Reflections on the increasing relevance of large-scale professional development.

This paper focuses on commonalities and differences of three approaches to large-scale professional development (PD) in mathematics education, based on two studies from Germany and one from the United States of America. All three initiatives break new ground in improving PD targeted at educating 'multipliers,' and in all three cases specific design principles for successful PD are defined, implemented, and discussed. All three teams systematically investigate the success of their PD activity and thereby discuss their theoretical assumptions, research questions, methods, and results. Given the goal of scaling up, the initiatives are pilot projects due to the relatively small number of participants. The paper highlights the diversity of approaches, each including various specific strengths but also some limitations. This is done by analyzing the three studies regarding the features 'large-scale PD and scientific knowledge on it', 'goals and design of PD', 'research design and methods', and 'research results and implications'. Overall, the studies help to understand the enormous challenges of the field when aiming at large-scale PD and systematically investigating and reflecting its impact. One prominent challenge is teacher educators' double role of intervening and investigating. All three studies recommend a continued or even stronger focus on participants' practice and its challenges. It makes sense to assume that the focus on participants' practice and strengths is even more important when starting further cascades. [ABSTRACT FROM AUTHOR]