The author observes that checking the closure property is redundant for most number systems and therefore hard for students to understand. He defines several systems which are not closed, develops two concepts related to closure, and provides many related examples. (SD)

This booklet was written to provide role models for young people. Included are stories of 13 interesting women who have worked in careers that require substantial training in mathematics, with the hope of encouraging students to aspire to careers in fields using mathematics. Both contemporary and noncontemporary women are included to provide…

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

This document contains 15 research papers presented at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics. The papers are organized into four sections. In part I, four position papers by Romberg, Engelhardt, Ashlock, and Heddens reflect research ideas which underlie the Council. Part II…

This publication is intended to serve as a resource for teachers who are responsible for selecting textbooks for general mathematics courses in high school. Contained are 18 factual textbook reviews. (The reviews do not contain assessments about the quality of the books). Each review includes four parts. Part 1 contains information furnished by…

This paper presents an overview of the Comprehensive School Mathematics Program (CSMP) elementary school mathematics curriculum. The philosophy behind the program, content goals, and teaching strategies are briefly discussed. Then ways in which the program develops facility in mathematics are described in discussions of the language of arrows, in…

Examines the prediction that the ordinal property of natural number symbols is more easily learned by preschoolers than the cardinal property of natural number symbols. (Author/ED)

Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)

In the fall of 1966, the School Mathematics Study Group embarked upon a four-year longitudinal study of mathematical learning in the primary grades, the Elementary Mathematics Project (ELMA). The primary purpose of the study was to assess children's progress in learning particular mathematical ideas during the beginning school years. This volume…

In the fall of 1966, the School Mathematics Study Group embarked upon a four-year longitudinal study of mathematical learning in the primary grades, the Elementary Mathematics Project (ELMA). The primary purpose of the study was to assess children's progress in learning particular mathematical ideas during the beginning school years. This volume…

In the fall of 1966, the School Mathematics Study Group embarked upon a four-year longitudinal study of mathematical learning in the primary grades, the Elementary Mathematics Project (ELMA). The primary purpose of the study was to assess children's progress in learning particular mathematical ideas during the beginning school years. This volume…

This book is designed to introduce the reader to some fundamental ideas about probability. The mathematical theory of probability plays an increasingly important role in science, government, industry, business, and economics. An understanding of the basic concepts of probability is essential for the study of statistical methods that are widely…