> I have recently discussed this with a couple of people at the places I 
> work. It seems teaching doing a square root by hand was removed from the 
> basic training about 40-50 years ago.

I think this was the case in the UK too, my maths teacher mentioned it as 
something they had to do "in the old days", but it certainly wasn't on the 
curriculum.  Of course long multiplication and long division were, also 
later on in school we had to do long division with algebraic expressions... 
fun!

> To get things in perspective: the majority of people training for teacher 
> fail the end test for our 12 year olds in maths.

"Those that can't do, teach, and those that can't teach... teach gym."

> One of the first courses at this university is in basic maths. Which is 
> simply trying to get them at the level of the end terms of the school they 
> have just finished (actually even less than that). We do start with 
> addition, subtraction, long multiplications and divisions, and 
> fractions...

Hmm at my University they send us a booklet over the summer holiday before 
we started, basically telling us we should know all of this and to learn the 
rest before you come.  It was more to just fill in the gaps between the 
different curriculums at different schools, but mostly we had covered it 
all.

> From my personal experience I know that also the writing skills are far 
> below what was thought in my days.

What makes it worse in the UK is that every year the media congratulates 
everyone with record pass rates for school exams.  You simply have to 
compare a maths exam paper (or even text book) with one from 20 years ago to 
realise how massively easier it is today.  Stuff that was in my A-level test 
(taken when you're 18) was the same stuff in my dad's O-level test (when 
you're 16).

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