Describes a new theoretical model of the learning process produced by the computer's strict reliance on procedure and its unique methods for managing data. The implications of this model for mathematics learning are illustrated through an experimental paradigm comparing the problem-solving skills of an expert and a novice. (MBR)

This book features a set of problems assembled to reflect the criteria of the mathematics portion of the North Carolina High School Comprehensive Test. The problems are not necessarily suited to timed situations but rather are intended for classroom use by teachers to review high school mathematics and build upon concepts and skills developed in…

The material is designed to help students build a cone model, visualize how its dimensions change as its shape changes, estimate maximum volume position, and develop problem-solving skills. Worksheets designed for duplication for classroom use are included. Part of the activity involves student analysis of a BASIC program. (MP)

The problem involves randomly breaking a stick into three pieces and using the pieces to form a triangle. The probability of getting a triangle is calculated using four different solution methods. Two unique problem interpretations are noted, and one solution method involves a BASIC program. (MP)

Two orientation problems and six sample worksheets that stimulate students to use a complete conjecture-proving sequence are shared. The view promoted is that pupils can gain experience in conjecturing and in writing proofs that mirror their logical thinking through work with a careful sequence of activities. (MP)

A discussion of a contest between the German mathematician Adam Riese and a draftsman involving the construction of as many perpendicular lines as possible in one minute leads to a review of some interesting constructions involving circles. It is suggested teachers challenge their students with the historic contest question. (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)

Three teaching ideas are presented: (1) the use of "factor cards" to teach the concept of greatest common factor; (2) examples and tools used in student graphing in three dimensions; and (3) ways to use cuisenaire rods, cubes, and flats to discover binomial expansions. (MP)

Seven activities designed to lead students to the idea that the ratio of the perimeter of a square and its diagonal is a fixed number for all squares are presented. The activities are groundwork for preparing students for the ratio between the circumference and diameter of a circle. (MP)

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)

Spatial concepts are important to the development of many skills, including reasoning and problem solving. Here are guidelines for making geometry learning more effective for elementary-grade students. (Editor)

"Pure" geometry is promoted as instructional material suitable for enriching the education of the mathematically gifted student. Examples of mathematical and logical concepts that can be highlighted with geometric presentations are given. (MP)