Online math courses and academic integrity

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.

Academic Integrity in Online Courses

View more presentations from Judy Baker.

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.

Counterexamples in Calculus

One way I motivate critical thinking in my Intro to Proofs class is by using counterexamples. The book, Using Counter-examples in Calculus by Mason and Klymchuk, provides an accessible set of ideas to think about. Producing counterexamples is an important step to thinking about proofs in general, especially for students who are used to computations. What I really liked about the book were the graphs that accompanied many of the counterexamples. Here is one statement to think about:

True or false: The tangent to a curve at a point is the line which touches the curve at that point but does not cross it there.

The book is actually intended for first year calculus students and could work in that context if the course emphasizes concepts along with the standard skill set.

 

And the counterexample for the statement quoted above is x cubed at the origin.