The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

When U.S. Secretary of Education Margaret Spelling announced in March the final report of the National Mathematics Advisory Panel, created by President Bush two years ago to address concerns that many students lack essential skills to become engineers and scientists, she highlighted the importance of algebra. "The panel's research showed that…

The public and educational communities are aware of the continuing crisis in math education in our middle schools and the convergence of technologies for teaching and learning. This paper presents a case study in which iPod Touch[R] was used to help middle school students learn about algebraic equations and, in particular, the concept of slope,…

In this article we describe a project that we used in our undergraduate linear algebra courses to help our students successfully master fundamental concepts and definitions and generate interest in the course. We describe our philosophy and discuss the projects overall success.

The study of a real function of two real variables can be supported by visualisation using a Computer Algebra System (CAS). One type of constraint of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the given function and can provide very…

The purpose of this study was to examine the effects of a schema-based instructional strategy that emphasizes prealgebraic conceptualization of multiplicative relations on solving arithmetic word problems with elementary students with learning disabilities or problems (LP). Introducing symbolic representation and algebraic thinking in earlier…

This article describes several distinct approaches taken by preservice elementary teachers to solving a classic rate problem. Their approaches incorporate a variety of mathematical concepts, ranging from proportions to infinite series, and illustrate the power of all five NCTM Process Standards. (Contains 8 figures.)

The equal sign is perhaps the most prevalent symbol in school mathematics, and developing an understanding of it has typically been considered mathematically straightforward. In fact, after its initial introduction during students' early elementary school education, little, if any instructional time is explicitly spent on the concept in the later…

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

Middle-to-high school transition activities improve retention and graduation rates, reduce academic challenges, and support student social development. The purpose of this study was to investigate ninth-grade algebra I and literature/composition end-of-course test performance, attendance, and discipline in relationship to transition strategies…

This document presents a summary of changes made to the 2008 Mathematics Standard for grade 8. The table presented in this document offers a summary of the: (1) Removed Performance Objectives (POs); (2) POs Moved to a Different Grade Level; (3) POs Moved within the Grade Level or from another Grade Level; and (4) New POs.

The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless…

Preparing students from low-income, minority families to graduate is a challenge that begins as early as elementary school but becomes a particular concern at the secondary level. Low-income students are twice as likely as higher-income students to be poorly prepared for grade-level work and 1.3 times more likely to have learning disabilities,…

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…