While all the requirements are not known by anyone at this time, there are some necessary conditions that seem without question.

Beginning level students of mathematics need textbook quality mathematics delivered to them. Lesser quality, even unfamiliar fonts, can throw students off track, causing more problems than solving.

Reading text, particularly mathematics from a video screen requires sustained, controlled, and concentrated attention. Pages of black (electronic) ink will not communicate with anyone over the long term. To keep the student involved requires an "interesting " interface that will hold the student’s interest and focus his/her concentration. Bright colors and exciting graphics are exactly what most students expect and demand if you are to engage them. They’ve been conditioned to this from years of watching TV; denying its impact is foolish.

Day-by-day, students learning from an on-line course need to know how they are doing, and you, the teacher, need to know, too. But with web learning this is not so straightforward. Once we enter the realm of television, i.e. video interface, we enter the world of instantaneous feedback. We believe that computer graded, rapidly returned test results are essential. The distance learner wants to know, and should know results right away. This will give him/her the confidence to proceed with diligence.

The course must be fully linked with definitions and examples. It is a daunting task to deliver great looking mathematics and (vector, not bitmapped) graphics over the internet in an acceptably short time frame. We believe this is the strongest suit of the software we are using. Most files, including those with much mathematical content are less than 12 kb, excluding graphics. Download times average well under than 10 seconds. This means the format is effective even over that "last mile" of travel; that is, from the local internet provider over a phone line to the school or home. For internet delivery, most video and audio must be limited because of file size. Limited animations (gif) and Java applets are possible. We use them when appropriate. We also pay close attention to whether they "work" for students.

This is the most complex of all the issues we consider. The on-line mathematics course must be the teacher, the mentor, the facilitator, the comforter, and the threat, and so much more. The course must do many things that mimic human interaction. To the student it must:

Think this is easy? It takes most of us teachers years of dedication to achieve this. The on-line course must try to be this and more. It must

The on-line course can never be the in situ teacher, but maybe it can do some things the teacher cannot. By actively encouraging and engaging in the use of the CAS, students can experiment with mathematics, answer by themselves those "what-if" questions that can mean the difference in true understanding. So we append our list with

Finally, and perhaps most unlikely,

The requirement to keep the student engaged day after day, month after month, through the whole term, drives this condition. To keep up the interest, exciting things must happen.

An important part of a new pedagogy should be an evaluation process. There are at least two simple ways to measure efficacy, test scores and surveys. Test scores between sections taught with and without the technology should be compared. At this stage of development, maintaining a par with traditional methods is a great victory for distance education. Short surveys are given every couple of weeks to find out what’s working and what’s not while it’s fresh in the student’s mind. It’s also good PR with the students; they appreciate knowing that we value their opinion. Data from these surveys is accumulating and results (which are remarkably interesting) will be reported at a future time.

This is the transition period for on-line education. In just a decade, many, many students will have learned much on-line and be as familiar with this format as they are today with television and teachers; students will have a completely different attitude. It is important to recognize that during its transition period a new idea can be defeated before it gets a fair chance. Therefore, consider this question. Even if we achieve all the above goals, and even if we get reasonable students, are we guaranteed success? The answer is "possibly not." Unless students can be convinced that the on-line course they are taking will generate expected results with the same amount of effort, they will likely reject the new format. They need to be convinced that it’s working. For instance, they should be assured that their learning is more in their own control than ever before, or that they are learning to use a powerful piece of software, or that they have at their disposal powerful new techniques for learning mathematics and solving mathematical problems.

We are in our second semester of using this course at Texas A&M. We use the facilitator model, which means that we are with the students in the computer laboratory three days per week. Circulating the lab for the full period and beyond, we see just which students are having problems, the types of problems they are having, and the nature of the problems. We see what course features need further authoring attention. We see how students interpret exercises and stumble trying to solve them. Compared with the "chalk talk" traditional method, the most remarkable difference is our increased interactivity with students. We know better than ever before what aspects of calculus cause our students the greatest conceptual and computational obstacles.

We feel an intimacy with the class, greater than before. We actually come to know students, including normally quiet students that now aren’t timid about asking a question when it’s just to the Professor. We also notice spontaneous team learning; one student asks another when troubled. They help each other. Often questions come from a pair of students, mutually stumped over some point.

However, some students do have difficulties with the new format. Some wish to be transferred to a traditionally taught section.

It is easy to imagine that some teaching models for an on-line course decrease required teaching resources. If the on-line course is good enough, it should carry much of the teaching burden. But, we are often asked, will this prepare the student for the next course, or their career? If the student is enrolled at a good or even great institution where dedicated and capable professors are available, then the on-line course will likely come in second. However, we note that that some (even highly paid) professors have been giving bad lectures for years. Does their teaching meet the criteria asked of distance education? Do their students concede value to this "live" course, or do they come away empty of mathematics except what they have actually learned by themselves and on their own? Bluntly, is what many instructors offer any better than a well crafted, well tested, on-line course? Probably not. The point is this: very good and great teachers will likely always be better than an on-line rendition of what they do, just as small class sizes are better than huge 150+ student lectures. However, fully half of all teachers are at most OK, not exceptional and certainly not great. We do our students a great service by offering them the on-line alternative. This is one case among several that illustrate the significance and importance for on-line mathematics courses, which no doubt will steadily improve over time. Finally, the issues of diminished teaching resources, which swirl around us all, provide another compelling case for serious, well-designed, on-line courses.