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There is very little research in mathematics education that is not anecdotal or ideologically driven. There is really no research support for constructivist approaches to teaching math that will stand up to close scrutiny.
The issue is not integrated mathematics but rather mathematics instruction that is constructivist in approach and is built around "problem-solving" rather than the mathematical method. There are great math curricula that are integrated - e.g., the Singapore curriculum. This kind of integrated math curriculum has little to do with the kind of instruction pushed by the NCTM and the NSF although it may also bear the name "integrated." In a real sense, this kind of curriculum is "disintegrated" becasue, at base, its proponents deny the very essence of mathematics itself - a kind of decontextualized knowledge that is rationally constructed.
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