The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)

Presents mathematical models to determine whether seven-game baseball playoff series are significantly fairer than five-game series. Compares the results obtained from the models to actual playoff results. (MDH)

Describes an experiment to determine which of four objects, hollow cylinders, solid cylinders, hollow balls, and solid balls, will reach the bottom of an inclined plane first when released simultaneously. Provides solutions to the problem and supplementary exercises. (MDH)

An open-ended data-analysis activity, prompted by a Royal Mail advertisement, explores the claim that the real cost of first class postage has fallen below the inflation rate. The activity provides realistic exercises in both arithmetic and statistical indices, and in logical interpretation of, and deduction from, the data. (JJK)

Presents illustrated examples that promote problem solving through the student's consideration of a visible predicament from a three-dimensional viewpoint rather than the typical planar perspective. Includes six student exercises involving rays, circles, quadrilaterals, and hexagons, with hints and solutions provided. (JJK)

Concepts from cognitive psychology are presented as an alternative framework to arithmetic instruction for students with disabilities. The approach, which emphasizes reasoning, communication, and problem solving, is applied to addition, division, multiplication, subtraction, and word problems. The purpose of arithmetic instruction is asserted to…

Two teachers compared eighth graders who solved math story problems using a strategies approach (several strategies), a strategies and traditional approach, or a traditional approach. Achievement test results improved with the strategies approach. Students who learned strategies considered themselves good problem solvers who liked challenge and…

A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)

Presents three problems that help students develop a repertoire of heuristics and persistence in problem solving: the water-jug problem; the missionaries-and-cannibals problem; and the census-taker problem. Discusses methods to encourage students to persist. (MDH)

Presents five activities for multiple grade levels and family use that connect mathematics and football by using the Super Bowl. Mathematical concepts involved in the activities include number sense, geometry, measurement, statistics, estimation, and problem solving. Includes reproducible worksheets. (MDH)

Presents an activity to investigate the dimensions of the maximum rectangular area given a fixed perimeter using mathematical modeling and manipulative materials. Students collect and compare data, find patterns, graph data, write functions, and discuss the meaning of the related mathematical model. Provides three reproducible worksheets for the…

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)

Describes a study that explores the relationship between affective variables and mathematics achievement among high-risk students enrolled in developmental-mathematics courses. Finds that time taken from traditional instruction in college algebra to encourage persistence and problem-solving skills enhances spatial visualization, promotes…

A study explored middle school students' (N=54) perceptions of problem difficulty, persistence, and knowledge, and use of problem-solving strategies in solving mathematical word problems. Students with learning disabilities rated problems as significantly more difficult and had a significantly lower total word problem score than both average and…

Integrating nutrition into elementary mathematics curricula can help students develop skills for healthful food choices that will prepare them for healthy adult life. Nutrition science incorporates numerous mathematical concepts and procedures. Curriculum integration provides a framework for children to apply knowledge from several disciplines and…