This is Part II 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. This volume contains two lectures: "The Geometric…

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

This text is one of the sequence of textbooks produced for low achievers in the seventh and eighth grades by the School Mathematics Study Group (SMSG). There are eight texts in the sequence, of which this is the last. This set of volumes differs from the regular editions of SMSG junior high school texts in that very little reading is required.…

This study was designed to determine if a group of five- and eight-year-old students' understanding of selected geometric ideas paralleled Piaget's topological, projective, and Euclidean thesis. Additional purposes were to investigate which geometric ideas the group learned easiest, and to examine the relationships between geometric understanding…

This paper presents the results of the second class to participate in the fast-paced mathematics program begun by the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University. Fast-paced mathematics classes were established to meet the needs of highly gifted junior high school students. Thirty-three students participated in the…

This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

This manual was designed for use with the second of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

This text is the third of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first of the two chapters in this text deals with equations, inequalities and radicals.…

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

This is a book of readings from the "Arithmetic Teacher" on selected topics in geometry. The articles chosen are samples of material published in the journal from its beginning in February 1954 through February 1970. The articles are of three major types. The first is classified "involvement." These articles describe geometry units in which the…

Reported is a comparison of the School Mathematics Study Group (SMSG) and Suppes' approaches to teaching informal geometry in grades three and four. Twenty-eight classes (617 students) were randomly assigned to an SMSG, Suppes, or control group. The students were from lower to middle socioeconomic backgrounds and measured at or below national…

Investigated was the relationship between teacher and student performance on selected mathematical tasks. A measure of teacher effectiveness was obtained by comparing teacher and student performance on identical geometric tasks. The sample for this study consisted of teachers and their students from 19 fifth-grade classes, designated as either…

This curriculum bulletin is one of a planned series of bulletins designed to meet the needs of teachers and supervisors who are working to improve the achievement level of mathematics in the schools. The eighty sequential units of this bulletin are organized into 3 categories - (1) Sets, number and numeration, (2) Operations, and (3) Geometry and…

A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of…

The primary goal of this study was to develop an instrument for measuring students' attitudes toward geometry at both the middle-school and the high-school levels. Sample items were solicited from both professional educators and students; from these, 67 pairs of Likert-type statements were created. These statements were tested for…