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August 2005, Volume 99, Issue 1

FEATURES

Using Open-Ended Problems for Assessments
Albert Goetz
This article describes in some depth a specific open-ended problem the author has used as a group assessment in his precalculus classes. The author utilizes cooperative learning groups during instructional class periods and during part of an exam period. Other possible problems that may be similarly used are discussed in lesser detail.

How Do We Know That's the Minimum?
Deborah Franzblau
How the author uses classic problems in discrete mathematics as a context for teaching and proof. The Map Coloring problem and the Traveling Salesman problem, two combinatorial optimization problems, are used to teach logical concepts and methods of proof.

Linking Theory and Practice in Teaching Geometry
Randall Groth
How the author used the van Hiele teaching phases to design and implement. The author used the hierarchy of five different levels of thinking during summer school instruction; holistic, analytic, abstract, deductive, and rigorous. The students successfully moved towards understanding abstractions in quadrilaterals and triangles.

Connecting Procedural and Conceptual Knowledge of Functions
Jon Davis
How teachers can promote both conceptual and procedural knowledge by connecting symbolic manipulation techniques with the real-world, tabular, and graphical representations of a linear function. Functions are used to demonstrate that students' understanding of the meaning of functions through real-world examples and other representations strengthens student ability to perform procedural operations.

Data-Driven Mathematics Investigations on Curved Data
Michael Bossé
Data-driven mathematical investigations are becoming more common. Often within these investigations, one is assigned to graph data points and investigate the relationship between variables. While linear regression is a valuable methodology when the scatter plot is more or less linear, additional techniques and tools are needed when the graphed data demonstrated some curvature. This article provides three techniques for determining the equation of a polynomial function through a number of points. This function can be utilized to analyze data and provide predictions.

Sharing Teaching Ideas: Solving Absolute Value Equations Algebraically and Geometrically
Shiyuan (Steve) Wei
A unique method for solving absolute value equations derived through the use of an ellipse. Geometrical method shows that the solutions of both absolute value equations |x - a| + |x - b| = c(b - a < c**) and ||x - a| - |x - b|| = c(b - a > c**) are given by a single formulas: x = [(a + b) - c]/2 or x = [(a + b) + c]/2.