Presents a technique for teaching the lower ninety percent in mathematics. Concentrates on converting English statements, both expressed and implied, into one or many mathematical statements. Emphasis on translating in a direct, piecemeal, pure, and complete manner (DPPC). This method differs from others in that it is concrete rather than…

An attempt is made to detail the nature of mathematics as perceived by mathematicians. Mathematics is viewed here as both abstract and an experimental science. The typical working mathematician is described as proceeding through problems with an attitude of discovery and examples of such an approach are given. (MP)

Teaching story problems is seen to offer opportunities for developing the problem-solving process. Four steps described by George Polya are interpreted for the classroom as: (1) Tell, (2) Show, (3) Solve, and (4) Check. The teacher's role is detailed and the process is viewed to work for all problem types. (MP)

A humorous approach to "mathematical applications" focuses on the activities of the housewife in doing domestic chores. Six "lessons" touch on the following topics: algebra, direct and indirect proportions, arithmetic progressions, trigonometry, and non-Euclidean geometry. (MP)

Four problems are given and discussed involving reflection about a line or the reflection properties of conic sections. Solutions are given. (MP)

The article seeks to illustrate that calculators and problem solving complement each other perfectly. (MK)

Methods of formulating mathematical models are discussed and problems, insights, and solutions are given. (PK)

Addresses a problem originally published in the September 1994 issue in an article entitled "Creative Teaching Will Produce Creative Students" by Krulik and Rudnick. Problem stated: "Find all rectangles with integral dimensions whose area A and perimeter P are numerically equal." Presents solution to a rectangular solid,…

Presents a measurement problem that can be explored by students of varying ability. Discusses aspects that make it accessible in a heterogeneous class. (YDS)

Discusses problem solutions for questions originally posed in the column "Food for Thought from Jay's Diner." (YDS)

Describes the entire process involved when an untried problem was presented to a group of teachers. The lessons learned from their struggles are helpful reminders that open-ended problems should be presented to high school students. (Author/NB)

Examines student solution strategies to a problem that appeared previously in this journal. (YDS)

Presents responses to the Average Days of Spring problem that appeared in the March 2002 issue of this journal. (Author/NB)

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)