Mathematical didactics focuses on the teaching and learning of mathematics within all age groups. It seeks to answer questions such as the following:

• What could, or should, students learn in mathematics education?
• How could, or should, mathematical contents be taught, how should mathematical ability be developed?
• In what way would the students' abilities and their inclination towards mathematics influence the answers with regards to the questions mentioned before?
• What would enable students to derive pleasure from mathematical activity?
• Should all students learn mathematics on all school levels? What role does mathematics play in schools preparing students for a tertiary education?
• In what way are the problems mentioned above related?

Mathematical didactics tries to find answers to such questions by

• critically investigating and justifying the contents and specific teaching aims within the framework of the general goals of mathematical education,
• conducting research on learning conditions and teaching and learning processes related to the development of suitable empirical methods and theoretical concepts,
• investigating and preparing mathematical content, with the aim of making it accessible to specific learning groups.

As you see, there is a wide range for research and development in this context, namely:

• the analysis of contents with regards to their meaning in applications,
• the analysis of contents with regards to developing concepts and understanding,
• the analysis of general mathematical practice and the creation of concepts to develop respective abilities (e.g. calculation, problem solving, and proof),
• the development of methodical instruments and of substantial educational units, as well as the research for their practical application with special reference to the quality of induced learning process,
• the analysis of the opportunities that new technologies bring, with respect to the learning or teaching of mathematics,
• the development of method for the preparation, form, and analysis of education,
• the development and evaluation of curricula,
• the development of concepts with regards to teacher-training.

Mathematics is of course the main subject of reference in mathematical didactics. But in order to fulfill its task, mathematical didactics also makes use of the results and methods of other human sciences, e.g. pedogogics, sociology, psychology, the history of science, etc. The foundation for scientific knowledge about the teaching and learning of mathematics is a specifically mathematic-didactical research. Considering different points of view, it can form an integrated picture of mathematical education, which can in turn be applied in practice.

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