Miroslava Mihajlov Carević

THE BOOK OF ABSTRACTS International Scientific and Professional Conference “ALFATECH“ Smart Cities and Modern Technologies 2026

Artificial Intelligence in Education: Using ChatGPT to Generate Math Problems

Sanja Rudić; Miroslava Mihajlov Carević; Miloš Todorov; Sanja Stankov

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This paper presents the findings of a study on the application of ChatGPT for generating mathematical assignments in primary education. The research aimed to investigate the responses of pupils of varying ages to mathematics challenges devised by the teacher and those generated by artificial intelligence. Emphasis was placed on variations in success, perceived difficulty, clarity of objectives, and pupil motivation in addressing both task types. Pupils completed two assessments, one devised by the instructor and the other produced by artificial intelligence. Upon completing both assessments, pupils completed a questionnaire regarding their attitudes. The findings indicate that artificial intelligence can enhance mathematics instruction, particularly for older pupils. Nevertheless, the results underscore the need for pedagogical oversight and for tailoring content according to pupils’ age, since assignments produced by artificial intelligence are not invariably didactically suitable. The research indicates that artificial intelligence can serve as a helpful aid for educators, but it cannot replace their professional and methodological roles in mathematics instruction.

ChatGPT; Mathematics Teaching; Motivation; Pupils Perception

Saopštenje sa međunarodnog skupa štampano u izvodu (M34)

GPH-International Journal of Educational Research

Personalized digital tools in the function of improving the learning of mathematics

Miroslava Mihajlov Carević; Katarina Arsenić

https://doi.org/10.5281/zenodo.18605331

This paper analyzes the role of personalized digital tools in modern mathematics teaching. The focus of the research was on determining how high school students use digital tools for learning, how much they help them understand the material, and what attitudes they have towards their use in class. The research was conducted by surveying a sample of 225 students from different grades of high school. The results showed that digital tools are most often used outside the classroom, that the use of simple tools such as YouTube and PhotoMath dominates, while tools that enable deeper understanding and interactive learning are less represented. Students showed a moderate level of motivation and recognition of certain advantages of digital tools, but also pointed out important disadvantages, such as misunderstanding of procedures and technical limitations. Based on the results and analysis, the paper offers guidelines for improving the teaching of mathematics through purposeful, personalized and digitally supported teaching.

digital tools; personalization; mathematics; teaching; motivation

Rad u naučnom časopisu (M53)

Ecologica

Graph theory helps ecology preserve the environment

Miroslava Mihajlov Carević

https://doi.org/10.18485/ecologica.2026.33.121.2

The application of graph theory allows ecologists and nature conservation organizations to mathematically model the distribution of resources and find optimal solutions for ecosystem management. At its core, graph theory studies the relationships between objects, represented by the nodes of a graph and connected by branches. In ecological contexts, nodes can be habitats, species or individual organisms, while branches symbolize interactions such as movement pathways, predation, symbiosis and competition. Using graphs, ecologists can model the spatial connectivity of habitats, migration routes and food chains, which facilitates a clearer understanding of ecosystem dynamics, resilience and vulnerability. The application of graph theory in ecology is diverse and includes the study of food webs, habitat connectivity and biodiversity protection planning, as well as the efficient allocation of limited resources for nature protection.

graph theory; modeling; ecosystem; habitat connectivity

Rad u časopisu nacionalnog značaja (M52)

Ukrainian Mathematical Journal

Dominating Numbers on an Octagonal Chain and an Octagonal Grid

Miroslava Mihajlov Carević

https://doi.org/10.1007/s11253-025-02432-0

Domination of graphs and topological indices are essential topics in graph theory. We analyze the problem of k-domination, k ∈ {1, 2, 3}, on octagonal chains and an octagonal grid. We determine the minimal k-dominating sets and k-domination numbers for a chain of octagons with two common vertices. Using the obtained results, we determine the k-domination numbers for the grid of octagons O_m×n, where m, n ∈ N.

