The notion of identity is often used in mathematics education research in an attempt to link individual and social understandings of mathematical learning. In this paper we review existing research making use of the notion of identity, and we point to some of the strengths and weaknesses in the ways the notion of identity is being constructed. We propose a conceptualization of the notion which points to the fragility and instability of identification processes as embedded into discourse. We contend that a notion of identity formulated from a poststructuralist perspective and emphasising the dialectic relationship between identification and discourse offers interesting possibilities for interpretations of mathematical learning as a fragile process characterised more by discontinuities and disruptions than by continuity and stability. We further argue that a poststructuralist notion of fragile identities in action allows us to bring attention to what is normally considered as ”noise” or ”impossibilities” in our understandings of mathematics education and classroom interaction.