Designing and scaling up an innovation in abstract algebra

• We describe our process of designing and scaling up an abstract algebra innovation.
• We provide an example of generalizing an innovation beyond the pilot test phase.
• We describe efforts to investigate the efficacy of a curriculum innovation.

In this paper, we describe the process of designing and scaling up the TAAFU group theory curriculum. This work unfolded in three overlapping stages of research and design. The initial designs emerged along with local instructional theories as the result of small-scale design experiments conducted with pairs of students. A second stage of the research and design process focused on generalizing from the initial laboratory design context to an authentic classroom setting. The third (ongoing) stage involves generalizing to instructors (mathematicians) who were not involved in the design process. We describe each of these stages, and our efforts to investigate the efficacy of the resulting curriculum, in order to provide an illustrative example of the process of scaling up an innovation.