Four teachers and a teacher educator move from guided notes to strings in a series of problems that support students in increased engagement, reasoning, sense making, and problem solving.

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

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.

### Erik Jacobson

Table representations of functions allow students to compare rows as well as values in the same row.

### Wendy B. Sanchez

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

This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This month in the Coaches' Corner, take a closer look at CCSS Standard 3 for Mathematical Practice, Explain and Justify. Coaches may want to demonstrate the integration of math and writing with Speak, Write, Reflect, Revise, a five-step approach for integrating problem solving and the writing process.

### Bobson Wong and Larisa Bukalov

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

### 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.

### Lisa Berger

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

### Sonali Raje, Gail Kaplan, and Michael Krach

The Chinese number pyramid puzzle serves as a means to develop students' critical thinking skills.