Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

The author advocates a return to the teaching of logic in the public schools. Methods of lessening student difficulties in learning are highlighted and current school projects are discussed. (MP)

After noting that accurate calculation is not the only reason for teaching arithmetic, innovative activities providing practice with basic facts, pattern spotting,'' and exploration are presented. (MS)

Details of a class exploration of graphs that drew upon knowledge about the behavior of particular kinds of functions and applied them in a new context are provided. (MP)

The problem of finding the maximum number of right angles a polygon can have, given the number of sides, is discussed in detail. (MP)

A lesson for secondary mathematics pupils on prime numbers designed to capture student interest is presented. The emphasis is on developing lessons that act as motivating forces in the classroom. (MP)

The author describes a dialogue with his three-year-old daughter about numbers. He discusses aspects of mathematics education and how his views about how students acquire mathematical knowledge have changed. (MP)