Human participants and recurrent ("connectionist") neural networks were both trained on a categorization system abstractly similar to natural language systems involving irregular ("strong") classes and a default class. Both the humans and the networks exhibited staged learning and a generalization pattern reminiscent of the…

In experiment 1, novice fourth-grade students (N = 92) who compared multiple examples that separately varied each critical aspect and then simultaneously varied all critical aspects developed better conceptual knowledge about the "altitude of a triangle" than students who compared multiple examples that did not separately vary each critical aspect…

Rats were trained to search for a food reward hidden under sawdust in the center of a square-shaped enclosure designed to force orientation on the basis of the overall geometry of the environment. They were then tested in a number of enclosures differing in shape and in size (rectangular-, double-side square-, and equilateral triangle-shaped…

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)

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