dominating set; domination number; chain of octagons; octagonal grid; coverage index

Rad u istaknutom međunarodnom časopisu (M22)

SMEPP 2025 — Zbornik radova

Pametni gradovi kao tendencija savremenog života

Miroslava Mihajlov Carević

https://doi.org/10.5281/zenodo.15790313

Pametni gradovi predstavljaju inovativan pristup urbanističkom planiranju i ukupnoj infrastrukturi, sa ciljem poboljšanja kvaliteta života građana, povećanja efikasnosti lokalnih usluga i smanjenja energetskih, komunalnih i drugih troškova. Koncept pametnog grada obuhvata širok spektar inicijativa — od efikasne rasvete, gradskog saobraćaja i komunalnih usluga, do zdravstvenih usluga, obrazovanja, kulture i interaktivne gradske uprave. Inicijative u realizaciji ovog koncepta podržane su savremenim tehnologijama zasnovanim na internetu, pametnim senzorima, veštačkoj inteligenciji (AI), bežičnim mrežama i aplikacijama. Svi učesnici u sistemu pametnog grada — građani, lokalna samouprava, zdravstvene ustanove, naučne i kulturne institucije itd. — povezani su sa gradskim resursima putem informaciono-komunikacionih tehnologija (ICT), koje imaju ključnu ulogu u realizaciji pametnog grada. U ovom radu prikazujemo rezultate desk-istraživanja o pametnim gradovima, njihovom značaju, ulozi, održivosti, prednostima i nedostacima.

pametni gradovi; pametne inovacije; životna sredina

Saopštenje sa međunarodnog skupa štampano u celini (M33)

International Journal of the Latest Research in Engineering and Technology (IJLRET)

Digital Tools and Personalization in the Learning Process

Miroslava Mihajlov Carević

www.ijlret.com • Volume 11 • Issue 10 • October 2025 • pp. 01–04

Modern technologies involved in the education process have led to significant changes in the approach to teaching and learning. The development of information and communication technologies has enabled the emergence of various digital tools that can contribute to easier and more efficient transfer and acquisition of knowledge. Purposeful integration of digital tools into the teaching and learning process is a current issue in the education system. Students have different levels of prior knowledge and motivation, which gives digital tools the opportunity to contribute to the quality of education when used appropriately. In this paper, we analyze the use of personalized tools in the teaching and learning process.

digital tools; personalization; teaching; learning

Rad u naučnom časopisu (M53)

Vojnotehnički glasnik / Military Technical Courier

Dominance Number on Cyclooctane Chains

Miroslava Mihajlov Carević

https://doi.org/10.5937/vojtehg72-48272

Chemical structures are conveniently represented by graphs where atoms are nodes (vertices) and chemical bonds are edges (lines) in the graph. A graphical representation of a molecule provides useful information about its chemical properties. It is known that numerous physical and chemical properties of molecules are highly correlated with theoretical graph invariants, called topological indices. One such invariant is the dominance number. The aim of this research is to determine the k-dominance number for cyclooctane chains COC_n1, COC_n2, COC_n3 and COC_n4, for k ∈ {1, 2, 3}, n ∈ N.

cyclooctane; cyclooctane chain; dominance number

Rad u časopisu međunarodnog značaja verifikovanog posebnom odlukom (M24)

International Thematic Proceedings STEAM-X24

STEAM Education as Practice-Driven Innovation

Miroslava Mihajlov Carević; Miloš Todorov

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Real-world problems necessitate intricate solutions that encompass the combination of science, technology, engineering, arts, and mathematics. Consequently, educational paradigms have shifted toward the adoption of the STEAM approach. STEAM combines the disciplines of science, technology, engineering, art/architecture, and mathematics, integrating them into a cohesive framework that offers a fresh method for addressing challenges within the educational system. The implementation of STEAM practices has garnered significant attention, particularly in higher education, and includes equipping students with interdisciplinary skills necessary for the job market. Across the world, STEAM education has become widely used. It is imperative to research and enhance the implementation of STEAM in both classroom settings and teacher education. This paper showcases instances of interdisciplinary instruction implemented at Alfa BK University in Belgrade. The first example illustrates directing students toward integrating mathematics, engineering, and the arts to achieve harmony and beauty in architecture and art. The second example demonstrates the use of data from the Statistical Office of the Republic of Serbia through mathematical techniques, computer programming, and visual representation.

