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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### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

### Wayne Nirode

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

### Chris Harrow and Lillian Chin

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

### Barbara M. Kinach

The meaningful use of symbols links context and generality.

### John H. Lamb

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

### Wendy B. Sanchez

Educating students—for life, not for tests—implies incorporating open-ended questions in your teaching to develop higher-order thinking.

### Bruce Frahm

Four graphing calculator games to entice your students to learn mathematics.

### Jeremy S. Zelkowski

Do you always have to check your answers when solving a radical equation?

### Michael Todd Edwards, Suzanne R. Harper, and Dana C. Cox

The Meeting for Lunch problem exemplifies how standards provide more than an outline of daily activities for an entire school year.

### Amy L. Nebesniak

When it comes to student achievement, teachers and instruction matter most.