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## Student Engagement with the “Into Math Graph" Tool

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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## Angry Birds Mathematics: Parabolas and Vectors

Vector properties and the birds' frictionless environment help students understand the mathematics behind the game.

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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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## Media Clips: Optimizing HDTV Viewing Angles; Onside Kicks

Students analyze items from the media to answer mathematical questions related to the items. This month's clips are from an ad for HDTVs, which involves trigonometry and calculus, and from a sportscast, which involves probability and the binomial distribution.

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## Reader Reflections – August 2013

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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## The Back Page: My Favorite Lesson – Slopes of Parallel and Perpendicular Lines: A Visual Justification

When teaching slopes of parallel and perpendicular lines, I want students to have a visual image of the lines, not just memorize a formula. A simple exercise with parallel lines can get the message across.

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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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## Integrating Mathematical, Technologic, and Pedgogical Knowledge in Teacher Preparation

In Principles and Standards for School Mathematics (NCTM 2000), the authors describe a vision for school mathematics in which “all students have access to high-quality, engaging mathematics instruction” (p. 3). Students deserve teachers who are knowledgeable about mathematical content, who understand and use a variety of teaching strategies appropriately, who can effectively integrate technology into classroom learning, and who continually progress as professionals. But what kinds of experiences lead to such professionalism?