This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

After appropriate research, 18 geometry lessons were created using a multicultural approach. The lessons were designed to replace portions of a middle grades geometry curriculum dependent upon standard textbooks, and were piloted in an independent New York City school. The study involved 46 students and lasted for six weeks. The lessons were…

Inuit children and children from an urban environment, inhabiting as they do differing spatial environments, contrasted with one another in terms of perception, representation, and the manifestation of geometric, topographic, and projective properties. The general hypothesis of this research is that the process of mathematical acculturation is…

This paper describes a classroom, instructor-led activity designed to show how graphic calculators can be used to explore coordinate geometry. The activity involves digitizing an image of a hand and transforming the image through geometrical transformations. Teaching notes and calculator instructions are included as are blackline masters. Also…

The purpose of this study is to compare the results achieved when a computer-managed learning program is used in high school mathematics classes with the results achieved when traditional teaching strategies are utilized. The control groups for Pre-algebra, Algebra 1, and Geometry received traditional classroom instruction. The intervention groups…

This report presents mathematics benchmarks organized into instructional sequences by topic. Each sequence is based upon an analysis of the order of content as it appears among a set of highly rated state standards. The report is intended to inform and guide state or district curriculum directors or others who, starting from content that is placed…

Original Russian version of this paper appeared in To Honor Roman Jakobson,'' II: The Hague, Mouton, 1967. (RS)

Criteria for a reasonable axiomatic system are discussed. A discussion of the historical attempts to prove the independence of Euclids parallel postulate introduces non-Euclidean geometries. Poincare's model for a non-Euclidean geometry is defined and analyzed. (LS)

The article is based upon the author's experiences in England and America. (JM)