Research
The core of the research activities consists of the development, testing and evaluation of learning environments and teaching concepts that are geared towards innovation. The development work has a systemic-evolutionary character with the aim of combining design, empirical research, teacher training and further training as well as lesson development. Under Publications you will find some publications for download.
The following research and development projects characterize the work at the Chair of Didactics of Mathematics:
School and lesson development
Mathematics teaching in heterogeneous and inclusive classes
Building on several years of research in this area, the results and concepts for teaching mathematics in heterogeneous and inclusive classes are being further developed and transferred to other school contexts and made usable. The concepts and materials developed in this process are used in teaching, in academic theses and in the design of further training courses. Parts of the overall project are carried out in close cooperation with the Carl-von-Ossietzky-Schule (community school) in Berlin Kreuzberg.
Development research at the Freie Evangelische Schule Dresden
Since 2023, the Chair of Mathematics Education has been supporting school and teaching development at the Freie Evangelische Schule Dresden with regard to differentiation and learning in heterogeneous groups. In this context, students are also involved in lesson development processes as part of their academic thesis.
Diagnosis and support
- Initiated by the GemeinschaftUnterstützt project of TU Dresden, a project on diagnosis and support in a pedagogically challenging and heterogeneous school context took place (2019-2020) in cooperation with the 139th elementary school in DD-Gorbitz. The project was carried out together with Frank Beier (ZLSB, Graduate Forum, TUD) and Elisa Wagner (Primary School Pedagogy, TUD). An article on the project can be found in the TU Dresden University Journal in issue 12/19 on page 5 below (completed).
- Design-Based Research Project: Development of a school concept for diagnosis 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 cooperation with the Carl-von-Ossietzky School - a secondary school in Berlin-Kreuzberg. The cooperation school is a community school in which joint learning is realized from the 1st to the 13th grade. Due to the status of a "community school", there is no external differentiation into G and E courses. This presents teachers with particular challenges in terms of heterogeneity and internal differentiation. In the developmental research project, teaching in the new Year 7 classes was monitored for a school year, diagnostic procedures were developed and applied, material for internally differentiated teaching was developed and a concept for creating differentiated class tests was developed and evaluated.
Development research at the Dresden University School
Since winter semester 21/22, theory-based teaching materials have been developed and implemented in cooperation with Dresden University School. Students are involved in the research and development process (research-based learning). The processes are accompanied by the University School Research Center.
Project: Building up subject-specific learning as the basis for internal differentiation in learning groups with pronounced heterogeneity - exemplified by the example of percentage calculation and the idea of proportion (completed)
This project took place in cooperation with Dirk Bresinsky and Annett Veit QUA-LiS NRW within the framework of SINUS NRW. In addition to working on a concept based on several years of research work at a Berlin community school, curricula and teaching materials were developed on the basis of theory, tested and passed on in special teacher training formats and tested for their effectiveness.
Didactics of analysis
One focus of the research work is the reorganization of analysis lessons in terms of content and methodology. Here, we are working on an overall concept for the teaching of analysis and on the question of the meaningful and fruitful integration of digital tools, also with regard to the development of ideas of the limit value. Due to the Chair's connection to the Institute of Analysis, problems relating to the transition from school to university are addressed in particular. There is cooperation in this project with the Centre for Educational Research in Mathematics and Technology(CERMAT), which is located at the University of Potsdam under the direction of Prof. Dr. Ulrich Kortenkamp. You can find some digital learning environments on the topic here.
Development of textbooks and teaching materials for mathematics lessons
The Chair is involved in many ways in the development and creation of textbooks for teaching mathematics: Some publications.
Conception and research of teacher training formats
The research and development work leads, among other things, to the development of teacher training formats. Concepts for teacher training in mathematics in Saxony have been and are being developed together with the Chair of Didactics of Mathematics at the University of Leipzig, the working group on school mathematics at the Saxon universities, the subject advisors at grammar schools and training institutions in Saxony. In particular, offers for young teachers were created to accompany the third phase of teacher training. (Previous training courses offered by the Chair).
University mathematics didactics
Understanding mathematical algorithms through tutorials and task feedback (MARTA2)
(Funded by the Digital Teaching and Learning Fund 2024/25 at TU Dresden, 9/2024 - 8/2025, together with Dr. Christian Zschalig)
Continuation of the MARTA project, which was funded in 2021/22 in the Digital Fellowship Program. It builds on the experience and expertise of the previous 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 task feedback (MARTA)
(Funded by the Digital Fellowship Program Saxony 7/21 - 12/22, together with Dr. Christian Zschalig)
The drop-out rate in mathematics is high and there are many reasons for this. The project aims to address some of the causes through a flipped classroom approach combined with formative feedback elements. Video tutorials with cognitively activating elements are designed, implemented and combined with randomized and performance-differentiated ONYX tasks including formative assessment. In terms of content, procedural knowledge elements of algebraic topics will initially be implemented in a course for teachers, which is particularly suitable for a flipped classroom approach. The resulting digital elements will be made available for other courses. The central goals are to increase feedback that is effective for learning, the independence of the students and their expectation of self-efficacy. In particular, the flipped classroom approach is intended to create space for active engagement with algebra concepts in the exercise.
Integration of material mathematical models into action-oriented teaching concepts for the mathematics teaching degree (special funding from the Society of Friends and Sponsors of TU Dresden, 10/18 - 9/19)
In cooperation with the Geometric Modelling 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 mathematics teaching students by integrating and further developing the collection of mathematical models(more).
Teaching innovations and university didactic workshops
The working group develops and tests teaching concepts for the training of future mathematics teachers. The special connection between subject training and subject-didactic training plays an important role here in order to emphasize the professional reference more strongly and to counteract the phenomenon of double discontinuity in mathematics teacher training.
The development work is based on preliminary work within the framework of the BMBF research project as part of the programme "University research as a contribution to the professionalization of university teaching - Zukunftswerkstatt Hochschullehre" SAiL-M (completed: February 2012) and on the joint conception and implementation of university didactic workshops in cooperation with Prof. Dr. Walther Paravicini.
Transition from school to university
As part of the school-university transition issue, the Chair works together with the School Mathematics Working Group of the Saxon universities and the mathematics advisors for grammar schools in the state of Saxony. The areas of development currently focus on the following topics: Curriculum development, advanced training concepts on basic mathematical knowledge, support for young teachers and entrance tests for degree programs containing mathematics. An initial press release on the topic can be found here.
The development work is based in part on preliminary work on mathematical pre-courses, which took place in cooperation with Dr. Jörn Schnieder, Prof. Dr. Walther Paravicini and Andreas Fest (see publications).