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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
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Stepanyants V., Andrey V. Fizulin, Chibirov A. et al., FUTURE TRANSPORTATION 2026 Vol. 6 No. 5 Article 225
Reliable Vehicle-to-Everything (V2X) evaluation requires propagation models that represent terrain and multilevel infrastructure. Most integrated vehicular simulators still rely on planar models, but the magnitude of the resulting bias is unclear. This study quantitatively compares flattened two-dimensional (2D) and terrain-aware three-dimensional (3D) variants of three scenarios using identical Sionna RT settings. The pipeline combines OpenStreetMap ...
Added: October 8, 2026
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Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
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Added: October 7, 2026
Groshev Maksim, Rybakov Petr, Teterin N. et al., Sensors 2026 Article 6171
Manual assessment of soybean yield components, such as pod number, is laborious, time-consuming, and subjective. Existing computer-vision approaches based on object detection or instance segmentation perform poorly on close-range RGB imagery of soybean canopies due to severe occlusions, ambiguous plant boundaries, and the high cost of bounding-box annotation. To address these challenges, we propose a ...
Added: October 7, 2026
Lysova-Golomzina E., Dobryakova M. S., Мир психологии. Научно-методический журнал 2026 № 3 С. 285–307
The study focuses on the cognitive mechanisms associated with teachers’ work with new, conceptually complex material, both when they are experts in philological analysis and when they design the acquisition of subject matter. The scientific novelty of the article lies in its interdisciplinary approach, which allows for an explanation of the interaction between “threshold” subject ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
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Материалы сборника Шестнадцатой Международной конференции «Новые информационные
технологии в исследовании сложных структур» (Москва, 21–25 сентября 2026 г.) ориентированы на
широкий круг специалистов, работающих на стыке теории информации, системного анализа и
прикладных предметных областей. В издание вошли результаты исследований, посвящённые
моделированию дискретных и стохастических структур управления и связи, разработке
высокопроизводительных вычислительных и телекоммуникационных систем, а также вопросам
цифровой трансформации образования, архитектурно-градостроительного проектирования,
экологического ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Lyu M., Omopekunola M., Wang F., / Series 2026.aimecon-wip.55 "Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con)". 2026.
Large language models (LLMs) have been proposed as a substitute for field trials in itemdifficulty estimation, but evidence about where they succeed is usually drawn from a single test form. We compare LLM difficulty predictions across three task types that make different language demands, grammar cloze, semantic cloze and reading comprehension, on two operational Grade ...
Added: October 5, 2026
Denisenko I., Petrenko O., Vasilyeva T., Киров: Межрегиональный центр инновационных технологий в образовании, 2026.
Монография посвящена преодолению разрыва между стратегическими целями развития образования и повседневной практикой школы. Научно-методическое сопровождение рассматривается как управленческий механизм перевода образовательных инициатив в устойчивые изменения педагогических и управленческих практик.
Представлена эмпирически апробированная модель научно-методического сопровождения, основанная на цикле: данные — интерпретация — гипотеза — педагогическая проба — анализ — корректировка или закрепление практики. Эмпирическая база включает ...
Added: October 5, 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 ...
Added: August 12, 2021
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 ...
Added: November 23, 2020
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
Poddiakov A., , in: Proceedings of the PME and Yandex Russian conference: Technology and Psychology for Mathematics Education.: M.: SU HSE Publishing House, 2019. P. 178–185.
Added: January 3, 2020