Say you have a person or student you've given an assignment to, and you want to have a talk with them while they are still working on the assignment, to discover their status and how they're doing in terms of the assignment.
Is there a word that describes this talk?
CLARIFICATION - I'm looking for a noun - how to describe such an act.
I would call such a meeting a review.
There's monitoring which involves any activity (including talking) to check the progress/status of something in progress. I've also seen tracking used in this sense but am not able to get an appropriate dictionary definition to quote here.
businessdictionary.com
Supervising activities in progress to ensure they are on-course and on-schedule in meeting the objectives and performance targets.
Conference. The Free Dictionary says:
a meeting for consultation or discussion: a conference between a student and her adviser (Emphasis added)
In other definitions, a conference is described as "a formal meeting...", and the OP wanted a formal word. Etymonline says, for conference:
1550s, "act of conferring," from Middle French conférence (15c.), from Medieval Latin conferentia, from Latin conferens, present participle of conferre "to bring together; deliberate, talk over" (see confer). Meaning "formal meeting for consultation" is from 1580s.
The word gives more status to the student than words that imply that you, the advisor, are checking up on the student. The student is more of an equal participant in a conference, and, if this is a research project, she may have information or insights that are new to you.
A conference often involves many people, but does not have to: You can confer with one other person, and have a conference with one other person. Merriam-Webster on conference:
a meeting of two or more persons for discussing matters of common concern
Example: He spent an hour in conference with the president
