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I posted a query on smt-announce asking if anyone had experience creating onine diagnostic exams for incoming master's students. I received some excellent feedback including the comment that the general music theory public might be interested in an open discussion of this question--it seems to be a trend now that so many courses are now online.
Our issue at Temple University is that we will soon have a Masters in Music Education that is offered entirely online (in addition to our current face-to-face degree). These students will never set foot on our campus, so our problem is to create online diagnostics for music history and music theory that (1) truly test their theory skills and (2) prevent plagiarism. Our current music history exam is a combination of multiple choice and a short essay, so that's easy to do in Blackboard (or in a platform that Temple is offering this year--Canvas), although I still worry about plagiarism. But our music theory exams (harmony, counterpoint, and aural theory) currently require a good bit of note writing. Examity.com has been suggested, but each student would have to arrange his/her exam, which would be proctored by examity. We want to offer something online that any of our incoming masters students (not just the online cohort) could take in the future in a more convenient way.
We created an online exam through Blackboard for our incoming freshmen, music minors, and musical theater majors and that has worked well in placing students in the proper level of theory. It actually has a simple (one-line) melodic dictation that the student answers using multiple choice questions; they can take a picture of their dictation and attach it as well. We also offer a second part to this exam that has a 2-part dictation, hearing chords, and a Roman Numerall analysis--all done through multiple choice questions; this helps us identify students who qualify for our honors theory section. Obviously, the graduate exams are so much more complex!
Once we create these diagnostics, we also need to make three online courses for remediation. This part should be easy by comparison.
Thank you to those who responded to my query on smt-announce. I look forward to hearing from others about how they are solving this problem.