Presents selected responses to the question "The Farmer's Dilemma" that represent the thinking of sixth-, seventh-, and eighth-grade students. Indicates that by being given the freedom to use a variety of methods, most students found at least one solution or demonstrated an understanding of the restrictions set by the problem. (ASK)

Reports a case study set in the context of a "function" curriculum approach to introductory algebra. The expectation that the teacher's actions would reflect the philosophy implied in the curriculum was not supported. The teacher gave priority to curriculum content coverage, emphasized methods and procedures, and adopted teacher-focused…

As times change, so has the role of algebra in the educational program. The Interactive Mathematics Program (IMP) offers secondary students an opportunity to learn algebra in a college preparatory sequence that combines basic skills, problem solving, and conceptual understanding while integrating algebra into a problem-based program. Designed for…

Presents five guided activities that use a graphing calculator to help students discover the fundamental theorem of algebra. Includes student worksheets and illustrates solutions. (KHR)

Presents a classification of factorable cubics and shows how the associated factor graphs determine domains of disconnected branches and furnish a skeletal framework for the number and shape of the branches. Illustrates three dimensional visualization and examines level curves and spikes of surfaces. (KHR)

Addresses a problem originally published in the September 1994 issue in an article entitled "Creative Teaching Will Produce Creative Students" by Krulik and Rudnick. Problem stated: "Find all rectangles with integral dimensions whose area A and perimeter P are numerically equal." Presents solution to a rectangular solid,…

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

Describes the two-year Transition toward Algebra project developed to help middle grade teachers experience and think through effective teaching strategies that promote a rich and positive learning environment and transition toward algebra. Teachers engaged in problem solving, discovering relationships, and translating among mathematical…

Reports on middle school students' use of dynamic physical models to interpret functions. Includes student creations of symbolic variables and function equations. (KHR)

Examines the balance model and identifies the issues that divide scientists. Describes learning situations that were the subject of the empirical study which involved 40 students in two 8th-grade classes. Shows the presence of negative numbers gave rise to many errors. Discusses the relevance of the balance model and analyzes the arguments put…

Presents an activity, "Lisa's Lemonade Stand," that actively engages students in algebraic thinking as they analyze change by investigating relationships between variables and gain experience describing and representing these relationships graphically. (YDS)

Presents a measurement problem that can be explored by students of varying ability. Discusses aspects that make it accessible in a heterogeneous class. (YDS)

Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)

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