Hi.
I currently use eCollege when I teach my courses. To date, I have used eCollege to augment all of my courses. In addition, I have used eCollege to teach courses entirely online in discrete mathematics, college algebra and statistics. I am also familiar with Blackboard and have used it to augment my courses as well.
Without a doubt, an online gradebook, available course documents, easy e-mail facilities, online assignment submission, and online discussion capabilities enhance a course. They are, however time consuming to construct, maintain and troubleshoot.
What is more problematic are the assessment features: online quizzes and exams. The problems stem from two areas. Without requiring proctored exams, there is virtually no way to prevent one student from taking an exam for another. There is virtually no way to prevent a student from using any technological device while taking the exam.
In addition, as online exams are more time-consuming to develop, I find myself unable to devote the time to modify my online materials, specifically exams and quizzes each semester. In a regular course, each quiz and exam has 3 different versions and I change these exams each semester. I hate to say that I cannot currently do this for my online courses.
Finally, one may debate about whether the online teaching medium is optimally suited to teaching a math course. However, the technology is available and I don't see it going away any time soon. It is similar to arguing against the use of calculators in the classroom. It does not appear like a debate that the anti-calculator and similarly the anti-online camp can win in the long run.
Those are my two cents. Remember as I continue to teach online my opinion will constantly evolve. Also, the online experience can be LARGELY affected by the software policies decided by your university's system administrators.
Dov