Considered is the open-ended question of the various means of marking an n-inch ruler so that the distance of any integral number of inches from 1 to n can be ascertained with a single measurement. The relationship between a sparsely marked ruler, which is one gracefully marked with the fewest number of marks, and specific discrete graphs is…

Clapping music for two performers provides the basis for a series of mathematical problems in combinatorics and group theory. A discussion provides insight about how to avoid overlooking global extrema in constrained max-min problems when solving systems of algebraic equations. (JJK)

To illustrate that the writing and utilizing of declarative language programs can be a straightforward task in a logic class, a logic system is defined and a truth-table generator and validator are implemented using PROLOG programing language. Also, using BASIC programing language, an example of a contour map is presented. (JJK)

The discrete mathematics topics of trees and computational complexity are implemented in a simple reliability program which illustrates the process advantages of the PASCAL programing language. The discussion focuses on the impact that reliability research can provide in assessment of the risks found in complex technological ventures. (Author/JJK)

Activities for teaching about the solar system, the earth's rotation, plants, pendulums, and animal adaptation are described. Included are suggestions for building scale models to illustrate the solar system's proportions and the earth's rotation speed, and for using playground swings to demonstrate pendulum motion. (PP)

Part I describes the presentation of six different proofs of the Pythagorean Theorem by groups of three students in a party atmosphere. Part II delineates the analysis behind a student conjecture concerning the area of certain closed polar-coordinate figures. Part III proposes a categorical worksheet for determining when to apply the proper rule…

Postulated here is the notion that the exploration of number patterns with calculators is a valuable mathematical learning activity that should be commenced in the primary grades. Various activities are presented that make use of the constant function key, which is available on many of the inexpensive four-function calculators. (JJK)

Examines results of a survey documenting the current state of adolescent programs in the Montessori schools of North America. Includes information on the students, adults, and physical environment of such programs, as well as the programs' enrollment, grouping, activities, and materials. (HTH)

The first idea concerns a board game similar to tic-tac-toe in which the strategy involves the knowledge of the factorization of quadratic polynomials. The second game uses the calculation of the surface areas of solid figures applying the specific examples of cigar boxes and cylindrical tin cans. (JJK)

The nine chapters of this theme issue show how, in diverse cultural settings, cooperative learning methods enhance learning and reduce frictions among learners. A second goal of these papers is to indicate how cooperative learning fits or doesn't fit in several societies. (SLD)

The focus of this article is patterns and pattern making using geometric figures. Included are sequentially planned activities for K-8 students that help them first to discover the attributes of various figures and later how to combine these figures into patterns. Finally, this information is applied to real world activities such as quilting and…

Focuses on the theme of change. Provides Web sites, CD-ROMs and software, videos, books, and magazines that are resources concerning personal, environmental, historical and social changes. Includes activities centered on change and a subject index. (AEF)

Presents resources for grades K-8, on the subject of Colonial America. Describes Web sites; CD-ROMs and software; videos; books; audios; magazines; and professional resources. Includes two articles, "Native Americans in the Colonies," and "The Golden Age of Pirates," which also highlight resources. Presents a Web activity focusing on daily life in…

Provided are student activities to introduce the geometric concepts of line symmetry and rotational symmetry as related to Hawaiian quilting patterns. Paper squares, scissors, and folding techniques afford the teacher the chance to stimulate class discussion about pattern recognition and to integrate mathematics with the cultural world outside the…