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alwaysaskingquestions
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 Posted: Wed Jun 04, 2008 11:01 am Post subject: Not Just the US With Education Problems |
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http://news.bbc.co.uk/1/hi/magazine/7435023.stm
The British are uniquely happy to admit being bad at maths, says a report.
Why is that and how can attitudes change?
Imagine a famous television presenter joking that they couldn't read.
It's an unlikely scenario, such would be their embarrassment, yet no such
reservations exist for mathematics, with self-confessed innumerates popping
up regularly.
"I've always been rubbish at maths" is usually accompanied by a cheeky grin.
The subtext is "I'm no boffin."
A report this week by think-tank Reform laments the drop in numbers of
people taking maths A-level, at an estimated cost to the economy of £9bn.
"The UK remains one of the few advanced nations where it is socially
acceptable, fashionable even, to profess an inability to cope with maths,"
it says, despite a maths A-level putting on average an extra £10,000 a year
on a salary. |
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Tim Norfolk
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| Posted: Thu Jun 05, 2008 12:03 am Post subject: Re: Not Just the US With Education Problems |
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On Jun 4, 3:43�pm, tgdenn...@earthlink.net wrote:
| Quote: |
On Jun 4, 12:15�pm, Thurisaz the Einherjer
MAILTOsecret...@carcosa.de> wrote:
alwaysaskingquestions:
"The UK remains one of the few advanced nations where it is socially
acceptable, fashionable even, to profess an inability to cope with maths,"
it says, despite a maths A-level putting on average an extra �10,000 a
year on a salary.
Well, some fields of advanced mathematics, judging from my own experience,
aren't that important to the average joe (though an engineer et cetera will
see things differently of course). I freely admit that I've forgotten quite
a bit of my own advanced math skills I once learned at school, for I simply
never needed them again in the now 20 years since I graduated.
But basic maths, of course, is another thing entirely. If you can't do
logarithmic maths in your head within seconds, chances are you aren't hurt
much (exception see above)
What are 'logarithmic maths that you do in your head'? �And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they mean
by 'advanced mathematics'?
-tg
, but you should be able to know what "%" means
and how you have to deal with it for example :)
--
Romans 2:24 revised: �
"For the name of God is blasphemed among the Gentiles through you
cretinists, as it is written on aig."
My personal judgment of monotheism:http://www.carcosa.de/nojebus- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text -
|
Here we go again. Like art appreciation, 'advanced mathematics'
depends on the audience. To my present PreCalculus class, who
apparently have never been shown how to take the reciprocal of a
fraction, it's trigonometry. To many people, it means Calculus and
above. To me, it means things like Potential Theory. |
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Paul J Gans
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| Posted: Thu Jun 05, 2008 1:01 am Post subject: Re: Not Just the US With Education Problems |
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Vernon Balbert <vbalbert@gmail.nospam.com> wrote:
| Quote: |
On 6/4/2008 9:52 AM, Therion Ware went clickity clack on the keyboard
and produced this interesting bit of text:
On Wed, 04 Jun 2008 08:10:18 -0700, Vernon Balbert
vbalbert@gmail.nospam.com> wrote:
On 6/4/2008 6:00 AM, Cheezits went clickity clack on the keyboard and
produced this interesting bit of text:
"alwaysaskingquestions" <alwaysaskingquestions@gmail.com> wrote:
[etc.]
"The UK remains one of the few advanced nations where it is socially
acceptable, fashionable even, to profess an inability to cope with
maths," it says, despite a maths A-level putting on average an extra
Å“10,000 a year on a salary.
I thought it was because being good at math is considered nerdy.
I think it's SEXY!
Alas I think we're talking imaginary numbers here...
I don't imagine that women who are good at math are sexy. It's my
opinion, but it's not imagination. Women scientists are HAWT!
|
You'd be very wrong. At least at my place quite a few
women majoring in science and math are "sexy". Indeed
one could argue that percentage wise they are sexier
than their sisters in other fields.
It ain't the 20th century any more.
--
--- Paul J. Gans |
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Shearwater
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| Posted: Thu Jun 05, 2008 8:59 am Post subject: Re: Not Just the US With Education Problems |
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"Tim Norfolk" <timsn274@aol.com> wrote in message
news:50efc7dc-ebc7-4917-95b8-9dddd00b7cf4@f36g2000hsa.googlegroups.com...
| Quote: |
On Jun 4, 3:43�pm, tgdenn...@earthlink.net wrote:
On Jun 4, 12:15�pm, Thurisaz the Einherjer
MAILTOsecret...@carcosa.de> wrote:
alwaysaskingquestions:
"The UK remains one of the few advanced nations where it is socially
acceptable, fashionable even, to profess an inability to cope with
maths,"
it says, despite a maths A-level putting on average an extra �10,000
a
year on a salary.
