General Tech Tool: Geometer's SketchPad & SketchPad Explorer for iPad

Geometer's SketchPad is a tool I was first introduced to a few years ago, but shied away from because I had no prior knowledge and limited technology available to me at the time. While I still have yet to implement this in the classroom, it is one of the tools I am looking at using for next year as we build a more blended-PBL classroom style of teaching at our school. Since I am not as familiar with this tool, I will leave it to a classmate of mine, Terry C. to explain and evaluate. I'll cover the iPad version after!

Original CEP Post

Specific Math Activities using Geometer's Sketchpad (GSP)

Overview

Curator: Terry C

Name of Tech Tool: The Geometer's Sketchpad (GSP)

Brief Description of Tech Tool: The Geometer's Sketchpad is a dynamic, interactive software that supports the teaching of mathematics through the creation, visualization, and manipulation of geometric shapes, mathematical models and graphical representations relevant to geometry, algebra, and calculus. The software is developed and sold by McGraw-Hill Education.

Additional Information

A multitude of resources, ranging from lesson plans and activity guides to tutorials and professional development/training sessions are available for Geometer's Sketchpad.

McGraw-Hill Education maintains several sites that offer tutorials on how to use the software, free classroom activities, and an online community to share new ideas on how to use Geometer's Sketchpad in the classroom:

• Geometer's Sketchpad Resources
• Geometer's Sketchpad Resources Center
• Sketch Exchange - Online Community

A community of Geometer's Sketchpad users have also posted their own lessons and activities for the software on the web:

• The Math Forum @Drexel: Sketchpad Resources at the Math Forum
• Kutztown Unversity: Geometer's Sketchpad Lessons
• Math Bits: Working with Geometer's Sketchpad
• The University of Georgia: GSP Lessons
• Technological Education Consulting: Sketchpad Sketches
• Nate Burchell's Dynamic Geometry Site
• University of Virginia Center for Technology and Teacher Education

Numerous videos and video tutorials for Geometer's Sketchpad are also available on YouTube:

• Geometer's Sketchpad YouTube Videos

System Requirements

Geometer's Sketchpad Installation Guide and Licensing Agreement

For Version 5:

Windows system requirements:

Pentium-based system or equivalent

Windows XP or later

300 MB free disk space

Optional: Internet connection*, Adobe® Reader or Adobe Acrobat®

Macintosh system requirements:

Intel-based system (Note: PowerPC users may use Sketchpad Version 5.04 or earlier, available on the download page.)

Mac OS 10.4 or later

300 MB free disk space

Optional: Internet connection*, Adobe® Reader or Adobe Acrobat®

• An internet connection is required for downloading Sketchpad 5, deregistering Sketchpad 5, and watching Sketchpad Movies.

Geometer's Sketchpad currently is not compatible with iPads and Android devices. Sketchpad Explorer is available as a free iPad app in the iTunes store.

SketchPad Explorer

Curator: Kristen (Me)

Overview: SketchPad explorer is the iPad version of Geometer's Sketchpad. While it does not have all of the same capabilities, it does provide a good amount of activities to explore using this dynamic modeling software. 

Technical Costs & Considerations: Aside from owning or having access to an iPad, there is no cost to download this app. 

Additional Information: I have downloaded the SketchPad Express app and find that I am very much enjoying it and the flexibility it gives me to model mathematics and to play with the modelings they provide. This is a great resource to take advantage of the Representing and the Automating affordances of technology. The app is easy to use and a free resource for you to use in your classroom. After following a brief tutorial and exploring some of the cooler features of mathematics that SketchPad can demonstrate, you get the opportunity to browse through the library and find various activities already created just for this app. Topics include:

• Elementary Mathematics
• Geometry: Constructions
• Geometry; Ellipse Constructions
• Algebra: Dynagraphs
• Algebra: Slope
• Sketch Exchange Community Site
• The Sketch Exchange Community site allows you to browse lessons created by other SketchPad users that are specifically geared toward use with the iPad app. Simply browse with the appropriate search, and you'll find a vast treasury of activities to use.

How this Supports & Supplements PBL/PrBL:

Geometer's SketchPad and it's iPad counterpart SketchPad Express both provide a dynamic workspace that allows students to get visual and study geometry synthetically (without coordinates), while manipulating their ideas to round out their reasoning. With Geometer's SketchPad, you have more freedom to create your own models than with the Express version, but the Express version has some very interesting lessons that require critical thinking and analysis to truly gain an understanding. In my opinion, I like Geometer's Sketchpad best for PBL because it allows for the user to create more independently and to model and play with their own thinking to draw conclusions. However, I like SketchPad Express a lot for PrBL as it provides solid lessons that are truly inquiry based placed into a dynamic environment where students can manipulate the tools and build their thinking.

