Classroom Tools - Geometer's Sketchpad

            Dynamic Geometry Software such as Geometer’s Sketchpad is a helpful tool for visualization. This helps not only the students but the teachers as well. Having a visualization tool available helps teacher explain concepts and ideas, which are difficult to put into words, in a way that is easier for students to comprehend.

            For example, Geometer’s Sketchpad can be used to illustrate the dynamic relationships between trigonometric functions (i.e. sine, cosine, tangent) and the unit circle. Trigonometric functions are taught at the high school level, usually introduced in Geometry (tenth grade) or Algebra II (eleventh grade) and explored more rigorously in Pre-Calculus (twelfth grade).

            I have just been introduced to Geometer’s Sketchpad so I am still learning its capabilities and exploring its potential. Unfortunately, one major drawback to Geometer’s Sketchpad is its price tag¹. Since the district I work for does not own a license for the software I have limited opportunity to familiarize myself with it.

            However, Geogebra is a completely free DGS with similar capabilities to Geometer’s Sketchpad. I will discuss Geogebra in my next blog.

Delicious Stacks

I have wanted to share these links for some time. I was able to organize and share them by creating "stacks" using delicious.com, a social bookmarking site. My hope is that you will find these links, not only helpful, but useful as well. Please share these stacks with your friends and contribute other links that you have found to be helpful and/or useful.

 
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Visualization Tools

            Visualization tools have been created because humans have no natural mechanism for visually representing ideas apart from mental images and dreams, which can be very difficult to communicate. Necessarily, they help people to visualize ideas and share those images with others.

In the classroom technologies are available and have proven useful for visualizing mathematical ideas and concepts. This is because, on a human level, visual images are effective facilitators of meaning. For many people, visualizing something helps them to make sense of it. This is especially true for the abstractness of mathematics. Furthermore, the ability to visualize ideas will prove particularly useful in clarifying and correcting common misconceptions of mathematical concepts. On a technological level, visualization tools automate some of the manual processes for creating images for those that lack the artistic skills necessary for generating original images.

There are two predominant roles of visualization tools. The first is interpretive, which helps “learners view and manipulate visuals, extracting meaning from the information being visualized.” The second role is expressive, which “helps learners to visually convey meaning in order to communicate a set of beliefs.”

In mathematics, dynamic geometry software (DGS) such as Geogebra, Geometer’s sketchpad, and Cabri Jr. app help learners to construct and manipulate geometric objects. Learners are also able to make conjectures about the relationships of objects and then test them for correctness.

I teach high school geometry but I am sad to say that I have never used any of these DGS packages. I hope to explore them in coming weeks to make my lessons more effective for all of my students.