The grammar point in the textbook was ‘future forms’ (strictly speaking, English doesn’t have a ‘future tense’), the section was be going to V, and the prompt was David and I ________ a movie. Many students saw I and wrote David and I am going to see/watch a movie. But David and I functions as we, so the sentence must be David and I (=we) are going to see/watch a movie.
One student asked “Should that be David and me are going to see/watch a movie?”. I’m aware of variation within English, but I had to be standard and say “No, David is going to watch a movie and I am going to watch a movie, so David and I are going to watch a movie”. I are sounds wrong even in that context, but so does me are.
The problem here is a coordinated noun phrase with a name and pronoun (starting with I/me) either as the subject of a sentence or the object of a verb or preposition.
So we might have:
1 David and I invited them.
2 I and David invited them.
3 David and me invited them.
4 Me and David invited them.
5 They invited David and I.
6 They invited I and David.
7 They invited David and me.
8 They invited me and David.
9 They sent an invitation to David and I.
10 They sent an invitation to I and David.
11 They sent an invitation to David and me.
12 They sent an invitation to me and David.
1 is correct. 2 is incorrect, not for any grammatical reason, but for the social politeness of not putting oneself first. 3 is ‘incorrect’ but widespread, particularly by younger, non-standard speakers in informal speech. The usual explanation is that if you take David and out of the sentence, you are left with Me invited them. But that only works in past tenses and with modal verbs (David and I will invite them). Taking David and out of our original sentence leaves I are going to see/watch a movie. 4 is doubly ‘incorrect’ but occasionally used in very informal speech.
The problem with teachers saying “Don’t say David and me” (as in 3) is that some people hyper-correct and say 5 and 9, for which the grammatically correct forms are 7 and 11: They invited (David and) me and They sent an invitation to (David and) me (= They sent me an invitation / ?They sent David and me an invitation). 6 and 10 are simply incorrect, grammatically and socially. 8 is possible, probably because of the juxtaposition of invited me, and 12 is more possible than 4, because of to me.
Grammar books, style guides and material for second language learners vary in their treatment of these points. 1, 7 and 11 are always correct, 2, 6 and 10 are always incorrect, while 3 (informal), 4 (very informal), 5 and 9 (hyper-correct) and 8 and 12 (somewhere between informal and very informal) vary in acceptability.
In A Student’s Introduction to English Grammar, Rodney Huddleston and Geoffrey Pullum say that their equivalent of my 3 “is not accepted as Standard English, though it is very common in non-standard speech”, and mark it with ‘!’ in front of it, meaning “non-standard”. Their equivalent of my 5 “is used by many highly educated people with social prestige in the community; it should be regarded as a variant Standard English form”, and marked with ‘%’ , meaning “grammatical in some dialects only” (in this case, the hyper-correct, prestige dialect).
With respect, I disagree. To me, 3 and 5 are equally ‘incorrect’ but are obviously both widely used by different groups of speakers. Hyper-correctness, education and the social prestige of the speakers shouldn’t affect our judgements of grammaticality. But then they wrote an internationally acclaimed grammar book and I haven’t yet, so take your pick.
To sum up: if in doubt, be ‘correct’ – David and I invited them, They invited David and me and They sent an invitation to David and me.
These issues are most evident when the pronoun is I/me, but also happen with she, he, us and they. We can also have two pronouns, which multiplies the possibilities: She and I, I and she, She and me, Me and she, Her and I, I and her, Her and me and me and her.
We can always say “I invited them, and she invited them as well” or “I invited them, and so did she” etc.
TS Eliot started one of his poems: “Let us go then, you and I, … through certain half-deserted streets”. But then he won a Nobel Prize and I haven’t yet.