The current research project is concerned with so-called “arrow chasing”, with which identities for recursively defined sequences (such as the binomial coefficients) are to be proven in a new way. Valid mathematical proofs already exist for these identities - some of which have been proven for centuries. But the alternative method of proof is much more visual than the classical methods. “I had the idea for this research topic during a session of the Bonn Math Club,” explains Regula Krapf, Senior Academic Advisor at the Institute of Mathematics at the University of Bonn, where she works in the Mathematics Education working group headed by Rainer Kaenders. “The students inspired me to do it. I later realized that you can find a lot of new proofs using the 'arrow chasing method' without any prior knowledge.”
Application with a letter of motivation
Mathematically gifted pupils were invited to apply for this first research project with a letter of motivation. The research group currently consists of Hannah Julia Gajdecka, Felix Göbel, Calum Kessler, Lorenz Röther and Lisa-Sophie Theemann - all 14 to 16 years old and attending secondary schools in Bonn and the surrounding area. The group is enthusiastic about the new experience, as Hannah describes on behalf of the group: “They are meetings of mathematical inspiration. I'm always happy to have the opportunity to exchange ideas with people interested in mathematics and experience joint successes.” The duration of this first research project has not yet been decided. However, the results should definitely lead to the first publications in mathematical journals, in which mathematics education and elementary mathematics topics are presented.
Participants test the possibilities of evidence methods
The offer differs from typical mathematical workshops in which compact educational units are presented or mathematical exercises are solved whose solutions are already known to the teachers. What comes out of the meetings of the new research group is not known beforehand. “Unlike traditional Olympic preparation, our focus is not on a single exercise, but on testing the possibilities and limits of a method of proof. It's exciting to see how the students come up with amazing results,” enthuses postdoctoral researcher Henning Heller, also a member of the Mathematics Education working group. After the “arrow chasing”, further research projects are planned, perhaps from completely different areas of mathematics. There will be further calls for participation in the future.