Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

In this article, the author features "Flatland," by Edwin Abbott, a fantastic story about a square who lives in a two-dimensional world and who receives a visitor from the third dimension. Written in 1884 by a teacher-theologian who dabbled in mathematics, the novel is full of rich themes, including social class structure, the treatment of people…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

Concepts in mathematics are often universally applicable to other fields. A critical aspect for success in high school or college is the ability to transfer content knowledge from one discipline to another. This is especially true for material learned in the sciences and mathematics. Several studies have suggested that strong mathematical skills…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

Calculus students have great trouble visualizing solids of revolution and their cross sections. Illustrates the use of props in order to help students understand the solid revolution. (ASK)

Discusses the need for three-dimensional ideas in geometry. Describes a three-year sequence of projects that help develop students' spatial skills. (ASK)

Presents a ping-pong activity to teach the coordinate plane that puts students in a position to experience and relate to the coordinate plane in a manner that evokes their visual, spatial, and physical senses while linking the plane with a familiar object. (ASK)

Discusses important lessons on the mathematics of manufacturing and how curriculum content and teaching can prepare students for working. Features concepts such as the importance of spatial and geometric reasoning, problem solving, numbers and computation, and measurement. (ASK)

Presents activities where students visualize three dimensional figures, construct tables, discover patterns in the tables, and use the patterns to make predictions. (PK)

Presents activities that utilize representations of the side, front, and top views of three-dimensional configurations of blocks to develop spatial-visualization skills and aspects of the concept of function. Provides worksheets of these open-ended investigations. (MDH)

Presents activities designed to give students an opportunity to solve concrete problems involving spatial relationships and logical thinking utilizing hands-on manipulatives. Provides teacher instructions and four reproducible worksheets. (MDH)