Argues that reasons for teaching geometry before second-year algebra include higher student achievement and attitude and better abstract thinking. (PK)

Describes and gives patterns for polyhedra other than the Platonic and Archimedean solids. The focus is on the deltahedra, but pyramids, prisms, and antiprisms are discussed first to help describe the deltahedra. (PK)

Presents examples of visual representations helpful in understanding number relationships and the algebraic statements of these relationships. Suggests that these representations can be used by teachers to aid students in discovering number relationships and in acquiring meaning for given mathematical statements. (PK)

Recounts a classroom experience which investigated whether any integral solutions for the law of cosines would be analogous to "Pythagorean triples." Several interesting relationships were discovered. (PK)

Describes a three-week summer course for academically talented high school students which explored the integers and some classical topics from number theory. (PK)

Suggests that the mathematics curriculum for young children can grow from children's literature. Examples given encourage children to use a variety of thinking skills including classifying, forming hypotheses, selecting strategies, and creating problems. (PK)

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

Presents three traditional problems from discrete mathematics with alternative solutions and discussion of those solutions. (PK)

Offers practical tips on teaching secondary mathematics topics. The ideas are classroom-tested approaches that offer new slants on familiar subjects. The topics discussed include the interpretation of mathematical symbolism in concrete terms, ellipses, and vectors. (PK)

One method (attributed to Archimedes) of approximating pi offers a simple yet interesting introduction to one of the basic ideas of numerical analysis, an iteration sequence. The method is described and elaborated. (PK)

Describes a study of the use of certain curriculum materials (SMP 11-16) with a third-year class of low attainers in mathematics. The study involved classroom observation and a student questionnaire. It was concluded that the materials were at least partially successful. (PK)

Describes an installation of Comprehensive Instructional Management System (CIMS), a management information system for the instruction of mathematics in a New York school system. Suggests that CIMS has yielded dramatic gains in mathematics performance. (PK)

This study describes the development and application of a needs assessment measure used to evaluate two inservice courses for Israeli mathematics teachers. Reliability and validity checks are presented through factor analysis, Cronbach alpha coefficents, and comparing instrument results with teachers' written comments. (BS)

What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

Principles on which the teaching of mathematics is based are discussed. Sections concern the skill principle, the curriculum principle, and learning strategy, with many classroom illustrations. (MNS)