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…

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)

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)

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)

Investigates how students interpret and analyze multivariate data organized in tables and the nature of external visual displays that they tend to create and use for this purpose. Reports that: (1) students based their conclusions on only part of the data; (2) students did not use either efficient or sufficient visual representations; and (3)…

Students often look for real-life situations where they can apply the concepts they learn. A project of measuring the speed of moving cars demonstrates that they learn communication skills, teamwork skills, and develop patience specially when work in a group with a common purpose.

The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

This article illustrates the fact that unless tempered by algebraic reasoning, a graphing calculator can lead one to erroneous conclusions. It also demonstrates that some problems can be solved by combining technology with algebra.

Students who have particular difficulty in mathematics are a growing concern for educators. Graphic organizers have been shown to improve reading comprehension and may be applied to upper level secondary mathematics content. In two systematic replications, one randomly assigned group was taught to solve systems of linear equations through direct…

This article illustrates how problem solving can be enhanced through careful planning and problem presentation. Often, students shut down or are turned off when presented with a problem to solve. The author describes how to motivate students to embrace a problem to be solved and provides helpful prompts to further the problem-solving process.…

Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…