On 09/24/09 14:14, andrel wrote:
>> 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,

	I doubt it was ever in basic training universally. Probably only in 
some countries. I know folks much older who know about it - seeing it at 
some point in their lives, but never were formally taught it.

	In my text book (7th or 8th grade), it was there in one of those 
special "fun" sections, and it's possible that the teacher even made us 
do a few problems using it, but it wasn't required to know, and I never 
memorized it.

> 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

	That's *really* bad. Long division is not something that can be 
replaced with calculators. You use it for algebraic expressions as well. 
Unless, of course, it's degraded to the point where you don't need 
algebra and you just let Maple do everything.

	I know a lot of people criticize some of the "new math". I'm not that 
certain in either direction. I find long multiplication and long 
division to be good for computing stuff fast, but gives virtually *no* 
insight into anything. The techniques in "new math" actually give you a 
fundamental understanding of what's going on, and has more "right" to be 
called mathematics. But it's likely not practical to do it that way each 
time.

	If I had kids, I'd try to make sure they learn both. I consider either 
approach alone to be seriously flawed.

	Reminds me of a bunch of math graduate students I've known. Fairly slow 
at doing integrals, etc. But a physics student or a good engineering 
student is much faster at doing them. It's because the math students are 
not concerned with calculations (for the most part) - but the others are.

	In any case, my advisor in grad school had a no-calculators policy for 
exams. And this was for engineering courses, where you have to calculate 
stuff with real numbers, and not just symbolically. I always felt that 
if I were a professor, I'd do likewise for exams. I wonder how long 
before such professors are shunned by their own colleagues.

> 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...

	I often wonder. A lot of people (including myself sometimes) feel that, 
say, mathematics education is degrading over time. In my undergrad 
institution, a few decades ago, the lowest math class was introductory 
calculus. As the years went by, they needed to put a remedial precalc 
course that was strictly not for credit. Then as time went by, they 
converted that to a proper course with credits, and put a remedial 
algebra course for no credits. Now that course is offered for credit.

	Likewise, some of the things they often teach in the first year of 
graduate school here in mathematics is often taught in the 4th year of 
undergrad in universities in other countries (I just saw one where it's 
taught in the 3rd year of undergrad).

	Is the math education at high school etc degrading, requiring all these 
remedial courses?

	Possibly.

	Another explanation is that as a percentage (and of course, in absolute 
numbers) of the population, more and more students are getting educated 
and graduating high school, and the education system is having trouble 
keeping up. Put another way, the percentage of people age 18 in this 
country who have a "solid" background in mathematics may have actually 
stayed the same (not gone worse) - it's just that the percentage 
graduating and moving on to university is higher (and not just because 
standards have gone down).

	I used to be firmly in the first camp, but I really don't have the 
data, and it wouldn't surprise me if the second reason is the bigger one.

> 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.

	I wonder how much of this really matters.

	Take a number of east European countries. And Russia. When it comes to 
mathematics, they used to (and probably still do) beat, say, the US 
handily. Not just the brilliant ones, but also the average high 
school/university graduate.

	In many technical areas (except perhaps engineering), the US has been 
consistently behind those and other countries for most of the 20th century.

	Yet it doesn't hurt the country much.

	I think what matters is maintaining a fairly good average (not just of 
students, but the whole population). I don't really know, but I suspect 
those countries tended to be elitist. Only the really good got to go to 
universities, whereas the rest went to simple trade schools. And that 
results in an overall lower average. An elite group of a few brilliant 
people cannot impact the country as much as a huge group of above 
average folks.

	I think the UK used to be like that and they probably changed it some 
decades ago. I've met a bunch of older people from there who couldn't 
get into university to become an engineer, but in terms of their 
abilities and grades, had they lived in the US, they would have.

-- 
If you think nobody cares, try missing a couple of payments.

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