Due to COVID-19, I have been planning to transition to online teaching (which, of course, includes online testing as well). The LMS that we use is Blackboard which is integrated with Proctorio. However, they work well for multiple choice problems not free response math problems. Any ideas on how to conduct online testing for course like Calculus in which we cannot give take-home exams as the answers are easily available online.

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    $\begingroup$ LMS = Learning management system? $\endgroup$ Mar 19 '20 at 1:29
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    $\begingroup$ I'd argue that everything is a take-exam now whether we like it or not. Perhaps explain why you think "we cannot give take-home exams" in your answer? $\endgroup$ Mar 19 '20 at 1:42
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    $\begingroup$ The answers are easily available online only if you ask easy questions and don't demand explanations. $\endgroup$ Mar 19 '20 at 6:30
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    $\begingroup$ Another reason why take-home exams are undesirable is that students will email the answers to each other, so it makes no difference how conceptual the questions are or how much explanation is required. $\endgroup$
    – Mike Z.
    Mar 19 '20 at 14:42
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    $\begingroup$ Any sort of online test of the traditional sort is completely compromised in terms of academic integrity. One's options are oral exams or the honor system. There is no evidence that the honor system works. $\endgroup$
    – Dan Fox
    Mar 21 '20 at 8:17

Well, one idea would be that of shifting to evaluating students through projects. For instance, there could be created a pool of project topics which will be randomly assigned to students. This may be way off the usual written examination, it makes it, however, necessary for the students to process the knowledge they have obtained conceptually and not only "copy-and-paste" from the internet or each other.

Some sample topics related to calculus could be the following:

  • The critical comparison of the several ways in which one may express the completeness axiom - e.g. through suprema or using Cantor's principle or using Bolzano-Weierstass's theorem orthrough Heine-Borel theorem etc.
  • Several proofs of Bolzano's theorem for continuous functions - related to the previous one.
  • A discussion upon the definitions of integrable functions using Riemann and Darboux sums - equivalence etc. This could be extended to include Riemann-Stieltjes integral.
  • The creation of a cognitive map connceting all the theorems of calculus the students have been exposed so far - e.g. in terms of which can be proved using some other(s).

A drawback of such a way of examination is that it is usually focused on some specific part of the topics discussed in a calculus course. To treat this, one could split each student's evaluation to two or more projects, coming from different areas of calculus.

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    $\begingroup$ I really love that this idea, but I'm wary right now of assigning extensive assignments that weren't on the original syllabus at a time when students are already overwhelmed with all the changes that are happening. This sounds like an excellent concept for a project-based calculus course, but that's not necessarily what students signed up for or agreed to when they decided to take one's course. $\endgroup$
    – James S.
    Mar 25 '20 at 23:32
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    $\begingroup$ Yes, that is also right. Possibly one could make such projects group projects rather than individual ones so as to split the workload of each student - with the risk, however, that only some students in some groups carry out the majority of the work needed. $\endgroup$ Mar 26 '20 at 8:51
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    $\begingroup$ @JamesS., you can do it, regardless. Just keep the thema(s) manageable in a reasonable period. $\endgroup$
    – vonbrand
    Apr 12 '20 at 18:16
  • $\begingroup$ While this answer was selected, I don't see how it answers the essential question of how to conduct online testing for calculus. $\endgroup$ Jun 20 '20 at 18:51

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