The teaching of mathematics has reached a dead end during the last decades, and at the same time it is still one of the basic subjects that determine the possibility of successfully continuing studies at many universities, not only in science and technology. Mathematics should teach students to think logically, analyze, describe problems from different points of view, and look for solutions. Unfortunately, the content is oversized and the connection to the real world is almost completely lost. Mathematical areas are learned abstractly, without overlap, and often students only memorize them. For that reason, STEM education is currently strongly supported, but teachers do not have enough experience or competence to lead such lesson.

It is therefore appropriate to think about breaking down old stereotypes in terms of content units in mathematics education and start setting up key topics in accordance with STEM ideas that will connect several areas and mathematics will be able to fulfill its main mission here.

The Faculty of Science of the University of Ostrava prepares future teachers of science subjects and mathematics. As part of their university studies, they have the opportunity to attend specialized workshops focused on STEM education. During the workshops, students focus on one topic, which they work on with their lecturers. The first of the thematic units, which will be part of the training of future teachers is shapes and patterns.

The content of the contribution will be the presentation of partial mathematical topics that are related to the thematic unit – from the exploration of geometric shapes in plane and in 3-dimension, their properties, especially in connection with the reasons why a given shape is advantageous in some cases. It will be in the form of a comparison of shapes and patterns preferred by nature and shapes and patterns preferred by humans. Why do we sometimes use different shapes and patterns than nature? How is it more beneficial for us? We will also deal with symmetry versus, for example, the golden ratio, up to fractals as patterns, from a structural, visual and mathematical point of view.

Keywords: STEM education, mathematics, science.