Activities used with seventh and eighth grade students in Western Australia are described. The instructor guides pupils towards experimental solutions and encourages discovery of solutions for similar and more general problems. Investigations include study and construction of polygons, polyhedra, and one and two-sided surfaces. Commercial kits are…

The author shares 12 problems he has found effective in stimulating the imagination of students. (MNS)

Geometrical probability deals with probability on infinite sample spaces where each outcome of an experiment is equally likely to occur. Geometry which identifies sample space regions and event subregions leads to a method of finding a desired probability. A collection of problems with solutions is presented. (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)

Rubik's Cube is viewed as a tool to generate student interest in applying rather sophisticated mathematics to generate some solution algorithms. Discussion begins with the creation of a notation method for the cube and develops into applications of permutations and set concepts. A special "cycle notation" is employed. (MP)

Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

Students' misconceptions in mathematics and how teaching may be directed to diagnose and eliminate these misconceptions are discussed. Four main types of misconceptions during problem-solving are noted. It is also noted that the basic mathematical processes of generalizing, representing, and explaining are used in selected student self-help…

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)

Problems designed to show the meaningful use of logarithms in the age of calculators are presented. The emphasis is placed on viewing a logarithm as an inverse operation to raising to a power. (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)

A project designed to stimulate analytical reasoning skills in elementary school students is described, with a sample of the developed exercises. The materials were found to generate and maintain an enthusiastic response from the group of gifted eight-year-olds with which they were used. (MP)

Three methods for using four-function, counting calculators for developing understanding of the meaning of square roots and operations on whole and rational numbers are described. (MP)

How the use of calculators can illuminate mathematics and improve the level of problem-solving discussion in classes is presented. (MP)

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

This study compared good and poor fourth-grade problem solvers on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…