The title is that of a course with the same name, designed for teachers of mathematics. The rational for a course specifically on geometry was that "many of those currently teaching mathematics in school had little geometrical education". Teachers on the course experience geometry through problem solving, and learning to pose geometrical problems.…

Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

Two problem-solving strategies involved in finding the area of a particular square formed on a geoboard are described in detail. (MP)

The problem of inscribing a square in a semicircle and related problems are discussed. Solutions to the problems are provided. (FL)

A discussion of intuition, doubt, and surprise in mathematics arising from a problem involving rational points and lines. (RS)

Describes the idea of teaching as active learning and defines direction in mathematics teaching as action and perception. Presents an example of a mathematics classroom activity in which students are centered. (KHR)

Tesselations and n-dimensional geometry problems are reviewed. The author discusses possible models which could be used to approach and understand these special aspects of geometry. (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)

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)