Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

This longitudinal study investigated the ways in which two groups of eight students used spreadsheets to represent and solve algebra problems and related this to their previous arithmetical experiences and evolving use of symbolic language. The spreadsheet environment supported students to move from specific to general thinking. Includes story…

The standards developed for reform in mathematics education by the National Council of Teachers of Mathematics (NCTM) de-emphasize the algorithmic manipulation of mathematical symbols. The NCTM takes the position that the rapidly changing workplace is an environment that requires problem-solving skills with computers being used to perform routine…

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Stresses using the features of graphing calculators to teach parametric equations much earlier in the curriculum than is presently done. Examples using parametric equations to teach slopes and lines in beginning algebra, inverse functions in advanced algebra, the wrapping function, and simulations of physical phenomena are presented. (MAZ)

By measuring the performance of 62 students enrolled in a community college introductory algebra course, this study challenges the generally accepted assumption among mathematics instructors that mastery of arithmetic is necessary for the learning of algebra. Study subjects were 35% male, 74% Hispanic, 16% Black, 8% white, and 2% other. A pretest,…

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

Examines 8th grade units from the Connected Mathematics Project (CMP). Identifies differences in older and newer conceptions, fundamental objects of study, typical problems, and typical solution methods in algebra. Also discusses where the issue of what is new in algebra is relevant to many other innovative middle school curricula. (KHR)

Discusses police officers' use of mathematics when reconstructing an accident scene; and the history of algebra, including al-Khwarizmi's works on the theory of equations, the Rhind Papyrus, a Chinese and an Indian manuscript on systems of linear and quadratic equations, and Diophantus'"syncopated algebra." (10 references) (EK)

Uses articles on children's thinking to find out and improve student teachers' thinking about algebra and proof. (ASK)

Presented are the results from a few of the writing prompts used in a study and some of the comments made by individual students in response to specific prompts. Background of the study, an intervention strategy, and categories used (prompts, responses, applications, and explanations to peers) are discussed. (CW)

The geometry problems of finding rectangles that have numerically equal areas and perimeters knowing when the plane can be tessellated by congruent regular polygons are connected by the equation: m = 2n/(n-2). Three graphic approaches to the solution of the problem when m and n are integers are discussed. (MDH)

An activity in which students use manipulative materials to help solve simple algebraic equations using the operations of adding inverses, removing opposites, and sharing equally is presented. Directions, examples, the rationale, and cautions are included. (KR)

Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)