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.
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.