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…

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)

Seventy fifth-grade students in Australia were observed as each solved a jigsaw puzzle. Boys obtained higher scores on a measure of cognitive style and took less time to complete the jigsaw task; the two measures were significantly correlated. Uses of tangrams are also discussed. (MNS)

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 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)

Describes three microcomputer programs that allow geology students to deform two-dimensional images on a computer screen and then to measure changes in angular relationships. Two of the programs simulate pure and simple shear and the third simulates variations in shear strain that occur in shear zones. (ML)

Science is suggested as an excellent content area for teaching primary students the creative and critical thinking skills that can help them become better problem solvers. J. P. Guilford's Structure of Intellect model and Benjamin Bloom's Taxonomy of Educational Objectives serve as the basis for developing exercises which lead to improvement of…

Reports on a study in which two spatial tests were given to science and engineering majors and to students in nursing and agriculture at Purdue University (Indiana). Scores from the tests consistently contributed a small but significant amount of success on measures of performance in chemistry. (TW)

The problem-solving skills of logical thinking, critical thinking, visualization, and communication skills are linked with some activities for students. Sample activities with logic, strategies and patterns, breaking fixed notions, open-minded problems, spatial visualization, and communication are described. (MNS)

Presents a distance and time map exercise designed as a crime scenario. Explains that students must determine whether one individual could have committed a series of crimes in a given time period. Includes graph production that gives practice in interpreting and expressing aspects of spatial information. (DK)

Reports on a study which examined the relationship between spatial ability and performance in organic chemistry. Results indicated that students with high spatial scores did significantly better on questions requiring problem solving skills, as well as on those requiring the mental manipulation of two-dimensional representations of a molecule. (TW)

Examines the hypothesis that there are preliminary stages in problem solving that are often neglected in teaching chemistry. Discusses correlations calculated between the student's ability to handle disembedding and cognitive restructuring tasks in the spatial domain and ability to solve chemistry problems. (TW)