Discusses concerns for mathematics education research on algebra and requestions methods that focus on the Piagetian concept of cognitive obstacles. Suggests the use of computer-based environments to develop the concept of variable and offers research findings indicating that experiences working with variables in LOGO influences student…

Presents an account of the historical evolution of the definition of variable and the way the concept is currently treated in textbooks. Shares activities to promote student discussion on the use of variables as constants, as quantities that vary, and as parameters. Provides a reproducible worksheet. (MDH)

Discusses how a single problem can be utilized to discuss mathematical skills and concepts at several different levels. Presents a problem involving fractions examined at the following four levels according to the abilities of the students: (1) finding solutions; (2) identifying methods for finding solutions; (3) exploring similar examples; and…

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Explores the role that symbolic-graphical calculators can play in the current calls for reform in the mathematics curriculum. Discusses symbolic calculators and graphing calculators in relation to problem solving, computational skills, and mathematics instruction. (MDH)

The problem-of-the-week (POW) and problem-solving class openers are exemplified as methods for the integration of course-relevant problem solving into a first-year algebra classroom without sacrificing time spent on developing skills and learning concepts. Illustrated examples, as well as problem sources, are included. (JJK)

Discussed is the classroom suitability of an open learning computer microworld centered around families of quadratic equations that provides a framework for exploring questions about parabolas to establish the link between the graphical and the algebraic representations of quadratic equations. (JJK)

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

Why should schools have a Family Math Night? It helps students learn essential math concepts. It gives parents a chance to serve as models of motivation, persistence and competence. It promotes math success in a supportive setting. With its step-by-step directions and suggestions for both teachers and parents, this book takes the worry out of…

This report summarizes evaluation results of the 2005-2006 Dell Math Academy Program at 5 high schools and 1 middle school in AISD.

Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at…

Recent changes in national and state mathematics standards have increased the level of algebraic thinking taught in younger grades. These changes have prompted more inclusive curriculum designs that open the opportunity to enroll in advanced mathematics courses at younger ages. Of particular interest to this study is the access to eighth-grade…

Alternative mathematical items administered as prototypes at the spring 1989 Field Trials of the Scholastic Aptitude Test (SAT) are evaluated for differential item functioning (DIF) and differential speededness. Results for Algebra Placement (AP) and Student Produced Response (SPR) items are presented and contrasted with results obtained on two…

Middle school prealgebra students (n=157) learned about functions in a 20-day unit that emphasized: (1) representing problems in multiple formats, (2) anchoring learning in a meaningful thematic context, and (3) discussing problem-solving processes in cooperative groups. They produced smaller pretest-to-posttest gains on symbol manipulation tasks,…

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…