Finding the shortest route between two points can be approached by vector methods. Several types of matrices modelling a map of 6 cities are described. (SD)

Activities in which students make and prove conjectures and devise their own geometric axiom systems are discussed. (SD)

Described are various common misconceptions about the nature of mathematics and suggests that courses or activities based on model building might help change these. Two examples are offered. (SD)

An introductory preservice teacher activity from a typical college geometry course is presented. This activity leads the preservice teachers to specific goals, including increased geometric awareness within the everyday environment, appreciation for mathematical modeling techniques, and awareness of methods for teaching geometric concepts to…