Excerpts from interviews with pupils in grades 1, 2, 3, and 6 to ascertain their interpretations of mathematical sentences and symbols are presented. Children were found to consider the equal sign as an operator symbol ("do something") and not as a relational symbol. Implications for teaching are briefly discussed. (MS)

This publication is a response to the need expressed by elementary teachers for a concise introduction to intuitive probability concepts and how they may be presented. Instruction is divided into five concept groups including: (1) basic understandings; (2) the probability of simple events; (3) the probability of compound events; (4) counting; and…

This 19-page workbook presents the elementary student with topological concepts through sequences of pictures with related questions. Generally the questions ask, "How are the pictures different?" and "How are they the same?" Several topological concepts are presented in this manner: connectivity, number of holes, closed and open curves, networks,…

The notions of topological equivalence for one-, two-, and three-dimensional figures, as well as for graphs and networks, are developed for classroom use with children between the ages of three and ten. Properties of open and closed curves are also examined. This manual, addressed to the teacher, describes several activities related to each…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functionl-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

Evaluated was grade 6 of a televised arithmetic program, "Patterns in Arithmetic." The major goal was to determine whether or not the technique of item-sampling could be incorporated into a design effective for formative curriculum evaluation. Approximately 60 classes near Madison, Wisconsin, participated in the study. Tests were administered at…

The series "Soviet Studies in the Psychology of Learning and Teaching Mathematics" is a collection of translations from the Soviet literature of the past twenty-five years on research in the psychology of mathematical instruction. Also included are works on methods of teaching mathematics directly influenced by this research. The aim of…

Reported are the results of an experimental course taught at the ninth grade level. The course included both modern and traditional topics in algebra. Presented are a rationale for the course, a list of the topics included in the course, a description of instructional techniques and methods used in presenting and developing some of the main ideas…

To investigate the efficacy of a training procedure designed to facilitate the attainment of the mathematical concept of number conservation, 43 children from grades 1 and 2 were tested for their ability to conserve. Some of the pupils were found to be nonconservers; some, transitional conservers; and some, conservers. Pupils of the first two…

Material included in this bulletin provides an overview of research studies which pertain to teaching addition and subtraction of whole numbers in the primary grades. The studies mentioned relate directly to the following questions: (1) What foundation for addition and subtraction do children have upon entering school? (2) What is the relative…

This series of booklets is designed for use by students of ninth grade general mathematics. The units are the result of experimental work done by the General Mathematics Writing Project of the National Council of Teachers of Mathematics. The series treats a variety of topics which are suitable for use with general mathematics students. Each unit…