Graph Theory: Enhancing Understanding of Mathematical Proofs Using Visual Tools

Abstract

Mathematical culture is an essential part of general culture, and mathematical proof is the essence of mathematical culture, which plays an essential role in education for sustainable development. The presented research focuses on the following issue: Can the use of visual tools contribute to a better understanding of mathematical proofs presented within the framework of courses in graph theory? The research focuses on Czech university students of computer science. The presented results were achieved in a pedagogical experiment based on a pre-test, treatment and post-test design carried out during three academic years before the COVID pandemic period. In the pre-test and post-test phases, students were tested to determine their level of mathematical logic knowledge. Visual applications were used in teaching in the treatment phase. The research results clearly showed that the use of visual tools supporting formal explanation of mathematical proofs results in better understanding of the abstraction of the presented process and thus contributes significantly to sustainability in mathematical education. Thanks to the use of the mentioned visual tools during the COVID pandemic period, when schools had to switch to on-line education, the students' results were comparable to those from face-to-face classes.