This article appeared in the Proceedings of the ICTMC 2000.

Gene Abrams and Jeremy Haefner
Department of Mathematics
University of Colorado at Colorado Springs
P.O. Box 7150
Colorado Springs, CO 80933-7150
gabrams@uccs.edu haefner@eas.uccs.edu

We describe in this article the MathOnline system, a learning delivery system which we have developed and implemented in order to provide courses in mathematics to students participating at a distance; that is, to students whose learning occurs outside either the time or the space domain of a traditional classroom setting. We have found that this system provides advantages to the traditional learner as well as to those students who, for various reasons, choose to learn at a distance.

There are essentially two types of students who enroll in these MathOnline-supported courses: the students who approach the course as ‘traditional’ (i.e., students who physically attend the live lectures on a regular basis), and the students who incorporate a substantial portion of the Internet / archiving component (i.e., students who view the lectures at a temporal or spatial distance on a regular basis). Our initial fears that the simultaneous servicing of both groups would result in the delivery of a lower quality course than we could deliver to each group individually were shown by survey results to be completely unfounded. Specifically, the in-class students benefit from the electronic whiteboard and archiving features of the approach (features missing from a ‘traditional’ presentation), while the distance students benefit from their ability to interact real-time or on a regular basis with a clearly identifiable instructor and classmates (features missing from many web-page based, computer tutorial driven on-line courses).

The courses taught using this delivery system are regular university mathematics courses which have appeared for many years in the standard course catalog. Currently these include Calculus I, Discrete Mathematics, Introduction to Differential Equations, and Introduction to Linear Algebra. Offerings will be expanded in Academic Year 2001/02 to include Calculus II, Calculus III, and Introduction to Statistics. (Additional courses which have been taught via the MathOnline system in previous semesters include Electronics I, Electronics II, and Calculus for Business and Economics.)

Classrooms in which these courses are taught are outfitted with an Instructor Station. This station consists of a lectern (in which is housed a computer with an attached graphics tablet) and a wireless microphone system. The computer output is fed through a projector mounted on the ceiling of the classroom. Aside from these pieces of hardware, all other aspects of the classroom are ‘traditional’. The instructor, rather than writing directly on a chalkboard, instead writes on the graphics tablet while standing at a podium in the front of the classroom. The images produced are then projected on the screen in front of the classroom, thus effecting an image very much like that of a traditional chalkboard. The image is simultaneously broadcast via the Internet, and is archived for future playback. Furthermore, the instructor’s voice is heard directly by those students who are sitting in the traditional classroom. By way of the instructor-worn wireless microphone, the instructor’s voice is also simultaneously broadcast via the Internet, and is archived for future playback. The wireless microphone allows free movement of the instructor throughout the classroom. Thus the traditional and distance students each receive the same sound and ‘board’ content, although the sound component is heard directly by one set of students, and via the Internet by the other.

The LearnLinc collaboration software product provides the backbone of the MathOnline system. Specifically, LearnLinc supports a synchronized learning environment which includes: multicast two-way audio, application sharing and viewing, web surfing, and presentation capabilities (including Powerpoint). This product supports the same sort of 'boardwork' which an instructor would normally produce in a classroom setting. In addition, the LearnLinc whiteboard allows the instructor to: incorporate various graphics features (e.g. draw lines or circles, change color); paste images (e.g. graphs or photos or images from a web site) into the whiteboard, and then annotate the image; archive hard-copy of the lecture notes; archive the 'live' lecture, specifically the voice and 'active' boardwork; recall any portion of the current lecture, or of previous lectures; know who is synchronously participating at a distance (as each participant at a distance logs in, and his/her name appears in a current list of users); and receive questions from any student synchronously participating at a distance, by means of a chatbox or two-way audio.

While a small minority of the in-class students feel the computer aided lecture system is somewhat ‘burdensome’, the following feedback from a survey of the 70 traditionally-enrolled students during Spring Semester 2000 is illuminating:

Suppose that during some future semester, two sections of the same course are taught by the same instructor. In one section, the instructor will use a traditional blackboard, while in the other, the computerized whiteboard system will be used. In which section would you choose to enroll?

