Discusses the process of mathematical iteration, its benefits as a problem-solving technique, and how to teach it. Presents a selection of mathematical ideas and problems that can be solved and explored using iteration, along with related BASIC computer programs. (MDH)

Examines aspects of language connections in the learning of mathematics in three sections that discuss the interaction between language, symbolism, and manipulatives; emphasis on context in language development; and language connections in problem solving. Presents implications for nonnative English speakers. (MDH)

This is a reprint of an address given at the Christmas National Council of Teachers of Mathematics (NCTM) meeting in 1958. It provides a critique of elementary instruction and discusses the changes necessary. It calls for fundamental change in the concept of mathematics teaching. (PDD)

According to Kilpatrick (1987), in the mathematics classrooms problem posing can be applied as a "goal" or as a means of instruction. Using problem posing as a goal of instruction involves asking students to respond to a range of problem-posing prompts. The main goal of this article is a classification of mathematics questions created by Years 8…

The paper examined the possibility of finding out if improvements in students' problem solving performance in simultaneous linear equation will be recorded with the use of procedural and conceptual learning strategies and in addition to find out which of the strategies will be more effective. The study adopted a pretest, post test control group…

Five different methods for determining the maximizing condition for x(a - x) are presented. Included is the ancient Greek version and a method attributed to Fermat. None of the proofs use calculus. (LS)

Article gives a brief history and suggestions for the proof of the theorem that of all plane figures with a common perimeter, the circle has the maximum area. (RS)

Presents a problem on nets and polyhedra and responses to the talking club problem. (YDS)

Presents solutions to the Bike Trike problem that appeared in the April 2002 issue of this journal. (Author/NB)

Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)

The preproblem pondering strategy of "anticipate the answer" involves attempts to anticipate the form of the answer and the answer's relationship to the conditions of the problem. It draws on the skills of recognition, identification, interpretation and builds confidence.

The origins of this paper lay in making beds by putting pieces of plywood on a frame: If beds need to be 4 feet 6 inches by 6 feet 3 inches, and plywood comes in 4-foot by 8-foot sheets, how should one cut the plywood to minimize waste (and have stable beds)? The problem is of course generalized.