Based on an analysis of 90 interviews with middle-school, high-school and undergraduate students in algebra, advanced algebra, discrete mathematics, and combinatorics, we have developed a framework characterizing three major forms of mathematical generalizing: Relating, Forming, and Extending.

 

The Relating-Forming-Extending Framework distinguishes between inter-contextual forms of generalizing, in which students establish relations of similarity across problems or contexts, and intra-contextual forms of generalizing, in which students form and extend similarities and regularities within one task. Our recent PME-NA paper introduces the framework and provides examples of student reasoning across the forms of generalization.