The aim of this monograph is to describe a program of research investigating the problem-solving responses of young children and to present in summary form the results of the analyses completed so far. Attention is given to characteristics of clinical studies which are thought to make the clinical method particularly useful with young children.…

Young children grow in an environment that is patterned in many different ways. These early experiences of pattern can be the basis for later understanding of the complex structures of mathematics. Teachers can structure experiences to encourage children to examine and analyze patterns, to discover symmetrical properties, to compare shapes and…

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

Instructors of 41 Navy electronics "C" courses were presented with a list of 70 mathematics skills and asked to indicate: (1) how important they were to successful course performance, and (2) whether required skills were prerequisite to, reviewed in, or taught in the course. Based on results obtained, a mathematical skills test was…

This study was conducted in order to identify some of the broad characteristics of achievement in science and mathematics by black students. A nationwide sample of nine, thirteen, and seventeen year old students was tested with a series of exercises that were developed to assess science and mathematics performance. The exercises were designed to…

THE PURPOSE OF THIS BOOK IS TO DESCRIBE LEARNING AIDS THAT MAY BE MADE BY A TEACHER OR CHILDREN FOR USE IN MATHEMATICS PROGRAMS IN THE ELEMENTARY SCHOOL. THESE AIDS ARE OF TWO TYPES--MANIPULATIVE AND VISUAL. DESCRIPTIONS IN THIS BOOK INCLUDE (1) THE PURPOSE OF THE TEACHING AID IN A MODERN MATHEMATICS PROGRAM, (2) EXAMPLES OF ITS USE, AND (3) ITS…

Six tests were constructed, four on a pictorial level and two on a symbolic level, to measure the performance of fourth-, fifth-, and sixth-grade children, in three different ability groups, on problems concerning ratios or fractions. Two variables were of interest in the four tests on a pictorial level: (a) "equal" ratio situations vs.…

This student discussion guide is intended to accompany "Explorations in Mathematics," a text for teachers. The materials in this booklet relate mainly to variables, graphs, signed numbers, logic, identities, functions and matrices. The materials were designed to be used as supplementary materials with students in grades 5 through 9. (RP)

This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…

Contained in this publication are seven items pertaining to the PMDC testing program: (1) scale and test administration directions for grade 1 and (2) for grade 2, (3) description of Hollingshead Socioeconomic Index, (4) School Profile and Class Profile Questionnaires, (5) master record forms, (6) pupil score sheet and report on the preliminary…

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…