This Brief Report describes a secondary analysis of the solutions written by 306 second-year algebra students to four constructed-response items representative of content at this level. The type of solution (symbolic, graphical, or numerical) used most frequently varied by item. Curriculum effects were observed. Students studying from the second…

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

This study was conducted to reveal how students at university level justify their solutions to tasks with various degrees of difficulty. The study is part of a larger study of students' concept formation of limits. The mathematical area is limits of functions. The study was carried out at a Swedish university at the first level of mathematics. The…

Should all students study algebra in eighth grade? Would offering early access to algebra to all students help close the achievement gap among minority populations? Traditional educational policies that provide eighth grade algebra to selected students raise questions about equitable access to advanced opportunities for all students. Even when…

Since 1994 when the General Law of Education was issued, educational authorities have been claiming that Colombia has embarked on an "educational revolution" [""La revolucion educativa"" (n.d.). From the Colombian Ministry of Education website: http://www.mineducacion.gov.co. Retrieved 23 Nov 2004] where schools have…

Leaders in professional development have called for more learner-centered professional development opportunities for teachers. These approaches allow teachers to have some choice about the content and pedagogies on which they focus during professional development courses. This paper shares case studies of three participants from InterMath, a …

This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement…

An individualized Computer Assisted Instruction (CAI) mastery learning format was offered to sections of Fundamentals of Mathematics and Basic Algebra courses over four semesters (two academic years). The effectiveness of this method compared to a traditional lecture approach was examined in the areas of passing the course, passing the final…

The main aim of this paper is to demonstrate that new and highly effective computer-based learning tools can be designed by adhering to a simple principle: Good learning tools conform to and support the processes and structures that comprise learning. The paper first discusses the processes involved in learning cognitive skills, then describes…

This paper is the sixth in a series designed to supplement the statistics training of students. The intended audience is social science undergraduate and graduate students studying applied statistics. The purpose of the applied statistics monographs is to provide selected proofs and derivations of important relationships or formulas that students…

Focusing on the question that is being discussed in a mathematics lesson is suggested as an approach to teaching developmental mathematics at the college level. Ways in which students can be involved with the question are described. First, some contagious cliches that are used by students are given. Then a few antidotal aphorisms and educational…

This document consists of three related items. The first brief paper describes the components of a cumulative daily review program and its origins, rationale, and outcomes. The review-as-you-go (RAYG) format entails planning cumulative examinations and providing review problems each day. The procedure once was routinely used; today it is…

This project was designed to improve the graphing competency of students in elementary algebra, intermediate algebra, and trigonometry courses at Virginia Commonwealth University. Computer graphics programs were designed using an Apple II Plus computer and implemented using Pascal. The software package is interactive and gives students control…