This study investigates student understanding of the part-whole concept in mathematics at an independent two-year post-secondary institution in New Mexico. The mathematics portion of the Tests of Adult Basic Education (TABE) Summary Form was used as the evaluative instrument. Evidence for a lack of part-whole concept understanding as a hidden…

When students confront arithmetic or algebraic word problems, they develop ideas and notations during the processes of solving them by using various arithmetic strategies. Those ideas and notations are the basis for solving that type of problems. Is it possible to aid the development of students' algebraic thinking during their transition from…

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…

This paper presents some ideas on how to utilize TI-83 Plus calculators to perform division of one polynomial (the divided) by another polynomial (the divisor) and how that procedure might be incorporated into a college algebra lesson. Four ways to obtain the quotient and remainder when dividing a polynomial by a first-degree polynomial are…

This paper focuses on student understanding and learning of the algebraic concept--rate of change. Teachers' knowledge about their students and current literature on students' understanding is used to design and assess the instruments. Data were obtained as part of two-year research program that focused on how the study of students' understanding…

This document summarizes the results of a dissertation (M. Alford, 1999) that focused on the success of Wake County Public School System (WCPSS), North Carolina, students who failed Algebra I in 1994-1995 and retook it during the 1995 summer session or the 1995-1996 regular school year. Success was defined by three measures of student learning:…

Given two interesecting lines, the "pencil" of this interesection is the family of all lines passing through the point of intersection. Presented is a characterization of all lines both in the plane and lying in opposite sectors of the plane as determined by one of the original intersecting lines. (JP)

Paper shows that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. (Author)

The results of a study of third-graders' performance in solving certain open sentences, and implications for teaching open sentences are discussed. (DT)