A dialog shows how student-teacher interaction on problems can help students learn. Fifty sample problems are provided as starting points for class discussions from grade three through college. Six purposes such problems can serve are identified. A method of classroom presentation, the mathematical scavenger hunt, is discussed. (MP)

The goal is to make some suggestions that may be useful to teachers in meeting the mathematics needs of the noncollege-bound student. It is felt teachers can motivate pupils with problems that are relevant and practical. Further, teachers need to approach mathematics from a realistic point of view. (MP)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

A mathematical treatment of the relationship between driving speed and fuel efficiency is presented. The material involves applications of exponentials, logarithms, and elementary calculus, and is intended to be enrichment material for secondary and lower college mathematics classes. (MP)

A report on the early stages of a research project, The Skills and Procedures of Mathematical Problem Solving in pupils of 9-13 years (SPMPS), is given. The article explores the background to the need for such a project, both from a mathematical and pedagogical point of view. (Author/MK)

The author promotes an earlier introduction of decimals than is currently standard practice in most elementary mathematics programs. Suggested activities and related skills are reviewed. (MP)

An exercise in applied mathematics that focuses on belt drives that is suitable for senior secondary pupils is presented. Some comments on classroom use and student reactions to this lesson are included. (MP)

Mathematical problems generated by 509 middle school students who were given story-problem descriptions and asked to pose questions that could be answered using the information were examined for solvability, linguistic and mathematical complexity, and relationships within the sets of posed problems. The multiple-step data analysis scheme can be…

This study examined effects of video-based, anchored instruction and applied problems on the ability of 11 low-achieving (LA) and 26 average-achieving (AA) eighth graders to solve computation and word problems. Performance for both groups was higher during anchored instruction than during baseline, but no differences were found between instruction…

Presents two ancient problems, trisecting any angle and dividing a circle into any number of equal parts. Illustrates how to use these problems to prompt students to think broadly and creatively about problems instead of letting the apparent boundaries of the problem limit their thoughts. Combines three-dimensional solutions to the problems to…

Four surface covering games are presented. These activities are designed to help children learn to develop mathematical theories. Directions for each activity and reproducible game boards are provided. Suggestions for the use of these games are given. (CW)

Presented are two exercises on the differential geometry of curves. A generalization dealing with smoothness conditions is given that relates the two exercises. Included are the definitions, theorems, propositions, and proofs. (KR)

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

Reports examples of the behaviors, including kinetic and vocal, used to facilitate problem-solving based on observations of four seventh-grade students. Discusses the use of the behaviors in problem-solving teaching. (YP)

Investigated the effect of the choice of a model's medium (algebraic expression or computer program) on the performance of students. Student programers did not transfer the qualities of a computer program approach to their algebraic models. Provides items for five tests. (YP)