Rule learning in mathematics among elementary school children is described. Samples of dialogue between experimenters and children are presented, and the concept of rule learning is described in relation to two subgroups, gifted children and "regular" ones. (MP)

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)

Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)

In workshops for teachers the author provides each participant with five sticks and challenges them to create a variety of configurations. In the process the teachers hypothesize and test a number of geometric notions. (SD)

Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (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)