One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

This study was designed to (1) analyze relationships between qualitative characteristics of ability in mathematics and success in a special interest-ability algebra program at the eighth grade level and (2) develop a rating scale for teachers to use in identification of students with high potential in mathematics. The "Iowa Test of Basic…

This is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a…

The second part of Course III includes a study of probability, polynomial, rational and circular functions, and informal space geometry. The chapter on probability presents such topics as probability measure, outcome sets and events, and overview of topics studied in Courses I and II. Chapters on functions include polynomial algebra concepts and…

Studied was the interaction between curriculum treatment and selected aptitude variables as predictors of learning and transfer scores. Visualization ability was measured by a paper folding test; general reasoning ability was measured by the Necessary Arithmetic Operations Test. Geometry students (191) were assigned to treatment groups for two…

Reported are the results of a study which investigated the effect of temporal position of review through two experiments. Experiment I involved one review; Experiment II involved two reviews. In Experiment I, eighth grade students were pretested, presented with the learning task (four rules from algebra and geometry), and randomly assigned to one…

The study was designed to develop, test, and refine a model of teaching behavior for teachers of a first course in algebra. The model described five categories of teaching behavior which should be exhibited by algebra teachers. To aid in observation of these behavior categories, a modified Flanders interaction Analysis instrument was developed and…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program see ED 086 545. In this guide, the teacher is provided with objectives for…

This study investigated differences in problem-solving performance following instruction varying in the type of heuristic advice given. The subjects, 176 college students with two years of high school mathematics experience, were provided programed instruction over a three-week period in three topic areas: finite geometry, Boolean algebra, and…

One chapter of the fifth unit in this SMSG series for the general mathematics student covers the topics of writing equations, solving linear equations, using graphs to solve equations, inequalities, and solving inequalities. The second chapter discusses ratios and percents, decimal notation, decimal representation for rational numbers, rounding…

The teacher's guide for Unit 13 of this SMSG series covers the chapter on systems of sentences in two variables and the chapter on exponents and logarithms. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral…

This guidebook on minimum course content for beginning algebra covers graphing, the distance formula, slope, the slope-intercept form of the equation of a straight line, algebraic and graphic solutions to systems of equations, functions, and variation. Overall goals for the course are stated; performance objectives for each unit, a course outline,…

The first of a series of three workbook texts on beginning algebra. Designed primarily for use by lower ability mathematics students, the texts have been used by average ability students as supplementary materials. Volume 1 contains material on multiplying, prime factors, signed numbers, problem solving involving addition, subtraction, and…

This guide provides a structured program for the slow learner in mathematics grades 6-11. Suggestions for implementing the program are included. The guide is divided into the following major areas of mathematical competency: Fundamental Operations, Geometry, Measurement, Graphing, Algebra, Probability and Statistics, and Logic. Recreation is the…

The purpose of this study was to investigate the effects of providing behavioral objectives on the learning, forgetting and retention of high school algebra. A sample of 52 algebra I students was randomly divided into two classes, both of which studied a programed course of instruction written in the framework of a learning hierarchy. The measures…