T 'n' T: Teaching and Techniques

Introduction
As a former Mathematics teacher at the junior and senior high levels, I have always been fascinated by the geometry of mosaics and the artistry of M.C. Escher. Pictures of his illusions decorated my classroom and tessellations (which can be defined as "an arrangement of closed shapes which cover a plane without gaps or overlaps") were always intriguing to my students. When I chanced upon Suzanne Alejandre's "Tessellation Tutorials" web site at:

http://forum.swarthmore.edu/sum95/suzanne/tess.intro.html

I immediately thought of designing this "Let's Get Connected" activity to encourage students to demonstrate their creativity in a "tessellation tournament"and share them over the world wide web.

The educational "big picture"
This activity involves the following steps:

1. On behalf of their student(s) or a class, teachers sign up as participants in the "T 'n' T: Tessellations and Telecommunications" activity as part of the "Let's Get Connected" event.
   
2. Teachers decide on whether they will utilize a Macintosh or Windows "Paintbrush/Paint" or "HyperStudio" (for either platform) software for creating the tessellations.
   
3. Each participating teacher follows the tessellation creation steps that are outlined in detail below to become familiar with the process. Once they are familiar with the procedure, they share the steps and instruct their students accordingly.
   
4. Once a student completes her/his tessellation, the teacher ensures that the resulting size conforms to the 512 x 342 pixel frame (which is the default size of a HyperStudio card). Strategies for ensuring that this standard is maintained are provided in the documentation below.
   
5. Students, who wish to "autograph" their creation, may wish to add their first name and ONLY the first letter of their surname as well as their school to their tessellation creation in its standard bitmap format. Some may even wish to name their creation.
   
6. Students must then convert their bitmap files to an Internet-ready GIF or JPEG format using software identified in the documentation. This conversion process automatically reduces the file size of the tessellation so that it can be e-mailed much faster.
   
7. It is recommended that the teacher send one sample tessellation as an e-mail attachment (using MIME compliance) to the host facilitator to ensure that the creation was received intact. Once the educator receives confirmation that the process is working flawlessly, then the remaining tessellations can be sent.
   
8. Once the tessellation is in a 512 x 342 pixel size GIF or JPEG format with the optional student's signature, it must be sent as an attachment to the activity facilitator by e-mail. It is important that the body of each e-mail message contain the student's first name and school of the student so that an index can be built to link to the creation of each contributor. For example, if you transfer by clicking on the "Talent 'n' Tessellations" link (and click on your browser's back button to return here) you will see how the contributing students' names and schools are entered in an index.

Software Selection
At this point educators need to determine which software will be utilized. Even though your students may be using a Macintosh computer, you may wish to review the detailed steps designed for Windows-based computers below since most concepts will transfer amazingly well. If, however you wish to examine Macintosh-specific commands for HyperStudio or other software such as Claris Works, HyperCard, or LogoWriter, detailed steps are also provided through a link to Suzanne Alejandre's phenomenal tessellation resource on the world wide web. You, of course, are reminded that if you link to a remote site or have difficulty navigating through this activity web, remember to click on your browser's "Back" button until you return to familiar surroundings. Select the appropriate "step-by-step" procedure and work through the steps to construct a tessellation.

Step by Step - Tessellation, Teaching & Tutorial
Click on the appropriate link below to learn a step by step procedure for creating a tessellation. It is recommended that "first-time creators" begin by making simpler tessellations. Avoid adding too many complex interior details. Rather work with two basic solid colored shapes in contrasting colors and use these as the basic building blocks in the tessellation construction. Once the process is understood, and if time permits, a student can choose to create more complex detailed tessellation building blocks. Based on the software available, choose the appropriate link from the three below. Once all the detailed steps have been completed in the appropriate link, return to this section and continue with the steps following the three links below.

• HyperStudio (for Windows)
• PC Paintbrush or Paint (for Windows)
• Tessellation Tutorials (Tutorials and templates for making your own tessellations with a variety of Macintosh software)

At this point, it is expected that the participant has worked his/her way through one of the above detailed procedures and has created a tessellation (in 512 x 342 pixel format) which has been saved to the hard drive or floppy in its "native format". One should now proceed to the next step by clicking on the "T 'n' T - Transfer 'n' Telecommunications" link below.