This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing…

This document contains detailed directions for constructing a device that mechanically produces the three-dimensional shape resulting from the rotation of any algebraic line or curve around either axis on the coordinate plant. The device was developed in response to student difficulty in visualizing, and thus grasping the mathematical principles…

Students enjoy learning by doing and by manipulating objects. This paper describes classroom activities using rods with various lengths and different colors. The activities included are: (1) preparation of rods; (2) elementary addition and subtraction; (3) fractions; (4) concept of greater than, less than, and equals; (5) simple division and…

This survey reflects new developments in the mathematics curriculum as emphasized in the curriculum frameworks and state-adopted textbooks. The first section describes the procedure for the development of the survey and the rationale for the topics and types of questions included on the mathematics portion of the test. The second section describes…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

The purpose of this project is to help teachers of mathematics get started using the computer to aid the teaching and learning of many mathematical concepts in a meaningful way. To this end, commercially available software packages are described which are versatile, cost effective, and easy to use. A review and several lessons, including homework…

This monograph is intended to be a practical introduction to computers for K-12 mathematics teachers, describing and illustrating ways in which computer technology can be used in the teaching of mathematics. It is organized according to the major ways computers are used in classrooms, and includes activities with suggested lesson outlines, BASIC…

Studies of methods of teaching statistics are reported. Three brief texts were written for the investigations; they varied in degree of explanation of basic concepts of elementary probability. Subjects were undergraduate students at the University of Massachusetts, Amherst. None of the subjects had had previous formal exposure to probability or…

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…

Instructors in the Navy's Basic Electricity and Electronics (BE/E) schools were presented with a list of 70 mathematical skills and asked to indicate: (1) how important they were to successful BE/E school performance, and (2) whether they were prerequisite, reviewed, or taught in the schools. Also, they were asked to state the number and type of…

This book is a guide for the reinforcement of the elementary mathematics laboratory program. It uses a hands-on and activity approach with maximum involvement of the students. Reinforcement strategies for the first three phases (concrete, semiconcrete, and semiabstract) of each mathematics concept are suggested. Also included are specific job…

Approaches to helping students remember concepts in secondary mathematics are presented. The eleven points listed are: 1) distinguishing between natural and whole numbers; 2) remembering isosceles triangles have two equal sides; 3) finding all possible pairs of integral factors of a given number; 4) recalling the meaning of reflexive, symmetric,…

This study was designed to extend the schema-theoretic perspective of understanding general discourse to include graph comprehension. The sample included 204 fourth-grade and 185 seventh-grade pupils. Data were collected on achievement in reading and mathematics, sex, prior knowledge of topic, mathematical content, graphical form, and graph…

This teaching guide suggests practical ideas for encouraging mathematics talent in preschool children. It is part of a series of similar guides developed by the RAPYHT Project (Retrieval and Acceleration of Promising Young Handicapped and Talented) for educating gifted/talented handicapped children and gifted children with no handicaps. A list of…