On 24-9-2009 12:24, Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> Well, I suppose you could argue that, in the real world, if you want to 
>> do a nontrivial calculation and you actually need an exact answer, 
>> you'll use some sort of computation device.
> 
>   But that's not the point. "Just use a calculator" is not didactic, it
> doesn't teach anything, and will only make people lazy. This will bite
> back in the future, when people won't become programmers because they
> lack the proper education and way of thinking.

agreed, see below.

>>>   The same is true for other mathematical operations, such as division
>>> and square root.
> 
>> Out of curiosity... how the hell *do* you actually calculate the square 
>> root of something? I've always wondered.
> 
>   Your lack of google skills don't surprise me. Slightly more surprising is
> that someone of your age hasn't been taught that at school.

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. It wasn't in my training anywhere, 
though I do know it after having sort of derived it myself. (That is of 
course why it is a particular favourite of mine).
I am now teaching digital technology to first years electronic 
engineering at an applied university (whatever that is in English). One 
of my colleagues that is a few years older and is teaching VHDL and that 
sort of stuff actually did not know it. Someone from my department in 
the hospital did know and he is about the same age. I wouldn't be 
surprised if the only reason he learned it was that his teacher liked it 
and not that it was in the official end terms. (BTW I am 47 and they are 
begin-mid 50s).

More disturbingly: I noticed that some of my students did not know long 
division. I haven't asked for long multiplication (yet). It seems to 
have dropped from the program for the same reasons as you mention for 
the US. The teachers don't understand it and don't see why an innocent 
kid needs to know such a overly complicated algorithm if they can use a 
pocket calculator. To get things in perspective: the majority of people 
training for teacher fail the end test for our 12 year olds in maths.

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...

>
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Digit_by_digit_calculation

>>>   They are missing the point. By teaching lazy rules of thumb, they are
>>> failing to teach a higher concept: Algorithmical thinking. You can't
>>> program a computer with just "rules of thumb".
> 
>> Well, most people won't ever need to be computer programmers. It _is_ a 
>> minority occupation. Indeed, most professions don't really involve 
>> higher mathematics in any way.
> 
>   Then you wonder why some countries are more proficient than others.
> It's probably a common trait in the more proficient countries that the
> schooling system is *not* driven by a "only very few people will ever
> need these skills, thus we'll just skip teaching them" ideology.

The common fear with those in teaching maths, physics and chemistry in 
the Netherlands  is that we will be with the countries at the bottom in 
a few years/decades. We are still doing OK but when the current 
generation retires we are left with an incompetent mathophobe group of 
teachers.
 From my personal experience I know that also the writing skills are far 
below what was thought in my days.

OTOH, every generation will say so.

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