Seymour Papert, creator of LOGO, explains how he came to create this important problem-solving language and how he intended it to be used to foster learning among children. What children can do with turtle geometry (indicated to be a natural approach to mathematics) is one topic considered. (Author/JN)

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

Discusses the uses of the computer and how it can enhance teaching productivity. (RK)

Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

Many students appear to enjoy mysteries at the same level that they hate proofs. It is felt that the solutions of the two can be so alike that their diagrammatic forms will coincide. One geometry and three mystery problems involving logic for solution are presented. (MP)

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)

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)

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)

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)

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)

Changes in the elementary and junior high school mathematics curriculum that have occurred in the last 20 years and that may occur in the future are discussed. (MK)

Describes a classroom activity designed to give students hands-on experience using technology and geometric visualization, as well as to explore fractal geometry in a cooperative classroom environment. Natural phenomena is the context of these activities. Enriches understanding of Euclidean geometry and infinite sequences. Lists materials,…