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## Delving Deeper: Pythagorean Triples: Avenues for Exploration

The article contains classroom enrichment suggestions related to Pythagorean triples. Topics discussed for student exploration can be adapted for any level from early algebra through early college.

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## The Human Unit Circle

When each student has become part of an ordered pair, we go outside to the school parking lot, where I chalk the outline of a Cartesian plane.

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## The Circle Approach to Trigonometry

A connected introduction of angle measure and the sine function entails quantitative reasoning.

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Readers comment on published articles or offer their own ideas.

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## Visible Thinking in High School Mathematics

Chalk Talk and Claim-Support-Question are two routines for developing students' ability to use multiple representations and encouraging classroom discussion.

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## Delving Deeper: Approximating π Using Similar Triangles

This article presents a method for approximating π using similar triangles that was inspired by the author's work with middle school teachers. The method relies on a repeated application of a geometric construction that allows us to inscribe regular polygons inside a unit circle with arbitrarily large number of sides.

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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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## Building Momentum by Starting Small

A university mathematics teacher educator and a math department chair reflect on how various assignments and structures can support early-career teachers in anticipating student thinking and solutions to purposefully plan lessons.

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## Do It Right – Strategies for Implementing Technology

Mathematics teachers can use a broad range of technologies—calculators, computers, display systems, and others—as teaching and learning tools. Although actual access is influenced by budgets and demand, the important thing is to make the best use of the technology available. Whether you have one computer station for demonstration, a classroom set of graphing calculators, or a fully wired classroom, you can take steps to make your technology implementation most effective and successful.

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## Students' Conceptions of Sine and Cosine Functions When Representing Periodic Motion in a Visual Programming Environment

In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. The author examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment. This study illustrates the range of prior knowledge and resources that students may draw on in their use of trigonometric functions as well as how the goals of students' work inform their reasoning about trigonometric functions.