This theoretical paper suggests identity as a nexus of research on affect and discourse in mathematical learning. It broadens Sfard and Prusak's (2005) discursive definition of identity by building on an analytical framework that examines positioning of students at three levels: the objects described, the interactions achieved, and the alignment with dominant discourses. The framework is exemplified on an excerpt of 7th grade students solving a problem, showing how a "gifted" identity is constructed through positioning at the three levels. At the meta-level, I propose this framework to be helpful for mapping studies of affect and discourse.