In those words, the diaeresis (¨) means that a vowel starts a new syllable. It is considered archaic in English, yet I still encounter it in books and articles.
What I think people do wrong is apply the rule ONLY to the word 'naïve'. If you're gonna use obscure grammar, at least be consistent with it. If I see 'naïve cooperation' written like that, it makes me think that you just wanna show off but can't be bothered to actually look up grammar.
Pick one or the other. Either use it in all words that warrant it or just drop it altogether.
Wikipedia, New Yorker on the subject
EDIT: Phrasing.
YSK that if you write 'naïve', then you should also write 'coöperate', 'reëlect', etc
![YSK that if you write 'naïve', then you should also write 'coöperate', 'reëlect', etc]()
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