REPRESENTATIONS OF MATHEMATICS TEACHING AND THEIR USE IN TRANSFORMING TEACHER EDUCATION: CONTRIBUTIONS TO A PEDAGOGICAL FRAMEWORK Patricio Herbst i , Wendy Aaron ii , Kristen Bieda iii , Gloriana González iv , Daniel Chazan v Discussion document for the Working Group “Representations of Mathematics Teaching” vi (a) Brief History of the Working Group This is the second meeting at PMENA of this RMT working group. The idea of this working group emerged during a series of three-day conferences on representations of mathematics teaching held in Ann Arbor, Michigan in 2009 and 2010,(and earlier workshops in 2007 and 2008) organized by ThEMaT (Thought Experiments in Mathematics Teaching), an NSF-funded research and development project directed by Herbst and Chazan. ThEMaT originally created animated representations of teaching using cartoon characters to be used for research, specifically to prompt experienced teachers to relay the rationality they draw upon to justify or indict actions in teaching. The original workshops were conceived to begin disseminating those animations to be used in teacher development. The (Representations of Mathematics Teaching) RMT conferences in 2009 and 2010 gathered developers and users of all kinds of representations of teaching to present their work and discuss issues that might be common to them. These conferences included users of video, written cases, dialogues, photographs, comic strips, and animations. An outcome of the 2009 RMT conference was a special issue (Volume 43, issue 1, 2011) of the journal ZDM—The International Journal of Mathematics Education, guest edited by Herbst and Chazan. Outcomes of the 2010 Conference included two sessions at the 2011 NCTM Research Presession. The 2011 Conference (June 13-15) will also work toward the goal of creating events related to the use of representations of mathematics teaching in other conferences. In proposing a continuation of the working group for PMENA 2011 we are interested in continuing the discussion and work we had in Columbus during PMENA 2010 around the elaboration and investigation of a pedagogical framework for teacher development that makes use of representations of teaching and work toward an edited book on the subject. (b) Issues in the Psychology of Mathematics Education that Will Be the Focus of the Work Review of Existing Work Relating the Theme of the Working Group to the Field The use of representations of mathematics teaching, particularly those that are maintained in a digital form, calls for specialized pedagogical practices from teacher developers. They also open new areas for investigation of how future professionals learn to practice and the role that various technologies play in scaffolding that learning. In the 2010 PMENA discussion paper, Herbst, Bieda, Chazan, and González (2010) briefly reviewed the literature on the use of video records and written cases in teacher education. We also noted that classroom scenarios sketched as cartoon animations have begun to be utilized for those purposes and argued that they have affordances that are distinct from those of video and written cases (see also Herbst, Chazan, Chen, Chieu, & Weiss, 2011). We also noted existing literature on the use of written and video cases in teacher education and cited examples that concern mostly face-to-face facilitation. We argued that the increased capabilities of information technologies for creating, manipulating, and collaborating over multimedia point to a promising future for teacher development assisted by representations of practice. In the special issue of ZDM referenced above, several new articles