S.H.O.W.M.E.
Spear-Heading Online Work in Mathematics Education
Gene Abrams Jeremy Haefner
Department of Mathematics
University of Colorado
Colorado Springs, CO 80933
Ph: 719.262.3311
Fax: 719.262.3605
gabrams@uccs.edu
haefner@eas.uccs.edu
Abstract: We discuss the history, motivation and technological issues regarding the development of our Mathematics Online program. This program features courses presented live and archived lectures via the Internet.
Biographies: Gene Abrams received his Ph.D. in mathematics from the University of Oregon in 1983. He is currently Professor and Chair of the Department of Mathematics at the University of Colorado at Colorado Springs. In 1996 he was designated as a University of Colorado Presidential Teaching Scholar.
Jeremy Haefner received his Ph.D in mathematics from the University of Wisconsin in 1986. He is currently Associate Professor of Mathematics at the University of Colorado at Colorado Springs. Since 1995 he has been the director of C.A.T.M.E., the Center for Applications of Technology in Mathematics Education.
Introduction. In the spring semester of 1998, the Department of Mathematics at the University of Colorado at Colorado Springs offered two courses over the Internet as the first stage in its Distance Learning program. The key feature of these two online courses was that live lectures were "broadcast" as audio and whiteboard feeds. In this article we discuss the motivation, details and results of this project.
History and Motivation. Our motivation for experimenting with offering courses ‘at-a-distance’ was fueled by a number of factors.
First, there is a natural constituency of potential students who require / desire courses from the University, for whom actual class attendance is difficult (if not impossible). Examples include: people who live far away from CU – Colorado Springs (e.g. students at junior or community colleges throughout Southern Colorado); people with physical disabilities; people whose work schedules do not allow them to attend class regularly; and high school students who wish to complete university courses during their junior or senior years. As a public institution, we felt that we have a responsibility to try to accommodate to some extent the members of these groups.
Second, there was an interest on our part to see just what the currently emerging technologies would allow us to do in regards to delivering courses at a distance. We have taught mathematics courses on television. But who was really out there watching? We have experienced distance learning courses which consist of nothing more than information scanned into a computer and reconfigured as web pages. So why not just read a textbook? We have observed some mathematics websites which seem to be fixated on presenting essentially nothing more than cute graphics and slick animation. Where’s the beef? In the end, we saw few (if any) instances where the successes of the traditional classroom were emulated online. Would the new technologies make it possible to somehow extend to a distance the things we view as the key elements of traditional classroom delivery (i.e., live instructor, student-instructor interaction, student-student interaction, human contact!)?
Third, we wanted to confront first hand some of the pedagogical issues surrounding Distance Learning. What are the advantages of this approach? What are the disadvantages? What differences are there between the performances of students who learn ‘at a distance’ versus those schooled in more traditional classroom settings?
Finally, and perhaps most importantly, we sensed the existence of giant administrative steamrollers charging ahead ‘pedal-to-the-metal’ in the effort to deliver Distance Education. While part of the justification for pursuing such an effort is quite honorable (‘education for the masses’), the jaundiced faculty eye sees administrative bean-counters drooling over a tasty cash cow. While parts of such a program can be viewed as improved pedagogy, the absence of traditional human interaction leads some faculty to view it as unacceptable McLearning. We felt (and still feel) strongly that in order to be effective participants in the discussion regarding the future direction and scope of distance learning, we should have some first-hand experience from which to draw. This project has supplied us with such experience, and then some. The acronym S.H.O.W.M.E. is thus a wholly appropriate moniker for this program: it indicates that our interest in this project is very real, but is mixed with healthy doses of caution and cynicism.
Philosophy: The philosophy which guides this effort is our attempt to approximate the traditional classroom as much as possible while simultaneously maximizing the advantages afforded by our use of the Internet. As a result, we always attempt to put pedagogy first, technology second. In addition, we constantly keep in mind the needs and requirements of the typical student as much as possible. This often requires a trade-off between what is technologically feasible for the instructors, and what is financially feasible for students.
