Research
The core of our research activities consists of the development, testing, and evaluation of learning environments and instructional approaches that are focused on innovation. The development work is systemic and evolutionary in nature, with the aim of integrating design, empirical research, teacher education and professional development, and instructional development. Under “Publications ,” you will find several papers available for download.
The following research and development projects shape the work at the Chair of Didactics of Mathematics:
School and Instructional Development
Mathematics Instruction in Heterogeneous and Inclusive Classrooms
Building on several years of research in this area, the findings and concepts regarding mathematics instruction in heterogeneous and inclusive classrooms are being further developed, adapted to other school contexts, and made accessible for practical use. The concepts and materials developed in this process are, in turn, incorporated into teaching, academic theses, and the design of professional development programs. Parts of the overall project are carried out in close cooperation with the Carl von Ossietzky School (comprehensive school) in Berlin Kreuzberg.
Development Research at the Freie Evangelische Schule Dresden
Since 2023, the Chair of Didactics has been supporting the school and instructional development at the Free Evangelical School in Dresden with regard to differentiation and learning in heterogeneous groups. In this context, students are also involved in instructional development processes as part of their academic theses.
Assessment and Support
- Initiated by the “GemeinschaftUnterstützt” project at TU Dresden, a project on assessment and support in a pedagogically challenging and heterogeneous school context took place (2019–2020) in cooperation with the 139th Elementary School in Dresden-Gorbitz. The project was carried out in collaboration with Frank Beier (ZLSB, Graduate Forum, TUD) and Elisa Wagner (Elementary School Education, TUD). An article on the project can be found in the TU Dresden University Journal, Issue 12/19, on page 5 at the bottom (completed).
- Design-Based Research Project: Development of a school concept for assessment and differentiation based on the New Zealand “Numeracy Project” (partially funded by the German Center for Mathematics Teacher Education).
This was a development research project in collaboration with the Carl-von-Ossietzky School—a secondary school in Berlin-Kreuzberg. The partner school is a comprehensive school where students learn together from 1st through 13th grade. Due to its status as a “community school,” there is no external differentiation into G and E courses. This presents teachers with particular challenges regarding student heterogeneity and internal differentiation. In the educational research project, instruction in the new 7th-grade classes was observed for one school year; diagnostic procedures were developed and applied; materials for internally differentiated instruction were created; and a concept for designing differentiated class tests was developed and evaluated.
Developmental Research at the Dresden University School
2021–2022: Development of instructional materials in cooperation with the Dresden University School, with the active involvement of students in the research and development process (inquiry-based learning).
Project: Cumulative subject-specific learning as the basis for in-class differentiation in highly heterogeneous learning groups—illustrated using the example of percentage calculations and the concept of proportion (completed)
This project was conducted in collaboration with Dirk Bresinsky and Annett Veit of QUA-LiS NRW as part of SINUS NRW. In addition to developing a conceptual framework based on several years of research at a Berlin comprehensive school, curricula and instructional materials were developed based on theory, tested, shared in specialized teacher training formats, and evaluated for their effectiveness.
Didactics of Calculus
A key focus of the research is the redesign of calculus instruction at both the content and methodological levels. In this context, we are working on an overarching concept for calculus instruction and on the question of how to meaningfully and effectively integrate digital tools, particularly with regard to the development of concepts related to limits. Because the Chair is affiliated with the Institute of Analysis, the project specifically addresses issues related to the transition from high school to college. This project involves a collaboration with the Centre for Educational Research in Mathematics and Technology (CERMAT), which is based at the University of Potsdam under the direction of Prof. Dr. Ulrich Kortenkamp. You can find some digital learning environments on this topic here.
Development of Textbooks and Teaching Materials for Mathematics Instruction
The Chair contributes in various ways to the development and creation of textbooks for mathematics instruction: Selected publications.
Design and Research on Teacher Professional Development Formats
The research and development work leads, among other things, to the development of teacher professional development programs. In this context, concepts for mathematics teacher professional development in Saxony have been and continue to be developed in collaboration with the Chair of Didactics at the University of Leipzig and the subject advisors for high schools and teacher training institutions in Saxony. In particular, programs are being created for new teachers to support the third phase of teacher education. (Current professional development offerings from the Chair).
