In 12 audio taped sessions, three kindergarten children engaged algebra in a teaching for understanding, thematic project. Toni, Asa, and Cornel had one-on-one lessons dealing with simple natural numbers, patterns, and relationships. Along the way, each child studied one of Toni Morrison's Who's got game books to explore repetition patterns in…

Why should prospective elementary and high school teachers study group theory in college? This paper examines applications of abstract algebra to the familiar algorithm for converting fractions to repeating decimals, revealing ideas of surprising substance beneath an innocent facade.

The algebraic concepts and major ideas that govern Newton's laws of motion can often be a challenge for the majority of ninth-grade students. Therefore, to make learning these concepts less task-oriented and more enjoyable, the author developed lessons that allow students to construct and express their understanding of these ideas through…

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

The purpose of this study is to apply the attribute hierarchy method (AHM) to a sample of SAT algebra items administered in March 2005. The AHM is a psychometric method for classifying examinees' test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance. An…

Data analysis plays a prominent role in various facets of modern life: Schools evaluate and revise programs on the basis of test scores; policymakers make decisions on the basis of information gleaned from polling data; supermarkets stock shelves on the basis of data collected at checkout lanes. Data analysis provides teachers with new tools and…

This book describes and illustrates learning paths for the mathematical concepts and skills of each grade 8 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about…

The study reported in this volume adds to the growing body of evaluation studies that focus on the use of NSF-funded Standards-based high school mathematics curricula. Most previous evaluations have studied the impact of field-test versions of a curriculum. Since these innovative curricula were so new at the time of many of these studies, students…

The purpose of this paper was to describe the process of development of assessment instruments for the Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project. The COSMIC project was a three-year longitudinal comparative study focusing on evaluating high school students' mathematics learning from two distinct…

One prohibitory component to graduation rates in college is the lack of student success in college algebra. The current national passing rate of college students enrolled in college algebra is approximately 40 percent. Lack of success in college algebra creating higher enrollments in remediation courses for students has also been linked to…

This "Third Annual Report Card" looks at improvements in the cradle-to-career educational pipeline, the areas where Boston has made modest progress but still has a great deal of work to do, and the places where observers have failed to see the gains that are needed to ensure that Boston is a city of opportunity for all. This report card…

his is the second volume of a series of textbooks on junior high-school mathematics. Like the first volume, it is organized on the principles that were stated in the preface of Book One. Geometry is the basis of the first part of this course. By actual measurement formulas are developed for finding the areas of triangles, quadrilaterals, and the…

This textbook's main objective is to provide a connecting link between the study of arithmetic and algebra, and to show how to solve problems. It seeks to show practical applications of the theory discussed. While this book was designed originally for the use of those whose educational training had been limited, it has been so remodeled as to…

This textbook is a young mathematician's guide to mathematics. The following five parts are presented: (1) Arithmetick, vulgar, and decimal, with all the useful rules; and a general method of extracting the roots of all single powers; (2) Algebra, or arithmetick in species; wherein the method of raising and resolving equations is rendered easie;…