Drawing connections: exploring graph theory as a tool for problem solving in high school
This work aims to explore graph theory as an innovative tool for problem solving in the context of high school. Graph Theory is a field of mathematics that studies the properties and relationships between connected elements (vertices and edges), and is widely used in various areas, such as mathematics, computer science, electronic circuits, finance, social networks, logistics, biology, genetics, etc. This dissertation presents in detail the main concepts of the theory of graofos, including Euler's theorem. The core idea is to provide high school students with the development of logical thinking, problem-solving, and communication skills. Although the National Common Curriculum Base (BNCC) does not explicitly address graph theory, it defends the importance of problem-solving as a fundamental skill for students. In this context, we have developed lesson plans that integrate graph theory into the high school curriculum, using the Geogebra platform as a technological support. We believe that a dynamic approach, coupled with the use of interactive tools, can transform a potentially complex topic into a pleasurable educational experience for students. Not only does this study fill a gap in the curriculum, but it also provides a valuable opportunity for students to develop problem-solving, critical thinking, and logical reasoning skills, thereby promoting meaningful learning in high school.