Representations of classroom practice offer the chance of referring to the teachers’ professional environment both when conceiving opportunities of professional development and when investigating aspects of teacher expertise. Representations of practice can stimulate teachers’ criteria-based analysis in environments that do not bring the full pressure and action constraints of the actual classroom. In professional development and in research, approaches which use representations of practice offer prospects and encounter challenges which can be explored along the following key questions: How can representations of practice encourage pre-service and in-service teacher professional development, e.g. through stimuli for reflection, criteria-based analysis, or structured observation? How can representations of practice help to investigate aspects of teacher expertise, such as e.g. criteria-based aspects of noticing or analyzing? What kinds of methodological challenges emerge when designing opportunities for professional learning, which make use of representations of practice? How can these challenges be addressed? What methodological challenges emerge when designing research settings based on representations of practice? How can these challenges be addressed?

By aspects of teacher expertise which can be in the scope of empirical research, we mean—an understanding which is as open and inclusive as possible—teacher characteristics which may be meaningful for supporting students’ learning, such as, components of professional knowledge of mathematics teachers, views and convictions (e.g. Shulman, 1986; Ball, Thames, & Phelps, 2008; Kuntze, 2012), competence facets such as “professional vision” (Sherin & van Es, 2009), “noticing” in the sense of “selective attention” (cf. e.g. Seidel, Blomberg, & Renkl, 2013) or in the sense of “knowledge-based reasoning” (Sherin, Jacobs, & Philipp, 2011), as well as the notion of “awareness” (Mason, 2002), and specific competences of analyzing classroom situations (e.g. Kuntze, Dreher, & Friesen, 2015). Opportunities and challenges related to the use of representations of practice for supporting aspects of teacher expertise have been explored in an ICME discussion group with contributions from Orly Buchbinder, Dan Chazan, Anika Dreher, Marita Friesen, Jessica Hoth, Sebastian Kuntze, Nanette Seago, Karen Skilling & Gabriel Stylianides, Corey Webel, Bill Zahner, and Rina Zazkis. Joint publications related to the theme of this discussion group are planned for the near future.