A colleague asked if the structure of the following phrases was the same:
- a group of the students
- the groups of students
- one of the students
This brought to mind a section from a paper I've been working on, which is reproduced below. Here, I'm discussing the category of determinatives as presented in The Grammar Book 2nd edition by Celce-Murcia and Larsen-Freeman.
Questions are treated in chapter 13, which implies at least the following additions: whose, which, what (p. 249). Quantifiers are covered in chapter 17. "Quantifiers can be determiners or when the referent is clear, pronouns" (p. 330). The following list is given: Positive: some, a few, several, a couple of, a little, quite a few, quite a little, (a great) many, a (good) number of, a lot of, a great deal of, a good deal of, almost all, most, and all; Negative: none, no, not any, few, hardly any, scarcely any, little, just a few, only a few, just a little, only a little, not many, not much, not all, many… not, and most… not. Other quantifiers are listed in TGB on pages 277, and 334-335.
Clearly, this list represents a significant expansion on what is considered a determiner by the dictionaries. The inclusion of adverbs such as hardly, just, and not suggest those expressions including them are determiner phrases rather than determiners per se, but it is harder to account for the complex items such as a good deal of and a lot of.  Far from being determiners, these items are not even constituents. Rather they are sequences of the form a (adj) N of, differing from other combinations like a box of, or a carload of chiefly in that they do not typically dictate subject verb agreement in cases like A lot of students understand the value of a university degree (not *A lot of students understands…).
The main reason to believe that they are not constituents is that unlike the core members such as many, every, and this, you cannot remove the following noun and have them stand on their own. Compare:
I ate too much sushi. à I ate too much.
I ate a lot of sushi à *I ate a lot of.
Moreover, in relative constructions, the of is placed at the front, before the relative pronoun:
a lot of the damage remains unseen à
the damage, of which a lot remains unseen
It is clear that of is part of the preposition phrase of which, in which case it cannot be part of a complex determiner a lot of. Add to this the fact that these exist in both singular and plural versions (e.g., a lot/lots of), and that they may be internally modified (e.g., a very great deal of), and it becomes clear the constructions with couple, number, lot, and deal are simply the structure a (adj) N of.
Beckner and Bybee (2009) argue that these kinds of chunks often become constituents over time. One could hardly question this claim, given such words as everyone, breakfast, and nonetheless. They further claim that changes are gradual rather than abrupt, which also seems undeniable if we're dealing with language across populations. But the simple observation that some strings become constituents is not evidence for any particular string having done so. In building their case, they take the example of in spite of, which bears some similarity to a lot of, and argue that it has become a compound preposition. In particular, they point out how commonly spite appears in this string: in spite is followed by of in 99.50% of its occurrences in the Corpus of Current American English (Davies, 2008-). It is possible that strings like a lot of, are on their way to lexicalization, but currently a lot is followed by of only 72.12% of the time (Davies, 2008-). They further argue that the meaning of in spite of is far from the original meaning of spite. The same cannot be said of a lot of and lot, in particular the meaning of the plural lots. So, while these are certainly collocations worth bringing students' attention to, they are not yet constituents, and thus, not determiners. In this respect, the dictionaries had it right.