003. Факультет інформатикиNo Descriptionhttps://ekmair.ukma.edu.ua/handle/123456789/242023-12-01T23:01:43Z2023-12-01T23:01:43Z4571Inquiry-based learning for enhancing students’ interest in mathematical research: a case study on approximation theory and Fourier seriesVlasenko, KaterynaRovenska, OlhaLovianova, IrynaKondratyeva, OksanaAchkan, VitaliyTkachenko, Yanahttps://ekmair.ukma.edu.ua/handle/123456789/273932023-12-01T01:01:21Z2023-01-01T00:00:00Zdc.title: Inquiry-based learning for enhancing students’ interest in mathematical research: a case study on approximation theory and Fourier series
dc.contributor.author: Vlasenko, Kateryna; Rovenska, Olha; Lovianova, Iryna; Kondratyeva, Oksana; Achkan, Vitaliy; Tkachenko, Yana
dc.description.abstract: This paper investigates how to develop students’ interest in mathematical research by using inquiry-based learning (IBL) as a pedagogical approach. We conducted a case study on the application of IBL to the teaching of approximation theory and Fourier series, which are important topics in mathematics and computer science. We surveyed the students who participated in the IBL workshops and measured their emotional state using the Differential Emotion Scale (DES) by Izard. The results showed that the IBL environment reduced the students’ negative emotions and increased their positive emotions, which in turn enhanced their engagement and motivation in the mathematical research activities. We conclude that IBL is an effective method for fostering students’ interest in mathematical research and suggest some implications for future practice and research.
2023-01-01T00:00:00ZThe method of using the online course "Creative Thinking through Learning Elementary Maths" in the Mathematics teacher training systemAchkan, VitaliyVlasenko, KaterynaLovianova, IrynaSitak, IrynaArmash, Tetianahttps://ekmair.ukma.edu.ua/handle/123456789/273902023-12-01T01:01:44Z2023-01-01T00:00:00Zdc.title: The method of using the online course "Creative Thinking through Learning Elementary Maths" in the Mathematics teacher training system
dc.contributor.author: Achkan, Vitaliy; Vlasenko, Kateryna; Lovianova, Iryna; Sitak, Iryna; Armash, Tetiana
dc.description.abstract: The article offers the method of using the online "Creative Thinking through Learning Elementary Maths" and the results of checking the effectiveness of the implementation of this course in the mathematics teacher training system. The research substantiates the possibility of three methodological options for combining educational materials of the online course with the study of the educational discipline "Elementary Mathematics". The methodological options are chosen depending on the number of credits assigned to the study of the elementary mathematics course at the university. Practical tasks of the course were focused on the organization of students' activities (recognition, classi cation, solving and creation) with Rich tasks of three levels of complexity. The results of control tests in Elementary Mathematics give grounds for concluding about the effectiveness of the developed method.
2023-01-01T00:00:00ZInterdisciplinary connections of Mathematics and Literature in the preparation for External Independent Assessment of Humanities studentsVlasenko, KaterynaLovianova, IrynaAchkan, VitaliyArmash, TetianaChumak, Olenahttps://ekmair.ukma.edu.ua/handle/123456789/273862023-12-01T01:00:12Z2023-01-01T00:00:00Zdc.title: Interdisciplinary connections of Mathematics and Literature in the preparation for External Independent Assessment of Humanities students
dc.contributor.author: Vlasenko, Kateryna; Lovianova, Iryna; Achkan, Vitaliy; Armash, Tetiana; Chumak, Olena
dc.description.abstract: This article examines the issue of finding new methodological approaches to the development of problems that can contribute to the preparation of ‘Humanities’ students to pass the state final certification in the format of External independent assessment (EIA). The study analyzes the existing development of methods of qualitative mathematical training of students of humanities classes who study Mathematics according to the basic level program. In particular, the authors of the article were interested in the use of interdisciplinary connections between Mathematics and humanitarian disciplines. The authors of the article identified crosscurricular problems as a means of forming students’ motivation to study Mathematics, as well as a toolkit for measuring their level of readiness to solve typical problems of EIA. The researchers set a goal to develop cross-curricular problems following the EIA program based on the plot of Bulgakov’s novel ‘The Master and Margarita’. An experiment was conducted to confirm the effectiveness of the use of the system of interdisciplinary problems in the preparation for the EIA of humanitarian students. The obtained results confirmed that the implementation of problems in which the intersubject connections of Mathematics and Literature are realized has a more significant effect on both increasing the motivation of students to study Mathematics and their mathematical preparation.
