The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

The content of the standards focusing on numbers and numeration for grades K-8 are discussed. Several activities for developing number concepts and skills are described. (YP)

This is unit three of a fifteen-unit secondary mathematics textbook. This unit contains two chapters. The first chapter discusses integers and the second chapter discusses rational numbers. Operations with both types of numbers as well as the structure of the systems are discussed. (MK)

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular…

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)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

Reviews two software packages; "Block It, An Instructional Game" and "Conquering Whole Numbers." The first is a simulation game which uses graphic representation of base-ten blocks to reinforce place value and regrouping. The second package is designed to give students in grades three through six practice in computation. (PK)

Examines the historical development of logarithm tables. Suggests that students should write computer programs to calculate logarithms. (PK)