Abstract:

The elliptic curve, sigmoid and gyroid –not presented in ordinary mathematics textbooks– are currently very progressive objects. Each of them is associated with one of three important research areas: elliptic curve with cryptography; sigmoid, as an activation functions, with artificial neural network; and open-structure, triple-periodic minimal surface gyroid, with material research, especially nano and metamaterials. That's why we believe it's worth introducing them to teenagers.

The publication presents tips on how to usefully incorporate the three elements listed above into linear algebra, single variable calculus and multivariable one. Examples, exercises, assignments were created with respect to the variability of object representation, e.g. verbal or graphical one, via the appropriate type of equation given by mathematical symbols; alternatively with help of real/virtual physical models, while taking into account revised Bloom’s taxonomy.

We focused on training a wide range of skills from manual calculations as well as freehand drawings to the critical use of digital applications for graphic and symbolic calculations. We have engaged Google Drive as a place for peer-to-peer observation and comparison of uploaded students‘ photos of real 3D printed gyroid or gyroid sketches. Feedback on selected details and viewpoints were realized via Slido web application.

For example, it has been shown that digital visualization of functions graphs, and 2D curves as such, here namely visualization of elliptic curve, is more attractive and goes to deeper diving of students to the theme if application offers continuously change of curve parameters. Interesting was also, that high school students’ group choce gyroid as a winner from a set of physical objects, as well as from a text list of terms.

Our experience shows opportunities for implementing, on the one hand, complex but on the other hand scientifically attractive geometric objects in teaching framework of a presence and also distance learning, also with the aim of increasing students' interest in STEM fields.

Keywords:

Mathematics, elliptic curve, sigmoid, gyroid, representation, equation, graph, verbal description, physical model, calculus, algebra, technical university.