September/October 2002 // Case Studies
Blending Online and Traditional Instruction in the Mathematics Classroom
by Gene Abrams and Jeremy Haefner
Note: This article was originally published in The Technology Source ( as: Gene Abrams and Jeremy Haefner "Blending Online and Traditional Instruction in the Mathematics Classroom" The Technology Source, September/October 2002. Available online at The article is reprinted here with permission of the publisher.

We describe in this case study the MathOnline system, a learning delivery system which has been developed and implemented at the Colorado Springs campus of the University of Colorado. This system simultaneously provides courses in mathematics both to traditional students (i.e., students who physically attend the lecture) and to distance students (i.e., students whose learning occurs outside either the time or the space boundaries of a traditional classroom setting). Student surveys indicate that the MathOnline system greatly enhances the educational experience of the traditional learner, while at the same time provides an opportunity for students who, for any number of reasons, choose to learn at a distance.

How the system works

Courses taught using the MathOnline delivery system are regular university mathematics courses which have appeared for many years in the standard course catalog, and currently include: Calculus I, Calculus II, Calculus III, Discrete Mathematics, Introduction to Differential Equations, and Introduction to Linear Algebra.

The MathOnline classroom environment is in most senses "traditional". The only difference which is readily apparent to the students is that the instructor, rather than writing directly on a chalkboard, instead writes on a graphics tablet which rests on a podium in the front of the classroom; the images so produced are then projected on a screen. While the in-class students are experiencing a relatively traditional classroom presentation, much is going on 'behind the scenes'. First, the images are simultaneously broadcast via the Internet, and are archived for future playback. Furthermore, by way of an instructor-worn wireless microphone, the instructor?¢‚Ǩ‚Ñ¢s voice is also simultaneously broadcast via the Internet and archived for future playback. (The wireless microphone allows unfettered movement of the instructor throughout the classroom.) Thus the in-class and distance students each receive the same audio and ?¢‚ǨÀúboard?¢‚Ǩ‚Ñ¢ content. (The LearnLinc software by Mentergy, Inc. is used by the instructor to deliver and archive the lectures, and is used by the student to view the lectures either synchronously or asynchronously).

Feedback from the traditional students.

The traditional students are quite enthusiastic about the MathOnline delivery system. In support of this opinion we present the response to a question which was included in a survey of the Spring 2001 traditional students enrolled in MathOnline supported courses:

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?

Traditional blackboard 12

Computerized whiteboard 104

When asked to ' ?¢‚Ǩ¬¶describe in detail the most important reason which influenced your choice between the two systems', the vast majority of students who preferred the computerized system cited one of these three things: the archiving feature (and availability of class notes from the Internet); the ability of the instructor to easily incorporate Internet material and graphics in the classroom; and the ease with which the screen image can be seen from everywhere in the classroom. The students who preferred the traditional blackboard cited less 'distraction' in that model.

Feedback from the distance students

Virtually all of our distance students fall into one of three cadres:

  • advanced high school students who enroll in these courses as 11th or 12th graders

  • middle school and high school mathematics teachers (or potential teachers)

  • standard University of Colorado at Colorado Springs degree-seeking students who, for any number of reasons, cannot attend the traditional class sessions for these courses.

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 and the middle and high school instructors complete exams at their school under the proctoring auspices of a ?¢‚ǨÀúCoordinating Math Teacher?¢‚Ǩ‚Ñ¢. Students in the third cadre come to campus to complete their exams alongside the traditional students.

The most 'general' question (and corresponding responses) among those included in a survey of the Academic Year 2000 / 2001 distance students is presented here.

LOW 1 2 3 4 5 HIGH Please rate your overall experience with the course.