University (Mathematics) Didactics
BeSOS Project (Counseling Tools for Strengthening or Restoring the Career Orientation Skills of Students with Mental Health Challenges)
The BeSOS project, which is currently in its second funding phase (through Dec. 2026) and is based at the TU Bergakademie Freiberg, has the following goal: To provide educational and career guidance professionals with a model and a toolbox that improve their ability to work with children and adolescents experiencing psychological distress, as well as to manage their own stress. The BeSOS model and toolbox have been integrated into courses on subject-specific pedagogy in mathematics, religious education, geography, and general social studies since the winter semester of 25/26. The contacts and partners at TU Dresden are Prof. Dr. Birte Platow (Religious Education) and Prof. Dr. Andrea Hoffkamp (Mathematics Education). The project staff member at TU Dresden is Mr. Jeremias Vahle, who also volunteers with the AufeinanderAchten project.
Understanding Mathematical Algorithms through Tutorials and Assignment Feedback (MARTA2)
(Funded by the Digital Teaching and Learning Fund 2024/25 at TU Dresden, 9/2024 – 8/2025, in collaboration with Dr. Christian Zschalig)
This is a continuation of the MARTA project, which was funded in 2021/22 as part of the Digital Fellowship Program. The project builds on the experience and expertise gained from the predecessor project. This time, the focus is not only on algorithms but also on essential mathematical concepts in which “standard proofs” play a role.
Understanding Mathematical Algorithms through Tutorials and Assignment Feedback (MARTA)
(Funded by the Saxony Digital Fellowship Program 7/21–12/22, in collaboration with Dr. Christian Zschalig)
Dropout rates in mathematics are high, and the reasons for this are varied. This project aims to address some of these causes through a flipped classroom approach combined with formative feedback elements. Video tutorials incorporating cognitively stimulating elements will be designed and implemented, and linked to randomized and ability-differentiated ONYX assignments that include formative assessment. In terms of content, procedural knowledge elements of algebraic topics will first be implemented in a course for teacher education students, which is particularly well-suited for a flipped classroom approach. The resulting digital resources will be made available for other courses. Key objectives include increasing effective learning feedback, fostering student independence, and enhancing students’ self-efficacy. The flipped classroom approach is intended, in particular, to create space for active engagement with algebraic concepts during the practice sessions.
Integration of physical mathematical models into action-oriented teaching concepts for mathematics teacher education (special funding from the Society of Friends and Supporters of TU Dresden, 10/18–9/19)
In cooperation with the Geometric Modeling and Visualization Working Group (Prof. Dr. Daniel Lordick and Robert Päßler, TUD) and Erlebnisland Mathematik, innovative and action-oriented teaching concepts are being developed and evaluated for students in the mathematics teacher education program by incorporating and further developing the collection of mathematical models (more).
Teaching Innovations and University Pedagogy Workshops
The research group develops and tests teaching concepts for the training of future mathematics teachers. In this context, the unique connection between subject-specific training and subject-specific pedagogical training plays a key role in emphasizing the professional relevance of the program and counteracting the phenomenon of “double discontinuity” in mathematics teacher education.
This development work builds on preliminary research conducted as part of the BMBF research project within the program “University Research as a Contribution to the Professionalization of University Teaching—Future Workshop on University Teaching” ( SAiL-M ) (completed: February 2012) and on the joint design and implementation of university pedagogy workshops in cooperation with Prof. Dr. Walther Paravicini.
Transition from High School to College
In addressing the challenges of the transition from high school to college, the Chair collaborates with the Working Group on High School Mathematics at Saxony’s universities and the mathematics subject advisors for high schools in the state of Saxony. The areas of development currently focus primarily on the following topics: curriculum development, professional development concepts for basic mathematical knowledge, support for new teachers, and placement tests for degree programs involving mathematics. An initial press release on this topic can be found here.
This development work is based in part on preliminary work on preparatory mathematics courses conducted in cooperation with Dr. Jörn Schnieder, Prof. Dr. Walther Paravicini, and Andreas Fest (see Publications).