Details and key features of program. Live lectures. A distinguishing feature of our program is our incorporation of a large dose of the traditional classroom elements into our presentations. We believe the two most important components of a mathematics classroom presentation are the use of some sort of ‘chalkboard’ (in order to visually, efficiently transmit mathematics), and the voice/words of the instructor (in order to describe, explain, and otherwise guide the students through the material). Thus, we believed that it was essential to provide both the "chalkboard experience" and the voice of the instructor to the students online.
We investigated video conferencing applications, hoping that we could possibly deliver both a live video and audio feed. The idea was to have a video camera record the lecture, while simultaneously broadcasting the lecture over the internet (using a product such as RealAudio or NetShow). In addition, we could archive the video lecture and permit students to view the lecture over the Internet at their convenience. However, our experimentation with this form of video conferencing quickly showed us that the video signal was far too large to transmit over the Internet in such a way that students with standard, widely used 28.8 baud modems could receive a coherent lecture. It was at this point we scaled back our aspirations and decided to try to deliver "only" an audio and a "whiteboard" feed.
During our search for a whiteboard product, we came across the LearnLinc product from Interactive Learning International Corp. The philosophy of this product was very much in line with our own pedagogical goals for distance learning. This product was a client/server application that included a teaching environment based around a whiteboard. At the time, it did not provide an audio feed although the company had told us that this feature was under development. The product, to our understanding, did not provide an archiving capability - a feature we had decided was critical to our project. Both cost and availability were determining factors in our decision to not pursue this product. (For a public institution of higher education, the cost of this product required to reach a class of 20 to 30 students was prohibitive.) Nonetheless, our experimentation with this product convinced us that we were on the right track.
Through an Internet search on "whiteboards" we became acquainted with the product Rendezvous by VisualTek Solutions, Inc. Like LearnLincTM , this too is a client/server application designed around whiteboard conferencing. VisualTek has written this product as a multiplatform application, meaning it could be used on a variety of computers (e.g. Suns, Macs, PCs). It even provided a Java applet for use from a web browser. Our initial tests indicated that this product seemed very stable and robust. We began a dialogue with Mr. Sanjay Dalal, a technical marketing representative at VisualTek. We soon realized that our distance learning project was appropriately suited to benefit both the University of Colorado and Visualtek. Subsequently, a very agreeable contract was formulated between the two parties and a very comfortable working relationship began.
Because the existing Rendezvous product did not exactly suit our needs, we asked the developers at VisualTek to make some modifications. These modifications included:
- a secure login feature (so that we could control the classroom environment)
- an audio "handshake" with the audio product of our choice (we later chose Microsoft's Netshow)
- an archive feature so that the whiteboard lecture could be replayed by students
- other minor modifications (e.g. keyboard equivalents to repetitive mouse movements)
We presented the developers with these requirements in early November 1997, with a deadline of mid-December for product delivery. To our pleasant surprise, the product was delivered in early December. This reinforced our choice of VisualTek as a partner in our distance learning endeavor.
In the meantime, we had selected Microsoft's Netshow application to deliver the audio feed of our lecture. This was motivated by the fact that we planned to use our NT webserver to perform the actual delivery. We felt that by using a product that was (in theory) designed to work well in an NT environment, we would be saving ourselves much time and effort later. In addition, the Netshow server 2.0 was free to us and came with adequate documentation. On the downside, the Netshow player was only available on the PC platform, so our decision to use Netshow precluded a Mac user from hearing the audio portion of our lecture. We considered this to be a major disadvantage, but as this was the first experiment in this project we felt our decision was justified. Our other audio option was the Realaudio product. The cost of this product would have been greater than the cost of Netshow (although Realaudio did provide a free 60 user server), but would have been available to multi-platforms, thereby enabling Mac and Sun users to hear our audio feed.
Finally, we investigated smart whiteboard hardware products that would allow us to write on a large whiteboard surface, digitize the markings, send the markings into our instructor station computer, and distribute them over the Internet via Rendezvous. While this technology may ultimately be viable, we opted for the simpler approach of using a large graphics tablet (made by Wacom). This product has proven very effective and reliable. We use the tablet for all of our drawing and mouse movements.
