In recent years, there has been an increased use of information and communication technologies and mathematical software in mathematics teaching. Numerous studies of the effectiveness of mathematical learning have shown the justification and usefulness of the implementation of new teaching AIDS. They also showed that learning with educational software has a great impact on students' achievement in the overall acquisition of mathematical knowledge during the school year as well as in the final exam at the end of primary education. Teaching realized by using computers and software packages is interesting for students, increases their interest and active participation. It is indisputable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by many researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is to develop constructive thinking of students. The results of the research we conducted with primary and secondary school students showed the lack of visual-logical approach of students during the learning of mathematics as well as in solving mathematical problems. Visualization and representation of mathematical laws are of great importance in the realization of mathematics teaching. They should be applied everywhere and whenever possible.

Razvoj nastave obuhvata celokupnost sistematičnih težnji da se praksa u nastavi optimalizuje u pravcu smisaonog i efektivnog učenja. Ovako shvaćeno učenje se u razmenama vođenog i samostalnog rada često bavi otvorenim i autentičnim problemima. Ova nastojanja otvaraju niz pitanja kojima se želi dati odgovor o tome koje uslove treba da uvaži uspešan classroommanagement, koji se u školi javlja u obliku širokog spektra direktnih i indirektnih aktivnosti koje nastavnik treba da realizuje, kako bi savladao raznovrsne i neočekivane zadatke školske svakodnevice. Dijapazon delovanja kreće se od perspektive nastavnika preko perspektive učenika do perspektive nastave i nastavnog procesa. Različiti elementi i oblici u kojima se pojavljuje classroom-management variraju s obzirom na intenzitet, rok i trajanje, a javljaju se u brojnim kombinacijama i sa različitim stepenom zastupljenosti. Da bi se razumeli efekti classroom management-a, potrebni su nam transparentni i izazovni ciljevi, razumevanje dinamike i strukture učenja, kriterijumi uspeha, dobra volja učenika i nastavnika, logika i strategija da se postignu željeni ciljevi. Pri tome, ne sme se zanemariti multidimenzionalnost nastavnog procesa: poučavanje i učenje imaju svoj fokus, efekat, težnju, tipove, svoj fidbek, kao vezivne niti složenih interakcija, komunikacije i odnosa koji se posreduju u procesu poučavanja i učenja.

Introduction/purpose: 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 dominant set and the dominance number on ortho and meta pentagonal cactus chains. Methods: When the corresponding destinations are treated as graph nodes and the connections between them as branches in the graph, the complete structure of the graph is obtained, to which the laws of graph theory are applied. The vertices of the pentagon are treated as nodes of the graph and the sides as branches in the graph. By applying mathematical methods, the dominance was determined on one pentagon, then on two pentagons with a common node, and then on ortho and meta pentagonal cactus chains. Results: The research has shown that the dominance number on the ortho chain 𝑂ℎ of the length h ≥ 2 is equal to the value of the expression ⌈ 3ℎ 2 ⌉ while on the meta chain 𝑀ℎ it is equal to the value of the expression h+1, which was proven in this paper. Conclusion: The results show that the dominant sets and the dominance numbers on ortho and meta pentagonal cactus chains are determined and explicitly expressed by mathematical expressions. They also point to the possibility of their application in the fields of science as well as in the spheres of business in which these structures appear.

The twenty-first century has brought the growing use of information and communication technologies in many spheres of human life. Also in education. In the learning process, students are increasingly focused on the use of modern technologies and software packages. Exploring the quality of maths teaching in primary school, we found students' knowledge of using modern technologies but also the lack of visual-logical approach in solving mathematical problems. In this paper, we show how the establishment of figurative numbers and selected examples that demonstrate the observation of legality, can direct students to a visual-logical approach to solving tasks with sets of numbers. We organized a three-hour exercise in experimental and control group, during which the experimental group was working with figurative numbers and the control group with selected examples. On the pre-test both groups showed a low degree of ability to observe legality among the numbers. On the post-test, both groups achieved progress compared to the pre-test, although the experimental group achieved greater progress. The research has shown that dealing with figurative numbers and selected examples that demonstrate the observation of legality, contributes to the development of pupils' abilities to perceive the laws of numbers and to apply the laws observed to solving problems with sets and arrays of numbers.