Kimberly over at Number Two Pencil has a really good discussion of the subtleties of building a good test, responding to news reports from Oregon, where 10th graders are failing a math test in massive numbers (unlike last year). Go read the whole thing.
I don't know if I'd call problem-solving tests in math "faddish," and such items are not automatically unsuitable for high-stakes testing. When the state's employers claim they need more citizens with solid problem-solving skills, they're right, and one way to test those skills is with this type of item.
But such items are more difficult to develop properly, and they may very well test a narrow area of the domain, making it hard to generalize the results to the overall math construct. What's more, that one item counts the same as the multiple-choice exam, so if none of the three options are appealing, an examinee is at a real disadvantage. There's research to suggest that examinees, when given a choice of topics, don't always do a good job of knowing what they're good at.
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