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Question: what is the past tense form of these two words? For example, if I wanted to know how many times someone has dived into the pool, that sounds fine to my ear. But what about dove? How many times have you doved into the pool? How many times have you doven into the pool? Neither of those sound correct to my ear. Do you know the correct past tense for dove?
You're talking about the past participle form, I think--that is the version you use with a helping verb like "has" or "had." For simple past tense, the form is "dived" or "dove," take your pick. For the past participle form, as in "How many times have you dived into the pool?" you overwhelmingly see "dived" used, not "dove." On the other hand, Webster's claims using "dove" as the past participle form is not completely out of line: http://www.merriam-webster.com/dictionary/dive. To my ear, though, I agree with you: "I have dove into the pool" sounds wrong, and "I have dived into the pool" sounds right.
There isn't one. However, create one. The past tense for dove is doved. Foreign students learning English as Second Language will immediately expedite a solution to the esotericism madness of the English language. Why not simply add every present tense with, 'ed'. Instead of writing, ' I had lain a carpet'. Simply write, 'I had lied a carpet'. Simple with an added, 'ed' to all present tense do away with all options to english correctness in past tense but one measly wordy past tense.