In mathematics education, geometry presents students with greater difficulties than other mathematical content, and one of the main reasons for this is the development and ability of visualization. Visualization refers to the ability to present ideas, information and concepts through graphical or pictorial representations. Many empirical studies as well as theoretical statements, for example van Hiel's theory, indicate that visualization or recognition is the first step in geometric thinking and reasoning, followed by analysis, informal deduction, deduction and rigor. Vectors as a concept and as a unit of instruction are learned in elementary school and appear in high school through to college classes, where the culmination of their application is reached in the analysis of stresses, strains, vibrations, fluid dynamics and many other segments of mechanical engineering. In the theoretical part of the paper, the mathematical and graphical representation of vectors is combined with the processing of arithmetic operations with vectors. How and in what way to explain and visualize certain vector quantities or formulas for scalar and vector products to students is a major challenge for professors. The experimental part of the paper shows some concrete examples of the application of vectors that students learn in mathematics but also in other professional courses at the Technical Department. The results of a survey of the first year of professional undergraduate studies at the Technical Department will also be presented, providing information about students attitudes and their approach to visualization and teaching content.
Science Journal 