Well, some fields of advanced mathematics, judging from my own
experience,
aren't that important to the average joe (though an engineer et cetera
will
see things differently of course). I freely admit that I've forgotten
quite
a bit of my own advanced math skills I once learned at school, for I
simply
never needed them again in the now 20 years since I graduated.
But basic maths, of course, is another thing entirely. If you can't do
logarithmic maths in your head within seconds, chances are you aren't
hurt
much (exception see above)
What are 'logarithmic maths that you do in your head'? �And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they mean
by 'advanced mathematics'?
-tg
, but you should be able to know what "%" means
and how you have to deal with it for example :)
--
Romans 2:24 revised: �
"For the name of God is blasphemed among the Gentiles through you
cretinists, as it is written on aig."
My personal judgment of monotheism:http://www.carcosa.de/nojebus- Hide
quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text -
Here we go again. Like art appreciation, 'advanced mathematics'
depends on the audience. To my present PreCalculus class, who
apparently have never been shown how to take the reciprocal of a
fraction, it's trigonometry. To many people, it means Calculus and
above. To me, it means things like Potential Theory.
|
-----------------------------------------------------------------------------
Differential equations, Physics and Physical Chemistry; they kicked
my butt. |
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Guest
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| Posted: Thu Jun 05, 2008 10:06 am Post subject: Re: Not Just the US With Education Problems |
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On Jun 5, 1:46 am, Thurisaz the Einherjer <MAILTOsecret...@carcosa.de>
wrote:
| Quote: |
tgdenn...@earthlink.net:
What are 'logarithmic maths that you do in your head'? And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they mean
by 'advanced mathematics'?
Hey I wrote that posting pretty spontaneously, okay? If my example doesn't
make much sense, so be it. You know what I mean, don't you? :)
|
I really had two points: One was simply that I *don't* know what you
might mean by 'logarithmic maths' so I was curious---I didn't think
that anyone did much about logarithms anymore ( even 20 ya), and I
thought maybe this was a case of 'the other English language' at
work. ;-)
The other was the serious one which is that despite math and science
being all about precision of language, when people talk about
education in those subjects they tend to be incredibly vague. To have
a serious discussion, it really does matter what engineers need to be
able to do, and what voters need to be able to do, and so on.
-tg
| Quote: |
--
Romans 2:24 revised:
"For the name of God is blasphemed among the Gentiles through you
cretinists, as it is written on aig."
My personal judgment of monotheism:http://www.carcosa.de/nojebus |
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Guest
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| Posted: Thu Jun 05, 2008 10:14 am Post subject: Re: Not Just the US With Education Problems |
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On Jun 5, 3:44 am, Douglas Clark <dgdcl...@dgdclynx.plus.com> wrote:
| Quote: |
I will just paste this in from Tuesday's UK Guardian....
Without the big maths stories our numbers are plummeting
Britain has been denied a generation of experts thanks to dumbed-down
teaching of what should be a magical subject
Marcus du Sautoy The Guardian, Tuesday June 3 2008
What is the point of studying mathematics? I have never used a sine or
cosine in my everyday life. And solving quadratic equations? Although a
footballer subconsciously solves one every time he works out where to
stand to volley a free kick, I don't think Wayne Rooney is using the
formula he was taught in school to make his decision. So should we be
worried by a new report out today claiming that the failure of
mathematics education in the UK has lead to the disappearance of half a
million mathematicians?
A study published by the thinktank Reform finds that since the 1980s,
mathematics has been dumbed down and made so anaemic that students are
being put off taking it beyond the compulsory tick in the box at GSCE.
City firms have certainly noticed the evidence of a lost tribe. The
great majority of the mathematicians they rely on are recruited from
overseas. Countries such as China and India have realised the crucial
role mathematicians play in the success of their economy and are pumping
out fantastically competent mathematicians that increasingly fill the
hole left in Britain. The report estimates that the cost to the UK
economy since 1990 of not raising homegrown mathematicians totals a
staggering £9bn.
