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Neeum Zawan <m.n### [at] ieee org> wrote:
> 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.
From my PDE's textbook:
"...Our efforts will be largely devoted to proving mathematically the existence
of solutions. ... This may seem like wasted or misguided effort, but in fact
mathematicians are like theologians: we regard existence as the prime attribute
of what we study. But unlike theologians, we need not always rely upon faith
alone."
> 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.
The professors I thought the most highly of were the ones who basically said,
"Open book, open notes, calculators allowed--but it won't help." I really do
think estimation is an undervalued skill though. The ability to stand there,
figure out orders of magnitude in your head, and come up with some quick
approximations can save a lot of time blindly pursuing totally inappropriate
methods. That sounds obvious, but it's really remarkable how completely some
people lack basic problem-solving and analysis skills.
> 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.
Maybe some people need a more remedial course, so they add a remedial course,
just to get everyone up to speed. Suddenly, the bottom rung of the ladder isn't
the bottom anymore, so all the people who were struggling in precalc move up a
step. And if you're not falling off the bottom, why worry? People just expand
to fit the container, in a sense.
> 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).
"it" being what? Just curious...
> 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).
This actually seems plausible. Still, they choose their program, so to allow
more people through, the standards must be relaxed. As I said above, relaxed
standards in turn reduce effort put forth by students, compounding the problem.
Just a guess, of course.
> I think what matters is maintaining a fairly good average (not just of
> students, but the whole population).
Let's hear it for mediocrity!
- Ricky
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> 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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"triple_r" <nomail@nomail> wrote:
> I really do
> think estimation is an undervalued skill though. The ability to stand there,
> figure out orders of magnitude in your head, and come up with some quick
> approximations can save a lot of time blindly pursuing totally inappropriate
> methods. That sounds obvious, but it's really remarkable how completely some
> people lack basic problem-solving and analysis skills.
My physics course at university included a weekly 'workshop' slot in the
teaching. Among other things, this focused on estimating order-of-magnitude
answers to complicated yet unspecific problems, using nothing but basic physics
formulae from memory, sensible guesses for data and paper & pencil for
calculation. Questions like 'how much water might be vaporised if an asteroid
hit the ocean?'
In hindsight, it was probably one of the most valuable skills I was taught in
that degree programme.
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scott wrote:
> 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!
I envy schools where they actually *teach* algebra.
Everything I know about algebra is what little I've been able to figure
out for myself and scrape out of library books.
> "Those that can't do, teach, and those that can't teach... teach gym."
Incidentally, our gym teacher was the most terrifying guy in the school.
Very fair, but... DO NOT get caught doing bad stuff! My God, the horror...
> What makes it worse in the UK is that every year the media congratulates
> everyone with record pass rates for school exams.
What happens is that every single year, the pass rate either goes up, or
it goes down. It is a statistical fact that it is almost impossible for
the pass rate to remain exactly the same.
If it goes up, even slightly, even by a statistically insignificant
amount, the media starts screaming about "exams are getting too easy".
Not, you know, that students are getting brighter or working harder or
new teaching methods or anything like that. No, exams are getting easier.
If it goes down, even by a statistically insignificant amount, the media
shrieks "schools are failing our children". Not, you know, that the
exams are getting harder, or that this was just a random fluctuation,
but that schools are failing us.
No matter what happens, the media will yell and shout about the terrible
moral decay of either failing schools or watered down exams. There is
apparently nothing the education system can do about this.
> 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.
I haven't had the opportunity to try that, so I really couldn't say.
When I did my exams, I didn't think they were especially easy. And I was
entered for the lower grades. (E.g., I got a B in science, and B is the
highest possible mark for the paper I took.)
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> Everything I know about algebra is what little I've been able to figure
> out for myself and scrape out of library books.
Do a maths evening class? You should sail through the GCSE, the A-level
might take a little bit of work to fill in the gaps of your knowledge. For
even further the Open University probably offer something.
> What happens is that every single year, the pass rate either goes up, or
> it goes down.
There is a strong upward trend though in the results:
http://2.bp.blogspot.com/_mJmwQtPmusk/Rt8ZqfEnvyI/AAAAAAAAA2U/TIGBotspDds/s400/gcse-scores--ns-2007.jpg
> I haven't had the opportunity to try that, so I really couldn't say.
Maybe one of your parents has an old text book from school? I also got my
dad's A level physics text book, and it went in to so much more detail about
*everything* that we did in A level physics, if I wanted to read further
about anything in school I used his books.
