Imagine a wooden cube painted and cut into "unit cubes." A typical activity consists of predicting the number of unit cubes with exactly three faces painted, two faces painted, etc. This article presents extensions of this activity designed to help students develop analyzing abilities and powers to generalize. (JP)

Investigated was student inability to understand mathematics across concepts, focusing on the processes by which students solve problems. In-depth clinical interviews were used with students during ninth-grade general mathematics. Mathematical abilities investigated were information gathering, generalization, reversibility, flexibility, and…

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)