11 Traditional blackboard 4 ‘50/50’

54 Computerized whiteboard (1 survey with no response)

The distance students learn in a number of different environments. Students who choose to participate at a distance are able to fully participate in the course provided they have, at a minimum: a hard drive running a standard operating system (e.g. a pentium-based PC), with a sound card; an Internet connection; 28.8 modem; email access; fax access; additional software as required to support computer algebra computations, e.g. Maple or Scientific Notebook; and the LearnLinc client. Registered students are provided with a CDRom of the LearnLinc client free of charge, while the computer algebra systems can be purchased by students for less than $50.

Over the six semesters we have delivered courses via the MathOnline system, two distinct cadres of distance students have emerged. The first such cadre consists mostly of advanced high school students who enroll in these courses during their junior or senior years. Typically these are students who have completed a calculus sequence prior to their senior year in high school, and find themselves having pushed through the envelope of mathematics courses offered at their school. The second cadre of distance students includes standard UCCS degree-seeking students who for spatial or temporal reasons cannot attend the traditional class sessions for these courses. Typically these reasons include employment concerns, family commitments, or course schedule conflicts.

Students at a distance are required to complete homework assignments on the same schedule as the in-class students; such work can be submitted either by fax or by attachments to emails. Proctoring arrangements are made at the start of the semester for any student who wishes to take exams at a distance. Typically, the high school students complete exams at their school under the proctoring auspices of a ‘Coordinating Math Teacher’, an individual who has agreed prior to the start of the semester to shoulder such duties. Most of the students in the second cadre come to campus to complete their exams. For both pedagogical and administrative reasons, we do not offer exams on-line.

The one major component of a traditional classroom experience which we have not been able to deliver at a distance is what might be called the personal factor. While this term is obviously somewhat nebulous, it seems to be the overriding reason for the response to the following survey question (Spring Semester 2000, n = 70):

Suppose that you had easy, free access to all the hardware and software required to view the lectures real time ‘at a distance’ via the Internet. (This means that you would see whatever was written on the whiteboard, and you would hear the instructor’s voice simultaneously.) Would you still choose to regularly attend the live lectures?

60 Yes 7 No (3 surveys with no response)

When asked to give the single most important reason which affected your choice of answers to the previous question, the majority of 'Yes' respondents indicated Teacher / student interaction or eye contact. Additional reasons are included these representative responses: I wouldn’t attend the electronic sessions regularly due to laziness; More distracting / detached to view a computer; Education is still a largely social experience for me; Can interact more and see more; Technical difficulties with the software; I like being in class; Just the personal note of it; Concentration; Class atmosphere; Learn faster in class; Learn better in class; and Personal interaction. The students who provided 'No' responses indicated Parking; Convenience; and Uncomfortable seats in classroom as primary reasons.

We broadcast from a system running Windows 2000 Advanced Server. The system consists of two Pentium III 500 MHz processors with 512 Megabytes of RAM and a
10-gig scsi hard drive. The server software requires an 850 Megabyte partition with 650 Megs of hard drive space free. Storing the audio and whiteboard files for playback access by students requires about 200 Megabytes of server hard drive space per semester per course. The LearnLinc server software requires 128 Megs of RAM, a 300 MHz processor or better, and 150 Megs of hard drive space. The amount of RAM used varies, depending on the number of channels (classrooms) and size of the whiteboard space used in each channel. Our Instructor Station consists of a projector and graphics tablet. This station uses the same version of the LearnLinc software as the client stations. The client on Windows 95 or 98 requires 24 Megabytes of RAM, and a 28.8 modem or faster. Windows 2000 requires 64 Megs of RAM, and a 28.8 modem or faster.

