Here's how it works:
* The mark: A dieresis is two dots placed over a vowel (¨).
* The purpose: It tells us that the vowel with the dieresis should be pronounced separately from the vowel that precedes it, rather than forming a diphthong.
Examples:
* Naïve: The dieresis over the "i" indicates that the "i" is pronounced separately as a short "i" sound, not as part of a diphthong.
* Coöperate: The dieresis over the "o" indicates that the "o" is pronounced separately as a short "o" sound, not as part of a diphthong.
Note: Dieresis is becoming less common in modern English writing, often replaced by a hyphen.