Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical argument and empirical examples of students generalizing graphing from R[superscript 2] to R[superscript 3]. The work presented here contributes to the field by (a) drawing attention to particular cognitive activities that underpin generalization, (b) explaining empirical findings (my own and others') occurring as a result of particular cognitive activities, and (c) providing implications for influencing student cognition in the classroom.