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Craig J. Cullen, Joshua T. Hertel, and Sheryl John

Technology can be used to manipulate mathematical objects dynamically while also facilitating and testing mathematical conjectures. We view these types of authentic mathematical explorations as closely aligned to the work of mathematicians and a valuable component of our students' educational experience. This viewpoint is supported by NCTM and the Common Core State Standards for Mathematics (CCSSM).

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Christine P. Trinter and Joe Garofalo

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. In our classes of precalculus students and preservice mathematics teachers, we have found that nonroutine tasks encourage our students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions.

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Jacqueline Coomes

Turn a light on the Rectangle Border problem and watch students make connections among multiple representations to better understand structure.

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Amy F. Hillen and LuAnn Malik

A card-sorting task can help students extend their understanding of functions and functional relationships.

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A set of problems of many types.

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