Beginning with a construction problem admitting a classical solution, the authors provide other solutions based on algorithmic estimation and transformational geometry. The latter methods are generalized to suggest solutions to other problems; hints to these solutions are provided. Teacher-student discussion could lead in many directions. (SD)

This document extracts ideas from research on the teaching of algebra and geometry which might prove useful to secondary school teachers. Part I reviews research on algebra; it is divided into sections on classroom instructional practices, cognitive factors, attitudes and affective factors, problem solving, computers and calculators, and testing…

This book is a translation of a Russian text. The translation is exact, and the language used by the author has not been brought up to date. The volume is probably most useful as a source of supplementary materials for high school mathematics. It is also useful for teachers to broaden their mathematical background. Chapters included in the text…

Vector space concepts are developed by consideration of solutions for linear homogeneous equations. (SD)

Four geoboard activities for elementary school students are described. (SD)

This textbook is a third-year high school mathematics course and is the third of the series of textbooks on secondary mathematics. It completes the study of high-school algebra, trigonometry, and solid geometry. The features of this course are: (1) Reviews are carried on at frequent intervals throughout the course; (2) At the end of each chapter…

A selection of 14 tests of five cognitive factors was administered to 95 senior high school geometry students. These cognitive factors were then related to six measures of performance in mathematics and subjected to correlation analysis and stepwise regression. The findings indicated that the selected cognitive factors correlated with all measures…

THE PURPOSE WAS THE DISCOVERY AND EVALUATION OF GENERAL PROGRAMING PRINCIPLES FOR TEACHING MACHINES. THE DEVELOPMENT OF A SELF-INSTRUCTIONAL PROGRAM IN INFORMAL GEOMETRY FOR SECOND-GRADERS WAS THE FIRST STEP OF THE PROCEDURE. THE 170-ITEM PROGRAM CONSISTED OF FIVE UNITS DESIGNED (1) TO FAMILIARIZE THE CHILD WITH MACHINE OPERATION AND (2) TO TEACH…

THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE (1) MEASURING VOLUMES OF RECTANGULAR SOLIDS, RIGHT RECTANGULAR…

This study was designed to evaluate the effect of the use of mathematical logic in high school geometry on (1) achievement of students in geometry, (2) achievement of students in reasoning in geometry, (3) critical thinking of students, and (4) attitude of students toward logic deduction, and proof in mathematics. The experimental group of six…

This is Part III of the first volume of the proceedings of the Committee on the Undergraduate Program in Mathematics (CUPM) Geometry Conference, held at Santa Barbara in June, 1967. The purpose of the conference was to consider the status of geometry in colleges at the undergraduate level. The conference, attended by undergraduate mathematics…

This study explored: (1) the opinions of secondary and postsecondary faculty on what ought to be included in the secondary geometry curriculum to prepare students for selected postsecondary courses, (2) the effect of feedback of participants' responses, and (3) the reasons given by the participants to support their judgments. The original sample…

In this study Piaget's method of the clinical interview was used to examine children's understanding of rotation about apoint at three age levels (6, 7, and 8). In two half-hour sessions, subjects (N = 108) were given four tasks: (1) an adaptation of Piaget's locus and circular motion experiment, and tasks concerned with (2) the circle as a locus…

This booklet explains the historical background and construction techniques for various sets of uniform polyhedra. The author indicates that the practical significance of the constructions arises in illustrations for the ideas of symmetry, reflection, rotation, translation, group theory and topology. Details for constructing hollow paper models…