Geometry Tech Tool: Geometer's Sketchpad Tessellations that use Rotations

You'll see in another post that the Geometer's Sketchpad and it's iPad version: Sketchpad Explorer are wonderful tools to use to complement a PBL/PrBL classroom. Below is a review of a specific tech tool that uses the software, written by a colleague of mine: Terry C.

Original CEP Posting

Overview

Curator: Terry C.

Name & Link to Tech Tool or Resource homepage: Tessellations That Use Rotations

Link to parent Wiki page: Geometer's Sketchpad

Link to Other GSP Activities: Geometer's Sketchpad Activities

Brief Description of Specific Math Activity: Students construct an irregularly shaped tile based on an equilateral triangle, and then use rotation to tessellate the plane with it (Key Curriculum Press, 2009).

Evaluation

Description of Learning Activity

By creating the tessellation and then dynamically changing the original tile to see the effects, students get a deeper understanding of what makes the tessellation work (Key Curriculum Press, 2009).

1. Learning Activity Types

• LA-Present - (read or attend to) presentation of new content/ideas
• LA-Present-Demo - demonstration
• LA-Present-Explain - explanation
• LA-Explore - exploring/investigating mathematical ideas
• LA-Apply - applying mathematics to problems and situations

2. What mathematics is being learned?

The objective of this activity is to use rotation to tessellate and to explore rotational symmetry (Key Curriculum Press, 2009).

NCTM Standards

• NCTM-Geo-analyze - analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;
• NCTM-Geo-specify locations - specify locations and describe spatial relationships using coordinate geometry and other representational systems;
• NCTM-Geo-visualization - use visualization, spatial reasoning, and geometric modeling to solve problems.

Proficiency Strands

• PS-conceptual understanding - Students work with a specific example but the activity tries to promote the idea that students can wander down a path of "What if I did this?" and still reach similar results.
• PS-adaptive reasoning - Throughout the construction and manipulation, students have to understand what is happening, how its happening, and why its happening.
• PS-productive disposition - Seeing the tessellation animated at the end of the activity is fun and rewarding.

Prerequisite Knowledge Required: Experience with equilateral triangles, translation, tessellation, and rotation.

3. How is the mathematics represented?

Mathematics can be represented symbolically and graphically in this activity. Geometer's Sketchpad allows for both dynamic and static representations of mathematics, and it depends on the inputs made by the creator how the mathematics is represented in the tool. Through the instructions, this activity guides students to creating graphical and symbolic representations of mathematics that act as virtual manipulatives.

4. What role does technology play?

Geometer's Sketchpad makes a unique contribution in that it automates tessellation of a plane through tile rotation, so that students can see the effects more easily and quickly.

Affordances of Technology for Supporting Learning

• Computing & Automating - Sketchpad allows students to construct shapes on a computer more easily than if they were drawing them with pencil and paper. Sketchpad also allows them to manipulate and change the shapes more easily than with pencil, paper, and eraser. The effect of rotating the tile to tessellate the plane is achieved through technology; this cannot be done on paper.
• Representing Ideas & Thinking - Sketchpad allows students to visualize and explore mathematics problems.
• Accessing Information -
• Communicating & Collaborating -
• Capturing & Creating -

5. How does the technology fit or interact with the social context of learning?

According to the instructions, this activity is meant to be performed in student pairs. It can also be modified for a whole class. The technology facilitates the ease in which students can construct tessellations together (or side-by-side on separate computers) and then share the results with each other. Using technology allows students to rotate the original tile dynamically, which certainly is not easily accomplished with pencil and paper.

6. What do teachers and learners need to know?

This activity requires that students and teachers have access to Geometer's Sketchpad, and intermediate knowledge of Sketchpad is required to do this activity. The suggested grade level is 9 to 10; however, advanced seventh or eighth grade students could work on this activity. The activity includes an introduction on the activity for the teacher, notes, instructions, and discussion points for the teacher to guide the class through the activity, and a worksheet for the students that will guide them through the activity in Sketchpad and ask them questions at various intervals. The recommended duration for this activity is 45 minutes.

How this Supports and Supplements PBL/PrBL

 This activity is a great way for students to work on developing a conceptual understanding of tessellations as well as the procedural process of making tessellations, both of which can be daunting and time consuming for students. A lot of great projects and problems can focus on tessellations, or can take a tessellation turn (try turning ANY tiling problem into a tessellation problem!). The exposure students get by using this tool and doing this activity helps familiarize them with the concepts well enough to prepare them for thinking this way in projects and problems.