Mathematics is rich in visual representations. Such visual representations are the means by which mathematical patterns "are recorded and analyzed." With respect to "vocabulary" and "symbols," numerous educators have focused on issues inherent in the language of mathematics that influence students' success with mathematics communication.…

Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…

Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…

This article draws out many mathematical ideas connected with a familiar game often used by middle school teachers. (Contains 5 figures and 1 table.)

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

Pattern work is now undertaken as early as kindergarten, and both researchers and teachers have discovered that children engage in pattern work with great enthusiasm and innate ability. Having some flexibility in pattern perception and selecting mathematically useful patterns require some training, although there is nothing particularly algebraic…

This article describes an innovative lesson that uses the biography "Barbara McClintock: Alone in her Field" (Heiligman, 1994) to integrate genetics, literature, and mathematics as a context for students to investigate patterns on Indian corn. This two-day lesson requires students to estimate, collect data, identify and describe patterns,…

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

Presents a problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)

Presents three sets of polygons marked so that visually appealing designs emerge when the polygons are assembled into tessellations that cover the plane. Provides ideas for using the different sets of tiles in the classroom and reactions of the students who assembled the patterns. (AIM)

Presents an activity involving the use of students' birth dates. Activity includes a classic binary representation of numerical values. In the Green Machine, Sorting Cards, and Window Cards, students observe, describe, and analyze patterns. (PVD)