It is understood that the child eats sitting down on his/her own in the school cafeteria.
The actual skill to sit down and eat around others... is not the issue.. or it doesn't appear to be at this point.
More detective work is needed:
Does this mean that the child just has not been able to generalize the skill of sitting at a table to eat - to the home setting - or it is not reinforcing (or worth it) to the child to sit at the table in the home setting - for some reason?
What could be encouraging the child to sit at school? Does he/she have an assigned seat? Is he/she only required to sit for a short amount of time?
What does the child actually "gain" by sitting at the table- at school?
Does the child sit alone at home when eating vs. school?
These are just a few questions you might want to think about at this time.
Another important factor to consider is the "eating" environment. A cafeteria is usually just used for eating. Unfortunately, at home, people can be coming and going through the eating area... the table may have newspapers, books, etc. on the "eating" table.
So... the table may not actually "look" like a place to eat - especially compared to the structured setting of a school cafeteria. However, it is highly possible to create a structured "eating" area in the home.
Also, what may be needed in the home setting to encourage the child to sit at the table?
Well... you might want to start by observing the child perform this skill in the school environment.
When observing, it might help to actually video tape or take a picture of the child performing the actual task.... sitting and eating at a table.
Below I've attached a form- Planning for Victories: Antecedent Checklist. This might help you prepare the home setting, supports, etc. to encourage the child to sit at the table.