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

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

## Can We Use a Mirror to Find Height?

### Christina Lundberg

My favorite lesson is based on a problem my geometry students encounter. When we study similar triangles, students use indirect measurement to determine the height of an object.

## Solving and Graphing Quadratics with Symmetry and Transformations

### Michael Weiss

One of the central components of high school algebra is the study of quadratic functions and equations. The Common Core State Standards (CCSSI 2010) for Mathematics states that students should learn to solve quadratic equations through a variety of methods (CCSSM A-REI.4b) and use the information learned from those methods to sketch the graphs of quadratic (and other polynomial) functions (CCSSM A-APR.3). More specifically, students learn to graph a quadratic function by doing some combination of the following:

Locating its zeros (x-intercepts)

Locating its y-intercept

Locating its vertex and axis of symmetry

Plotting additional points, as needed

## What Does It Mean to Do Something Randomly?

### Yating Liu and Mary C. Enderson

Similar assumptions seem to give rise to conflicting answers when students approach probability questions differently.

## Conic Connections with Polar Functions

### Kent Thele

Encourage investigation of the conic-section attributes of focus, eccentricity, directrix, and semi-latus rectum using polar coordinates and projective geometry.

## Creating a Hybrid Immersive Mathematics Experience

### Miriam Gates, Tracy Cordner, Bowen Kerins, Al Cuoco, Eden Badertscher, and Gail Burrill

With this professional development program, teachers work with colleagues and experience a manner of teaching that embeds habits of mind.

## Happy Families, Continued

### James Metz, Lance Hemlow, and Anita Schuloff

Explore the relationship between families of quadratic expressions factorable over the integers and Pythagorean triples.

## Correlation Revelation: The Search for Meaning in Pearson's Coefficient

### Craig Huhn

Lesson planning leads to a deeper consideration of what it means to study and learn mathematics.

## Snapshots of Equitable Teaching in a Highly Diverse Classroom

### Ruth N. Urbina-Lilback

Two instructional principles–being open to students' input and building on misconceptions–can open the door for mathematics learning in community college.

## Strategically Fostering Dynamic Interactive Environments

### S. Asli Özgün-Koca

Student interviews inform us about their use of technology in multiple representations of linear functions.