The paper presented relates to a study done examining the ability of children from grades one through six to locate a point in one, two, and three dimensions and to order a temporal series of events in one, two, and three dimensions. The performance of the subjects was also used to examine a small part of Piaget's theory of cognitive development.…

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 materials 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…

In this report, the theoretical background and procedures for a study of concept learning are discussed. Several definitions of the term "concept" are analyzed, and the relations among concepts, chains of concepts, and hierarchies of concepts are explored. Conceptual learning is discussed from several points of view, and axiom systems for the…

In this volume, the results of a study of concept learning are presented. (The background for the study, and descriptions of the treatments--rote reception, rote discovery, conceptual reception, and conceptual discovery--are provided in Part 1.) Several hypotheses concerning the effectiveness of these treatments in learning concepts and on the…

Using this guide and the four popular books noted in it, a student, working independently, will learn about some of the classical ideas and problems of topology: the Meobius strip and Klein bottle, the four color problem, genus of a surface, networks, Euler's formula, and the Jordan Curve Theorem. The unit culminates in a project of the students'…

This volume contains abstracts of 33 research papers presented at the 53rd Annual Meeting of the National Council of Teachers of Mathematics. Most papers concerned instructional strategies; fourteen were concerned with sequencing of instruction and/or hierarchical analysis of learning. Four papers dealt with strategies for reviewing and…

Reported are the results of a study to ascertain if verbal, visual-spatial, and numerical abilities were related to the learning of function concepts when taught by instructional approaches thought to be consistent with these abilities. A secondary purpose was to determine the efficacy of these approaches at the eighth grade level. Three subtests…

This teaching guide outlines a college algebra course for use in the secondary school. Units studied are: mathematical induction, functions, groups and fields, linear algebra, and limits. Special emphasis is given to the study of functions and linear algebra. Sequence, textbook references and assignments, and time allotments are suggested. Some…

A pilot study was conducted of the understanding of prospective elementary school teachers of mathematical concepts. Purposes were to test the diagnostic instrument used to measure comprehension of concepts and to determine whether American College Test mathematics scores of student teachers could be used to predict ability to understand concepts…

A series of experiments, all concerned with the topic of mathematical concept learning by the young child, were conducted. The concept mainly focused upon was that of inequalities. Five experiments were run. These are: (1) acquisition of mathematical concepts under experimental situation and in traditional pedagogical situation, (2) cued vs.…

This programmed text of self-instruction is one of a series of manuals on techniques describing procedures for planning and executing specialized work in water-resources investigations. It has been prepared on the assumption that the reader has completed standard courses in calculus and college physics and is presented in eight parts. Part I…

This article states that children in the first grade have usually not developed the thought processes which would enable them to understand the typical first-grade math curriculum. (CD)

The history of mathematics education is examined, especially as it relates to the understanding of mathematical concepts. Earlier segments of this article appear as SE 515 504 and SE 516 064. (SD)