Three sessions at the Joint Meetings revealed either poor or improving communication between high schools and colleges about what courses colleges want students to take in high school.

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### Paul Laumakis

Students bring the real world into the classroom by studying speeding data collected on two Pennsylvania highways.

### Michael J. Bossé and Kwaku Adu-Gyamfi

A geometry course for teachers—easily adaptable to a high school geometry class—integrates technology, reasoning, communication, collaboration, reading, writing, and multiple representations.

### Renee Parker and M. Lynn Breyfogle

This student-friendly rubric helped improve third graders' competencies when explaining solution strategies in writing.

Discourse is the mathematical communication that occurs in a classroom. Effective discourse happens when students articulate their own ideas and seriously consider their peers' mathematical perspectives as a way to construct mathematical understandings. Encouraging students to construct their own mathematical understanding through discourse is an effective way to teach mathematics, especially since the role of the teacher has transformed from being a transmitter of knowledge to one who presents worthwhile and engaging mathematical tasks.

### Samuel Otten

Our answers to students' questions about the relevance of what we teach might paint mathematics into an undesirable corner.

### Beth Cory and Ken W. Smith

Through these calculus activities, students reach an understanding of the formal limit concept in a way that enables them to construct the formal symbolic definition on their own.

### Colin Foster

Exploring even something as simple as a straight-line graph leads to various mathematical possibilities that students can uncover through their own questions.

### Carol J. Bell

Reasoning and Proof is one of the process standards set forth in NCTM's *principles and standards for school mathematics* (2000).