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

Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.

### Catherine Tabor

A programming activity helps students give meaning to the abstract concept of slope.

### Barbara M. Kinach

The meaningful use of symbols links context and generality.

### Anderson Norton, Jesse L. M. Wilkins, Michael A. Evans, Kirby Deater-Deckard, Osman Balci, and Mido Chang

Explore a new app that allows students to develop a more sophisticated understanding of fractions.

### Rachel Levy

The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.

### Sabrina R. Goldberg

Introduce mixed-ability classes to a project exploring famous mathematicians and scientists and ignite students' math interest.

### Clayton M. Edwards

This guide to an individually paced classroom, containing suggested technology resource ideas, is meant to help students of differing ability levels succeed.

### Jason Lee O'Roark

After teaching high school mathematics in Maryland for three years, I began teaching sixth-grade mathematics in one of the best school districts in Pennsylvania (according to state test scores) and have been teaching there for the past six years. My high school teaching background led me to differentiate differently from my colleagues. I share my observations of the result of the differences in methodology and my conclusions from those observations, and I offer a plan to implement changes in the way that mathematics is taught.

### Emily Sliman

Chalk Talk and Claim-Support-Question are two routines for developing students' ability to use multiple representations and encouraging classroom discussion.