1 - 0 responses

2 - 3 responses

3 - 3 responses

4 - 8 responses

5 - 6 responses

Average response: 3.85

(Note: Of the 8 students enrolled during Spring 2001, a majority of whom were also enrolled during Fall 2000, the average response to this question was 4.375. )

General observations

Recent news reports (e.g., Jason, Wall Street Journal, August 22, 2001) indicate that many professors are experiencing a drop in student classroom attendance and participation in those courses for which the lectures are made available for asynchronous viewing. We have found no such drop in attendance. Indeed, the responses to the following survey question (Spring 2001) are illuminating:

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

106 Yes 8 No

When asked to give the single most important reason which affected the choice of answers to the previous question, the majority of 'Yes' respondents indicated either " teacher / student interaction", or a response represented appropriately by " ?¢‚Ǩ¬¶education is still a largely social experience for me".

The course instructor shoulders an initially large but rapidly diminishing burden in the MathOnline delivery process. Our experience is that the instructor?¢‚Ǩ‚Ñ¢s learning curve vis-?É -vis the use of the graphics tablet, microphone, and whiteboard product 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. The MathOnline delivery system affords the instructor numerous 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. Thus a major advantage to the MathOnline distance learning system compared to others currently in use is that the development costs associated with bringing a new course online are virtually nonexistent.

The major costs associated with supporting the MathOnline delivery system include: technical support; instructor stipends; campus-wide administration fees; office overhead; proctoring services; and advertising / marketing. The total amount charged to distance students to enroll in a MathOnline-supported course ($577 for a 3 semester credit hour course; $683 for a 4 s.c.h. course) is roughly the same amount that a traditional Colorado resident student would pay in tuition plus fees for the same course. With this price structure the MathOnline program manages to essentially break even financially. As the program grows (for Fall 2001 there are 28 students enrolled, compared to 18 in Fall 2000) we expect some economies of scale to allow the program to generate a profit. Thus the MathOnline program has avoided the fiscal traps which have plagued many of the high profile (and admittedly much larger scale) distance education programs throughout the country (see e.g. Blumenstyk, The Chronicle of Higher Education, July 20, 2001

There are a number of issues regarding the MathOnline system on which we will focus our attention in the near future. First, due to pedagogical and identification verification issues, we have not yet implemented a secure online exam procedure. The current 'Coordinating Math Teacher' model works perfectly well for proctored exams at a distance, but this arrangement does introduce logical complications and overhead, issues which we seek to eliminate.

Second, 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 synchronously at a spatial distance can ask questions via the LearnLinc chatbox. However, this can be rather cumbersome, especially when mathematics symbols are required to pose a question.) A promising form for interaction is the 2-way audio feature that is supported by the LearnLinc platform. We have used this feature for online office hours but we would like to integrate it into the classroom lecture. Another possible interaction involves creating ?¢‚ǨÀústudent learning groups?¢‚Ǩ‚Ñ¢ that would enable students to 'virtually?¢‚Ǩ‚Ñ¢ come together in order to discuss problems and work on projects.

Third, we hope to gather data that measures the effectiveness of the product being delivered 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 demographics, further analysis is warranted.

Finally, the archiving feature of the MathOnline system threatens to open a Pandora?¢‚Ǩ‚Ñ¢s Box of issues, including copyright, ownership, instructor remuneration, and professional obsolescence. The simultaneous goals of ?¢‚ǨÀúease of access for students?¢‚Ǩ‚Ñ¢ versus ?¢‚ǨÀúprotection of creative work?¢‚Ǩ‚Ñ¢ seem to be meeting at loggerheads here. As one example, CDRoms containing all of the Spring 2001 lectures from the five MathOnline supported courses were made available for sale to students in the CU - Colorado Springs bookstore for the Fall 2001 semester. Who should determine whether such sales are appropriate? Who should profit from such sales? Existing copyright law is relatively ill-suited for this type of electronic environment. The University of Colorado system is currently preparing a policy statement which may address some of these issues.


Blumenstyk, G. (2001, July 20). Temple U. shuts down for-profit distance-education company [Electronic version]. The Chronicle of Higher Education

Jason, L. (2001, August 22). Web lectures make it easier for students to skip classes [Electronic Version]. The Wall Street Journal

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