I can't imagine them demanding that their children learn whether a particular ablative is an ablative of origin or an ablative of accordance.

The difference between learning a language and learning to translate. >.< Reggie Foster teaches Latin as a living language and he does go into the various forms of the ablative, but it's more in the vein of "So you told me that you came to class from the market--now, HOW WOULD YOU SAY THAT IN LATIN? DIC MIHI!"