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During the last six years, we were engaged in professional development programme for mathematics teachers of special schools for students with intellectual disabilities (IDs). We were able to observe that mathematics teachers of students with IDs are left in a difficult situation where support in subject specific knowledge is lacking. Although the knowledge of the characteristics learners with special educational needs (SENs) as provided by psychology does help to open the door to successful teaching and learning of these students, how to teach subject content with constraints of students' disabilities is left open. This paper reports some qualitative data collected from the programme, which sorts out several key challenges in the field of mathematics education for students with IDs and demonstrates how the design science of mathematics education helps teachers to address teaching problems. Based on the data, we claim that: (a) teachers' ability to figure out milestones and intermediate learning states within a prolonged process of knowledge construction is crucial to teach students with IDs; and (b) using a design science approach to create carefully designed teaching units serves a dual role of providing teachers with teaching ideas as well as facilitating their understanding of mathematical knowledge structure.

1 from design research but also pursue particular accentuations: The first contribution (Sect. 2.2) reports on a project that positions design science between normative and descriptive theories. That is, mathematical learning opportunities have been designed from a normative viewpoint while learning processes have been explained on the basis of descriptive theories. Examples are provided that illustrate such a proceeding. The second contribution (Sect. 2.3) also reports on a developmental research project. Here, studying carefully designed teaching units is in the focus while paying explicit attention to problems that teachers face in the classroom. One main goal of the research is to help teachers to develop their mathematical knowledge and to ultimately enhance their teaching. Subsequently, in Sect. 2.4 Wittmann elaborates on the conception of empirical studies within design research that start from the mathematics involved in terms of structure-genetic didactical analyses. Particularly, bridging didactical theories and practice is pursued by collective teaching experiments. Finally, Sect. 2.5 takes up the strands presented so far and sheds light on developments of design science from a national and international perspective. Thereby, particular emphasis is assigned to design research from a learning perspective as extending characteristics from design research. The chapter ends with a summary and an outlook on further developments.