My 7 year old has started using sentences which go "Methink ..." and "Methought ..." which has had the teacher try to correct him. But he has looked something up online and claims this is correct English according to Milton/Shakespeare and does not want to change. Can some English expert advice?

Personally, I think that's adorable! At home, I would probably leave it alone. If it's really causing problems with his teacher or elsewhere, though, I think I would have the communication conversation:

Communication consists of three parts:
1. the sender
2. the message
3. the recipient

It is not enough for the sender (you) to know exactly what you are saying, and to say it correctly; you must also consider your audience, and whether they are receiving your message as you intend it to be received. Regardless of the technical correctness and sophistication of your communication as it leaves you, it is a failed communication if the recipient does not receive it intact. So if your objective is to communicate, you have to make adjustments to your audience. If your objective is simply self-expression for its own sake, then by all means use language that is incomprehensible to your listeners, if that's what you want to say! (With due consideration for language that would endanger yourself or unduly hurt others, of course.)

And then, of course, there are just some things that we save for home...

I love this! He might have to save it for appreciate audiences and avoid using it around his teacher? Alternatively, this may be an opportunity for beginning to teach self-advocacy.

He might be interested in how languages evolve? You could illustrate how what was proper language use in the past is confusing now. He might pick up some other words or phrases though. 😂

He might benefit from learning about how good communicators and authors modify their language for their audience. I don't recall if this is age appropriate, but "Mother Tongue" by Amy Tan discusses the topic of how ordinary people speak different versions of English depending on their audience or environment.

The correct pronunciation is mi-thinks - short i vowel sound. A change in pronunciation may pacify the teacher.

Audio here: https://www.merriam-webster.com/dictionary/methinks

Also, he might enjoy vocabulary.com. It's a free platform to learn new words (and spelling!). There are thousands of lists already, or you can make your own list from whatever he is reading. My son likes to practice spelling words there and I love playing on the GRE vocabulary lists. So many words! There is audio for correct pronunciation too. There might be a word list for Shakespearean insults. 😇

It s a perfectly valid (if archaic) English verb, methinks. Using it overly would be considered an affectation but if the teacher is under the impression that it is grammatically incorrect then, sadly, she isn't at all well read.

Personally, I would have the 'communication' conversation as outlined by Aeh as it is broadly applicable not just to conversation but all forms of expression even Art.

Also, I myself wouldn't encourage my child in riling the teacher or proving them wrong - nobody likes a smart Alec and unnecessarily souring the relationship with the teacher is not something that I would encourage, frankly. Learning to appreciate and respect the likes and mores of the 'receiver' of one's outputs is a valuable Life Skill, methinks.

YMMV

Thank you all the feedback. This form is invaluable. I will try to make him understand the concept of archaic usage. I do not think he understands the concept yet.

The weird part here is that I do not think he learnt this from any literature reference. He just started using it and then went to check on it only after he was corrected. Also is methink an exception or are there other verbs which start with me?