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| 1 | 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 | 1891 | ||||
| 2 | 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 | 1841 | ||||
| 3 | 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 | 1466 | ||||
| 4 | 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 | 1272 | ||||
| 5 | The paper is devoted to the problem of developing computational skills necessary for solving computational problems in physics. The problem is especially relevant for participants in the state final certification in physics, balancing on the verge of the minimum score. The source of the problem leading to insufficient development of computational skills in students is identified: starting from the 7th grade, little attention is paid to computational work. The results of testing computer simulators created by the author are presented. The testing took place on students of preparatory courses for the state certification in physics. The simulator “Formulas in Physics” develops the skill of finding unknown physical quantities. Its substantive basis is physics formulas that must be remembered for successful passing of the state final certification. 92 such formulas were selected. There are formulas for the solution of which one action is required. For example, Newton’s Second Law. There are formulas for the solution of which three or more actions are required. For example, the formula of a thin lens. The student sequentially finds each physical quantity included in the formula, based on the known others. In case of an error, it is recommended to repeat the exercise. The problem of computational errors remains when solving equations in three or more steps for students with insufficient working memory, while the probability of errors decreases to 10 %. There are about 6–13 % of such students. The “Rounding Numbers” trainer develops the skill of rounding the obtained result to the required digit. During testing, the trainer was changed: a reminder of the rounding rules was added for each error, which increased its effectiveness: students began to master this computational skill faster. Keywords: computational skills, solving physics problems, computer trainers, working memory | 524 | ||||
| 6 | The article presents the results of a study of the use of neural networks in teaching mathematical disciplines and a comparison of their capabilities with products based on programmable algorithms: task databases, computer simulators, and mind maps. The questions are considered: can neural networks effectively generate educational content, develop students’ computational skills, provide reliable reference information, and act as tutors in preparation for exams, including the Unified State Exam and the Basic State Exam. The use of artificial intelligence (AI) in educational practice is growing, especially among schoolchildren and students who use neural networks to do homework and cheat on exams. However, experiments show that AI-generated tasks often contain arithmetic errors and logical inconsistencies, and the hallucinations of neural networks make them an unreliable source of information. Comparative tests of ChatGPT, DeepSeek, GigaChat, and Alisa Yandex on Unified State Exam tasks revealed the limited ability of neural networks to solve complex problems of the second part and the inability to solve problems whose condition is specified by a drawing. Computer simulators, task databases and mind maps remain indispensable for the formation of stable mathematical skills: assimilation of the logical structure of disciplines and memorization of mathematical facts. Important advantages of these tools: generation of an unlimited number of reliable exercises for the development of mathematical skills; interface providing instant feedback; tracking of students’ progress through a database. It has been shown that neural networks can be useful for generating educational materials and analyzing large unrefined data, identifying non-trivial recommendations for improving the educational process. However, they are not able to monitor the student’s activity, identify individual gaps and adjust the educational trajectory, which makes them a weak substitute for a teacher or tutor. The optimal strategy for integrating AI into the educational process is to combine the capabilities of neural networks with proven tools based on programmable algorithms. The teacher, adjusting and checking the results of the AI, can increase the effectiveness of the educational process, while maintaining the reliability and quality of the formation of knowledge and skills. Keywords: neural networks, artificial intelligence, programmable algorithms, teaching mathematics, computational skills, generation of educational content, Unified State Exam, Basic State Exam, mind maps, computer simulators | 282 | ||||