A Pragmatic Approach to Theorizing Interdisciplinary Design Research on Interactive Math Learning Systems: The Case of a Multimodal Algebra Learning System with Tangible User Interfaces

The design of digital curriculum resources for the teaching and learning of a mathematical concept often requires including knowledge from mathematics education early into the technological design process. In the MAL project, researchers from Human-Computer Interaction and Mathematics Education established an interdisciplinary approach to develop a Multimodal Algebra Learning system (MAL system) in order to integrate necessary knowledge from both disciplines from the beginning. This chapter presents three layers of theorizing necessary to guide the scientific research and development in such an interdisciplinary design approach. The first layer is about theorizing the notion of design. It informs theorizing on the second layer which ties the two disciplines together by a topic-specific design approach, where the MAL system serves as a boundary object whose development requires researchers to cross the boundary between the two disciplines. Within this approach, a third layer of theorizing focuses on the construction of a pragmatic theory frame for our user-centered design of the MAL system. The pragmatic theory frame is set up, philosophically grounded in pragmatism and further developed over the course of the design research leading to design guidelines. We elaborate this frame, illustrate how we applied it in the design research, and improve it by formative evaluation studies. The resulting design research path enriches and tunes design choices. With the help of the Toulmin scheme, we illustrate our local pragmatic theory that describes and predicts under which conditions the final design guidelines for the MAL system would foster teaching/learning algebra conceptually. Tying the parts together, we extract a theoretical template for the transfer.