Application of graph theory in teaching and understanding of the mathematical problems

The basic aim of mathematics education was described as “to bring mathematical knowledge and skills that are required by daily life to the individual, to teach students problem solving and to bring them a way of thinking that handles incidents including a problem-solving approach”. For this reason, problem-solving skills take an important place among mathematical skills. Mathematics (NCTM) standards also indicate that problem-solving skills have higher priority in teaching mathematics. One of the mathematical disciplines which has great application for solving of the real problems is the graph theory. Graph theory as a part of mathematics has the potential to become a popular tool for teaching and learning mathematics in elementary and secondary school for solving and understanding of many logical puzzles. This kind of puzzles are very complicated and present complex problems for understanding by the students at elementary and secondary level. But, by using the basic concept of graph theory the students can easily make visualization of such kind of problems and can easily prepare for different kind of mathematical competitions. The graph theory can facilitate the learning process, because it provides good illustrations by which the applications of the ideas can be shown and presented to the children. In this paper we are considering a methodology that improve the students’ ability for logical thinking. For that purpose, we will consider some kind of logical mathematical problems which are usually given at the mathematical classes but especially for gifted and talented students.