Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)

An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (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)

The use of a ruler with two parallel Straight edges as a tool in geometric constructions is presented, based on ideas that are fairly standard in high school geometry courses. The constructions are seen as potential challenges that provide opportunities for inventiveness by students. (MP)

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)

These exercises are designed to expose students to the nature and effects of inflation and consumption rates. Pupils are expected to see how long it takes for costs to increase to certain levels, and how quickly various growth rates can deplete a finite resource. Worksheets suitable for duplication are provided. (MP)

A problem that is seen to allow room for student discovery and exploration is detailed. A discussion starts with an examination of the generation of a general equation for the sum of a set of consecutive integers, and leads to an exploration of more complex sums. (MP)

The unmarked protractor appears to have been ignored in considerations of construction tools other than the standard straightedge and compass. Some geometric problems are presented which are designed to be done using only the unmarked protractor. They are thought to provide challenges to better students. (MP)

Describes a mathematics trail created on the campus of Exeter Academy and in the town of Exeter, New Hampshire. A series of problems and puzzles enabled teachers to teach mathematics outdoors. Novel questions were created to permit students to look at things from a different perspective. Participants were often inspired to create questions of…

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Four specific problems are presented, discussed, and extended to illustrate how diverse instructional strategies, materials, and resources can be used to develop problem-solving skills. (MP)