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.

### Emily Sliman

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

### Walter J. Whiteley and Ami Mamolo

Investigating rates of change in volume without calculation leads to an enriched sense of the optimization process and encourages reflection and connection among different approaches.

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month the editors consider photographs of African bowls made of recycled telephone wire. The mathematics involves trigonometry, parametric equations and their graphs, and linear regression.

### Daniel R. Ilaria

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.

### Thomas E. Hodges and Elizabeth Conner

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.