Mathematical investigations pursued by two gifted students are presented. One is written by a boy age 9 with his follow-up at 11; he studied patterns to derive the factors for the difference of two squares. Another boy of 11 discovered formulas for slopes of tangent lines and areas under curves. (LS)

Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)

Much constructive computer and programable calculator activity can be stimulated by BASIC programs that are only three or four lines in length. This article illustrates several ideas with accompanying BASIC program, particularly related to the learning of algebraic concepts, that can be explored with both elementary and secondary mathematics…