For those of you old enough to remember using geoboards in elementary and middle school in order to learn shapes and patterns, GeoGebra is an application about which to get excited. As a free, web-based dynamic geometry environment, the GeoGebra software is accessible via a desktop computer or a free app for your tablet or smart phone. The software gives the user a toolbar with which one can create geometric figures, measure lengths and angles, manipulate objects, and explore many other geometric properties. The student-friendly interface is simple to use and perfect for students seeking to investigate geometric properties and theorems. To experience GeoGebra for yourself, click here.

GeoGebra exemplifies the type of technology that is perfect for classroom use. According to the text *Focus in High School Mathematics: Technology to Support Reasoning and Sense Making*, instructional technology should serve to “push or probe” students’ mathematical thinking. Specifically, GeoGebra aligns perfectly with several of the guidelines set forth in *Focus in High School Mathematics*:

- Purposeful, thoughtful, and deliberate action is required to create, manipulate, and analyze geometric figures
- No special skills are required to utilize the software
- Consequences of input into GeoGebra are immediate, visual, and mathematically meaningful
- Connection between action and mathematic consequence is clear
- Use of this software enables precision unable to be attained with traditional paper and pencil

As with most technology, GeoGebra can be most effectively used when paired with guided worksheets or teacher demonstrations. For example, a guided worksheet might step a student through the process of creating an “apparent” isosceles triangle by dragging together line segments, followed by creating an inherently isosceles triangle through its construction using a circle.

The guidelines set forth in *Focus in High School Mathematics *function as an important tool in evaluating whether or not given technology enhances student learning. WolframAlpha is an example of such technology and was discussed in the last post. While WolframAlpha meets much of the criteria suggested by *Focus in High School Mathematics*, it requires special knowledge of how it functions to make a meaningful tool, unlike GeoGebra.

Overall, GeoGebra is a worthwhile application with the potential to radically change the way in which geometry is taught in elementary and secondary schools. Go check it out!

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