Colleagues are writing "always/sometimes/never" questions, because they're easy to automatically mark. (You give the student a statement, and they have to decide if it's always/sometimes/never true)
They say it's hard to come up with "sometimes" statements, but 90% of what they thought were "always" statements have counterexamples.
Never get an applied mathematician to do a pure mathematician's job.
@christianp Fwiw -- and this depends a lot on the class -- I find that some students are actually confused by understanding those words (sometimes, always, etc) with a temporal meaning. The questions do a better job on several fronts if they are phrased with appropriate quantifiers, like "for every positive integer n / for at least one positive integer n / not for any positive integer n" (or whatever's appropriate to the problem).
@jsiehler yes, an important point: we'll make sure to say "always" means "for every possible value of the free variables", etc.
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!