A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

Fractions and algebra are critically important components of the mathematics education of the youth. Unfortunately, however, students have typically struggled in these areas. For this reason, teachers and researchers have focused their attention on these topics for at least the past century. This article discusses what research shows regarding…

In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage,…

The racial achievement gap has been at the center of the educational debate for decades in the United States. Although disparities in educational outcomes have declined in part of the 20th century, the process has stalled in this decade. For instance, in mathematics the gap in raw scores for students aged 13 has decline from 41 points in 1978 to…

The purpose of this report is to examine results in mathematics for the ACT Educational Planning and Assessment System (EPAS) in schools nationwide. EPAS consists of three programs: EXPLORE[R] (for students in grade 8 or 9), PLAN[R] (for students in grade 10), and the ACT[R] test (for students in grade 11 or 12). The following questions are…

We face a world in which a college degree increasingly dictates the likelihood of life success. At the same time, there has been an ever increasing population of students who have not been prepared adequately through their high school education to meet the rigors of college/university-level content. The present study investigated the effects of a…

The typical path of instruction in high school algebra courses for the study of polynomial functions has been from linear functions, to quadratic functions, to polynomial functions of degree greater than two. This paper reports results of clinical interviews with an Algebra II student. The interviews were used to probe into the student's…

Mathematical meanings can be developed when individuals construct translations between algebra symbol systems and physical systems that represent one another. Previous research studies indicated (1) few high school students connect whole number manipulations to algebraic manipulations and (2) students who encounter algebraic ideas through…

This book brings together papers by scholars from around the globe on the historiography and history of mathematics and their integration with mathematical pedagogy. Of the three articles in Part 1, "Historiography and Sources", one identifies research trends in the history of mathematics, the second discusses the centrality of problems, and the…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

This paper discusses three dimensions of algebra reform: breadth, integration, and pedagogy. Breadth of algebra includes algebra as: generalizing and formalizing patterns and constraints; syntactically-guided manipulation of formalisms; study of structures abstracted from computations and relations; study of functions, relations, and joint…

This paper is a reaction to a plenary address, "A Research Base Supporting Long Term Algebra Reform?" by James Kaput (SE 057 182). Three dimensions of algebra reform identified by Kaput (breadth, integration, and pedagogy) are discussed and contrasted with the draft version of the Algebra Document from the National Council of Teachers of…

This paper is a reaction to a plenary address, "A Research Base Supporting Long Term Algebra Reform?" by James Kaput (SE 057 182). The reactions fall into three categories: comments on Kaput's dimensions of algebra reform, a brief discussion of algebra and algebra reform from the viewpoint of a curriculum developer of the Connected…

This high technology quality assurance and statistics training module is a part of the statistics unit for an algebra I or algebra II course. This module fits into high school math classes in which students compute and display measures of central tendency and variability. The module contains a description, objectives, and content outline--phase I…

The life of Fibonacci is summarized, and his importance in the development of mathematics is assessed. Several problems first solved by Fibonacci are posed. (SD)