Summary In modern education, the roles, functions, strategies and recommendations for the use of models and modeling in the search for authentic STEM education and improvement of STEM literacy are elaborated. This requires interaction between STEM subjects such as mathematics and physics to contribute to integrated STEM literacy. Through mathematical and physical modeling, students are introduced to the process by which mathematicians and physicists investigate real-world problems. As a pedagogical approach, mathematical modeling emphasizes students’ ideas and their choice of representations and the way they communicate their mathematical thinking about problems. With material models, students can explore behaviors, patterns, and relationships, and can make predictions. Material models encourage peer-to-peer, external and internal communication. The Geoplate is an example of a material model that can have numerous applications in the teaching of mathematics and physics. The Geoplate makes it easier to visualize, set up and solve math and physics problems. It encourages them to research, be systematic, creative and persistent in their work, so that they become active participants in the learning process. In this diploma thesis, we have given some examples related to vectors. There are numerous other application possibilities. In the context of too much exposure of students to digital content, the Geoplate is an example of an educational tool that does not have to be digital, but that improves teaching in the direction of the development of modern education.