2023-01-01T00:00:00ZThe Wheel of Mathematics Learning MethodsVlasenko, KaterynaLovianova, IrynaChumak, OlenaSitak, IrynaKovalenko, Dariahttps://ekmair.ukma.edu.ua/handle/123456789/273842023-12-01T01:01:11Z2023-01-01T00:00:00Zdc.title: The Wheel of Mathematics Learning Methods
dc.contributor.author: Vlasenko, Kateryna; Lovianova, Iryna; Chumak, Olena; Sitak, Iryna; Kovalenko, Daria
dc.description.abstract: The article is devoted to the creation of a wheel of mathematics learning methods. The study analyzed how Bloom's taxonomy is used by the educational community. Special attention is paid to the study of the issue of bringing to a single system a set of disparate goals and tasks of learning in new models of education, which provide for the openness of learning to new technologies. Analysis of scienti c works and resources helped to determine the structuring of the Wheel of Mathematics Learning Methods (WMLM). The authors of the article identi ed the areas of didactics that should ll the wheel: Competencies, Motivation, Bloom's Taxonomy, Activities, and Technologies. A structured set of hints for the teacher is presented in the form of 5 sectors of the wheel: Apply, Analyze, Evaluate, Create, Remember Understand. Each sector is a set of constituent components Methods, Forms, Tools, Activities and Active Verbs. The analysis of the results of the survey of 58 respondents proved that Bloom's taxonomy is important both in the selection of teaching methods and means and in the determination of e ective forms of organization of educational activities. It was concluded that the idea of developing a methodology wheel should be based on the structuring of a set of tips for the teacher at all stages of activity from planning to implementation of mathematics education.
2023-01-01T00:00:00ZAn optimal lower bound for the size of periodic digraphsKozerenko, Sergiyhttps://ekmair.ukma.edu.ua/handle/123456789/265712023-10-20T00:00:34Z2023-01-01T00:00:00Zdc.title: An optimal lower bound for the size of periodic digraphs
dc.contributor.author: Kozerenko, Sergiy
dc.description.abstract: A periodic digraph is the digraph associated with a periodic point of a continuous map from the unit interval to itself. This digraph encodes "covering" relation between minimal intervals in the corresponding orbit, which allows the application of purely combinatorial arguments in establishing results on the existence and co-existence of periods of periodic points (for example, in proving the famous Sharkovsky’s theorem). In this article, an optimal lower bound for the size of periodic digraphs is provided and thus some previous results of Pavlenko are tightened.
2023-01-01T00:00:00ZUnique eccentric point graphs and their eccentric digraphsHak, ArtemHaponenko, VladyslavKozerenko, SergiySerdiuk, Andriihttps://ekmair.ukma.edu.ua/handle/123456789/263302023-10-07T00:00:46Z2023-01-01T00:00:00Zdc.title: Unique eccentric point graphs and their eccentric digraphs
dc.contributor.author: Hak, Artem; Haponenko, Vladyslav; Kozerenko, Sergiy; Serdiuk, Andrii
dc.description.abstract: We study graph-theoretic properties of eccentric digraphs of unique eccentric point graphs (shortly, uep-graphs). The latter are the connected graphs in which every vertex has a unique eccentric vertex. In particular, we characterize uep-graphs and the corresponding eccentric digraphs in the following classes: self-centered graphs having the number of vertices twice as diameter, block graphs, and graphs with diameter three. Also, we obtain non-trivial properties of weak components in eccentric digraphs of uep-graphs with diameter four and pose several open questions in this direction.
2023-01-01T00:00:00ZThe first boundary value problem for the nonlinear equation of heat conduction with deviation of the argumentDrin, YaroslavDrin, IrynaDrin, SvitlanaStetsko, Yuriyhttps://ekmair.ukma.edu.ua/handle/123456789/258052023-09-23T13:34:44Z2022-01-01T00:00:00Zdc.title: The first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument
dc.contributor.author: Drin, Yaroslav; Drin, Iryna; Drin, Svitlana; Stetsko, Yuriy
dc.description.abstract: The initial-boundary problem for the heat conduction equation with the inversion of the argument are considered. The Green’s function of considered problem are determined. The theorem about the Poisson integral limitation is proved. The theorem declared that the Poisson integral determine the solution of the first boundary problem considered and proved.
