British magical education outside of Hogwarts

[Bruce Alan Wilson]

No: HPFGUIDX 156839

Irene:
"And I still want to know what happens if a muggle family refuses to send their
child to Hogwarts. Do they always dispatch Hagrid to deal with difficult
customers?"

BAW:
JKR says that a Hogwarts professor or someone from the Ministry of Magic comes
to explain matters.  A Muggle family that threw a wizardling sport would have
seen 'breakouts' as the child grew up.  How many 'Aunt Marge' incidents would it
take for a pair of reasonably bright parents to realize that there was something
wrong with the kid, and be actually glad to hear that (a) there was an
explanation and that (b) there was a place the child could go to get the
necessary training to bring the talent under control.
All fiction that I have read involving a functioning system of magic contains a
saying containing some variant of "To keep dark the mind of the mageborn is ill
done," or "An untrained sorcerer is a danger to himself and others."  It would
not be hard to persuade parents who had experienced an 'Aunt Marge' incident, or
something like the snake in the zoo, or even things like a child teleporting
himself to the roof of the school or an ugly sweater shrinking to doll-clothing
size that the kid needs to get the gift under control NOW.
Now, what of parents who are opposed to sending their children away--would not
have even considered boarding school if the child were nonmagical?  JKR does not
tell us because it is not relevant to the story--she's a storyteller, after all,
not an encylopedist--but she does say that some wizardling children are
homeschooled rather than sent to Hogwarts.  
Perhaps there is some scheme whereby Muggleborn wizardlets can attend Muggle
schools and have regular visits from teaching wizards and witches; we know that
the OWLs and NEWTs are administered not by Hogwarts, but by some outside
agency--so HOW a candidate prepares for the exams is not so important as that
they can pass.  Perhaps that is what Lupin did before he came to
Hogwarts--private tutor to young witches or wizards whose parents did not want
to send them to Hogwarts.  The mechanics of this will only be told to us if it
becomes important to the story.

BAW.