I'm teaching calculus 1 online this term and anticipate being plagued by the perennial problem of cheaters. I have seen suggestions for how to arrange the testing time to accommodate for traditional tests (such as this previous question and the questions it mentions) but I would rather improve my question-writing instead of impose onerous requirements on my students in terms of time. I would hope that by making these sorts of questions common in all assessment levels that this would also improve my students' learning, especially as they learn that I expect them to understand instead of merely regurgitate. I've also contemplated moving to projects, but have come to similar conclusions that it is difficult to evaluate students on procedural fluency with projects, and devising effective projects is probably going to take me more time than simply writing better questions.
So, with that said, what are some examples of types of questions which are suited for an online exam? A requirement here is that WolframAlpha & other solving websites often do in an unnatural way, or in a way which we do not ask the students to do it. Or equivalently, what ways of formulating questions are there that are difficult to put in to WolframAlpha?
The goal here is to make it less desirable to cheat (because it is difficult to do so) and to make it easier to catch those who cheat. I also do not think entirely avoiding mechanical differentiation problems is possible or desirable, as students need to develop the pattern-recognition to be able to learn integration in the next term, where it is possible we may end up going back face-to-face.
Some types of problems that I can think of include:
In a question, requiring logarithmic differentiation to simplify problems which would involve large numbers of products and quotients.
Differentiation of absolute value problems, if you ask for it to be done in the "piecewise" method instead of teaching them that the derivative of |x| is x/|x|
Finding the value of a constant which makes a function continuous, or perhaps even its derivative continuous.
"Abstract" Problems with chain rule, quotient rule, etc. that involve having a formula for one function and a simple f(x) for the other, represented as table or a graph.
Find the place where a made-up student made an error, and complete the problem from that point on correctly. Or, explain what is wrong with a specific step and what should be done to correct it.
Of course, applications problems. But these do not necessarily test their knowledge of the symbol manipulation and the deeper algebraic fluency which should come from a well-taught calculus class.
I have difficulty coming up with lower-DOK questions in this same vein, however!