Research projects
Concept-Tests in abstract algebra courses:
Alexander Unger and I develop Concept-Test questions for abstract algebra courses that aim at supporting students to gain a deep understanding of the basic concepts in group and ring theory. Furhermore, we investigate empirically students' usage of quizzes with such questions as well as to what extent these quizzes actually help students to acquire an understanding of the corresponding concepts.
Learning of university mathematics in a Flipped Classroom:
In traditional mathematics lectures the lecturer normally puts definitions, theorems and proofs on the board while the students are busy with copying the lecturer's notes from the board. For the development of an understanding of the content the students need to carefully process their lecture notes at home. However, students often do not rework through their notes in the way it would be necessary, and do not process the information presented in the lecture sufficiently. The idea of the Flipped Classroom model now is to change the in-class and the out-of-class activities: The students concern themselves with the content first at home before the lecture. The lecture can then be used for activities that can help to gain an understanding of the content.
Luise Fehlinger and I investigate to what extent students more likely (can) perform activities that are essential for a succesful learning in mathematics lectures in a flipped classroom course than in a traditional lecture.
Guided notes in mathematics lectures:
In traditional mathematics lectures the instructor writes the complete content down at the board. The students are mostly busy with copying the instructor's notes and cannot follow his explanations. On the contrary, in the case of the provision of a complete script, students tend to stay absent from the lecture. Hence, it seems reasonable to provide the students just with parts of the lecturer's notes with blanks at certain spaces (so called guided notes). Anja Panse and I investigate how students' note-taking differs in a lecture based on guided notes compared to traditional lectures.
Support of students in developing mathematical study skills at university:
I work together with Prof. Dr. Hans-Michael Dietz at the project "Support of study skills in Mathematics for economics students" at the Centre for Higher Mathematics Education in Germany (khdm). In this project the methodological suppot program of Prof. Dietz is evaluated and refined. Further information can be found here.
Ph.D. project:
My Ph.D. project (supervisor: Prof. Dr. Rolf Biehler at the University of Paderborn) is about students' of economics understanding of the derivative. It has the aim that students of economics can apply this concept in a reflective manner after their mathematics course. Further information can be found here.
Project about students uinderstanding of the vector concept at the transition from school to university:
Together with Tobias Mai I do research on students' understanding of the vector concept at the transition from school to university. It has the aim to find out how the concept can be taught for university freshmen in a way that it is based on the students' previous knowlege of the concept from school on the one hand, but can also be embedded into formal vector space theory properly and concistently on the other hand.
Diploma Thesis:
In meiner diploma theses I did research on stress intensity coefficient of solutions of mixed elliptic boundary value problems. I showed that these coefficients depend smoothly from the data of the domain if the boundary is smooth, even if the solution itself is not smooth. I showed the result if the boundary is locally straght, but it can easiliy be generalized by using alocal transformation of the domain. A pdf-version can be found here.