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

### Courtney Starling and Ian Whitacre

Introduce your students to a fun and innovative game to encourage precise communication

### Melissa D. Gunter

Writing about mathematics holds a wealth of benefits for students. When students are given opportunities to write in math class, it helps develop mathematical thinking and language (Carter 2009; McCarthy 2008; Yang 2005), encourages self-reflection (Carter 2009; Danielson 2010; O'Kelley 2013), and provides a better way to organize ideas (Linhart 2014; Rogers 2014). Many teachers incorporate journaling and other types of reflective writing into their instruction already (Sjoberg, Slavit, and Coon 2004; Sanders 2009), but what about other forms of writing? NCTM states the importance of writing, in that students in the middle grades should be “more explicit about basing their writing on a sense of audience and purpose” (NCTM 2000, p. 62). How can we help students develop this important skill in math class?.

## Mathematical Explorations: A New Twist on Collaborative Learning

### classroom-ready activities

### Stephanie M. Butman

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

### D. Bruce Jackson

Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.

### Pamela J. Dunston and Andrew M. Tyminski

Techniques for teaching mathematics terminology allow adolescents to expand their abstract reasoning ability and move beyond operations into problem solving.

### Terri L. Kurz and Barbara Bartholomew

To support mathematical investigations, use this framework to guide students in constructing art-based and technology-based literature.

### Gloriana González and Anna F. DeJarnette

Students develop ownership and increase their understanding of mathematics when they are allowed to discuss alternative perspectives.

### Leigh Haltiwanger and Amber M. Simpson

Allowing students to write in mathematics class can promote critical thinking, illustrate an awareness of mathematical connections, and result in clear communication as they share ideas comfortably with peers.

### Kara J. Jackson, Emily C. Shahan, Lynsey K. Gibbons, and Paul A. Cobb

Consider four important elements of setting up challenging mathematics problems to support all students' learning.