Their analysis of exam papers from the 1950s to the present day
concludes that the current generation of students are not being
stretched mathematically in the same way their predecessors were. An
attempt to make the mathematics more "relevant" has ended up just making
it boring. The move away from rigour and logic, the bedrock of
mathematics, has emasculated the subject. But it is precisely this
ability to think logically that employers are so thirsty for. And it is
not just the financial sphere that values such skills. Mathematics is
much more than an ability to manipulate numbers and perform arithmetic
computations. Trigonometry and quadratic equations are important because
they teach people an analytic way of thinking that can be applied in all
walks of life.
|
Excellent. But the question is, if the analytic way of thinking can be
applied in all walks of life, then why is it necessary to teach it
through trigonometry and quadratic equations?
| Quote: |
But if we want to ensure we don't lose another generation of
mathematicians it must also be an inspiring subject, forming a
springboard for the dive into deeper mathematics. We are being too timid
in what we are challenging students with. It is like teaching someone to
play a musical instrument and only making them play scales and
arpeggios, never letting them listen to real music. Even if you can't
yet play Bach or the blues, at least you realise what you are aiming for.
In mathematics we are missing telling the kids the big stories of maths.
Students should be exposed to the wonders of four-dimensional shapes,
the fascination of the primes, the mysteries of topology.
|
Absolutely. And that's why time should not be wasted doing monkey-
tricks that are not even as necessary as scales and arpeggios.
-tg
| Quote: |
One can
motivate these as essential tools in modern life: they are key to the
way mobile phones change voices into a stream of 0s and 1s, how credit
card numbers are kept secure on the internet, how Google works. But they
also have an exciting quality in their own right which, regardless of
practical applications, can challenge students to see the world in new ways.
It was these big stories that turned me on to mathematics. A teacher at
my comprehensive school when I was about 13 recommended a couple of
books that explored maths beyond the long division of the classroom.
He pointed me towards Martin Gardner's column in Scientific American,
which slipped in fascinating bits of maths on the back of puzzles. I
attended the Christmas lectures at the Royal Institution, that year
given by Christopher Zeeman, the first time they were ever given on
maths. He made it all look so exciting I came away knowing that I wanted
to be a mathematician when I grew up.
It is a lack of teachers who can tell the big stories that is part of
the problem. But it is one that government is trying to address with the
introduction of the National Centre for Excellence in the Teaching of
Mathematics, a coordinated attempt to enrich teachers, who can in turn
inspire their pupils.
It's not as if mathematics is completely isolated in our society. There
seems to be a real thirst recently for things mathematical. Last year
Complicite's play A Disappearing Number about mathematics was a sell out
at the Barbican in London, won the Olivier best play award and returns
for a rerun this autumn. On television, Ridley Scott's Numb3rs does for
maths what CSI did for forensic medicine.
Maths even has a starring role in two recent Hollywood movies, 21 and
the Oxford Murders, with Kevin Spacey and Elijah Wood showing how maths
can be used to break Vegas and crack crimes. And how many people sit
down every morning to stimulate their brain cells with the logical
challenges of the sudokus that fill our newspapers? Perhaps it is time
to find innovative ways to bring this thirst for mathematical stories
and games from the adult playground into the classroom and transform
mathematics from geek to chic.
· Marcus du Sautoy is professor of mathematics at Wadham College, Oxford
and author of Finding Moonshine
--
Douglas Clark ..................... Bath, Somerset, UK ......http://usergroup.plus.net..........http://www.dgdclynx.plus.com |
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Thurisaz the Einherjer
Guest
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| Posted: Thu Jun 05, 2008 10:46 am Post subject: Re: Not Just the US With Education Problems |
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|
tgdenning@earthlink.net:
| Quote: |
What are 'logarithmic maths that you do in your head'? And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they mean
by 'advanced mathematics'?
|
Hey I wrote that posting pretty spontaneously, okay? If my example doesn't
make much sense, so be it. You know what I mean, don't you? :)
--
Romans 2:24 revised:
"For the name of God is blasphemed among the Gentiles through you
cretinists, as it is written on aig."
My personal judgment of monotheism: http://www.carcosa.de/nojebus |
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Douglas Clark
Guest
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| Posted: Thu Jun 05, 2008 11:01 am Post subject: Re: Not Just the US With Education Problems |
|
|
I will just paste this in from Tuesday's UK Guardian....