2022-01-01T00:00:00ZA Model of Information Influences on the Base of Rectangular Stochastic Matrices in Chains of Reasoning with Possible ContradictionsOletsky, Oleksiyhttps://ekmair.ukma.edu.ua/handle/123456789/251912023-09-23T13:34:37Z2021-01-01T00:00:00Zdc.title: A Model of Information Influences on the Base of Rectangular Stochastic Matrices in Chains of Reasoning with Possible Contradictions
dc.contributor.author: Oletsky, Oleksiy
dc.description.abstract: A way of implementing the model "state-probability of choice", which describes probabilities of making a choice between certain alternatives, into chains of uncertain reasoning has been
suggested. That means associating a special matrix, called rectangular stochastic matrix, with each node of the reasoning chain, whereas a node corresponds either to a given fact or to a rule of inference, maybe uncertain. A binary case, when a resolution has to be either rejected or accepted, has been regarded. A situation of a dynamic equilibrium, which means that none of these alternatives has advantage over the other, and possible ways of how agents of influence can break such a situation, have been demonstrated. Some ways of resolving conflicts between contradictory sources of evidence have been suggested.
2021-01-01T00:00:00ZІнформаційно-аналітичний майданчик підтримки публікаційної активності як інструмент підвищення якості наукових досліджень в умовах воєнного стануПриходнюк, ВіталійГорборуков, Вячеславhttps://ekmair.ukma.edu.ua/handle/123456789/250982023-09-23T13:34:39Z2022-01-01T00:00:00Zdc.title: Інформаційно-аналітичний майданчик підтримки публікаційної активності як інструмент підвищення якості наукових досліджень в умовах воєнного стану
dc.contributor.author: Приходнюк, Віталій; Горборуков, Вячеслав
dc.description.abstract: Значною мірою потенціал країни залежить від спроможності забезпечити високий рівень та якість наукових досліджень. Особливу актуальність ця проблема має в умовах воєнного стану, оскільки в цей період суттєво зростає необхідність розвитку різноманітних інноваційних рішень. Таким чином, виникає потреба у створенні спеціалізованих засобів підтримки наукових працівників для підвищенні ефективності їхньої роботи. Запропоновано підхід до оперативного створення та розгортання інформаційно-аналітичних майданчиків на базі онтологокерованих лексикографічних систем. На основі цього підходу розроблено систему підтримки публікаційної активності, яка надає інформаційну підтримку в рамках науково-дослідної діяльності. База знань та інформаційний кластер цієї системи забезпечують ефективний трансфер знань між науковцями, що сприяє підвищенню їхньої кваліфікації та якості роботи.
2022-01-01T00:00:00ZAnalysis of the Shape of Wave Packets in the "Half Space–Layer–Layer with Rigid Lid" Three-Layer Hydrodynamic SystemAvramenko, OlgaLunyova, Мariiahttps://ekmair.ukma.edu.ua/handle/123456789/250822023-09-23T13:34:46Z2022-01-01T00:00:00Zdc.title: Analysis of the Shape of Wave Packets in the "Half Space–Layer–Layer with Rigid Lid" Three-Layer Hydrodynamic System
dc.contributor.author: Avramenko, Olga; Lunyova, Мariia
dc.description.abstract: We study the process of propagation of weakly nonlinear wave packets on the contact surfaces of a "half space–layer–layer with rigid lid" hydrodynamic system by the method of multiscale expansions. The solutions of the weakly nonlinear problem are obtained in the second approximation. The condition of solvability of this problem is established. For each frequency of the wave packet, we construct the domains of sign constancy for the coefficient for the second harmonic on the bottom and top contact surfaces. The regularities of wave formation are determined depending on the geometric and physical parameters of the hydrodynamic system. We also analyze the plots of the shapes of deviations of the bottom
and top contact surfaces typical of the constructed domains of sign-constancy of the coefficient. We discover the domains where the waves become ∪ - and ∩ -shaped and reveal a significant influence of wavelength on the shapes of deviations of the contact surfaces of the analyzed hydrodynamic system.
2022-01-01T00:00:00Z