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## Using Covariation Reasoning to Support Mathematical Modeling

Table representations of functions allow students to compare rows as well as values in the same row.

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## Spaghetti Sine Curves: Virtual Environments for Reasoning and Sense Making

The Spaghetti Sine Curves activity, which uses GeoGebra applets to enhance student learning, illustrates how technology supports effective use of physical materials.

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## Sorting Out Ideas about Function

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

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## Stop Teaching and Let Students Learn Geometry

A geometry course for teachers—easily adaptable to a high school geometry class—integrates technology, reasoning, communication, collaboration, reading, writing, and multiple representations.

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## Delving into Limits of Sequences

Through these calculus activities, students reach an understanding of the formal limit concept in a way that enables them to construct the formal symbolic definition on their own.

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## Proofs without Words: A Visual Application of Reasoning and Proof

Reasoning and Proof is one of the process standards set forth in NCTM's principles and standards for school mathematics (2000).

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## A Conceptual Approach to Absolute Value Equations and Inequalities

Sitting in the back of Ms. Corey's sixthgrade mathematics class, I enjoyed seeing students enthusiastically demonstrate their understanding of absolute value. On the giant number line on the classroom floor, they counted the steps that they needed to take to get back to zero. The old definition of absolute value of a number as its distance from zero—learned by students and teachers of the previous generation—has long ago been replaced with this algebraic statement: |x| = x if x ≤ 0 or − x if x < 0. The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. However, I cannot remember students attacking the task with enthusiasm or having any understanding beyond “make the inside positive.”