This document is intended to describe several software learning environments in an order that parallels a reasonable sequence of use by students. It also describes a planned an designed, but not yet implemented, extension of these environments from the discrete to the continuous case. Each of the implemented environments was developed in…

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…

The demand for more valid and useful educational indicators has grown significantly as national, state, and local agencies have moved to improve the quality of elementary and secondary education. At the national level, there is a growing need for more systematic information about student performance in mathematics and science, about the content of…

A large body of research literature has indicated that parents exert a strong influence on their children's development of achievement attitudes. It is suggested that children's beliefs about achievement appear to be related to parents' expectations about their childrens' achievement but not to parent's attitudes regarding their own abilities and…

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 is a part of the Manitoba Mathematics Assessment Program 1987. Actual testing material and the manual for grade 12 are provided. The test (38 items) requires 75 minutes to be taken. Part A (30 items) has core items for every student and Part B has optional items on which students write only two sections (8 items) from those designated by the…

This is a part of the Manitoba Mathematics Assessment Program 1987. Actual testing material and the manual for grade 12 are provided. The test (39 items) requires 90 minutes to be taken. Part A (31 items) has core items for every student and Part B has optional items on which students write only two sections (8 items) from those designated by the…

The author states that this book was written for anyone who wants to know what calculus is all about, and that those with knowledge of some algebra and geometry should be able to understand it. That calculus should be called "slope finding" is discussed, and this term is used extensively. The book is divided into three chapters: (1) the…

This guide for teachers in the Houston schools outlines the first semester of a two-semester course on computer mathematics. Course objectives are listed, and a scope-and-sequence chart correlates topics in the course with the textbook ("Computer Programming in the BASIC Language") and suggests time allotments. An objectives-by-topic…

This guide for teachers in the Houston schools outlines the second semester of a two-semester course on computer mathematics. Course objectives are listed, and a scope-and-sequence chart correlates topics in the course with the textbook ("Computer Programming in the BASIC Language") and suggests vocabulary and time allotments. An…

The purpose of this paper is to report the research that took place during the development of the "ENRIGHT Diagnostic Inventory of Basic Arithmetic Skills." This is a criterion-referenced test designed to provide educators with information useful for changing instructional strategies based on known error patterns of students in grades 1 through 9.…

For almost 20 years, student achievement in the United States has been measured by the National Assessment of Educational Progress (NAEP) reported in recent years as "The Nation's Report Card." Based on a sample size of 25,000 students at each of three grade levels, it has provided the only data that reflect in a comprehensive way what…

Interest in state level assessment compared with national assessment is increasing in many states. This report makes 12 recommendations to the U.S. Department of Education and to the National Assessment of Educational Progress (NAEP) grantee on how state achievement data from 1990 mathematics assessments should be measured and reported by NAEP,…