In this study with four sections of preservice teachers, both spatial visualization and cognitive development correlated significantly with achievement. However, in an analysis of variance, only cognitive development was significant, and no interaction was found. Spatial visualization was greater at the end of the geometry course than at the…

Describes techniques intended to provide the teacher (or student) with insights to the solution of the problems of constructibility of squares of area c and determination of the numbers of squares, and a method for the construction of constructible integers of area c. (DS)

A discussion of the reasons for the new design of international standard typing paper (AY) with dimensions of 210 mm by 297 mm leads to a discussion of the ratio of the sides and geometric concepts involving similar rectangles. (MP)

The nature and contents of a school's mathematics exhibition is discussed. It is presented to show what was done and to serve as a rough guide for others. The program was viewed as a very successful venture. (MP)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

Teachers are encouraged to have pupils examine the symmetry of crystals when instruction is given on three-dimensional geometry and polyhedra. Crystals are noted to provide students with three-dimensional applications of transformational geometry, and the pupils also learn mineral identification. Suppliers of mineral models and specimens are…

The construction of a pentagon is divided into three problems, designed to enhance the traditional high school geometry class. The material is seen to serve as a potential springboard for many other activities. It is felt most students could not realistically be expected to solve the third problem by themselves. (MP)

The unmarked protractor appears to have been ignored in considerations of construction tools other than the standard straightedge and compass. Some geometric problems are presented which are designed to be done using only the unmarked protractor. They are thought to provide challenges to better students. (MP)

Ways different subsets of a large set of geometric shapes can be applied to the development of concepts and skills appropriate for children from preschool through the primary grades are presented. It is suggested teachers consider their curriculum and textbook while selecting specific activities to use. (MP)

An approach to the instruction of maxima and minima problems that works with tools of geometry and algebra is presented. The focus is on a classic pie-cutting problem, which is viewed as an interesting and instructive task that is an excellent application of transformation geometry. (MP)

Details of a class exploration of graphs that drew upon knowledge about the behavior of particular kinds of functions and applied them in a new context are provided. (MP)

Some methods of proof of traditional algebra problems using geometric methods are explored. The techniques used come from the original Greek approaches to these mathematical questions. (MP)

In a classroom investigation of the teaching of transformation geometry, an attempt was made to generate aptitude-treatment interactions by using various teaching methods among groups of students. (CJ)

Helping students notice the geometric shapes and symbols around them and in the world's cultures is a fascinating way to make mathematics meaningful. (Editor/SJL)

The development of the new mathematics curriculum of the late 1950s is examined in light of current calls for changes in the instructional program. Thoughtful, imaginative reform that offers radically new models of approach to teaching mathematics is called for. (MP)