I can't help but think this is a phenomenon unique to the US where education has been completely devalued. If the only point of education is to fulfill a requirement to make more money then it makes sense to shortcut as much as possible.

The solution is of course no computer

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[–] Tomorrow_Farewell@hexbear.net 4 points 3 days ago* (last edited 3 days ago) (1 children)

There is more to math than just acting like a human calculator.

I know. I literally am a mathematician by education. I made a couple of math-related posts on Hexbear last year. That's why I excluded relevant tests in my question.

You can create word problems or case studies in math where the student has to figure out what algorithm to apply, why, and how.

Okay, but I did exclude this sort of test in my question.

What I am much more curious about is students proving that they understand things like what Taylor series is (including its significance and relation to polynomials), or basic theorems about planes in the context of linear algebra. How does one test that students do understand that without limiting their access to notes and textbooks?

[–] sodium_nitride@hexbear.net 3 points 3 days ago (1 children)

I don't believe that closed book tests should literally never be used.

I just believe that for a lot of things, the typical test provides very limited or low quality information on the abilities of the student.

In the case of the Taylor expansion, you can test if the student has correctly memorised the formula and can plug and chug, which is what a lot of my closed book tests were like. But these tests were easy because all I had to do was memorise a few basic formulas. The home assignments and labs tested my full skills much more.

[–] Tomorrow_Farewell@hexbear.net 4 points 3 days ago* (last edited 3 days ago)

In the case of the Taylor expansion, you can test if the student has correctly memorised the formula and can plug and chug, which is what a lot of my closed book tests were like. But these tests were easy because all I had to do was memorise a few basic formulas.

You can also ask a student to actually explain the motivation for it, as well as its significance. My university exams were all in the form of explaining a few assigned topics to a teacher after being given some time to prepare notes and remember things, without access to prior notes and textbooks. Being able to use notes without restrictions would trivialise that.
Rote memorisation would not work in the case of the exams that I took.