This study was an investigation of a standardized 8th grade Algebra I placement policy across multiple educational districts. Researchers have documented benefits of students' 8th grade Algebra I education, while others have detailed the consequences of algebra enrollment without necessary prerequisite skills. The purpose of this study was to…

The Wake County Public School System (WCPSS) in North Carolina recently addressed the issue of advancement in and equitable access to advanced mathematics. Under a recent policy, WCPSS uses a SAS-generated predicted probabilities of students' success in obtaining a passing score on the NC Algebra I End-of-Course (EOC) exam, to determine…

Guided by the principles of lesson study as applied to microteaching, this paper discusses the results and conclusions of a series of activities done by some graduate students of De La Salle University, Philippines, in an attempt to test the applicability of the lesson--Sequence and Patterns--to facilitate the transition of seventh graders from…

This article reports on a study which investigated first year university engineering students' construction of the definition of the concept of the chain rule in differential calculus at a University of Technology in South Africa. An APOS (Action-Process-Objects-Schema) approach was used to explore conceptual understanding displayed by students in…

This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

Although high school geometry could be a meaningful course in exploring, reasoning, proving, and communicating, it often lacks authentic proof and has become just another course in algebra. This article examines why geometry is important to learn and provides an outline of what that learning experience should be.

In this article, a classroom teacher discusses ambiguities in mathematics vocabulary and strategies for ELL students in building understanding. The authors note that mathematics vocabulary may be more difficult to learn than other academic vocabulary for several reasons: (1) definitions are filled with technical vocabulary, symbols, and diagrams;…

While an algebraic expression is typically assigned a regular structure, this article introduces the concept of personal structure ("Strukturierung"); here, the structuring of an algebraic expression is understood as the act of forming relationships between its parts. This concept is used for the analysis of interviews in which experts and novices…

Concern about students' math achievement is nothing new, and debates about the mathematical training of the nation's youth date back a century or more. In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the "new math" movement sought,…

The ACT College Readiness Benchmarks are the minimum ACT® college readiness assessment scores required for students to have a high probability of success in credit-bearing college courses--English Composition, social sciences courses, College Algebra, or Biology. This report identifies the College Readiness Benchmarks on the ACT Compass scale…

The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how…

Students with learning disabilities are most typically characterized as struggling readers (i.e., 80-90% of students are identified on the basis of reading failure; LD OnLine, 2008 Lerner, 1989; Lyon, Fletcher, Shaywitz, Torgesen, Wood, et al., 2001); however, as many as 50% of students with learning disabilities have IEP goals in the area of…

A plethora of laboratory studies have shown that including the study of worked examples during problem-solving practice improves learning (Sweller, 1999; Sweller & Cooper, 1985). While most worked-example research focuses on the use of correct examples, recent work suggests that asking children to explain a combination of correct and incorrect…

In this study, we build on previous work on conceptualizations of slope to suggest a framework of slope across the landscape of the mathematics curriculum. Data from multiple studies on students', teachers', and college instructors' conceptualizations of slope are revisited in light of theory on procedural versus conceptual understanding and…