> When I did my exams, I didn't think they were especially easy.
I'm not talking about individuals, I'm talking about the entire population.
When something stupid like 40% gets an A grade, how is anyone meant to tell
the difference between the hard working kids and the really clever ones?
They introduced the A* grade at GCSE, but the % of people getting A* has
been steadily rising. How are Universities meant to choose the best
students when more and more are applying with the highest possible grades?
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>> Everything I know about algebra is what little I've been able to
>> figure out for myself and scrape out of library books.
>
> Do a maths evening class? You should sail through the GCSE, the A-level
> might take a little bit of work to fill in the gaps of your knowledge.
> For even further the Open University probably offer something.
My mum suggested I do a maths A-level. Personally, I'm not sure where
I'd find the money or the time. Nice idea though...
>> What happens is that every single year, the pass rate either goes up,
>> or it goes down.
>
> There is a strong upward trend though in the results:
Is this a fact, or just hype? It's hard to tell just by listening to the
news. (If you believed them, bird flu is a deadly world-wide pandemic
which is killing everything in sight...)
>
http://2.bp.blogspot.com/_mJmwQtPmusk/Rt8ZqfEnvyI/AAAAAAAAA2U/TIGBotspDds/s400/gcse-scores--ns-2007.jpg
This isn't grades, it's point scores. You can get a higher GSCE point
score by taking more subjects.
>> I haven't had the opportunity to try that, so I really couldn't say.
>
> Maybe one of your parents has an old text book from school? I also got
> my dad's A level physics text book, and it went in to so much more
> detail about *everything* that we did in A level physics, if I wanted to
> read further about anything in school I used his books.
I have my mum's O-level maths books. (Plural.) And her logarithm tables.
(They're very brown and crumbly.) The books talk about a lot of stuff I
either already know or don't understand. I guess because I don't know
the stuff that's supposed to come *before* an O-level. The books talk a
lot about trigonometry and triangle rules; damn, at my school, maths
classes didn't even mention triangles!
> When something stupid like 40% gets an A grade
It's that high??
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> Is this a fact, or just hype? It's hard to tell just by listening to the
> news. (If you believed them, bird flu is a deadly world-wide pandemic
> which is killing everything in sight...)
Or that HIV had just been cured because 51 got HIV who took the vaccine
compared to 74 otherwise.
Anyway, I'm sure you can actually look up the real GCSE pass rates rather
than simply reading the text of news reports. The bbc site has a graph on
this page:
http://news.bbc.co.uk/2/hi/uk_news/education/4202327.stm
>> When something stupid like 40% gets an A grade
>
> It's that high??
I was just making that bit up, after checking it's actually 20%.
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>> Is this a fact, or just hype? It's hard to tell just by listening to
>> the news. (If you believed them, bird flu is a deadly world-wide
>> pandemic which is killing everything in sight...)
>
> Or that HIV had just been cured because 51 got HIV who took the vaccine
> compared to 74 otherwise.
Or that, yes.
> Anyway, I'm sure you can actually look up the real GCSE pass rates
> rather than simply reading the text of news reports.
Somewhere somebody probably has all sorts of interesting statistics.
Damned if I know how to find them though...
>>> When something stupid like 40% gets an A grade
>>
>> It's that high??
>
> I was just making that bit up, after checking it's actually 20%.
Hmm, I take your point. That *is* pretty high. I was expecting A grades
to be nearer to 0.02%. (Let's face it, most people are very, very stupid.)
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On 09/24/09 22:57, triple_r wrote:
>> 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).
>
> "it" being what? Just curious...
Kinda forgot which one. Best guess was either what is introductory grad
real analysis in the US (measure theory, Fatou's Lemma, etc) - or
introductory grad algebra course.
> This actually seems plausible. Still, they choose their program, so to allow
> more people through, the standards must be relaxed. As I said above, relaxed
And they relax it because allowing more people through (thus far) has
proven to be a good thing. Most engineers in the real world don't use
calculus, for example. Why make that the starting point in university?
--
Would the capacity of a Palaeozoic Hard Dive be measured in Trilobites?
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triple_r wrote:
> people lack basic problem-solving and analysis skills.
My favorite was in some store where the clerk had to use a calculator to
calculate 60% off a $20 item. And then she couldn't figure out whether to
charge us $12 or give us back $12.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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