Why do the youngest Cratchits cram spoons into their mouths after they finish setting the table in Stave III of "A Christmas Carol"?
As noted in the previous answer, the children had to wait their turn and they were obviously very excited.
They are trying to avoid shrieking because,
"Such a bustle ensued that you might have thought a goose the rarest of all birds; a feathered phenomenon, to which a black swan was a matter of course—and in truth it was something very like it in that house" (Stave III).
The Cratchits are very poor and so this is truly a feast for them. The children are not simply excited because it is Christmas dinner, but because this is really an exception in their household. They cannot afford to eat this well but once a year, so their excitement is even more accentuated here. In many ways, that goose is their Christmas present. They do not want to risk shrieking and being admonished, which might not only get them sent form the table, but also show disrespect. These children are very respectful and very obedient, so putting the spoons in their mouths is another way of showing both their excitement and their ability to control themselves in spite of that excitement.
The younger children knew they must keep quiet until it was their turn to be served goose. In order to prevent themselves from "shrieking" out before it they were served. Dickens writes:
:the two young Cratchits set chairs for everybody, not forgetting themselves, and mounting guard upon their posts, crammed spoons into their mouths, lest they should shriek for goose before their turn came to be helped."
If they had yelled or screamed it would be considered very bad manners and they might risk being sent from the table.