You descriptivists are a pox on the corpus of effective communication.
What do you mean by 'correct'?
The quantifying phrase "a (large) number of", despite taking the singular indefinite article 'a', is plural. It's much the same as 'a flock', 'a group' etc., which although singular countable nouns, imply plurality, so I suppose the appropriate option would be 'there are' in both cases.
However, this concept of 'correct' is entirely prescriptive. It's only 'correct' because someone decided it was, not for any intrinsic reason of language. Thankfully, modern linguists are now less concerned with telling people how to say things than with studying how people say things and I imagine in your example there would be a fairly even split.
Language is replete with ambiguity and perhaps the question one should ask is not whether what one's saying is 'correct' or not, but whether it is communicatively effective, which is a far harder skill to achieve yet one that is infinitely more useful.
People cannot communicate effectively unless there is a common understanding of meaning and structure.
Though the language cops do skew pedantic, the are fundamentally correct in their assumption poor usage leads to ineffective communication.
Studying how people say things is an interesting and important discipline. It in no way eclipses the need to teach people how they should say things.
Are you suggesting that linguists prefigured language?
Personally, I am of the opinion that grammar is an explicit explanation of a language system that necessarily prefigured it. Not knowing grammatical terminology and 'rules' in no way impedes communicative ability. Indeed, self-conscious use of prescriptive grammar may even obstruct understanding, hence such campaigns as Plain English. Also, as any etymological dictionary will tell you, Shakespeare, Milton, Spenser etc. are not only literary giants but those who most altered the language to suit their needs. Fooling around with syntax and morphology is, by your definition, 'incorrect'.
I realize that there is a compelling need for consensus on how to teach language, and not every teacher can be his or her own arbiter of acceptability. Nevertheless, I don't believe that using a subject pronoun instead of and object pronoun, or ending a sentence with a preposition is 'incorrect', 'wrong' or anything else. Neither do I believe that, as Orik appeared to suggest earlier, that language is the preserve of the middle classes, and letting standards go will result in mutual unintelligibility.
No one, including the Middle Classes, has the right to demand a style of usage from another person. One has to remember that modern English grammar is only some 300 years old, and was extrapolated from Latin models, an inflected language of relatively free syntax, that has little in common with English. Not only this, but when grammar was fixed it was fixed onto one varietal of English, that of southern England's middle classes. Thus in one blow every variety that differed from this nascent Standard English became instantly 'incorrect'. This Standard English is still the variety of authority today, which is ironic because it is an utterly artificial class construct more in keeping with past imperialism than with the multicultural tolerance of today.