research (in Sect. 2.1) and identify dimensions of variability (Sect. 2.2). Distinguishing two archetypes, 'design research with a focus on curriculum products', and 'design research with a focus on learning processes' (in Sect. 2.3), this thematic issue and the overview on achievements and challenges mainly concerns the elaboration of the latter archetype for mathematics education, where it is the dominant approach.We first characterize this approach by grounding it in background theories that require an active role of students in constructing their own knowledge (Sect. 3). This is followed by a methodological reflection on this type of design research (Sect. 4), which takes its starting point in some of the critique on design research. As generating theories is crucial for design research with a focus on learning processes, we discuss the variety of theories that play a role, and the process of developing theories in design research. We close with an overview of how those considerations play out, elucidated with reference to the contributions to this thematic issue (Sect. 5).
Design research as a research program of increasing importance in general education and mathematics education 2.1 Different origins of design researchDesign research emerged in different places, under different names (e.g., "design research", "design-based research", "design experiments", "design theories", "educational design research", and "developmental research"), and-what is more important-to serve different needs, resulting in different characteristics. In this article we use the term "design research" as a generic, symmetric term, Abstract Design research continues to gain prominence as a significant methodology in the mathematics education research community. This overview summarizes the origins and the current state of design research practices focusing on methodological requirements and processes of theorizing. While recognizing the rich variations in the foci and scale of design research, it also emphasizes the fundamental core of understanding and investigating learning processes. That is why the article distinguishes two archetypes of design research, one being focused on curriculum innovations, one being focused on developing theories on the learning processes, which is the main focus of the thematic issue. For deepening the methodological discussion on design research, it is worth to distinguish aims and quality criteria along the archetypes and elaborate achievement and challenges for the future.