Both you and your informant are correct in different circumstances.
The difference lies in the character of the verb involved. With a telic verb—one which includes an end, a specific goal or point of completion—there is a marked difference between the simple form and the progressive form: the progressive form marks the action as incomplete. Eat, fall, take are telic verbs.
With an atelic verb, which does not include an end, there is no practical difference. Stand, run, think are ordinarily atelic verbs (although in some circumstances they may be ‘recategorized’).
See the tag-wiki entry on aspect.
Yes, 'increase' is being used as a verb. If there are more enrollments over time, then enrollments are increasing, and someone observing this would "see enrollments increase".
If you added a 'that', like so:
...while the ACA continues to see that enrollments increase, there are a lot...
It makes it sound like the ACA is causing enrollments to increase. Right now, I am seeing that this question is answered. Someone observing me answer the question would be seeing this question answered.
To convert to this other structure, you are correct that you would remove the 's' from the end of enrollment. But that's not all. With just that change, we have:
...while the ACA continues to see enrollment increase, there are a lot...
In this sentence, "enrollment" represents the total number of students enrolled, rather than "enrollments" representing individual instances of people enrolling. So, "increase" is still a verb describing what that number is doing.
To make the full switch, you would also need to add an 's' to the end of 'increase':
...while the ACA continues to see enrollment increases, there are a lot...
Now the ACA is is seeing "increases", and the type of increases they are seeing are "enrollment increases".
Other possible phrasings include:
...while the ACA continues to see an increase in enrollment, there are a lot...
...while the ACA continues to see that enrollment is increasing, there are a lot...
...while the ACA continues to see increased enrollment, there are a lot...
Best Answer
It depends on the context; its position in the sentence. 1) If the word with ing comes as a subject or an object, it's a noun. eg. Smiling is an act of kindness. 2) If it comes after the auxiliary "be" it's a verb. eg. The girl is smiling. 3) If it comes before a noun, describing that noun, then it's an adjective. eg. Smiling faces are lovely.
Some words with ing are always adjectives like 'interesting' and 'exciting'.