Provides an activity as an example of how matrices can be introduced from finite graphs and how finite graphs can be analyzed by examining their matrix representations. Presents the materials, objectives, prerequisites, directions, extension activities, answers, and worksheets. (YP)

Outlines various subtraction methods, such as the decomposition method, equal-addends method, and low-stress algorithm. Describes a subtraction method by addition of complements. Discusses the advantages and disadvantages of the method. (YP)

A problem concerning circles and points from a comic strip is presented. Its solution, using coordinate geometry, is then presented. The problem demonstrates how much one can learn by looking beyond the simple or partial solutions to a problem. (MNS)

An easier-to-understand alternative to the usual proofs of inequalities in triangles is presented. (MNS)

Discusses the use of truth tables to help students establish valid or invalid conclusions under a given set of premises. Provides several inference examples using the truth table. (YP)

Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

Some uncomplicated illustrations of how probability yields results that seem in conflict with traditional intuition are given. (MNS)

The technique of using "seed problems" involves starting with a simple problem and seeing how far it leads. It may inspire different, related problems, or it may be approached with varied tools. Problems related to points and lines, pyramids, Pythagorean quadruples, and regular pentagons are discussed. (MNS)

Eight skill-oriented principles designed to assist the teacher in the everyday task of marking work are discussed. (MNS)

An approach to teaching factors and terms is offered that builds directly on students' knowledge of arithmetic. Errors arising from factor and term confusions are noted, followed by the pedagogical strategy of exploration, invention, and discovery. (MNS)

Proposes a tested approach to creating rich and powerful learning situations by modifying standard tasks into open-ended ones with multiple correct answers. Several examples of modified tasks are included in an appendix. (MKR)

Presents classroom curriculum and student projects that use dynamical systems--something that changes over time, such as weather or populations--to capture students' attention. (MKR)

Promotes the use of worked examples to help students learn and strengthen their knowledge of mathematics. Discusses modeling effective use of worked examples, formats, and benefits. (MKR)

Discusses the geometric interpretation of the roots of a quadratic equation. (MKR)

Originally written near the beginning of the "new math" movement, this article reflects on the role of student discovery, intuition, mathematics as an analytic language, and the problem of student readiness. (MKR)