An introductory activity for the limit concept with a geometrical and historical foundation. A connection among Geometry, Measurement and Calculus is highlighted with the help of technology. The geometrical drawing, measurement and graphing capabilities of both TI-89 and Geometer's Sketchpad make it possible for students to experience Archimedes' process for determining circular area.

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### S. Asli Özgün-Koca

Student interviews inform us about their use of technology in multiple representations of linear functions.

### Thomas G. Edwards

### Edited by S. Asli Ozgun-Koca

The latest advances in instructional technology have enabled teachers to use interactive, dynamic tools to explore mathematical representations in ways they cannot when using chalkboard or paper and pencil. With these new tools, the technology itself performs the computations required to translate actions across representations, leaving the student free to perform the actions and monitor the consequences. The effectiveness of these learning tools lies in being able to represent the same mathematical concept by using many representations and making explicit the relationships among those representations by dynamically linking them (Kaput 1986, 1994), although multiplylinked representations have possible disadvantages (Ainsworth 1999; van der Meij and de Jong 2006). Dynamic linking may make students passive by doing too much for them, and providing too much information may result in cognitive overload. Thus, these powerful instructional tools must be used with great care and preparation.

## Mathematical Explorations: Interpreting Box Plots with Multiple Linked Representations

### classroom-ready activities

### S. Asli Özgün-Koca and Thomas G. Edwards

A box plot activity is driven by a TI-Nspire calculator.

### Thomas G. Edwards and S. Aslı Özgün-Koca

Using quadratic functions as an example, see how the evolution of technology has altered the expectations of students' understanding and critical thinking.

### S. Asli Özgün-Koca and Thomas G. Edwards

Students make a slam dunk, first with spaghetti and a scatter plot, then with a graphing calculator.

### S. Asli Özgün-Koca and Thomas G. Edwards

Extend a well-known circle-exploration activity using technology to connect geometry and algebra.

### Jennifer M. Lewis and S. Asli Özgün-Koca

This research department describes strategies for helping students persevere in solving complex mathematics problems.

### Matt Enlow and S. Asli Özgün-Koca

This month's Growing Problem Solvers focuses on Data Analysis across all grades beginning with visual representations of categorical data and moving to measures of central tendency using a “working backwards” approach.

### Matt Enlow and S. Asli Özgün-Koca

Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?