This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…

This study was designed to compare the effects of the traditional teacher-centered mathematics classroom with that of a laboratory-based program, on achievement and attitudes of low-achieving seventh graders. Five teachers and 87 pupils participated in the study for 101 days. Mental ability was measured by the SRA Primary Mental Abilities Test,…

The purpose of this study was to measure the effects of tutoring low achievers on the concepts of carrying and borrowing before they were introduced in the classroom. Twelve low-achieving second-grade students were tutored on these concepts. The tutored children, along with members of two control groups, participated in a pretest covering these…

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…

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…

Reported are the results of a study designed to test the effects of a programed unit in fundamentals of logic on the ability of college capable junior high school students to verbalize mathematical generalizations. The independent variables were the presence or absence of study of the logic unit, and ability level being college capable (I.Q.…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

This is the first of the NCTM yearbooks to be written by a single author. He traces the history of the terms "variable" and "function" and discusses the meaning of functionality. The logical and psychological bases are examined followed by a general discussion of the psychology of reasoning. Two chapters outline the history of…

Expanded abstracts and critical analyses are given for each of 14 research articles. Four articles involve variables affecting student achievement and attitudes; two each on teaching abstract concepts to young children, problem solving, conservation in young children, and children's understanding of logic and mathematical relations; one on…

The purpose of this study was to test the effects of an experimental method of instruction upon the cognitive development of disadvantaged first grade children. The hypotheses formulated were: (1) there is no difference between the medians of the control and experimental groups or between the numbers of subjects in each group placing at the…

A sequence of problem solving tasks of classification of geometric forms and biological organisms based on Piaget's theory of learning were developed and tested with elementary school children. One experiment involved third grade subjects with one treatment group directed to learn both simple and hierarchical operations, a second group directed to…

This compilation consists of a collection of reports on models and studies in the area of manpower management and planning. Part One contains a doctoral dissertation, "The Application of Computer-Assisted Multi-Level Manpower Planning Models in the Federal Government" by R. J. Niehaus, which provides a comprehensive summary of the U.S.…

The procedures utilized in constructing test items designed to measure intermediate grade children's level of attainment of selected classificatory science concepts are described. Tests were prepared to measure children's level of concept mastery for 30 concepts, 10 each from the areas of biological science, earth science, and physical science.…

A model for the analysis of simple human conceptual behavior, based on the apparent similarities of human conceptual behavior and that of infrahuman subjects, is developed. A minimum definition of conceptual behavior is given: A single response, verbal or nonverbal, under the discriminative control of a group of stimuli whose parameters are…

This replication study negates Bruner's finding that older subjects (age 15 and adult) understand the mathematical concept of ratio as exemplified by comparing judgments of fullness in pairs of glasses differing in height, diameter, and water volume. Weaknesses in Bruner's design and procedure that explain the discrepancy between the two studies…