STEAM; interdisciplinary access; higher education; statistics

Saopštenje sa međunarodnog skupa štampano u celini (M33)

Proceedings of International Scientific and Professional Conference “ALFATECH” — Smart Cities and Modern Technologies

Modern Technologies and Their Application in “Smart Houses”

Miroslava Mihajlov Carević; Milica Varšandan; Čaba Varšandan

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The rapid development of information and communication technologies in the 21st century and their wide spread increasingly affect people's daily lives. We are living in an era of application of artificial intelligence in most aspects of human life. Smartphones have long been indispensable companions that help in carrying out numerous activities. Smart systems have become an imperative of modern life. Surveillance cameras, door-opening sensors, and smart home appliances are only part of the smart systems increasingly entering households. In an effort to gain insight into citizens’ interest in using smart devices in their homes, we conducted a survey on a group of citizens. Using the questionnaire and the provided answers, we identified needs and interests regarding improving living comfort with smart devices. The received answers were statistically processed. Based on the calculated statistical indicators, we analyzed the obtained data and drew conclusions about the number of smart devices used in households, citizens’ interest in their use, and the reasons why they have not used them so far.

modern technologies; smart devices; smart house

Saopštenje sa međunarodnog skupa štampano u celini (M33)

Vojnotehnički glasnik

Domination on Cactus Chains of Pentagons

Miroslava Mihajlov Carević

https://doi.org/10.5937/vojtehg70-36576

A graph, as a mathematical object, occupies a special place in science. Graph theory is increasingly used in many spheres of business and scientific fields. This paper analyzes pentagonal cactus chains, a special type of graphs composed of pentagonal cycles in which two adjacent cycles have only one node in common. The aim of the research is to determine the dominating set and the domination number on ortho and meta pentagonal cactus chains.

graph; pentagonal cactus-chain; dominating set; domination number

Rad u vodećem časopisu nacionalnog značaja (M51)

Mathematical Problems in Engineering

Dominating Number on Icosahedral-Hexagonal Network

Miroslava Mihajlov Carević

https://doi.org/10.1155/2021/6663389

In this paper, we deal with the dominating set and the domination number on an icosahedral-hexagonal network. We consider all cases of successive halving of the edges of triangles that are the sides of icosahedrons and thus obtain icosahedral-hexagonal networks.

Dominating number; Icosahedral-hexagonal network

Rad u međunarodnom časopisu (M23)

Trendovi u poslovanju

Visualization of solving problems with sequences of numbers: Statistical comparison of the two methods

Mihajlov Carević Miroslava; Milojević Nataša; Rešić Sead

https://enauka.gov.rs/handle/123456789/903523

The twenty-first century has brought the growing use of information and communication technologies in many spheres of human life, including education. In the learning process, students are increasingly focused on the use of modern technologies and software packages. Exploring the quality of mathematics teaching in primary school, we found students' knowledge of using modern technologies, but also the lack of a visual-logical approach in solving mathematical problems. This paper shows how figurative numbers and selected examples that demonstrate the observation of regularities can direct students to a visual-logical approach to solving tasks with sets and sequences of numbers. A three-hour exercise was organized in experimental and control groups, where the experimental group worked with figurative numbers and the control group with selected examples. On the pre-test, both groups showed a low degree of ability to observe regularities among numbers. On the post-test, both groups progressed, although the experimental group achieved greater progress. The research showed that dealing with figurative numbers and selected examples contributes to the development of pupils’ ability to perceive numerical laws and apply them in solving problems with sets and arrays of numbers.

visual-logical approach; perception of laws; figurative numbers

Rad u časopisu nacionalnog značaja (M52)