Considering What We Want to Represent

Both the fields of mathematics teacher education and research on mathematics teachers have been making extensive use of representations of teaching, whether through written cases, video clips of actual practice, or a range of designed representations (like storyboards or animations with cartoon characters, e.g., Chazan and Herbst in Teachers Coll Rec 114(3):1–34, 2012). This reflection on the contributions to this monograph suggests that as mathematics educators continue to grapple with what representations of teaching are and might be, we give greater attention to the objects to which these representations, as signs, refer.