An exploratory problem is presented which involves the identification of all the ways a unit fraction with prime denominator can be written as a sum of two unit fractions. (MN)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (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)

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)

The exploration mode of content presentation is discussed. (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)

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)

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)

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)