Did you see the photo of (Jim and) me? is therefore correct

(Jim and) I took some photos is also correct

PS my goodness, there are some ignoramuses on here today. Please ignore those saying Jim and I is correct. They don’t know their grammar from their elbow.

the only way you could use ‘Jim and I’ is if it was at the beginning of the sentence. for example:

“Jim and I went for a walk through the park.”

here, if you were to take off Jim, you would say “I went for a walk through the park” and it makes sense.

but if you were to use it in the sentence you have and take off Jim, it would read “Did you see the photograph of I?” and that clearly doesn’t make sense.

so you sir, are completely correct.

and all these other people who are telling you that it’s ‘Jim and I’ are dumb and need to go back to school.

*edit*

I is always used as the subject of a sentence which why your son’s logic doesn’t work.

Me is usually used as a direct/indirect object and in your sentence, “you” is the subject of the sentence, making your usage correct.

For example” You would say “Did you see the photograph of me?”….but you wouldn’t say “Did you see the photograph of I?”

You would say: “Jim and I are going to the fair” because it is correct to say “I am going to the fair”.

Just imagine you were just talking about yourself….

Did you see the photograph of me ? or

Did you see the photograph of I ?

Did you see the photograph of me..is correct!..You are correct!

You also have to go by what makes sense!

You could also say..Did you see the photograph of me and Jim….You can’t say..Did you see the photograph of I and Jim ?

I hope this helps..

Enjoy the rest of your summer!

Jim and I is the correct term.

If you drop Jim:

Did you see my photograph?

Did you see the photograph of Jim?

Did you see the photograph of Jim and I?

And as far as dropping Jim, the first and secondary person change a sentence completely.

Jim and I were drinking lemonade.

Jim was drinking lemonade.

I was drinking lemonade.

See that taking away something can change a sentence. It is fun though. Give your son a hug and say your right, BUT I TAUGHT YOU EVERYTHING YOU KNOW. SO, I FORGOT FOR A MINUTE AND SMILE. I have four that think they are smarter than thou, I home school them and send them to regular school, and they are always ahead of the pack.

I found some information that might be helpful:

I/ME/MYSELF

In the old days when people studied traditional grammar, we could simply say, “The first person singular pronoun is “I” when it’s a subject and “me” when it’s an object,” but now few people know what that means. Let’s see if we can apply some common sense here. The misuse of “I” and “myself” for “me” is caused by nervousness about “me.” Educated people know that “Jim and me is goin’ down to slop the hogs,” is not elegant speech, not “correct.” It should be “Jim and I” because if I were slopping the hogs alone I would never say “Me is going. . . .” If you refer to yourself first, the same rule applies: It’s not “Me and Jim are going” but “I and Jim are going.”

So far so good. But the notion that there is something wrong with “me” leads people to overcorrect and avoid it where it is perfectly appropriate. People will say “The document had to be signed by both Susan and I” when the correct statement would be, “The document had to be signed by both Susan and me.” Trying even harder to avoid the lowly “me,” many people will substitute “myself,” as in “The suspect uttered epithets at Officer O’Leary and myself.”

“Myself” is no better than “I” as an object. “Myself” is not a sort of all-purpose intensive form of “me” or “I.” Use “myself” only when you have used “I” earlier in the same sentence: “I am not particularly fond of goat cheese myself.” “I kept half the loot for myself.” All this confusion can easily be avoided if you just remove the second party from the sentences where you feel tempted to use “myself” as an object or feel nervous about “me.” You wouldn’t say, “The IRS sent the refund check to I,” so you shouldn’t say “The IRS sent the refund check to my wife and I” either. And you shouldn’t say “to my wife and myself.” The only correct way to say this is, “The IRS sent the refund check to my wife and me.” Still sounds too casual? Get over it.

On a related point, those who continue to announce “It is I” have traditional grammatical correctness on their side, but they are vastly outnumbered by those who proudly boast “it’s me!” There’s not much that can be done about this now. Similarly, if a caller asks for Susan and Susan answers “This is she,” her somewhat antiquated correctness is likely to startle the questioner into confusion.

If Jim and I/me is the subject then its (Jim and I)

but

If Jim and i/me is the object then it (Jim and me)

Which it is in this case.

The easy way is leave out the and to see which sounds better

“Did you see the photograph of me” (GOOD)

“Did you see the photograph of I” (NOT SO GOOD)

hope this helps