Explores differences between mathematical definitions and non-mathematical definitions by contrasting three approaches to mathematical reasoning. Examines the consequences of the use of those approaches in a first course in real analysis. Analyzes students' reasoning behavior during analysis and suggests reasons for students' difficulties with the…

After describing desirable characteristics of a student's first encounter with proof, and listing skills prerequisite for the proposed lesson (knowledge of some operational systems), the author describes in detail an introductory session in which students prove consequences of commutativity and associativity for a system supposedly encountered on…

The scope and planned publications concerning a critical review of the past ten years of change in the school mathematics programs are outlined. Background material, resource materials, and reviews of books and syllabus will be included. Classroom teachers will have a major part in the survey. (LS)

A UNIT OF STUDY FOR MODERN MATH WAS DESIGNED TO ALLOW FOR A SMOOTHER TRANSITION FROM OLD TEXTBOOKS INTO THE NEW SILVER BURDETT SERIES, "MODERN ARITHMETIC THROUGH DISCOVERY." EACH CONCEPT PRESENTED IS BASED UPON FAMILIAR CONCEPTS, DEVELOPED GRADUALLY, AND DIRECTED TOWARD PARTICULAR FUNDAMENTAL PRINCIPLES. THE FIRST CONCEPT DEVELOPED IS…

TEACHER-STUDENT INTERACTIONS WERE STUDIED IN (1) A TRADITIONAL MATHEMATICS PROGRAM, AND (2) A NEW MATHEMATICS PROGRAM BASED ON PROCEDURES ASSOCIATED WITH THE PROCESS OF DISCOVERY AND INQUIRY AND THE USE OF SYMBOLIC LOGIC. FORTY CLASSES OF REGULARLY ENROLLED FOURTH-GRADE STUDENTS PARTICIPATED IN THE STUDY. DURING OBSERVATIONS OF EACH CLASS, THE…

Sampled were 309 principals and 737 teachers. Modern mathematics was taught at 76 percent of the schools. Responders indicated it was easier to place in the curriculum in schools that were not consolidated. A majority of the teachers felt it was easy to teach. (RS)

This is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a…

The second part of Course III includes a study of probability, polynomial, rational and circular functions, and informal space geometry. The chapter on probability presents such topics as probability measure, outcome sets and events, and overview of topics studied in Courses I and II. Chapters on functions include polynomial algebra concepts and…

This study interprets and evaluates elementary mathematics research literature and current teaching practice. The list contains three related documents: (11-A) gives answers from research on elementary mathematics. It is the authors synthesis and interpretation of research findings in question-and-answer format; (11-B) offers generalizations and…

This publication provides reports from several mathematics educators on the gains that have been made, and the problems still unsolved, related to curriculum activities in mathematics. Answers to certain key questions which are basic in curriculum development are explored--(1) What are the goals of teaching mathematics, (2) What mathematical…

A grammar school arithmetic textbook published in the 1890's is described. Many elements of current "modern" mathematics programs were present in this book. (SD)