Didactics of Mathematics

Mathematics is a central element of school education, and training (future) mathematics teachers is therefore an important task. The research groups in the Didactics of Mathematics contribute significantly in this context with work covering many aspects of mathematics teaching at all school levels. The Didactics of Mathematics is currently being restructured. In the process, Prof. Lisa Hefendehl-Hebeker and Prof. Hans Niels Jahnke remain at the Faculty as senior professors and have been joined in the past year by Prof. Bärbel Barzel, Prof. Andreas Büchter and Jun. Prof. Benjamin Rott.

The “Learning process and teaching research” group (Prof. Petra Scherer) conducts projects to analyse teaching processes and individual learning processes, paying particular attention to learning difficulties and dealing with heterogeneity in mathematics teaching. The head of the research group also leads the “Inclusion and Students at Risk” department of the German Centre for Mathematics Teacher Education (DZLM, funded by Deutsche Telekom Stiftung). This project is mainly concerned with the professionalisation of teaching (for example in inclusive mathematics instruction) and conceptual developments in continuing professional development for teachers, including a subproject exploring diagnostic skills among elementary and special school teachers in inclusive mathematics. Other research activities are also planned under the “Teacher Education Quality Offensive”. The research group also offers experiment mornings for elementary school classes as part of its “Maths Detectives” project. This particular offering is being extended, and the ­accompanying evaluation includes subprojects such as “Use of substantial learning environments in heterogeneous groups of learners” and “Handling heterogeneity – development and evaluation of a concept to promote mathematical learning processes in and out of school”. The other subprojects currently in progress are: “Teacher’s ­Notions regarding Negatives Prior to Instruction”, “Everyday Mathematics at Nursery – Discovering and Using Opportunities to Learn Mathematics in Picture Books”, “Learning Processes in Hetero­genous Study Groups – Analysis in Mixed Age Mathematics Classes”, and “Comparative Study about the Use of Mathematical Learning Material in Germany and Korea”.

One of the projects successfully conducted by the research group of Prof. Barzel is its cooperation with the DZLM in organising training and continuing development for multipliers, i. e., for teachers and educators who train other teachers and educators. Another is FaSMED (Improving Progress for Lower Achievers through Formative Assessment in Science and Mathematics Education), which is funded by the European Union and works to improve mathematics and natural science skills in Europe and South Africa. The group is also supervising the VisDeM (Visualisations in German and Mathematics Teaching) doctoral project in cooperation with the PH Freiburg. Other successful, long-running projects include T³ (Teachers Teaching with Technology) – a worldwide network of teacher education organisations with its focus on media-assisted teaching, KOSIMA (Contexts for Constructive Mathematics Learning) – a project in which schools, higher education and a textbook publisher jointly develop and analyse learning arrangements for the lower secondary level –, and the doctoral training group ProMatNat (Teacher Professionalism in Mathematics and Natural ­Sciences), which drew to a close in July 2014.
The research group of Prof. Büchter is contributing to the research concentration on “Language competence and learning mathematics” with its project “Examination of the interplay between linguistic and conceptual features in mathematics tasks – Empirical Analysis with Experimental Design” in collaboration with ProDaZ at the UDE (project funding by QUA-LiS NRW, the Quality and Support Agency – Regional Institute for School). As part of the research on “Material-assisted perception building in mathematics education”, a mathematics school laboratory is being set up and equipped by the end of 2014 as a basis for high-quality teaching and learning research in this area. The research group’s involvement in the “Studienverläufe” (student experience) subproject of the BMBF-funded UDE project “Focus on Educational Justice” is also being extended and deepened. Its new qualitative studies on special challenges and means of support for students in the early stages of their studies supplement the existing quantitative analyses. The leader of the research group is also intensifying work on the key topic, “Curriculum research and development”, with particular ­attention to the transition from school to higher education.

The work of Jun. Prof. Rott’s research group is dedicated to exploring mathematical problem-solving processes (with a focus on heurism and process regulation) and – in cooperation with the PH Freiburg – epistemological beliefs in relation to mathematics.

In “Epistemological Interaction Research on Mathematical Teaching and Learning Processes (EInmaL)” (research group of Prof. Heinz Steinbring), projects deal with the interpretative reconstruction of mathematical knowledge ­constructions (in elementary schools) and the professionalisation of teaching. The following subprojects are presently underway: “Testing and Evaluation of Focussed Teaching Strategies in ­Elementary Level Mathematics Classes”, “Elementary stochastic Vision in Elementary Schools – Epistemological Foundation and Empirical Testing of a Theoretical Construct”, and “Elementary School Children Interpret Visual Aids: An Epis­temological Analysis of Context and Framework Regarding the Promotion of the Visual Structuring Competence”.
In the group of Prof. Lisa Hefendehl-Hebeker, the research concentration on “Development of Algebraic Thinking for Grades 5–7” was brought to its conclusion in December 2012 with Dagmar Melzig’s dissertation. The research and development project funded by Deutsche Telekom Stiftung to mentor aspiring teachers during the basic stages of their degree programme has completed its third round and drew to a close at the end of the summer semester 2013 (running from 1 September 2009 to 31 August 2013 overall).