Number sequence patterns for counting boundaries of familiar figures are extended to higher dimensions. (JP)

Some patterns in prime numbers and their implications for general theorems are presented. Much of the material is taken from "The Strong Law of Small Numbers," an unpublished paper by Richard Kenneth Guy. (MP)

The Spirograph, a device used for artwork and designs, is utilized to explore the mathematical topics of symmetry, ratio, divisibility, and modular arithmetic. A worksheet for each topic is included along with pedagogic information and extensions and also the answer key. (JJK)

It is noted that students sometimes have the misconception that square roots of integers are evenly spaced. The difficulty seems suited to approaches with calculators and computers, and is viewed arithmetically, graphically, and algebraically. It is suggested that differences between roots of successive pairs of consecutive integers be examined…

Patterns generated by the set of natural or counting numbers are discussed. Included are quartic, odd, square, and triangular numbers. (MK)

This article first explains a "number trick" using algebra and then extends the ideas by use of a computer program. (PK)

What often catches student interest and provides needed motivation for learning is the remarkable patterns and unexpected, interesting ideas that fill mathematics. It is felt mathematics should be taught as an enchanting and multifaceted art as well as a tool and a science. (MP)

Exponential growth is examined through an example describing the number pattern formed by postage stamp issuance. Number tables and graphs are used to discover the functional relationship between the number of new stamps issued and time. (MDH)

Describes two activities to introduce or extend the concept of the natural number e. Students conduct a lottery using either a table of random numbers or a computer simulation to link experimental probability results to the theoretical probability and to the number e. (MDH)

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…

This material was produced by a task force of the National Council of Teachers of Mathematics to provide independent study projects for use in grades four through six. The major goals are as follows: (1) to encourage student research, investigation, and communication of mathematics through reporting and writing; (2) to provide activities that are…

Describes three activities to teach mathematical concepts involving probabilities related to outcomes using "Sicherman" and other dice; geometric representations of algebraic identities; and the volume of a cone. (MDH)

Forces created by the proliferation of computer hardware and software, by innovative methods of mathematical modelling and applications, by broader demographic considerations, and by schools themselves are profoundly changing the way mathematics is practiced, the way mathematics is taught, and the way mathematics is learned. In this volume, a…

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…