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

### Aaron Trocki

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI 2010).

### Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

Classroom communities should embrace individuals and foster communication; to this end, the MT Editorial Panel requests submissions on how to capitalize on the strengths that cultural, racial, and linguistic diversity bring to the classroom.

### Kasi C. Allen

Students today come to first-year algebra with considerable prior experience and a wide range of skills. Teachers need to modify their instructional strategies accordingly.

### Wendy B. Sanchez

Educating students—for life, not for tests—implies incorporating open-ended questions in your teaching to develop higher-order thinking.

This call solicits manuscripts on the dynamic relationship between physical phenomena and mathematical structure.

### Nancy S. Roberts and Mary P. Truxaw

A classroom teacher discusses ambiguities in mathematics vocabulary and strategies for ELL students in building understanding.

### Heather Lynn Johnson

This article explores quantitative reasoning used by students working on a bottle- filling task. Two forms of reasoning are highlighted: simultaneous-independent reasoning and change-dependent reasoning.

### David A. Yopp

Asked to “fix” a false conjecture, students combine their reasoning and observations about absolute value inequalities, signed numbers, and distance to write true mathematical statements.