Reflecting on representations which reflect practice – a preface -- Representations of practice in teacher education and research – spotlights on different approaches -- Representations of practice to support teacher instruction: video case mathematics professional development -- A situated approach to assess teachers' professional competencies using classroom videos -- Representations of practice in a video-based in-service teacher professional development project and in its evaluation -- Concept Cartoons as a representation of practice -- Simulations as a Tool for Practicing Questioning -- Competence assessment with representations of practice in text, comic and video format.-  Examining the mathematical knowledge for teaching of proving in scenarios written by pre-service teachers -- Ceci n'est pas une pratique: A commentary -- Considering what we want to represent.

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.