Archived lectures. With the archiving feature of Rendezvous and the saving feature of Netshow, we are in a position to record the lectures that we broadcast live over the Internet for later playback. The files are significantly compressed and can be archived synchronously so that when they are played back the student experiences a lecture that is similar to the live version.
Mathematics via the Internet. Since HTML (hyper text markup language) does not currently support mathematics symbols, we needed a way to transmit mathematics over the Internet. This is necessary if students want to send mathematics (in the form of assignments and projects) via email or obtain lecture notes from our server. Our choice was Scientific Notebook by TCI, a relatively inexpensive software application that allows the user to download mathematics (in the form of Scientific Notebook documents) from remote locations. (The price of Scientific Notebook has risen significantly since our decision to adopt it.) In addition to being a computer algebra system, Scientific Notebook is actually a browser for the Internet. However, it cannot read standard HTML documents; for this, the program calls up a specified web browser. In addition, the application could not be automatically invoked from a standard web browser such as Internet Explorer or Netscape's Navigator. Consequently, we found it necessary to maintain two distinct websites - one for standard HTML and another for Scientific Notebook documents such as lecture notes. While this is not a desirable solution to the problem of transmitting mathematics over the Internet, we found this configuration workable and we expect new products (hopefully available within the next three to six months) to rectify this situation.
Operating the system. We teach two online courses (freshman level Business Calculus and junior level Differential Equations) in our Hewlett Packard Mathematics Learning Center computer lab. The lab consists of 24 Hewlett Packard Pentium PCs running Windows NT and connected to an NT server. In addition the lab also contains the "Instructor station", which is a 200Mz Hewlett Packard PC with 96 Meg ram that serves as the computer from which the lecturer instructs. Attached to the instructor station is the graphics tablet and a LCD projection system that is used to project the image of the monitor of the instructor station onto a large screen at the head of the class. This setup allows the instructor to teach an essentially traditional math class, with a maximum of 24 students. The students in the classroom can either watch their personal monitor or watch the screen onto which is projected the activity that occurs on the instructor station. In the meantime, the lecture is broadcast out onto the Internet and the students outside the classroom see the whiteboard activity and hear the lecturer via the audio feed.
Online students initially experienced a time delay between the whiteboard and the audio feeds. The amount of delay experienced depended on a number of factors, including the particulars of the student’s home system and the ISP (or university dial-in line) used to access the data. This delay occurs because the whiteboard activity is more efficient to send over the Internet than the audio information. Working with the developers at Visualtek, we were able to offer the student a version of the Rendezvous client that allowed the user to set a delay in receiving the whiteboard. After a little experimentation, the student could synchronize the audio and whiteboard feeds.
Interaction occurs via the built-in "chatbox" feature of Rendezvous. The chatbox consists of an input window and a log window. Each time a user types in a sentence into the input window, the message appears in the log window with the name attached. In this manner, students can ask questions or get the attention of the instructor. Students in the classroom can also ask questions in the usual way. The instructor must repeat the question for the benefit of the online students, but such rewording and rephrasing of student questions typically occurs in a traditional classroom as well. Finally, the students can have chatbox conversations amongst themselves both during and outside the lecture via the ‘private message’ feature.
Interaction is also possible by granting whiteboard privileges to a student. Normally, students have access to the chatbox but only have 'read-only' privileges to the whiteboard. On those occasions when the class can benefit from having a student write on the whiteboard, the instructor can easily grant privileges to a specified student. Of course, the student will not necessarily have the benefit of a graphics tablet and so the output may appear very crude. Nonetheless, it can be an effective form of classroom participation.
When combined with the output of Scientific Notebook, the whiteboard can be a very robust delivery system of mathematics. In addition to handwritten mathematics, the instructor can easily and quickly paste in prepared mathematics text, graphics, complex numeric computations, and even symbolic manipulation. This makes the online experience more of a multimedia experience than the traditional mathematics classroom.
Finally, as the instructor is preoccupied with delivering mathematical content and answering mathematical queries from students, we found it convenient to have one of the course assistants monitor both the classroom and online chatroom in order to assist those students who may be having technical difficulties. This individual need not attend the entire lecture, only the first 30 minutes or so.
