Education

[cockneyrebe1]

No: HPFGUIDX 44746

Apologies if this has been brought up numerous times in the past, 
this is my first post on here :)

With the exception of muggle-born wizards, it seems that members of 
the magical community receive no education before joining Hogwarts.  
I believe J. K. Rowling has said in an interview (I don't know the 
link) that wizard primary schools and universities don't exist.  If 
this is true, then:

- Just what do child wizards do with their time pre-Hogwarts?

Perhaps they are taught at home by a private tutor, but presumably 
this would be costly.  If no free education exists, then what of the 
Weasleys, who surely couldn't afford to pay a teacher?  Mrs. Weasley 
is a housewife, but how could she make the time to teach her seven 
children?  
If they did in fact receive no education, how come they're not, well, 
a bit dim?

- Are we to assume that wizards have no concept of mathematics, 
history, geography, etc. etc.?

Literacy and numeracy are generally considered the foundations of 
intelligence in the muggle world, so why do wizards not hold the same 
view?
In PS, Hermione tells Harry that most wizards don't have an ounce of 
logic.  Later, in PoA, we learn she is taking arithmancy, but Ron and 
Harry are not.  Mathematics, it seems, is optional at Hogwarts.  Why 
is it not considered important?
Perhaps, since magic *is* illogical, science subjects become 
irrelevant.  But language is surely just as important to wizards and 
muggles alike?  Presumably Beaubatons and Durmstrang teach English, 
but Hogwarts does not seem to teach foreign languages or english 
literature.  

Lastly, if no universities exist in the wizard world, how did 
Hogwarts teachers become Professors?  Is "professor" just a throw-
away term in the books?  Can anyone become one?  Is Hagrid a 
Professor?  
Do Hogwarts-leavers go straight into work, like Percy did?  

That's it for now - sorry it's long and I'm even more sorry if this 
has all been said before.  There's nothing worse than someone new 
rattling on about, say, Dumbledore's gleam of triumph in GoF!