This is just the third semester I've been teaching, but I've been tutoring for many years. At the moment I'm teaching to community college students a "Business Calculus" course whose curriculum is attempting to cram an entire semester of calculus into eleven four-hour sessions. I've always had problems taking timed exams myself and find the anxiety crippling, so for this reason, coupled with the brevity and density of the course, I prefer to administer take-home exams. They seem to go over well with the students, and they don't take precious time away from class. And usually people do not perform "unexplainedly better" on my take-homes versus in-class.
However I've run into a snag. One of my students handed in his take-home exam based on the algebra review in the beginning of the course, and did fairly well on it. But his homework is atrocious. Tonight I helped him through a basic problem in front of the class, and I realized as I watched him cluelessly push the marker around the board that he has no idea what he is doing even on a rudimentary level. And I suspect that he had a great deal of help from someone on that initial test. Disappointing to say the least.
Then my question is this: do I need to switch to in-class exams because of this one guy? The take-homes work for everyone else and I much prefer them; they allow for longer, more comprehensive testing of the material, and they don't take time out of a class into which I'm struggling desperately to fit the entire curriculum. Can anything else be done?
Any words of wisdom would be greatly appreciated.
Edit: Thank you all so much for your consideration and thoughtful responses. They have definitely provided me with invaluable insight, and given me a lot to consider.