A discussion of what constitutes proof is given. Methods of teaching proof in a more intuitive and informal way than is usually done are suggested. (MK)

The inhibiting effect of symbols on the learning of mathematics is discussed. (MK)

An inconsistency between American and British accounting methods led the author to this problem whose solution involves linear equations and geometric series. (SD)

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)

Students were given the problem: Given a deck of cards in a certain order, after how many shuffles will it return to its original order? They worked with small decks of cards to develop a general formula, but were unhappy with the results. (SD)

How the use of calculators can illuminate mathematics and improve the level of problem-solving discussion in classes is presented. (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 use of the Computer to Help In Problem Solving (CHIPS) is described, along with Small Computers Aiding Mathematical Problem-solving and Investigations (SCAMPI). Sample activities involving combinations and "shuffles" of elements are used to highlight the use of computers, with the BASIC programing language featured. (MP)

A one-to-one teaching session with a student is described and analyzed in an attempt to communicate how student attempts at discovery in mathematics can be thwarted by teachers who do not allow room for creativity. (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)

Several examples of games and enrichment activities designed to be used with calculators in an elementary school setting are presented. Some possible difficulties students may encounter while carrying out the activities are reviewed. (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)