S.H.O.W.M.E.: Spear-Heading Online Work in Mathematics Education


In the springsemester of 1998, the Department of Mathematics at the University ofColorado at Colorado Springs offered two courses over the Internet asthe first stage in its Distance Learning program. The key feature ofthese two online courses was that live lectures were "broadcast" asaudio and whiteboard feeds. In this article we discuss themotivation, details and results of this project.

Our motivation forexperimenting with offering courses "at-a-distance" was fueled by anumber of factors. First, there is a natural constituency ofpotential students who require or desire courses from the University,and for whom actual class attendance is difficult (if notimpossible). Examples include: people who live far away from CU -Colorado Springs (e.g. students at junior or community collegesthroughout Southern Colorado); people with physical disabilities;people whose work schedules do not allow them to attend classregularly; and high school students who wish to complete universitycourses during their junior or senior years. As a public institution,we felt that we have a responsibility to try to accommodate themembers of these groups.

Second, there was aninterest on our part to see just what the currently emergingtechnologies would allow us to do in regards to delivering courses ata distance. We have taught mathematics courses on television. But whowas really out there watching? We have experienced distance learningcourses that consist of nothing more than information scanned into acomputer and reconfigured as Web pages. So why not just read atextbook? We have observed some mathematics Web sites which seem tobe fixated on presenting essentially nothing more than cute graphicsand slick animation. Where's the beef? In the end, we saw few (ifany) instances where the successes of the traditional classroom wereemulated online. Would the new technologies make it possible tosomehow extend to a distance the things we view as the key elementsof traditional classroom delivery (i.e., live instructor,student-instructor interaction, student-student interaction, humancontact)?

Third, we wanted toconfront first hand some of the pedagogical issues surroundingdistance learning. What are the advantages of this approach? What arethe disadvantages? What differences are there between theperformances of students who learn "at a distance" versus thoseschooled in more traditional classroom settings?

Finally, and perhapsmost importantly, we sensed the existence of giant administrativesteamrollers charging ahead "pedal-to-the-metal" in the effort todeliver distance education. While part of the justification forpursuing such an effort is quite honorable ("education for themasses"), the jaundiced faculty eye sees administrative bean-countersdrooling over a tasty cash cow. While parts of such a program can beviewed as improved pedagogy, the absence of traditional humaninteraction leads some faculty to view it as unacceptableMcLearning.

We felt (and stillfeel) strongly that in order to be effective participants in thediscussion regarding the future direction and scope of distancelearning, we should have some first-hand experience from which todraw. This project has supplied us with such experience, and thensome. The acronym S.H.O.W.M.E. is thus a wholly appropriate monikerfor this program: it indicates that our interest in this project isvery real, but is mixed with healthy doses of caution andcynicism. 

A ChalkboardExperience

A distinguishingfeature of our program is our incorporation of a large dose of thetraditional classroom elements into our presentations. We believe thetwo most important components of a mathematics classroom presentationare the use of some sort of "chalkboard" (in order to visually,efficiently transmit mathematics), and the voice/words of theinstructor (in order to describe, explain and otherwise guide thestudents through the material). Thus, we believed that it wasessential to provide both the "chalkboard experience" and the voiceof the instructor to the students online.

We investigatedvideoconferencing applications, hoping that we could possibly deliverboth a live video and audio feed. The idea was to have a video camerarecord the lecture, while simultaneously broadcasting the lectureover the Internet (using a product such as RealAudio or NetShow). Inaddition, we could archive the video lecture and permit students toview the lecture over the Internet at their convenience. However, ourexperimentation with this form of videoconferencing quickly showed usthat the video signal was far too large to transmit over the Internetin such a way that students with standard 28.8 baud modems couldreceive a coherent lecture. It was at this point we scaled back ouraspirations and decided to try to deliver only an audio and a"whiteboard" feed.

Through an Internetsearch on "whiteboards" we became acquainted with the productRendezvous by VisualTek Solutions, Inc. Like LearnLinc, fromInteractive Learning International Corp., this too is a client/serverapplication designed around whiteboard conferencing. VisualTek haswritten this product as a multi-platform application, meaning itcould be used on a variety of computers (e.g. Suns, Macs, PCs). Iteven provided a Java applet for use from a Web browser. Our initialtests indicated that this product seemed very stable and robust. Webegan a dialogue with Mr. Sanjay Dalal, a technical marketingrepresentative at VisualTek. We soon realized that our distancelearning project was appropriately suited to benefit both theUniversity of Colorado and VisualTek. Subsequently, a very agreeablecontract was formulated between the two parties and a verycomfortable working relationship began.

