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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.
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Sorokin P., Morozova E., Goshin M. E. et al., Высшее образование в России 2026 Т. 35 № 3 С. 63–89
The purpose of this study is to empirically identify the potential of contemporary educators involved in university entrepreneurship support initiatives as potential drivers of ecosystem development. This is achieved through an analysis of their key individual characteristics, professional experience, pedagogical practices, and the institutional context of the university environment. To this end, based on a ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Nisskaya A., Беляевская Е. С., Современная зарубежная психология 2026 Т. 3 № 15 С. 89–97
Context. The preschool period is a critical stage for the development of prosocial behavior. Children begin to understand the feelings of others, and the foundations of empathy and mutual assistance are formed. Situation-specific expressions of care can develop into more stable forms when children are embedded in a system of social relationships. However, the specific characteristics ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
М.: Национальный исследовательский университет "Высшая школа экономики", 2026.
The next collection “Cases of Russian Universities” contains cases developed in the master’s program “Management in Higher Education,” which has been offered since 2011 by the Institute of Education at the National Research University Higher School of Economics. The program is intended for university staff aiming for a managerial career or seeking to develop their ...
Added: October 1, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are
reduced to discrete-time random dynamical systems generated by time-one maps, so that
the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Мичурина А. А., Гуманитарные науки и образование 2026 Т. 17 № 3 С. 82–87
China pays special attention to the application of artificial intelligence (AI) technologies in various spheres of life, including education. The integration of AI into the field of education carries many opportunities. At the same time, this process is associated with a large number of risks, which raises the issue of the need for legal regulation ...
Added: October 1, 2026
Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1174–1178
Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...
Added: September 30, 2026
Dvoinin A., Развитие личности 2025 № Спецвыпуск С. 17–20
The article outlines A.M. Dvoinin’s personal reminiscences of his teacher, the prominent psychologist Valeria Sergeevna Mukhina ...
Added: September 30, 2026
Beldiev I., Тимашёв Д. А., Алгебра и анализ 2026 Т. 38 № 5 С. 1–10
An algebraic variety X is called a homogeneous space if there exists a transitive regular action of an algebraic group on X. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number. ...
Added: September 30, 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