Introduces human graphing by having students standing on certain coordinates instead of points plotted in ink. Includes teacher tips for success and possible graphing explorations. (KHR)

Discusses the relevance of teaching algebra to all students. Issues examined include the desperate need for reform in the algebra curriculum, developing a curriculum for a broad range of people, and rethinking how mathematics courses are structured and taught. Concludes that teaching algebra to students previously unsuccessful in mathematics will…

Illustrates the qualitative nature of the differences between reform courses and traditional courses based on the types of student questions and comments generated in reform classes ranging from college algebra to multivariable calculus. (AIM)

Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

Reports on a study designed to build instructional software to improve estimation, reasoning, and problem solving skills using an animation-based tutor for algebra word problems. Concludes that estimation and the solution of simpler problems (i.e., decomposition) are effective strategies. (Author/MM)

Using Longitudinal Study of American Youth data, researchers investigated factors related to middle and high school students' learning or growth in statistics, algebra, and geometry. Results indicated substantial growth in all three content areas in both middle and high school. Factors related to student learning included student characteristics…

Considers how students' mathematical thinking evolves as a result of their actions and everyday experiences and from increasing reliance on introduced mathematical principles and representations. Exemplifies how 8- to 10-year-olds' personal representations come to face with representations involving algebraic concepts. Explores implications for…

Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Describes how students can be guided to find an explicit rule for a pattern from a recursive rule. (YDS)

Presents action research in the classroom that involves a semantic feature analysis task to help students develop reasoning skills. (YDS)

Helps students develop new insights into mathematical relationships through alternative representations. Examines patterns, symbolic, and functions approaches. (Contains 11 references.) (YDS)

Investigates problems called "cranium crackers" and focuses on number sense, logical reasoning, data analysis, geometry, measurement, and algebraic thinking. (Author/NB)

Investigates ways to analyze change in various contexts. Focuses on computer technology providing contexts for children's investigations of patterns of change and helping to develop foundational ideas of algebra and calculus. Discusses relationships between patterns of change, fundamental algebraic notions as linear and nonlinear functions, and…