Students enrolled in two sections of college algebra (Math 110) at the University of Maryland in spring 1984 were informed about assistance available from the Math Lab. They were also informed that a sticker would be attached to any one of the four semester exams when grades indicated that the student should pursue one or more of the Lab services.…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

This project had three major goals: (1) investigate the extent to which introductory physics students misuse or misunderstand formulas; (2) catalogue the typical ways in which they do this; and (3) begin the larger task of identifying key types of knowledge that successful problem solvers use to give formulas meaning. Exploratory interviews and…

Robert Tinker, President of The Concord Consortium, announces that through a series of grants from the National Science Foundation (NSF) and the US Department of Education, the Concord Consortium has been able to produce amazing and innovative software packages and have incorporated them into hundreds of powerful learning activities. Whatever…

Part II of a continued article. (DD)

Author discusses how he introduced a mix of traditional and programed instructional methods to the problem of teaching algebra to a slow-track ninth grade class which contained many inner city learning problems. (Author)

Mathematical investigations pursued by two gifted students are presented. One is written by a boy age 9 with his follow-up at 11; he studied patterns to derive the factors for the difference of two squares. Another boy of 11 discovered formulas for slopes of tangent lines and areas under curves. (LS)

This book is designed to introduce the reader to some fundamental ideas about probability. It is assumed that the reader has completed chapters 1 to 7 of SMSG Introduction to Probability, Part 1. While the book is designed for junior high school students, some elementary algebra is required for a number of the exercises. The difficult exercises…

The purpose of this text is to teach learning and understanding of mathematics at grades seven through nine through the use of science experiments. Previous knowledge of science on the part of students or teachers is not necessary. The text is designed to be usable with any mathematics textbook in common use. The material can be covered in four…

These materials are intended to explain the approach adopted by the writers of the SMSG textbook, First Course in Algebra. This book is not a ninth-grade textbook or teacher's commentary. Many of the ideas presented are too difficult for most beginning students, but they are ideas which the author believes teachers should master. It is assumed…

This volume was prepared by the School Mathematics Study Group (SMSG) to help elementary teachers develop a sufficient subject matter competence in the mathematics of the elementary school program. Background material for related SMSG materials for grades four through eight are included. Chapters in the book are: (1) What is Mathematics; (2)…

Subjects were randomly assigned to a deductively structured verbal-symbolic-numeric treatment or an inductively structured verbal-spatial-numeric treatment for a unit on quadratic inequalities. Success on the deductive symbolic approach was associated with general reasoning ability; success on the inductive spatial approach was associated with…

This study was designed to compare the relative effectiveness of word problem instruction based on Polya's approach to problem solving with Dahmus' word by word translation approach. When ninth-grade students were randomly assigned to one of these approaches, no differences in mean number of problems solved were observed. (SD)

This textbook is third in a series of three volumes presenting a mathematics course for junior high school and six-year high schools. This volume covers college-preparatory algebra, trigonometry, and demonstrative geometry. [For Book I, see ED623224. For Book II, see ED623225.]

This text is based on the idea that teachers of mathematics at any level will find it advantageous to be able to point to interesting, useful, and diverse applications of the mathematics they teach. The first chapter describes several graphing techniques used for displaying data and finding meaningful relationships as a result. Subsequent chapters…