[BobaFloutist]

That's because midterms are specifically supposed to assess how well you learned the material presented (or at least directed to), not your overall ability to reason. If you teach a general reasoning class, getting creative with the midterm is one thing, but if you're teaching someone how to solve differential equations, they're learning to the very edge of their ability in a given amount of time, and you present them with an example outside of what's been described, it kind of makes sense that they can't just already solve it. I mean, that's kind of the whole premise of education, that you can't just present someone with something completely outside of their experience and expect them to derive from first principles how it works.

[throwway120385]

I would argue that on a math midterm it's entirely reasonable to show a problem they've never seen before and test whether they've made the connection between that problem and the problems they've seen before. We did that all the time in upper division Physics.

[BobaFloutist]

A problem they've never seen before, of course. A problem that requires a solving strategy or tool they've never seen before (above and beyond synthesis of multiple things they have seen before) is another matter entirely.

It's like the difference between teaching kids rate problems and then putting ones with negative values or nested rates on a test versus giving them a continuous compound interest problem and expecting them to derive e, because it is fundamentally about rates of change, isn't it?