How the concept of function sheds new light on one of the central tasks of algebra, that of solving equations, is discussed. Many specific examples are presented, and a theoretical basis is included. (MNS)

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)

By changing the Euclidean metric definition, a new geometry is developed. Properties of figures are analyzed and theorems are proven in this new system. (DT)

An approach to teaching problem solving to preservice and in-service middle school teachers is described. They examined an unsolved question as a class research project. The process of developing the solution is detailed, and difficulties contained within the process are noted. (MP)

A class of seldom-seen real-world applications of high school mathematics is described. The problems considered are viewed as more substantial than ordinary word problems and thus are thought to require a greater commitment of time and energy. Suggestions for student extensions of the project are made. (MP)

Three closely related problems are presented, which can be solved using only the formula for circumference. It is felt the solving of these genuine problems with the mathematical tools at their command should give pupils a feeling of power and accomplishment and a sense that mathematics is a useful subject. (MP)