SANAMA1 TONGUE TWISTER

The article analyzes the common features of the sanama and tongue twister genres which are based on word games of children's folklore their close examples of these genres to each other and their transmission as an example of the Uzbek, Karakalpak, Kazakh and Kyrgyz peopl

The Implementation of Using Fairy Tales in Learning Foreign Language in Elementary School

The article considers the material of fairy-tale texts as a valuable resource in the study of foreign languages, in particular English. It consists in substantiating and revealing the possibilities of including fairy tales in the educational process to improve the effectiveness of teaching English in primary school

Convergence Analysis of a Numerical Method for a Fractional Model of Fluid Flow in Fractured Porous Media

The present paper is devoted to the construction and study of numerical methods for solving an initial boundary value problem for a differential equation containing several terms with fractional time derivatives in the sense of Caputo. This equation is suitable for describing the process of fluid flow in fractured porous media under some physical assumptions, and has an important applied significance in petroleum engineering. Two different approaches to constructing numerical schemes depending on orders of the fractional derivatives are proposed. The semi-discrete and fully discrete numerical schemes for solving the problem are analyzed. The construction of a fully discrete scheme is based on applying the finite difference approximation to time derivatives and the finite element method in the spatial direction. The approximation of the fractional derivatives in the sense of Caputo is carried out using the L1-method. The convergence of both numerical schemes is rigorously proved. The results of numerical tests conducted for model problems are provided to confirm the theoretical analysis. In addition, the proposed computational method is applied to study the flow of oil in a fractured porous medium within the framework of the considered model. Based on the results of the numerical tests, it was concluded that the model reproduces the characteristic features of the fluid flow process in the medium under consideration

Leveraging digital tools to advance mathematics competencies among construction students

AbstractThis study investigated the impact of integrating design-technological activities on developing mathematical competencies among construction engineering students. A mixed methods approach compared curriculum delivery with and without digital tools across universities in Kazakhstan and Turkey. First, semi-structured interviews of faculty provided qualitative insights concerning technology adoption barriers. Next, an experimental group leveraging graphing calculators was tested against a control group using traditional techniques for solving straight line mathematics problems. Results showed the experimental group scored significantly higher at both Mukhtar Auezov South Kazakhstan University and MEF University, demonstrating enhanced conceptual understanding and problem-solving abilities when utilizing educational technologies. Interviews also suggested current training programs at Mukhtar Auezov South Kazakhstan University more extensively cover instructional design with mathematical digital tools. Findings highlight measurable learning benefits from incorporating technologies like dynamic geometry software and graphing calculators to improve construction engineering education

Probabilistyczne i statystyczne modelowanie rozprzestrzeniania się w atmosferze szkodliwych zanieczyszczeń z pojazdów silnikowych

The aim of the work is to create a mathematical model for the distribution of emissions from vehicles. In this article, it was proposed to use the probabilistic and statistical approach for modelling the distribution of harmful impurities in the atmosphere from vehicles using the example of the Ust-Kamenogorsk city. Using a simplified methodology of stochastic modelling, it is possible to construct effective numerical computational algorithms that significantly reduce the amount of computation without losing their accuracy.Celem pracy jest stworzenie matematycznego modelu rozprzestrzeniania się zanieczyszczeń z pojazdów. W tym artykule zaproponowano zastosowanie podejścia probabilistycznego i statystycznego do modelowania rozprzestrzeniania się szkodliwych zanieczyszczeń w atmosferze z pojazdów na przykładzie miasta Ust-Kamenogorsk. Stosując uproszczoną metodologię modelowania stochastycznego, można konstruować skuteczne numeryczne algorytmy obliczeniowe, które znacznie redukują ilość obliczeń bez utraty dokładności