During several years of experimentation, we accumulated a large collection of data on the analysis of problems generally encountered in algebra and on the reasoning developed by students at different levels when confronted with these problems. Analysis of this data led us to a new way of looking at differences among word problems, and to the…

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…

A discussion of some number patterns which arose from a consideration of the number of diagonals of a general polygon. (MM)

A Norman window consists of a semi-circular section mounted surmounting a rectangular section. Modifications to a simple problem are presented that assume parts of the window are made with stained glass. The goal is to maximize the level of light transmission with a fixed perimeter. (MP)

Describes an activity which introduces students to each other while introducing the concept of Cartesian coordinates. Also describes an activity for finding the least common multiple, and computer programs (with listings) for generating shapes resembling windowpanes and for determining amounts wagered in a golf game. (JN)

Work centered on open-ended problem solving was developed. Activities for students aged 14 focused on measurement of length are described, with problems on pygmies and giants. (MNS)

Good writing is seen as part of the problem-solving process and a device that can stimulate creative thought in students. Many ways of helping pupils use and refine writing skills in a mathematical context are discussed. It is felt teachers of mathematics need to see students' use of such skills. (MP)

An approach to teaching problem solving to preservice and in-service middle school teachers is described. They examined an unsolved question as a class research project. The process of developing the solution is detailed, and difficulties contained within the process are noted. (MP)

As calculators and computer use increases in mathematics education, more educators are recognizing a shift in emphasis from computation to problem solving. Ways to generate problems that can be used to develop pupil creativity and insight are suggested, and process-oriented instruction is promoted. (MP)

Details are provided about the American High School Mathematics Examination (AHSME), the American Invitational Mathematics Examination (AIME), and the USA Mathematical Olympiad (USAMO). The AIME will first be offered in 1983 as an intermediate examination between the AHSME and the USAMO. An appendix provides several sample problems. (MP)

Five reasons why graph work is effective are given, followed by suggestions for making bar, picto-, and line graphs. (MS)

A problem-posing approach is used to change a door problem that involves a linear hallway into one in which doors are in a circle. The new problem is noted to relate mathematically to concepts behind the spirograph. It is hoped the material will encourage teachers to use problem-posing. (MP)