Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

This activity involved constructing parallelograms on the sides of an arbitrary triangle and discovering a relationship between the areas of the parallelograms. (MP)

A number of traditional topics covered in school mathematics are examined, their origins discussed, and justifications sought for teaching them today. (MP)

Two well-known theorems from geometry are shown to be essentially the same using the principle of duality of lines and points. (MP)

Six conjectures are established concerning a rectangular solid with the lengths of all its face diagonals and the lengths of all its edges being positive integers. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

This model is useful in identifying specific learning problems and in providing techniques for the teacher to motivate and teach students at all levels. What it is and how it can be used are discussed, illustrated by specific strategies for geometry and science. (MNS)

Geometric analysis of a cube can motivate formulae for factoring algebraic expressions involving sums and differences of cubes. (SD)

After a brief discussion of the history of mathematical astronomy, the author introduces problems concerning aspects and distances of the planets. The problems presented can be solved without use of trigonometry. (SD)