It also seems that the now increasingly common format of multiple choice quizzes would be a "railroad" to designing bad placement tests - ones that verify remembering irrelevant details and how things are named/ordered/classified versus ones that verify skills and understanding of core concepts.

Quizzes (both single and multiple choice) are the worst possible way of testing student's knowledge, because they are sooo... easy.

Trouble here is that human memory is an associative memory - being given one piece of information helps you recall other, related piece. So when the correct answer is written down just few lines below the question you'll probably be able to identify it, even if your overall recall of the material is very bad. This strongly encourages learn-pass-forget style of learning.

To better test student's knowledge you need harder tasks: practical exam, asking to actually apply your knowledge. Or write an essay, which at the very least forces you to put your knowledge in some logical structure. Or the oral exam, where it's evident whether you can have intelligent discussion on the topic or not.

The only advantage of quizzes is that they are quick to do, quick to check, and give the teacher illusion of fairness (because there cannot be any debate whether or not answer is correct and complete).

> Quizzes (both single and multiple choice) are the worst possible way of testing student's knowledge, because they are sooo... easy.

Very much depends.

"Name members of X" is an easy question (unless there is a great amount of material that could be covered).

"Mark the following statements as correct or incorrect. Correct classification adds, wrong classification deducts points." can be a quite difficult type of checkbox-test.

Often there are ways to deduce the likely correct answer due to the way the questions and alternatives are formulated.

It is soooo hard to design a good multiple choice math test. I am trying to do exactly that right now, and resign myself to knowing that it will just be one non-comprehensive piece of evidence.

I did not-so-well on the math subject GRE myself. It was the first time I'd done multiple choice higher(ish) math questions and I just didn't train to triple-integrate fast enough or answer questions about the properties of ring homomorphisms. Write a proof? Sure! I did fine actually getting the PhD. I also placed into 'remedial' math at Caltech according to their placement test; fortunately they let me switch out and up in the first week as it really wasn't appropriate.