Because the existingRendezvous product did not exactly suit our needs, we asked thedevelopers at VisualTek to make some modifications. Thesemodifications 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; and
  • other minor modifications (e.g. keyboard equivalents to repetitive mouse movements).

We presented thedevelopers with these requirements in early November 1997, with adeadline of mid-December for product delivery. To our pleasantsurprise, the product was delivered in early December. Thisreinforced our choice of VisualTek as a partner in our distancelearning endeavor.

In the meantime, wehad selected Microsoft's NetShow application to deliver the audiofeed of our lecture. This was motivated by the fact that we plannedto use our NT Web server to perform the actual delivery. We felt thatby using a product that was (in theory) designed to work well in anNT environment, we would be saving ourselves much time and effortlater. In addition, the NetShow server 2.0 was free to us and camewith adequate documentation. On the downside, the NetShow player wasonly available on the PC platform, so our decision to use NetShowprecluded a Mac user from hearing the audio portion of our lecture.We considered this to be a major disadvantage, but as this was thefirst experiment in this project we felt our decision was justified.Our other audio option was RealAudio. The cost of RealAudio wouldhave been greater than the cost of NetShow, but it would have beenavailable to multiple platforms.

With the archivingfeature of Rendezvous and the saving feature of NetShow, we are in aposition to record the lectures that we broadcast live over theInternet for later playback. The files are significantly compressedand can be archived synchronously so that when they are played backthe student experiences a lecture that is similar to the liveversion.

Finally, weinvestigated smart whiteboard hardware products that would allow usto write on a large whiteboard surface, digitize the markings, sendthe markings into our instructor station computer and distribute themover the Internet via Rendezvous. While this technology mayultimately be viable, we opted for the simpler approach of using alarge graphics tablet (made by Wacom). This product has proven veryeffective and reliable. We use the tablet for all of our drawing andmouse movements.

Since HTML d'es notcurrently support mathematics symbols, we needed a way to transmitmathematics over the Internet. This is necessary if students want tosend mathematics (in the form of assignments and projects) via e-mailor obtain lecture notes from our server. Our choice was ScientificNotebook by TCI, a relatively inexpensive software application thatallows the user to download mathematics (in the form of ScientificNotebook documents) from remote locations. (The price of ScientificNotebook has risen since our decision to adopt it.)

In addition to beinga computer algebra system, Scientific Notebook serves as a browserfor 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 standardWeb browser such as Internet Explorer or Netscape Navigator.Consequently, we found it necessary to maintain two distinct Websites &emdash; one for standard HTML and another for ScientificNotebook documents such as lecture notes. While this is not an idealsolution to transmit mathematics over the Internet, we found thisconfiguration workable and we expect new products to rectify thissituation.

Interacting withthe Instructor

We teach two onlinecourses (freshman-level Business Calculus and junior-levelDifferential Equations) in our Hewlett-Packard Mathematics LearningCenter computer lab. The lab consists of 24 Hewlett-Packard PentiumPCs running Windows NT and connected to an NT server. In addition,the lab contains the "instructor station", a 200MHz Hewlett-PackardPC with 96MB of RAM. Attached to the instructor station are thegraphics tablet and an LCD projection system, used to project theinstructor's monitor onto a large screen at the head of the class.This setup allows the instructor to teach an essentially traditionalmath class, with a maximum of 24 students. The students in theclassroom can either watch their personal monitor or watch the largescreen to follow the instructor's activity. At the same time, thelecture is broadcast onto the Internet, and the students outside theclassroom see the whiteboard activity and hear the lecturer via theaudio feed.

Online studentsinitially experienced a time delay between the whiteboard and theaudio feeds. The amount of delay experienced depended on a number offactors, including the particulars of the student's home system andthe ISP (or university dial-in line) used to access the data. Thisdelay occurs because the whiteboard data is more efficient to sendover the Internet than the audio information. Working with thedevelopers at VisualTek, we were able to offer students a version ofthe Rendezvous client that allowed the user to set a delay inreceiving the whiteboard. After a little experimentation, the studentcould synchronize the audio and whiteboard feeds.

