This book presents innovative approaches and state-of-the-art empirical studies on mathematics teacher learning. It highlights the advantages and challenges of such tools as classroom videos, concept cartoons, simulations, and scenarios. The book details how representations of practice encourage and afford professional development, and describes how these tools help to investigate aspects of teacher expertise, beliefs, and conceptions.  In addition, the book identifies the methodological challenges that can emerge and the obstacles educators might encounter when using representations of practice. The book examines the nature of these challenges and provides suggestions for solving them. It offers a variety of different approaches that can help educators to develop professional learning activities for prospective and in-service teachers.