This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)

This paper discusses the overall design of the PIXIE Intelligent Tutoring System, and more specifically a series of recent enhancements. The original system has been implemented to involve three separate phases: the offline, or model generation phase; the online, or tutoring, phase; and the analysis phase. The offline phase, which is completed…

First-year algebra high school students of various ability levels were presented lessons concerning the application of geometry theorems. The lessons varied in terms of the complexity of the examples that were shown. After the lessons, students completed a questionnaire concerning their perceptions of the lessons, and then they were tested over…

The North Carolina End-of-Course Testing Program was established to provide student, school, and school system information about achievement in high school courses. It appears that more than 40 percent of a class of students and approximately 60 percent of Algebra I students take Algebra II. Each Algebra II student took a test containing one of…

This document was developed as a resource for secondary mathematics educators. The supplemental guide is designed to help educators challenge their students and provide each student with learning experiences to help them achieve success. Chapters reflect the mathematics curriculum and within each subject, activities are listed in the common…

This book, written primarily for college students who feel uncomfortable with mathematics, attempts to provide its readers with new ways of thinking about mathematics, reading mathematics, studying mathematics, talking the language of mathematics and appreciating the power of using mathematics. Chapter 1 deals directly with the problem of math…

To provide information to support school district considerations of changes in mathematics and science instruction, three issues were considered: (1) the adequacy of the California Basic Education Data System (CBEDS) for supporting an analysis of subject matter instruction; (2) the distribution of teaching effort and student enrollments among…

Utilizing data compiled from records of 33 students who had completed Algebra I in 1974 and 1976, the study examined the California Algebra Aptitude Test (CAAT) and other possible predictors of success for freshmen students entering Algebra I in a small rural high school. The CAAT and the Iowa Test of Basic Skills (ITBS) were taken by these…

Research on routine problem solving (e.g. the typical "story" problem) was reviewed to facilitate the identification and dissemination of promising practices for teaching routine problem solving, and to provide suggestions and directions for further research in the area. Promising teaching practices which were identified included giving attention…

Instructional techniques are outlined, as utilized in a remedial algebra course offered at the Community College of Allegheny County. The paper first provides background information concerning the college, the characteristics of its students, the content of the remedial course, and the testing procedures used to place students in the course. The…

THE EFFECTS OF TWO POSTULATED COMPETITIVE CONDITIONS ON GROUPS OF RELATIVELY SLOW LEARNERS WERE EXAMINED DURING THE REPORTED RESEARCH. THE TWO COMPETITIVE CONDITIONS WERE--(1) HOMOGENEOUS GROUPING, AS OPPOSED TO HETEROGENEOUS GROUPING AND (2) PUBLIC DISPLAY OF THE PERFORMANCE OF ALL MEMBERS OF A GROUP, AS OPPOSED TO INDIVIDUALIZED FEEDBACK. FOUR…

This document provides items to assess student competencies in the mathematics skills which need to be mastered as a requisite to passing the Test of General Educational Development (GED). The items are tailored to the skills outlined in the taxonomy; two items are given for each of the 74 topics. Two multiple-choice response sheets are included,…

A series of 10 teacher-prepared Learning Activity Packages (LAPs) in advanced algebra and trigonometry, these units cover absolute value, inequalities, exponents, radicals, and complex numbers; functions; higher degree equations and the derivative; the trigonometric functions; graphs and applications of the trigonometric functions; sequences and…

A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation…

This self-study program for high-school level contains lessons on: Algebra, Powers and Roots, Geometry, and Number Series. Each of the lessons concludes with a Mastery Test to be completed by the student. (DB)