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Mathematical Elements of Elementary Education
Doklady Mathematics. 2023. Vol. 107. No. 1. P. S10–S41.
Posicelskaya M. A., Rudchenko T. A., Semenov A.
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 range of activities also expands due to, for example, the introduction of strategies for enumeration, game winning, and algorithms (also operating in a visual environment). At the same time, the student’s position changes: they independently discover and build mathematics and constantly solve personally new, but feasible tasks that are “not-known-how-to-solve.” The student’s resources are saved by using a computer to perform routine arithmetic operations that have already been discovered and understood. The implementation of this approach is discussed in detail and is illustrated by examples of actual tasks that are representative of the program under consideration and the whole approach.
Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4
In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...
Added: October 12, 2026
Ogundele K. S., Durodola F. A., Social Psychology of Education 2026 No. 29 Article 127
This study examines the association between teacher expectations and mathematics growth among first-grade students in Russia. The sample included 1,155 students and 48 teachers from public schools in two Siberian regions. Students’ mathematics performance was assessed using START, with vertical test alignment used to measure individual growth. Multilevel regression models estimated on 20 multiply imputed ...
Added: October 12, 2026
Gusein-Zade S., М.: МЦНМО, 2026.
Книга содержит курс лекций по дифференциальной геометрии и топологии, читавшихся автором на механико-математическом факультете МГУ в разные годы. В дополнениях приводятся некоторые сюжеты (связности в расслоениях, теорема Фробениуса, производные Ли и др.), которые были включены в курс в отдельные годы либо содержались в аналогичных курсах лекций в Независимом московском университете.
Для студентов математических и физических специальностей. ...
Added: October 12, 2026
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
М.: Юрайт, 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
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
Korchak A., Hughes C., Costley J., Journal of Research on Technology in Education 2026 P. 1–17
Generative artificial intelligence (Gen-AI) is increasingly used in higher education, yet its role in collaborative learning remains unclear. This study examines how students use Gen-AI during group lesson-planning tasks in an undergraduate education course. Drawing on Vygotsky’s sociocultural theory, we introduce the concept of “an effort space” and apply the categories of appropriate, over-, and ...
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
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
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
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
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
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
Akhmedjanova D., Kanonire T., Zakharov A., Plos One 2026 Vol. 21 No. 2 Article e0341318
Research evidence exists on associations of subjective well-being, self-efficacy and various academic and non-academic outcomes with older students; however, there is a research gap on how these variables relate to each other in elementary school students. The goal of this cross-sectional study within a larger longitudinal project was to examine the role of subjective well-being ...
Added: February 3, 2026
Akhmedjanova D., Educational Studies 2026 Vol. 52 No. 3 P. 271–291
Self-regulated learning (SRL) and self-efficacy (SE) relate to the improvement of students’ academic outcomes in diverse cultural contexts. In Russia, the research on SRL is well established; however, most of the studies are focused on the university and middle/high school students. The research on SRL and self-efficacy in elementary schools is rather scarce. The novelty ...
Added: March 12, 2025
Bochaver A. A., Akhmedjanova D., Bayramyan R. et al., Социальная психология и общество 2024 Т. 15 № 3 С. 201–221
Objective. Adaptation of the Parental Stress Scale by J. Berry and V. Jones on a sample of mothers of Russian schoolchildren — first and fourth grade students of elementary schools in Nizhny Novgorod and the Nizhny Novgorod region.
Background. Modern parenting research highlights the complex nature of parenting experiences, the diversity of parental practices, the changes associated with ...
Added: October 18, 2024
Istomina A., Arsalidou M., Developmental Cognitive Neuroscience 2024 Vol. 69 Article 101419
Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that ...
Added: August 12, 2024
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
Vishnyakov Y. S., Semenov A., Shabat G. B., Doklady Mathematics 2023 Vol. 107 No. 1 P. S78–S91
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, ...
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