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The Work of a Mathematician As a Prefiguring of Mastering Mathematics by Students: the Role of Experiments
Doklady Mathematics. 2023. Vol. 107. No. 1. P. S78–S91.
Vishnyakov Y. S., Semenov A., Shabat G. B.
This paper considers an approach to mathematical education adequate to the task of developing mathematics and its applications in the 21th century. This approach is based on improving the efficiency of the educational process by maintaining the motivation of students of various categories. The basis for the formation of motivation is, on the one hand, independent design; invention of mathematical objects, methods of action, and models of the world around us; and the discovery of facts of mathematical reality and, on the other hand, solving of new, unexpected, and feasible tasks for the student. The student’s work is similar to the work of a mathematician–researcher and programmer. The possibilities of research work in educational mathematics are significantly expanded due to computer-based intramathematic experiments. Debugging a computer program is a special kind of mathematical experiment.
Language:
English
Flamarion M. V., Pelinovsky E., Wave Motion 2027 Vol. 148 Article 103867
We consider the interaction of two solitary waves in the modified Benjamin–Bona–Mahony
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modified Korteweg–de Vries (mKdV) equation. A regular perturbation method is used to
analyze the modification of the two-soliton wave field induced by the weak non-integrability of
the mBBM equation. We show that, ...
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Gavrilenko P. A., Янис С. О., Педагогика и психология образования 2026 № 2 С. 26–42
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system is an important area of modern pedagogy. The article presents
the results of an empirical study aimed at identifying ways for teachers to frame
time and group work in the context of supporting three basic psychological needs of schoolchildren, namely, autonomy, competence, and relatedness.
The theoretical basis of the research ...
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Sergei P. Zhdanov, Contemporary Educational Technology 2026 No. 18(4) Article 701
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challenges for educators and learners. Therefore, in terms of GenAI for education this
bibliometric analysis will characterize the change and development by mapping trends and
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Obsie E. Y., Zhan Y., Liu Y., Engineering Research Express 2026 Article 7
Maintaining plant health is crucial for crop quality, food security, and agricultural productivity. Although deep learning methods have shown strong potential for species, disease, and severity classification, most existing approaches tackle these tasks separately, failing to exploit shared representations and interdependencies among them. Furthermore, the variability of disease symptoms, such as subtle differences in size, ...
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Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
Added: October 19, 2026
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Added: October 19, 2026
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Roman Avdeev, Yulia Zaitseva, Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
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Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
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Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Posicelskaya M. A., Rudchenko T. A., Semenov A., Mathematics in School 2023 Vol. 2 No. 115 P. 7–12
The problem of values is becoming more central in education today than ever before. The main questions facing the teacher today:
• What value system will the student form as a result of education?
• What values are the driving motive for a student in the learning process? ...
Added: March 14, 2024
Posicelskaya M. A., Rudchenko T. A., Semenov A., Doklady Mathematics 2023 Vol. 107 No. 1 P. S10–S41
In recent decades, several Russian schools have been implementing a world-unique education program of mathematics for elementary schools. In it, the landscape of school arithmetic is radically expanded due to the basic objects of modern mathematics and computer science. These objects and their operations are visual, making them much more comprehensible than traditional arithmetic. The ...
Added: March 14, 2024
Shabat G. B., Semenov A., Doklady Mathematics 2023 Vol. 107 No. 1 P. S92–S116
A mathematical experiment has always been a key source for a mathematical discovery. Over the past 50 years, thanks to digital technologies, its role in mathematical research has grown significantly. Digital technologies have opened up fundamentally new opportunities for experimentation in mathematics education, bringing mathematical education closer to mathematical research for the majority of students. This tendency is ...
Added: March 14, 2024
A. L. Semenov, Soprunov S. F., Ivanov-Pogodaev I. A., Doklady Mathematics 2023 Vol. 107 No. 1 P. S132–S136
The paper discusses an example of an educational project in modern mathematics in which school students create mathematics that is new to them. The mathematical results produced by the students in the theory of definability also have an “absolute” novelty, i.e., are the basis for professional publications. The described course was based on recent results of this ...
Added: March 14, 2024
Semenov A., , in: The 6th International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev.: [б.и.], 2023. P. 19–20.
The report examines the views of Corresponding Member of the Academy of Sciences of the USSR, Professor L. D. Kudryavtsev on higher education and education in general, which are of great relevance today. For L. D. Kudryavtsev, mathematical education was the most important element and type of education, but the principles he developed certainly have ...
Added: March 13, 2024
[б.и.], 2023.
Abstracts, The 6th International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev Moscow, Russia, November 14–19, 2023 ...
Added: March 13, 2024
Bogolepova S., Шадрова Е. В., Педагогика и психология образования 2021 № 3 С. 73–94
Professional activities of a university instructor are multifaceted though not comprehensively examined yet. Competency indicators for instructors’ performance and the indicators of teaching excellency are still to be identified. This study aims to reveal and compare the competencies students from two Russian universities of different types characterise their best instructors with. The research included the ...
Added: September 18, 2021
Bogolepova S., Отечественная и зарубежная педагогика 2021 Т. 1 № 4 (77) С. 107–122
Introduction. In spring 2020 tertiary education in Russia underwent an unexpected transition online. The second transition, which was not that sudden, happened in autumn 2020. This study aims to examine students’ experience of online learning in these periods of study. Having revealed the features of online instruction, the author analysed if these aspects were taken ...
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Peresetsky A., Брайнин В. Б., Волков С. Е. et al., Математика в школе 2020 № 7 С. 69–80
В этом году Борису Соломоновичу Гельруду исполнилось бы 90 лет. Нам, группе его учеников, досталась от его внука Б.Е. Гельруда фотокопия его мемуаров, написанных более 35 лет назад. В них рассказывается о том, каким было математическое образование в СССР – не в столице, не в областном центре, а в Нижнем Тагиле – сравнительно небольшом индустриальном городе на Урале, о людях, с которыми жизнь ...
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Larina G., Kapuza A., , in: Proceedings of the PME and Yandex Russian conference: Technology and Psychology for Mathematics Education.: M.: SU HSE Publishing House, 2019. P. 278–278.
The competence of mathematical modelling is well conceptualized, thought a much-debated question is how to develop it in schools. International achievement test PISA consider mathematics achievements from the modelling perspective (formulating, employing and interpreting), and provides us with comprehensive data to analyze school factors in math results from the comparative perspective. The goal of our ...
Added: February 5, 2020