This fall I'll be teaching a standard "Introduction to Proofs" course and administration is advising us to be ready at any time to switch from in-person to fully online (or anything in between). I've been able to translate most of what I do into various modalities, but I'm having trouble with the memorization quizzes.
In a typical face-to-face version of the course I give weekly 10-question, 10-minute quizzes that require students to have memorized important definitions and/or theorem statements. I find this essential to developing their proof-writing skills. But if I give this in an online modality, what's to prevent them from just looking up the definition/theorem? (In my other courses I take the attitude that any online assessment is written to be open book/internet.)
Perhaps there's a better/alternate way to get students to really absorb the definitions/theorems and place importance on having them mentally readily-accessible. Perhaps in the modern age, all memorization is moot. I'm open to radical viewpoints/suggestions.
Note: I find myself rereading "How, now, shall we teach math online?" almost daily; mining for things I might have missed/forgotten and hoping that more people will post helpful ideas there.