Mathematics at school

GROUP ACTIVITY IN THE COURSE MATHEMATICS 4

SAMVEL HAROUTUNIAN — 2025-07-21

The present article to one of main practical components of the modern pedagogical teaching technologies is devoted. The group activity of pupils plays an important role in the process of Mathematics instruction since the first year of study. Introduction of this activity in primary school stimulate the development of different abilities of pupils necessary for the successful study of Mathematics and other disciplines. Besides, it develops communicative, researching, creative abilities of children. Concentration of learning, pedagogical, psychological, social and other components in the content of this activity transforms it in a very effective instrument in the process of the Mathematics instruction in the primary school. In the first part of the present article, some examples of the problems necessary to study with application of modern teaching technologies are presented. Individual properties of each teaching technology affects directly on the procedure of the group activity. Application of this activity in different teaching technologies adds to it some specific features. Other side the teachers must apply this activity carefully: three – four groups, 7-8 pupils in each group, it is important to change the staff every times. Implementation of these technologies (where the group activity is one of essential components) in the teaching process stimulates the progress of pupils in studying Mathematics. Other side the teacher develops his (or her) prof ssional level.

COORDINATE METHOD IN GEOMETRIC TASKS

LERNIK PETROSYAN — 2025-07-21

The article reveals the possibilities of solving geometric tasks by means of the coordinate method. The essence of the coordinate method in geometry is that, based on direct coordinate points, geometric objects are given analytically, i.e. by means of numbers, equations and inequalities or their systems, and thus, analytical methods are used to prove theorems or solve geometric tasks. This significantly simplifies judgments and often allows, using a certain algorithm, to prove theorems or solve tasks, make certain calculations in the case when the traditionally used geometric (comparative) method in many cases requires the use of artificial techniques. Currently the requirement to master general educational actions is also included in the current educational standards and used subject programs.

The use of the coordinate method in solving geometric tasks opens the wide opportunities for solving tasks not included in the traditional course of school geometry, but quite valuable in their usefulness, which can be considered to be of great success in groups with advanced training in mathematics or in amateur courses. In this regard particular theorems and a number of examples of study tasks are presented, substantiating the importance and necessity of applying the coordinate method in the secondary school.

APPLICATION OF GRAPHICAL REPRESENTATION OF ALGORITHMS IN SOLVING PARAMETRIC EQUATIONS

GYULNARA ADAMYAN — 2025-07-21

The work is dedicated to the interdisciplinary connections between mathematics and computer science. Block diagrams are considered as a factor for increasing the effectiveness of teaching parametric equations. It is shown that higher efficiency can be achieved if the solution of parametric equations is carried out using block diagrams. The process of effectively using block diagrams to solve parametric equations is described. The development of students’ algorithmic thinking and their mastery of algebraic language are emphasized. The importance of student participation in creating a general algorithm for solving parametric equations, as well as constructing its corresponding block diagram, is also highlighted.

This approach fosters students' abilities to research, experiment, combine various tools, analyze cause-and-effect relationships, and make informed decisions. It helps them develop teamwork skills, structured thinking, and the ability to assess both their own and others’ opinions and arguments. The approach directly contributes to the understanding and reinforcement of cross-cutting concepts such as patterns, cause and effect, mechanisms and prediction, systems and models, structure and function, thereby promoting a foundational understanding of the digitalization process.

The work can be useful in making the learning of parametric problems—typically considered difficult for students—more engaging and effective.

EQUATION IN THE SECONDARY SCHOOL ALGEBRA COURSE

HAMLET MIKAYELYAN — 2025-07-21

The paper considers the problem of identifying rational fractions within the framework of the secondary school algebra course. First, the importance of the idea of equality in the field of algebraic expressions is shown as one of the main ways of revealing the properties of these objects. Next, the second way of identification is presented as such a way - the identity of algebraic expressions. Finally, it is shown that these two methods of identification lead to the same result. In secondary school algebra textbooks, this fact is usually not paid attention to, and the student does not understand the difference between equality and identity. Moreover, the proof of the main result presented here is very simple and is taken from a textbook written for secondary schools by one of the authors. We also consider it necessary to mention the issue of addressing not only the applied, technical-training significance of algebra, but also its cultural, philosophical, and value-based potential, which is what this work, in part, and the aforementioned textbook are aimed at.

THE IDEA OF EQUATION IN THE MIDDLE SCHOOL CALCULUS TEACHING PROCESSL

ALVACHD MURADYAN — 2025-07-21

The work considers the idea of equation in the process of teaching algebra in middle school. First, a brief overview is made of the application of equations in mathematics. The experience of the ancient world, Ancient Greece, and the Middle Ages is presented. The problem of addressing the idea of equation in the section of the RA mathematics program dedicated to middle school is presented in detail, including the topics, goals, and learning outcomes. An experimental study on the concept of equation in teacher and student perceptions is also presented. The survey method is applied. The obtained data is analyzed.

ABOUT THIRD PEDAL QUADRANGLE

AVAG KOSTANYAN — 2025-07-21

It was proved in previous article that with respect of any point in the interior of any convex quadrangle the fourth pedal quadrangle is similar to the initial quadrangle. In the present work the following problem is discussed. Is there a point in the interior of any convex quadrangle such that the third pedal quadrangle with respect of this point is similar to the initial quadrangle? The answer is positive. It is established, that there is a point O in the interior of any convex quadrangle ABCD such that the third pedal quadrangle is similar to ABCD. In the second part of the present article, this result is applied for the class of semi canonical trapeziums. First, it is proved that the first, second, third pedal quadrangles with respect of midpoints of diagonals of semi canonical trapeziums are similar to the initial trapezium. Then it is established, that there is a point O on the middle perpendicular of the base of semi canonical trapezium ABCD such that the second pedal quadrangle with respect of this point is a square.

MATHEMATICS AS AN INSTRUMENTAL VALUE

MAMIKON ABGARYAN — 2025-07-21

In this paper, mathematics is considered as an instrumental value. It is shown that, on the one hand, it serves as an important source of worldview, satisfaction of needs, realization of goals, formation of beliefs, formation of truth, aesthetic, moral, spiritual, national and universal values. On the other hand, it serves as a tool for collecting and transforming information in the socio-legal information system, in everyday life, in economics, healthcare, in various sciences: physics, chemistry, geography, biology and others. The role of mathematics as a tool in the field of music is also discussed. Emphasis is placed on the role of mathematics as a tool in the mental development of a student. Its role in the formation of character, attention, individual-volitional qualities and other mental processes is considered.

OBJECTIVE FEATURES OF SCIENTIFIC BEAUTY IN MATHEMATICS AND IN MATHEMATICAL EDUCATION

HAMLET MIKAYELYAN — 2025-07-21

The work considers the issue of the relationship between mathematics and beauty from the perspective of the role of mathematics in the formation of beauty and the existential nature of mathematics and its teaching process. The work clarifies the problem from the perspective of satisfying the scientific or mathematical characteristics of beauty. The characteristics of scientific beauty were first put into circulation by the eighteenth-century Scottish artist Frebsis Hatcheson. Both Hutcheson and his numerous followers, proposing certain characteristics, evaluate the beauty of scientific or mathematical objects from the perspective of satisfying these characteristics. Over time, a fairly large number of such characteristics or signs have emerged, and the problem of their classification has become relevant. The author, having made a similar classification, based on the objective and subjective aspects of beauty. The work considers only the objective aspect, and the existing signs are divided into three groups: forming, unifying, and groups of logical antonyms. The work mainly systematically presents the author's previously obtained results in this direction, and some new emphases are made.