- function machine
Copyright (c) 2019 Allison Dorko
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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 R2 to R3. 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.