REPRESENTATIONS OF MATHEMATICS TEACHING AND THEIR USE IN TRANSFORMING TEACHER EDUCATION: CONTRIBUTIONS TO A PEDAGOGICAL FRAMEWORK

Abstract

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 discussion paper for the PMENA working group on representations of mathematics teaching, Herbst, Bieda, Chazan, and González (2010) reviewed literature on the use of video records and written cases in teacher education and noted that classroom scenarios sketched as cartoon animations have begun to be utilized for those purposes, arguing that they have affordances that are distinct from those of video and written cases. That document 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 and 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 this document we complement the previous year’s review by briefly accounting for three areas of emerging scholarship: (1) information technologies that support teachers’ learning from representations of practice; (2) the particular challenge of helping prospective teachers understand students’ thinking; and (3) research and theory about what is important or possible to achieve in having prospective teachers look at or work with representations of teaching. We also describe present developments in the articulation of a pedagogical framework.