Teaching and learning about political boundaries in an effective, engaging manner can be enriched through the use of webGIS mapping tools and spatial data. WebGIS enabled tools bring problem solving, critical thinking, and spatial analysis to education. Teaching with GIS is conducive to a multi-disciplinary, problem-solving learning environment…

We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

A holiday quilt project in a kindergarten classroom becomes a focus for exploring patterns, shapes, measurement, spatial relationships, and number sense. Cooperative group work, problem solving, and communication of mathematical ideas enhance the completion of the project. (Contains 5 figures.)

Features responses to a problem that appeared in the January, 2001 issue of this journal. The problem concerned finding all of the shape combinations of two colors of blocks in four-block combinations. (KHR)

Presents a problem of tetras made with four cubes, mathematical ideas involved in this problem, and guiding questions for teachers. (KHR)

This book introduces students to the types of problems and processes used throughout the "Reshaping Mathematics for Understanding" series. The problems in this unit deepen students' understanding of mathematics by encouraging them to clarify concepts and challenge their own assumptions. Additionally, by providing opportunities to give and follow…

Presents the Picasso Masterpiece problem to develop spatial reasoning in students. Addresses the National Council of Teachers of Mathematics (NCTM) Geometry Content Standards. (Author/NB)

Eleven activities with a puzzle consisting of 12 five-square shapes are presented, with some solutions illustrated. (MNS)

Students are asked to find different tiles that could be manufactured and show how a particular tile can be used to cover a floor. Thus, tessellations are explored. (MNS)

Spatial concepts are important to the development of many skills, including reasoning and problem solving. Here are guidelines for making geometry learning more effective for elementary-grade students. (Editor)

It is suggested that there are three levels of difficulty posing barriers to successful problem-solving performance: (1) entry into the problem; (2) basic skills; and (3) general cognitive skills. The levels are described in some detail and suggestions for instructional methods are given. (MP)

Activities designed to help pupils develop spatial abilities with cubes and right angles are presented. Instructions for manufacturing the special three-dimensional objects described are included. (MP)

Presents a methodology designed to strengthen the cognitive effects of using graphing calculators to solve polynomial equations using pattern matching, searching, and heuristics. Discusses pattern matching as a problem-solving strategy useful in the physical, social, political, and economic worlds of today's students. (DDR)

Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)