There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

In the first part to this article, the author described three stages that he believes are effective starting points for translating familiar classroom activities into mathematics-with-information and communications technology (ICT) lessons that exploit the power of variation to focus student attention. In this second part, the author continues to…

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)

Each of the primary problems described in this article encourage children to "get into" the process of problem solving, and all can be introduced without written instructions. A demonstration by the teacher with large hands-on materials can involve all the children effectively and give him/her the opportunity to highlight key points and deal with…

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)

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 computer program named BUGGY is described. The program is designed to duplicate "traditional" student mathematical mistakes; pupils are to identify the nature of the errors the computer makes. (MP)