Evaluation of Student Work. Homework and projects can be submitted in class, by fax, or by email (provided the homework was written as a Scientific Notebook document). We generally return homework or projects in the same format as it was turned in: in class, by fax, or by email. Exams pose another problem for which we have not yet found a completely satisfactory solution. Presently, exams are administered on campus to all students. Those students who normally experience the class at a distance must therefore come to campus on the designated dates.
Program implementation. There are four identifiable factors that contributed to the success of the implementation of our online program.
Development grants. We applied for and were awarded two grants that helped support the purchase of equipment and provided partial off-load time for this project. Without this and other forms of support from the administration of our campus, we neither would not nor could not have attempted this project.
Creative use of students for the technical details. From the very start it was apparent that we did not possess the technical expertise necessary to implement the software utilized for this project. Considerable testing of software, as well as installing and monitoring the software, were required. We were fortunate to have a group of students that could help us with these technical details. Moreover, since our Department of Electrical and Computer Engineering requires a Senior Design project, we were able to make an agreement with the ECE department that would allow a student to work on our project and get credit for such work as part of his Senior Design project. As an added bonus, this was the kind of project that ignited the enthusiasm of the student.
Use of Mathematics students for teaching assistance. For the day-to-day activities (e.g. collecting and grading homework, helping students log onto the system, monitoring the lectures) and for handling online ("virtual") office hours, we employed a mathematics graduate student and a mathematics undergraduate student. These students have received beneficial training and experience in computer systems, networks, and pedagogical issues.
Autonomy of decision making. One of the most significant factors in the success of this project was our ability to make decisions without wading through a vast hierarchy of administrative layers. Since Abrams is chair of the department, we could make decisions and implement those decisions immediately. In addition, many of our computer resources, such as our web server, are administered within the department. Thus we did not have to appeal to an administrator from outside our realm in order to affect changes to the existing system. This resulted in extremely quick implementation time for many aspects of the project.
Conclusion. Although we are pleased with the product we are currently delivering, the S.H.O.W.M.E. project can still be considered very much as a ‘work in progress’. For example:
We have not yet fully implemented the archiving system which would allow students to play back the lecture at future times. We are currently considering a switch to the RealAudio product (despite its relatively high cost), as we have experienced much difficulty with the functionality of NetShow and quality of the audio delivered via NetShow. The number of students who are taking the course truly at a distance is not large enough to gather significant statistical data regarding such students’ performances.
We will be offering these two online courses again during Fall Semester 1998. At that time we hope to have addressed the above issues.
In conclusion, we feel that our experience with these courses justified and legitimized the basic tenets of our philosophy of distance learning. In particular, while it is certainly possible to put mathematics on the Internet in an extremely passive mode, a successful online course emulates the interactivity of the traditional classroom. In the future, when the bandwidth of the Internet significantly increases, it may be possible to incorporate the entire range of visual and audio interplay of a traditional classroom into the online mathematics course. Our experience with distance learning seems to provide a step in the right direction.
Further Information:
Webpages of Department of Mathematics at CU – Colorado Springs
http://www.uccs.edu/
http://www.math.uccs.edu/mathonline
VisualTek Solutions, Inc. (for the Rendezvous whiteboard product)
VisualTek Solutions, Inc.,
46750 Fremont Blvd. #207,
Fremont, CA 94538
phone: 510.353.0952
fax: 510.353.0954
http://www.visualtek.com/
TCI, Inc. (for Scientific Notebook)
http://scinotebook.tcisoft.com/
Hewlett Packard, Inc. (for information regarding networked PCs)
http://www.hp.com
Wacom, Inc. (for the graphics tablet)
http://www.wacom.com
Microsoft, Inc. (for Netshow)
http://www.microsoft.com/netshow
Interactive Learning International Corporation (for LearnLincTM)
385 Jordan Road
Troy, NY 12180
(518) 283-8799
(518) 286-2439 fax
RealMedia, Inc. (for RealAudio)
http://www.real.com
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