Discusses mathematical thinking and problems posed by seventh- grade students as part of a unit on the study of algebraic ideas. The unit involves showing how variables cause changes and also incorporates the solving of systems of equations by constructing line-graph drawings and combination charts. (AIM)

Describes some basic difficulties in early algebra and their causes and presents some strategies for overcoming them. Lists five areas as being essential foundations for learning algebra: (1) seeing the operation, not just the answer; (2) understanding the equals sign; (3) understanding the properties of numbers; (4) being able to use all numbers;…

Suggests that the differences existing between the view of algebra as a mandated course at a specified grade level and the view of algebra as a way of mathematical thinking and reasoning developed gradually over time must be positively integrated to help students develop a genuine capacity for algebraic thinking and reasoning. (AIM)

Explains big ideas in algebra that help students connect ideas with procedures in different mathematical topics to build a relational understanding of algebra. (Contains 10 references.) (YDS)

Describes a series of lessons in which 6th grade students explore notions of rates of change and their effect on the shapes of graphs. Addresses aspects of the algebra content standard for the middle grades. (YDS)

Describes an action research project conducted in eighth-grade algebra and prealgebra classes. Suggests ways in which students can use their creativity to progress from a simple solution method to a method that produces a generalization and a formula. (AIM)

Describes student work with linear and nonlinear relationships illustrating algebra skills and understanding which are important to introductory algebra. (YDS)

Presents an algebra project in which students build a dance club. Reveals how this project motivates students and makes algebra more accessible, dynamic, and relevant to their society. (ASK)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

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)

Introduces mathematical guessing games to teach algebra that motivate students in learning mathematics by stimulating their curiosity and problem-solving abilities. (ASK)

Presents sample lab activities in algebra for representing functions in concrete, tabular, graphic, algebraic, and word format. Activities described actively involve students in hands-on models. Problem-solving techniques and technology help to form algebraic-thinking skills. (AIM)

Identifies big ideas for the informal study of algebra-related topics in the middle grades including notation, variable, function, and properties of number. Suggests meaningful ways to accomplish them. (YDS)

Presents 14 problems organized into three levels of difficulty. Topics include algebra, pattern identification, probability, and geometry. Includes solutions to the problems. (DDR)