This article examines the level of understanding by children (six- to seven-year-olds) of the addition and equality symbols. The article reports that about half of the subjects were unable to write the mathematical expression of simple addition while they were able to do it verbally. (YP)

This article discusses the classroom use of discovery of number pattern. Provided are examples of a table of squares, multiplications of numbers, and algebraic expressions. (YP)

Discusses the emergence of chaos as a major scientific subject and its place in historical, scientific, and technological context. Three sections provide (1) an overview of the scientific paradigm; (2) a review of the ideology of classical mechanics; and (3) examples of classical systems behaving in peculiar, nonintuitive manners. (MDH)

Presents one way, using simple materials available in hardware stores, to obtain accurate measurements of gravity acceleration in student laboratories. Analyzes a time-of-flight measuring scheme and discusses the experimental arrangements to make the measurements. (MDH)

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)

Discusses 4 numerical patterns occurring in the decimal expansions of 2 raised to a negative exponent. Includes two row patterns, one diagonal pattern, and a pattern in the sum of the digits of the expansions. Conjectures are presented for each pattern and subsequently proved. (MDH)

Discussed are properties possessed by polygons inscribed in the lattice parabola y=x, including the area of a triangle, triangles of minimum area, conditions for right triangles, triangles whose area is the cube of an integer, and implications of Pick's Theorem. Further directions to pursue are suggested. (MDH)

Traces the efforts of the Division of Continuing Studies at a large northeastern state university to regain fiscal solvency through business and leadership techniques including management by objectives, section management, and a course confirmation formula. Warns program administrators about potential problems with break-even registration…

The harmonic mean, neglected in favor of arithmetic and geometric means in modern mathematics, is defined and its historical relationship to music as presented by Pythagoras is described. Two geometric constructions present a picture of harmony, and an application in calculating the square root of a number is given. (MDH)

Doing mathematics includes the activities of making observations, searching for patterns, formulating conclusions called conjectures, and verifying these conjectures. Presented is an activity that develops pattern discovery and measurement skills using a protractor, compass, and ruler by drawing various stars. Appropriate worksheets and directions…

From the equality of the ratios of the surface areas and volumes of a sphere and its circumscribed cylinder, the exploration of theorems relating the ratios of surface areas and volumes of a sphere and other circumscribed solids in three dimensions, and analogous questions relating two-dimensional concepts of perimeter and area is recounted. (MDH)

Presents an experiment to investigate centripetal force and acceleration that utilizes an airplane suspended on a string from a spring balance. Investigates the possibility that lift on the wings of the airplane accounts for the differences between calculated tension and measured tension on the string. (MDH)

Describes software, hardware, and devices that were designed to provide students with an environment to experiment with basic ideas of mechanics, including nonlinear dynamics. Examines the behavior of a Lorenzian water wheel by comparing experimental data with theoretical results obtained from computer-based sensors. (MDH)

Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)