Many ways exist to engage students without detracting from the mathematics. Certainly some are high-tech options, such as video games, online trivia sites, and PowerPoint® presentations that follow the same model as Jeopardy; but sometimes low-tech options can be just as powerful. One exciting way to connect with students is by incorporating…

The purpose of mathematics competitions, and in our case the South African Mathematics Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest and enthusiasm for mathematics and to identify the most talented mathematical minds. SAMO is organised in two divisions--a junior and a senior division--over three rounds.…

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12-15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). "Cabri-Geometry (software)," Universite de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct:…

A series of problems concerning a geoboard with "holes" is suggested. (SD)

The process that Hippasus of Metapontum (ca. 470 B.C.) may have used to discover irrational numbers is reconstructed. (MP)

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (MP)

A journal called the Ladies' Diary published from 1704 to 1841, presented mathematical problems, and solutions to the problems. The purposes of the journal are compared to those of Scientific American today. (SD)

Problems involving the generation and counting of isosceles triangles interior to a given isosceles triangle are described. (SD)

A series of maps is presented for coloring with the fewest possible colors. (SD)

A Norman window consists of a semi-circular section mounted surmounting a rectangular section. Modifications to a simple problem are presented that assume parts of the window are made with stained glass. The goal is to maximize the level of light transmission with a fixed perimeter. (MP)

Ideas and activities are presented which are designed to help students gain better understanding of area and area formulas. It is felt many pupils have developed extremely vague or false notions about the concepts, and fail to understand why areas of certain regions can be determined through linear measurement tools. (MP)

Some ways of thinking and acting geometrically are described which are related to the approach used by ancient humans. The focus is on intuitive geometric imagery, an attempt to resurrect a way of describing possible viewpoints of geometry outside of those commonly accepted. (MP)

Activities designed to lead pupils through the process of using the basic measuring and drawing devices of geometry are presented and move to the discovery of several surprising generalizations about arbitrary triangles. (MP)

The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)