This project represents my vision of a way in which the geometric concept of properties of parallelograms can be effectively taught in a virtual classroom setting. Each investigation provides enough guidance to help students independently discover, conjecture, and prove important properties of parallelograms. There are many Web page editors on the market that allow users, even those with very little experience, to easily develop lessons that will reach any student that has access to the World Wide Web (WWW). These Web pages have been designed using the Internet Explorer editor, FrontPage Express.

Electronic Communication
Once the investigations are available to students on the WWW, the key to promoting a productive, successful virtual classroom is electronic communication. This type of communication parallels the one-on-one, small group, and class discussions that take place in a traditional classroom. Teachers and students need to extensively utilize electronic communication in order to create a classroom environment where ideas can be shared, questions explored, and feedback provided. The most basic way students and teachers can communicate with one another electronically is through e-mail. The communication is quick with the major advantage that attachments can be made. Therefore, a student can ask questions and send a "rough draft" of an investigation and receive a relatively quick reply with teacher suggestions. Teachers should also create a policy with students that they will monitor their e-mail during specified periods, so that students know when the teacher can be reached. This leads into the concept of instant messaging, a free service provided by most e-mail providers. An example is Yahoo! Messenger, which allows groups of people to "talk" almost as quickly as they can type. This feature allows for a group, including or not including the teacher, to discuss problems faced in the investigations. Again, teachers should create a policy with students that instant messaging "chats" will take place regularly at specified times. One last aspect of electronic communication that I would like to briefly mention deals with networks. Almost all schools are networked, which allows teachers to create various folders within the system to help students communicate. For instance, a class could be set up with two main folders, completed investigations and "works in progress." The completed investigations folder can be set up with security, so that students do not have access, while the "works in progress" folder can be known as a folder for students to share their ideas. However, most importantly, e-mail and instant messaging must be used extensively to create a virtual classroom that maximizes students' success.

Electronic Whiteboards
A relatively new technology that I would like to incorporate to enhance a virtual classroom is the electronic whiteboard. Teamboard and MicroTouch are two companies that are leaders in developing this technology. An electronic whiteboard interfaces with your computer and allows you to better convey a concept to your students and allows for collaborative work to take place electronically. This is accomplished by the ability of the whiteboard to automatically capture everything that is written on it in a file. Once this information is captured, the file can be e-mailed to your students. For example, if a student has a question, it can be placed on the whiteboard and all ideas and suggestions that are written on the whiteboard are automatically collected for easy electronic distribution to your students. The electronic whiteboard works with other software programs, such as GSP and Excel. You can enter information into the whiteboard through your keyboard, or with an electronic pen. The electronic pen allows you to quickly write commments and sketch ideas that are important for your students. Additionally, the whiteboard has a touch feature that allows you to erase and use point and click options. Therefore, using a combination of e-mail, instant messaging and an electronic whiteboard can allow teachers to interact with their students more efficiently and effectively. Furthermore, the use of an electronic whiteboard in conjunction with data, audio, and videoconferencing software can transform a virtual classroom into one that rivals a traditional classroom in its effectiveness.

Audio-, Data- and Video-conferencing
Free long distance is now available through the WWW which allows students and teachers to communicate verbally while working through questions raised in working on the investigations. There is also a great deal of audio-conferencing software on the market that is continually improving in quality. This provides students and teachers with the ability to verbally exhange ideas in close to the same manner as if they were all in the same classroom. Video- and data-conferencing software is improving quickly and dramatically to the point where students and teachers will soon be able to interact with one another in a virtual classroom that emulates the traditional classroom. For example, Microsoft already has a data, audio, and video-conferencing software package, NetMeeting, that interacts with the electronic whiteboard to allow students and teachers to conduct virtual classes that model effective traditional classes. Whiteboard and conferencing technology will transform distance learning into a fully interactive environment.

WebCT
It is very possible to develop a Web-based course independently; however, if I were to pursue this goal, I would strongly consider producing a course with the help of WebCT. WebCT provides a stong support system for teachers and students and provides the added advantage of being a part of a "community." WebCT employs trainers and developers to help teachers create and implement a virtual course. Teachers have the opportunity to pursue workshops and training courses in effectively using WebCT, and students are provided with a users' guide to maximize their efficiency. WebCT is divided into communities of which mathematics, online teaching and learning, student resource center, and Web support are the most important to teachers and students engaged in mathematics Web courses. Within each community, a library, directory, and forum link is provided to help with browsing and searching of topics. This design helps stimulate the sharing of ideas for teaching and learning. The forum link even has an "ask the expert" feature to field specific questions. Additionally, WebCT recently purchased Math Forum, a leading mathematics site that provides resources for students and teachers of all levels. I feel that the support and communities that WebCT offers would be a great asset in developing a Web-based course.

Assessment
With this particular project, my main form of assessment would be the development of portfolios. I would want the students to create an electronic portfolio of the work they have accomplished. I believe that through formalizing their findings from the investigations students will most successfully learn the desired mathematical concepts.

If you have any questions while trying to complete this investigation, or suggestions that would be useful, especially for use at the high school level, please send e-mail to esiwdivad@yahoo.com.

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