There are three main constituencies which comprise the human effort required to deliver courses using MathOnline: the technology support staff, the administrative support staff, and the course instructor. Duties of the technology support staff include direct instructor support with the classroom delivery, lecture archiving, and provision of technical support to students who wish to use the system. In addition to these regularly occurring duties, the technical support staff must assist in the initial setup of the server at the beginning of each semester for each class. Such setup tasks include maintaining and modifying the LearnLinc server, allocating passwords, readying the web server for archiving capability, and initializing the Instructor Station and client software packages. Administrative services required to deliver MathOnline-supported courses which can be viewed as ‘above and beyond’ the usual services required to support a standard mathematics course include standard office administration (e.g. receiving faxed homework assignments and distributing them to appropriate professors’ mailboxes, mailing graded homework assignments back to students, ensuring timely delivery of exams to the at-a-distance proctors) and internal processing of registration forms for distance students.

The course instructor shoulders a large but diminishing burden in the MathOnline delivery process. On a rather mundane level, the instructor spends approximately two or three minutes immediately preceding each lecture ‘launching’ the system (e.g. booting the instructor’s computer, opening LearnLinc, Scientific Notebook, etc.). Similarly, the instructor spends approximately one minute immediately after each lecture ‘powering down’ the system (closing the files, saving the files for archiving, storing the graphics tablet, etc.). Our experience is that the instructor’s learning curve vis-à-vis the use of the graphics tablet, microphone, whiteboard product, and the like is somewhat steep: once the initial five or six lectures have been delivered, the ‘electronic’ system becomes rather transparent, and the instructor feels relatively comfortable in the new environment. On a more grandiose level, this delivery system allows the instructor a cornucopia of pedagogical possibilities, from producing pre-lecture notes and mathematics graphics to organizing and facilitating student group work at a distance. Obviously each of these tasks can consume an enormous amount of instructor time. However, the marginal time required (over and above the initial learning curve) to teach a course using the MathOnline delivery system versus a standard chalkboard delivery is essentially zero.

For the future. There are a number of issues regarding this system on which we will focus our attention in the near future. For instance, we have not yet implemented an exam procedure which is truly at a distance. The nature of the exams we give (full written answers, computations shown, very few multiple choice questions), together with identity verification issues, do not lend themselves well to giving exams in an on-line environment. Most importantly, we would like to engender more student-student and faculty-student interaction than currently takes place among the students at a distance. Students who are participating real-time at a spatial distance can ask questions via the LearnLinc chatbox. However, this can be rather cumbersome, especially when technical writing is required to pose a question. As the cost of graphics tablets decreases, it may become appropriate to require students at a distance to purchase such devices in order to better interact with the instructor. Such interaction can take place both in the real-time setting as well as during electronic office hours. With a microphone, students can communicate with the instructor via audio as well; this is a useful feature during online office hours.

In the near term we hope to gather some data which reflects the effectiveness of the product we deliver at a distance, versus the effectiveness of the traditional in-class delivery. As a crude initial estimate, we have found that there is no statistically significant difference between the grades earned by in-class students in MathOnline delivered courses, versus those earned by distance students. However, as these groups of students typically have different backgrounds and demographic makeup (e.g., many of the distance students are still in high school), further analysis is warranted.

Finally, the archiving feature of the MathOnline system threatens to open a Pandora’s Box of issues, including copyright, ownership, instructor remuneration, and professional obsolescence. The simultaneous goals of ‘ease of access for students’ versus ‘protection of creative work’ seem to be meeting at loggerheads here. Existing copyright law is relatively ill-suited for this environment, mostly due to the ease of portability of the material being produced (i.e., electronic files). We are currently working with various faculty representative groups and university legal counsel to establish some guidelines and procedures in these areas.

Various additional information:

·         For questions about the MathOnline delivery system, or requests for guest accounts to view the system:  mathon@uccs.edu

·         University of Colorado at Colorado Springs Department of Mathematics MathOnline Program: http://www.uccs.edu/~math/mathonline

·         The gateway page to MathOnline-supported materials: http://online.uccs.edu

·         Complete results of the aforementioned student surveys can be found at: http://www.uccs.edu/~math/mathonline/surveys/SurveyResultsfromSpring2000.ppt

·         Information about LearnLinc: http://www.learnlinc.com