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## Exploring Geometric Sequences

Use popular culture to draw students' attention to mathematical topics.

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## Factor and Remainder Theorems: An Appreciation

Core content provides opportunities to focus on the structure of mathematical theory, proof, and anticipation of subsequent topics.

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## Working the System

Two teachers discuss the planning and observed results of an introductory problem to help students nail a conceptual approach to solving systems of equations.

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## Algebraic Activities Aid Discovery Lessons

Three graphing activities lead students to discover the shapes and properties of the graphs for linear, quadratic, and absolute value functions and inequalities.

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## Exploring Function Transformations Using the Common Core

Tying your teaching approach to the Common Core Standard for Geometry and Congruence will help students understand why functions behave as they do.

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## Teaching Absolute Value Meaningfully

What is the meaning of absolute value? And why do we teach students how to solve absolute value equations? Absolute value is a concept introduced in first-year algebra and then reinforced in later courses. Various authors have suggested instructional methods for teaching absolute value to high school students (Wei 2005; Stallings-Roberts 1991; Friedlander and Hadas 1988), but here we focus on an investigation that will help students make meaning of the absolute value equation in the context of a practical situation. We connect absolute value to the concepts of rate, time, distance, and slope.

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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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## Technology Tips – Piecewise-Defined Functions on the TI–Nspire

Students generally first encounter piecewise–defined functions in the form of a step function (perhaps the postage stamp function) in an algebra class. Piecewise–defined functions do not play a central role in mathematics before calculus although they can serve as challenging examples in the precalculus curriculum. Before the advent of the TI–Nspire, entering piecewise–defined functions on the calculator was time consuming and not particularly user friendly. That has changed.

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## Inverse Functions: What Our Teachers Didn't Tell Us

Our teachers misled us, but we don't blame them. They were only teaching what was in the textbook. And as new teachers—because of our lack of experience and our reliance on the textbook—we continued to teach the procedure we had learned as students. It wasn't until we began writing textbooks ourselves (Wilson 2007; Wilson et al. forthcoming) that we were compelled to confront the inverse function falsehoods in our intellectual past. These contradictions were difficult to detect because they were broadly accepted and perpetuated in widely used textbooks

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## Reflections on a Technology–Rich Mathematics Classroom

Integrating technology into the mathematics classroom means more than just new teaching tools—it is an opportunity to redefine what it means to teach and learn mathematics. Yet deciding when a particular form of technology may be appropriate for a specific mathematics topic can be difficult. Such decisions center on what is commonly being referred to as TPACK (Technological Pedagogical and Content Knowledge), the intersection of technology, pedagogy, and content (Niess 2005). Making decisions about technology use influences not only students' conceptual and procedural understandings of mathematics content but also the ways in which students think about and identify with the subject.