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

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### 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.

### 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.

### Tutita M. Casa

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.

### AnnaMarie Conner

Engaging prospective secondary teachers in mathematical argumentation is important, so that they can begin to learn to engage their own students in creating and critiquing arguments. Often, when we attempt to engage prospective secondary teachers in argumentation around topics from secondary mathematics classes, the argumentation is not authentic, as they believe they already know the answers. I suggest that there are problems related to the secondary curriculum around which we can engage students in authentic argumentation, and I propose one of them is whether 0.999… = 1. Purposefully engaging and supporting students in discussing this problem, and others like it, can lead to productive discussions that go beyond the answer to the question, including, for instance, what counts as evidence in mathematics.

### Nicole R. Rigelman

Take a page from the humanities and have your students investigate mathematics in writing.

### Lisa Berger

An analysis of problems from state assessments and other sources helps preservice teachers discover analogous mathematical representations.

### Nesrin Cengiz

Capitalize on student thinking to create opportunities to further their mathematical reasoning.

## Math For Real:The Half-Lives of Medicines

### when will I ever use this?

### Alyssa Hoslar

Calculating a half-life, the approximate time it takes for the body to remove one-half the active ingredient in a medicine, provides the real-life tie-in to this activity.