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.
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.
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.
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.
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.