Their current research project is all about “arrow hunts,” which are intended to prove the identities of recursively defined sequences (such as binomial coefficients) in a new way. Although these statements are already backed up by valid mathematical proof, some of which was established hundreds of years ago, the alternative method is much more visual than its classical counterparts. “I had the idea for the topic we’re currently researching during a Bonn Math Club session,” explains Dr. Regula Krapf, an Akademische Oberrätin (senior lecturer with civil servant status) at the Mathematical Institute of the University of Bonn, where she is part of the Mathematics Education working group led by Professor Rainer Kaenders. “It was the schoolchildren who gave me the inspiration for it. Later on, I realized that you can use the ‘arrow hunt’ method to come up with lots of new forms of proof without needing any prior knowledge.”
Applying with a letter of motivation
Schoolchildren with a talent for mathematics were able to apply for this first research project by submitting a letter of motivation. The research group is currently made up of Hannah Julia Gajdecka, Felix Göbel, Calum Kessler, Lorenz Röther and Lisa-Sophie Theemann, all of whom are between 14 and 16 and attend Gymnasien in and around Bonn. Speaking for the whole group, Hannah describes the enjoyment that their new experience is bringing them: “The meetings give us mathematical inspiration. It’s always fantastic to have the opportunity to chat with like-minded people who are interested in math and enjoy our shared successes.” Although the length of this first research project has yet to be finalized, its findings are definitely being lined up for publication in some initial mathematical journals that cover topics from the fields of mathematics education and elementary mathematics.
Participants test the possibilities of proof methods
The program differs from typical mathematical workshops, where participants learn about a single, self-contained topic each time or solve puzzles to which the workshop leaders already know the answers. With the new research group, by contrast, nobody knows in advance what its meetings will produce. “Unlike the traditional method for preparing for an Olympiad, we don’t focus on a single problem but instead test the possibilities and limits of a certain method of proof,” says an enthusiastic Dr. Henning Heller, who is likewise a member of the Mathematics Education working group. “It’s exciting to watch the schoolchildren coming up with some astonishing results.”
More research projects are planned for when the “arrow hunts” have finished, perhaps from completely different areas of mathematics, with more calls for applications being issued in due course. See https://www.mathematics.uni-bonn.de/de/outreach/fuer-schuelerinnen-und-lehrerinnen/schueler-innen-forschungsgruppe for more information.
Media representatives are warmly invited to come and observe the schoolchildren’s research group on a Monday. Please let Stefan Hartmann (stefan.hartmann@hcm.uni-bonn.de) know in advance.