An approach is described for teaching formulation of mathematical models to undergraduates with no modeling experience. Instruction is based on observation of successful patterns of behavior. (MP)

A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

The action in a British sporting event (bumping races) was used to motivate a simple method of computing the correlation between starting and finishing positions. The method is generalized to other situations. (SD)

Methods of constructing polyhedra models are described. (DT)

Using a staircase to introduce the concept of slope is discussed. (DT)

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)

Presented is the design of an electrical analogue of the simple pendulum--a one-dimensional oscillator resonating within a frequency range which can be generated and observed with readily available instruments. One possible study sequence is outlined. (Author/MA)

Directions are given for making a model of a three-dimensional coordinate graph. (DT)

Mathematical modelling activities related to everyday situations (e.g., traffic lights) can be used to develop probability concepts. (SD)

By considering colors as sets of wavelengths and using Boolean Algebra of sets, the effects of combining colors can be represented in a formal mathematical system. (SD)

A series of simple games can be analyzed inductively to determine strategies. Students explore possibilities, hypothesize solutions, prove their solutions correct, and then generalize to more complex games. (SD)

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (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)

Several activities consistent with the error analysis method of teaching measurement are described. These activities illustrate the method which is then discussed in some detail. (SD)