Interaction occursvia the built-in "chatbox" feature of Rendezvous. The chatboxconsists of an input window and a log window. Each time a user typesa sentence into the input window, the message appears in the logwindow with the name attached. In this manner, students can askquestions or get the attention of the instructor. Students in theclassroom can also ask questions in the usual way. The instructormust repeat the question for the benefit of the online students, butsuch rewording and rephrasing of student questions typically occursin a traditional classroom as well. Finally, the students can havechatbox conversations amongst themselves both during and outside thelecture via the "private message" feature.

Interaction is alsopossible 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 canbenefit from having a student write on the whiteboard, the instructorcan easily grant privileges to a specified student. Of course, thestudent will not necessarily have the benefit of a graphics tabletand so the output may appear very crude. Nonetheless, it can be aneffective form of classroom participation.

When combined withthe output of Scientific Notebook, the whiteboard can be a veryrobust delivery system of mathematics. In addition to handwrittenmathematics, the instructor can easily and quickly paste in preparedmathematics text, graphics, complex numeric computations and evensymbolic manipulation. This makes the online lecture more of amultimedia experience than the traditional mathematicsclassroom.

Finally, as theinstructor is preoccupied with delivering mathematical content andanswering mathematical queries from students, we found it convenientto have one of the course assistants monitor both the classroom andonline chatroom in order to assist those students who may be havingtechnical difficulties. This individual need not attend the entirelecture, only the first 30 minutes or so.

Evaluation ofStudent Work

Homework andprojects can be submitted in class, by fax, or by e-mail (providedthe homework was written as a Scientific Notebook document). Wegenerally return homework or projects in the same format as it wasturned in. Exams pose another problem for which we have not yet founda completely satisfactory solution. Presently, exams are administeredon campus to all students. Those students who normally experience theclass at a distance must therefore come to campus on the designateddates.

There are fouridentifiable factors that contributed to the success of theimplementation of our online program:

  1. 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 could not have attempted this project.
  2. 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 that would allow an ECE student to work on our project and get credit as part of his Senior Design project. As an added bonus, this was the kind of project that ignited the enthusiasm of the student.
  3. 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.
  4. 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 one of us chairs 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.

 A Work inProgress

Although we arepleased with the product we are currently delivering, theS.H.O.W.M.E. project can still be considered very much a "work inprogress." For example, we have not yet fully implemented thearchiving system, which would allow students to play back the lectureat future times. The number of students who are taking the coursetruly at a distance is not large enough to gather significantstatistical data regarding such students' performances. We will beoffering these two online courses again during Fall Semester 1998. Atthat time we hope to have addressed the issues discussed in thisarticle.

In conclusion, wefeel that our experience with these courses justified and legitimizedthe basic tenets of our philosophy of distance learning. Inparticular, while it is certainly possible to put mathematics on theInternet in an extremely passive mode, a successful online courseemulates the interactivity of the traditional classroom. In thefuture, when the bandwidth of the Internet significantly increases,it may be possible to incorporate the entire range of visual andaudio interplay of a traditional classroom into the onlinemathematics course. Our experience with distance learning seems toprovide a step in the right direction.

Gene Abrams receivedhis Ph.D. in mathematics from the University of Oregon in 1983. He iscurrently Professor and Chair of the Department of Mathematics at theUniversity of Colorado at Colorado Springs. In 1996 he was designatedas a University of Colorado Presidential Teaching Scholar.
E-mail: abrams@math.uccs.edu 

Jeremy Haefnerreceived his Ph.D. in mathematics from the University of Wisconsin in1986. He is currently Associate Professor of Mathematics at theUniversity of Colorado at Colorado Springs. Since 1995 he has beenthe director of C.A.T.M.E., the Center for Applications of Technologyin Mathematics Education.
E-mail: haefner@math.uccs.edu 

URLs forDepartment of Mathematics:





VisualTek Solutions,Fremont, CA, (510) 353-0952, www.visualtek.com.
TCI, Inc., Pacific Grove, CA, (800) 874-2383, http://scinotebook.tcisoft.com/.
Hewlett Packard, Inc., Palo Alto, CA, (800) 839-6850,www.hp.com.
Wacom, Inc., Vancouver, WA, (800) 922-9348, www.wacom.com.
Microsoft, Inc., Redmond, WA, (424) 882-8080, www.microsoft.com/netshow.
Interactive Learning International Corp., Troy, NY, (518) 283-8799,www.ilinc.com.
RealNetworks, Seattle, WA, (800) 444-8011, www.real.com.

This article originally appeared in the 05/01/1998 issue of THE Journal.

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