Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)

Learning to think logically and present ideas in a logical fashion has always been considered a central part of becoming a mathematician. In this paper we compare the performance of three groups: mathematics undergraduates, mathematics staff and history undergraduates (representative of a "general population"). These groups were asked to solve…

Word problems can be especially difficult for elementary students. This resource provides busy teachers with a new problem for every day of the school year. Period quizzes assess how well the students are mastering the problems. Tips for working the problems are provided to the students. This is ideal for improving math skills while giving…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for curriculum…

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

Forty-eight mathematicians in industry, business, and government replied to a questionnaire on the relative merits of the traditional undergraduate curriculum, advanced topics in pure mathematics, computer programing, additional computer science, and specialized or applied topics. They favored programing and applied mathematics, along with a…

The approach discussed intuitively illustrates how a problem can be analyzed by breaking it down into parts. The method makes extensive use of graphs of absolute value functions and is broken down into three stages. Each stage is covered in some detail. (MP)

A technique for teaching the graphing of polar coordinate equations is presented. This approach involves the use of an auxiliary graph in rectangular coordinates and is thought to aid students in understanding of problem-solving situations such as in dealing with points of intersection and determination of limits of integration. (MP)

An approach to equation solving using calculators that promotes the trial-and-error method as a useful strategy when combined with calculators is presented. The approach is specifically geared towards the secondary schools as a way of moving to harder equations that the linear and quadratic ones traditionally used. (MP)

A method of organizing data known as a stem-leaf plot is presented in detail. This method is viewed to overcome many of the disadvantages associated with the traditional methods of grouping in the frequency distribution table and provides a convenient introduction to data organization. (MP)

Materials designed to promote student investigation of factoring quadratic polynomials over the integers through using a physical model are presented. Pupils are expected to discover regularities that will permit them to factor such polynomials at the symbolic level. Worksheet masters designed for classroom use are provided. (MP)

The relationship between logic and mathematics is examined. Four basic concepts inherent in symbolic logic that are typically included in ninth- and tenth-grade mathematics programs are reviewed. Symbolic logic is advocated for all students who will study algebra and/or geometry. (MP)

Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)