EXAMPLES OF USING GRAPHS IN SOLVING MATHEMATICAL AND LOGICAL PROBLEMS IN 5-6 CLASSES

Authors

  • Olga Yakovlieva South Ukrainian National Pedagogical University named after K. D. Ushynsky, Ukraine https://orcid.org/0000-0003-0750-9769
  • Юлія Банна Communal institution «Sumy specialized school of I-III degrees No. 17», Ukraine

DOI:

https://doi.org/10.31110/2616-650X-vol11i9-011

Keywords:

graph, algorithm, math, logic, Computer Science

Abstract

Graph theory is a branch of mathematics that lies at the intersection of algebra, geometry, combinatorics, and a number of other mathematical disciplines and uses their methods to solve both mathematical problems and programming problems, problems of information theory, physics, etc. In recent years, at school mathematical competitions, Olympiads, and tournaments, there occur problems that can be solved by means of graph theory, in addition, such problems can be found also at computer science Olympiads. In the school mathematics course, graphs and their properties are not studied, however, they can be studied and used to solve problems in mathematics electives, in mathematics circles, in logic lessons. The article considers the use of some methods and algorithms of graph theory to solve mathematical and logical problems at school, which, according to the authors, can be offered to schoolchildren of grades 5-6. The authors consider route construction problems, problems using weighted graphs, procedures of Kruskal's algorithm, Prim's algorithm, problems solved using a greedy algorithm, problems of analysis of obtained solutions using Prim's algorithm, problems using properties of chains and cycles, problems solved using the handshake lemma. For teachers, the necessary theoretical information on graph theory, which was used in solving problems, is given. The article provides a brief historical overview of the development of graph theory. The proposed problems have simple solutions and can be used in logic lessons, optional mathematics classes for schoolchildren of grades 5-6. It is advisable to consider problems in the solution of which graphs are used in computer science classes to introduce students to one of the powerful mathematical tools for solving problems. Such lessons can become integrated from the point of view of an interdisciplinary approach, and the teacher in the lesson will implement interdisciplinary integration, which is relevant in modern conditions.

References

Anderson I. A First Course in Discrete Mathematics. Springer Verlag. 2002, 200 p. URL: http://www.fen.bilkent.edu.tr/~franz/dm/DM1.pdf

Карнаух Т. О., Ставровський А. Б. Теорія графів у задачах. К. : КНУ, 2012. 90 с.

Скляр І. В. Теорія графів у школі : задачі : посібник. К. : Шкільний світ, 2010. 128 с.

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Published

2023-11-30

How to Cite

Yakovlieva О., & Банна, Ю. (2023). EXAMPLES OF USING GRAPHS IN SOLVING MATHEMATICAL AND LOGICAL PROBLEMS IN 5-6 CLASSES. Education. Innovation. Practice, 11(9), 79–85. https://doi.org/10.31110/2616-650X-vol11i9-011

Issue

Vol. 11 No. 9 (2023)

Section

Статті

License

Copyright (c) 2023 Ольга Яковлєва, Юлія Банна

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