**The following series** of learning activities are from an afterschool math club called Go Go Gizmos that focuses on modeling mathematics with the use of technologies. This account describes how a classroom teacher and a math educator taught and assessed students' understanding of the rate of change using a variety of technologies. In particular, we chose data collection probeware called Go!Motion, which is a stand-alone motion-data-collection device from Vernier that sends data to the computer for analysis and simulation applets from http://explorelearning.com. The Go!Motion device can be connected to a computer and displays an interactive real-time spreadsheet with graphing capabilities. The objectives in the unit were for students to investigate physical representations of slope as a rate of change in mathematics and as velocity in science and the y-intercept as the initial condition, or starting position. In these investigations, students and teachers become partners in developing mathematical ideas and solving math problems (NCTM 2000).

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### Jennifer Suh and Kerri Fulginiti

### Patricia Wallace-Gomez

When teaching slopes of parallel and perpendicular lines, I want students to have a visual image of the lines, not just memorize a formula. A simple exercise with parallel lines can get the message across.

### Karen D. Campe

Mathematics teachers can use a broad range of technologies—calculators, computers, display systems, and others—as teaching and learning tools. Although actual access is influenced by budgets and demand, the important thing is to make the best use of the technology available. Whether you have one computer station for demonstration, a classroom set of graphing calculators, or a fully wired classroom, you can take steps to make your technology implementation most effective and successful.

## Connecting Research to Teaching: Why Did You Do That?

### Reasoning in Algebra Classrooms

### Daniel Chazan and Dara Sandow

Secondary school mathematics teachers are often exhorted to incorporate reasoning into all mathematics courses. However, many feel that a focus on reasoning is easier to develop in geometry than in other courses. This article explores ways in which reasoning might naturally arise when solving equations in algebra courses.