The Geometric Supposer

4	Generalization in Geometry

Michal Yerushalmy

The University of Haifa

GENERALIZATION, INDUCTION, AND CONJECTURING: A THEORETICAL PERSPECTIVE

A major obstacle in teaching plausible reasoning skills is the confusion among the terms generalization, induction, and conjecturing. First, generalization is a label for both a process and the products of this process: The process of generalization creates a generalization. This confusion is compounded by the custom of labeling the product of induction as a generalization as well. Conjectures can be developed through both induction and generalization. Second, the words generalization (in its process meaning) and induction are often used interchangeably. For example, “A further simplification ...