Generalization is a key aspect of doing mathematics, with policy makers recommending that it be a central component of instruction from elementary school through undergraduate mathematics. This recommendation poses serious challenges, however, given students’ difficulties in creating and expressing correct generalizations. Furthermore, how to foster productive generalization is not well understood. This symposium addresses these challenges by introducing a comprehensive framework characterizing productive mathematical generalization in grades 8–16. Four related projects across the domains of algebra, geometry and combinatorics share results on students’ generalizing activity in interview settings, identifying (a) categories of mental content making up the basis of students’ operating, and (b) categories of activity types supporting the formation of generalizations. The presentations will be followed by a discussion of the links between insight, generalizing, and justifying.

Session Type: Research Symposium