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.

# Browse

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

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

## Students' Understanding of Counterexamples

### Rebecca Vinsonhaler and Alison G. Lynch

This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.

## Capturing Mathematical Curiosity with Notice and Wonder

### Aaron M. Rumack and DeAnn Huinker

Capturing students' own observations before solving a problem propelled a culture of sense making by meeting needs typical of middle school learners.

## Connecting Quadratics, Line Segments, Continued Fractions, and Matrices

### Lee Melvin M. Peralta

One of the many benefits of teaching mathematics is having the opportunity to encounter unexpected mathematical connections while planning lessons or exploring ideas with students and colleagues. Consider the two problems in **figure 1**.

## Designing for Voice and Agency

### Laurie Speranzo and Erik Tillema

Specific teacher moves and lesson planning can facilitate student empowerment in the middle school classroom.

## Letters to the editor

## License to Do Math with a Full Tank

### Ron Lancaster

Since its inception, the Mathematical Lens column has provided teachers with resources to use with their students to make connections between mathematics and the world around us through the use of photographs. The editors and the dozens of teachers who submitted material for columns have taken all of us on a journey around the world to discover where mathematics lives. These columns have offered teachers a license to do mathematics everywhere and to travel far with their students with a full tank of resources.

## May 2019 Calendar and Solutions

## Problems

### Stephen Phelps

### Edited by Anna F. DeJarnette

A monthly set of problems targets a variety of ability levels.

## Prove It to Me!

### Jo Boaler

Engage your learners through tasks proven to significantly promote reasoning and problem solving, which touch on many of the Mathematics Teaching Practices in *Principles to Actions: Ensuring Mathematical Success for All*. These tasks are discussed in this article, another installment in the series.