the performance of untrained tests for working memory, but it may not lead to noticeable changes in learning indicators associated with the working memory of the student. Accordingly, it remains to reduce the load on working memory in the educational process. Well known methods that reduce the load on working memory when studying mathematics are described. Automation of basic computing skills (arithmetic, trigonometric, geometric) is achieved with the help of computer trainers developed by the author: the mental calculations trainer, the trainer for developing skills in working with a trigonometric circle, the trainer for developing skills of using reduction formulas and the rectangular triangle solving trainer. The technique of working with trainers is based on the interval repetition method. Empirical data on the results of their implementation are presented.

Keywords: mathematical abilities, teaching mathematics, working memory, computer trainer, interval repetition

IMPLEMENTING COGNITIVE TRAINING IN THE PROCESS OF LEARNING MATHEMATICS // Pedagogical Review. 2022. Issue 1 (41). P. 36-43

Lack of working memory leads to a persistent inability to learn mathematics. Additional lessons with a teacher do not solve the problem of lagging behind the program. Correction of working memory or adaptation of the curriculum to the characteristics of a given student is required. Working memory can be trained, however, cognitive improvement does not automatically translate into academic performance due to the deep lag behind these students from the program. It is proposed to train working memory in the context of mathematical knowledge. The author has created a system of computer trainers for working memory based on the key sections of the school curriculum in mathematics. There are eight trainers: mental counting and skills in working with a trigonometric circle, solving proportions and square inequalities, solving a right-angled triangle. Trainers are available free of charge on the website https://www.workingmemory.ru/ (registration is required). Embedding cognitive training in educational content removes the problem of far transfer, since the positive effect on academic performance is immediately apparent. The problem of motivation for training working memory also disappears, since the content basis of the trainers is the requirements of the school curriculum. The time limit for one exercise, the number and duration of exercise to reach the limit values vary widely. This confirms the significant individual differences in working memory. The hypothesis was confirmed that the strategy of using resources of working memory is improved as a result of training (not the volume of its short-term storage). The conclusion is made on the analysis of statistical data on working with the “Forest Marathon” trainer, in which it is required to hold and transform in the mind from one to five numbers.

Keywords: teaching mathematics, working memory, computer trainer, interval repetition

Computer trainers as a tool to overcome difficulties in learning mathematics // Pedagogical Review. 2023. Issue 5 (51). P. 102-110

It is the lack of working memory that is considered as the main reason for the difficulties in mastering mathematics. To overcome difficulties in mastering mathematics, computer trainers of working memory based on mathematical content are offered. If trainers do not have a mathematical component, but are aimed only at improving the functioning of the main components of a person’s working memory (articulation loop, visual-spatial notepad and central administrator), then classes with them do not lead to a noticeable improvement in academic performance, perhaps due to a significant lag behind current program. The computer trainers developed by the author and available on the site workingmemory.ru are aimed at both developing basic computing skills and training working memory. The subject of trainers was determined both on the basis of the author’s own observations and on the basis of an analysis of typical mistakes of USE participants published on the Federal Institute of Pedagogical Measurements website (fipi.ru). At the time of publication, nine trainers have been created and tested. The trainers are available at workingmemory.ru immediately after registration. The paper presents the data of approbation of trainers in the preparation courses for the Unified State Examination and their comparison with the results of studies by other authors. The average time to complete one calculation task is presented, practical recommendations are given. The use of author’s trainers as a tool for developing computational skills, increasing the efficiency of mathematics classes and training the working memory of students is substantiated.

Keywords: teaching mathematics, working memory, mental counting, digitalization of education