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## The Do Nothing Machine

The Trammel of Archimedes traces an ellipse as the machine’s lever is rotated. Specific measurements of the machine are used to compare the machine’s actions on GeoGebra with the graph of the ellipse and an ellipse formed by the string method.

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## Point-Line Ellipses and Hyperbolas

The author alters the definitions of ellipses and hyperbolas by using a line and a point not on the line as the foci, instead of two points. He develops the resulting prototypical diagrams from both synthetic and analytic perspectives, as well as making use of technology.

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## An Alternative Approach for Defining a Quadratic Function

Defining a quadratic function through the slopes of its secant/tangent lines leads to the fundamental theorem of calculus (FTC) and an alternative way of understanding integration.

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## Area of a Changing Triangle: Piecing It Together

Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.

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## Taking a Cue from Conic Sections

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## Parameters, Sliders, Marble Slides, Oh My!

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

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## The Structure of the Quadratic Formula

Lessons that focus on a conceptual understanding offer an opportunity for students to learn about mathematical structure, not just computation.

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## Visualizing Complex Roots of a Quadratic Equation

A quadratic equation was the basis for activities involving both concrete and technological representations.

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## Focusing on Visual Representations in Mathematics

The authors outline the importance of using variety when teaching mathematics.

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## NCTM Leadership Then and Now

How has NCTM leadership shaped the evolution of teaching and learning mathematics? What are your expectations for NCTM leadership?