For the past three years, I have been teaching an online math course every semester. To ensure that the students taking the class are really the ones who signed up, I have always used in class midterm and final exams. I check their ID and my grading system system reflects a heavy weighting toward the in-class tests. I encourage students to use whatever resources are available, including Wolfram Alpha, to study and do their online homework. They know that the in class exams are closed book and so the outside resources mainly serve as a study guide. All information about my online classes are publicized well before the class starts, and so the students know what is expected.
I do wish there was a better way to monitor academic integrity other than in-class tests. A presentation by Judy Baker, Dean at Foothill College, CA, discusses many aspects of online learning and academic integrity.
I tend to agree with her that most students are honest. But the anonymity of an online course can certainly tempt students to compromise their sense of ethics, especially those who are math-phobic. High tech security measures are too cost-prohibitive to use in an academic online setting. As online programs and courses are expanding in colleges and universities, there certainly needs to be a discussion on how to check identities of the students in the classes, and to ensure that they are the ones doing the work. One suggestion is to require students to make a presentation using a webcam. Would a one-on-one short oral exam using something like vyew.com and a webcam work for math courses? It is worth thinking about. But I think that an online course with no face to face interaction, either virtual or real, is opening itself to all sorts of compromises.