Without the big maths stories our numbers are plummeting
Britain has been denied a generation of experts thanks to dumbed-down
teaching of what should be a magical subject
Marcus du Sautoy The Guardian, Tuesday June 3 2008
What is the point of studying mathematics? I have never used a sine or
cosine in my everyday life. And solving quadratic equations? Although a
footballer subconsciously solves one every time he works out where to
stand to volley a free kick, I don't think Wayne Rooney is using the
formula he was taught in school to make his decision. So should we be
worried by a new report out today claiming that the failure of
mathematics education in the UK has lead to the disappearance of half a
million mathematicians?
A study published by the thinktank Reform finds that since the 1980s,
mathematics has been dumbed down and made so anaemic that students are
being put off taking it beyond the compulsory tick in the box at GSCE.
City firms have certainly noticed the evidence of a lost tribe. The
great majority of the mathematicians they rely on are recruited from
overseas. Countries such as China and India have realised the crucial
role mathematicians play in the success of their economy and are pumping
out fantastically competent mathematicians that increasingly fill the
hole left in Britain. The report estimates that the cost to the UK
economy since 1990 of not raising homegrown mathematicians totals a
staggering £9bn.
Their analysis of exam papers from the 1950s to the present day
concludes that the current generation of students are not being
stretched mathematically in the same way their predecessors were. An
attempt to make the mathematics more "relevant" has ended up just making
it boring. The move away from rigour and logic, the bedrock of
mathematics, has emasculated the subject. But it is precisely this
ability to think logically that employers are so thirsty for. And it is
not just the financial sphere that values such skills. Mathematics is
much more than an ability to manipulate numbers and perform arithmetic
computations. Trigonometry and quadratic equations are important because
they teach people an analytic way of thinking that can be applied in all
walks of life.
But if we want to ensure we don't lose another generation of
mathematicians it must also be an inspiring subject, forming a
springboard for the dive into deeper mathematics. We are being too timid
in what we are challenging students with. It is like teaching someone to
play a musical instrument and only making them play scales and
arpeggios, never letting them listen to real music. Even if you can't
yet play Bach or the blues, at least you realise what you are aiming for.
In mathematics we are missing telling the kids the big stories of maths.
Students should be exposed to the wonders of four-dimensional shapes,
the fascination of the primes, the mysteries of topology. One can
motivate these as essential tools in modern life: they are key to the
way mobile phones change voices into a stream of 0s and 1s, how credit
card numbers are kept secure on the internet, how Google works. But they
also have an exciting quality in their own right which, regardless of
practical applications, can challenge students to see the world in new ways.
It was these big stories that turned me on to mathematics. A teacher at
my comprehensive school when I was about 13 recommended a couple of
books that explored maths beyond the long division of the classroom.
He pointed me towards Martin Gardner's column in Scientific American,
which slipped in fascinating bits of maths on the back of puzzles. I
attended the Christmas lectures at the Royal Institution, that year
given by Christopher Zeeman, the first time they were ever given on
maths. He made it all look so exciting I came away knowing that I wanted
to be a mathematician when I grew up.
It is a lack of teachers who can tell the big stories that is part of
the problem. But it is one that government is trying to address with the
introduction of the National Centre for Excellence in the Teaching of
Mathematics, a coordinated attempt to enrich teachers, who can in turn
inspire their pupils.
It's not as if mathematics is completely isolated in our society. There
seems to be a real thirst recently for things mathematical. Last year
Complicite's play A Disappearing Number about mathematics was a sell out
at the Barbican in London, won the Olivier best play award and returns
for a rerun this autumn. On television, Ridley Scott's Numb3rs does for
maths what CSI did for forensic medicine.
Maths even has a starring role in two recent Hollywood movies, 21 and
the Oxford Murders, with Kevin Spacey and Elijah Wood showing how maths
can be used to break Vegas and crack crimes. And how many people sit
down every morning to stimulate their brain cells with the logical
challenges of the sudokus that fill our newspapers? Perhaps it is time
to find innovative ways to bring this thirst for mathematical stories
and games from the adult playground into the classroom and transform
mathematics from geek to chic.
· Marcus du Sautoy is professor of mathematics at Wadham College, Oxford
and author of Finding Moonshine
--
Douglas Clark ..................... Bath, Somerset, UK ......
http://usergroup.plus.net .......... http://www.dgdclynx.plus.com |
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alwaysaskingquestions
Guest
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| Posted: Thu Jun 05, 2008 11:01 am Post subject: Re: Not Just the US With Education Problems |
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"Bob Casanova" <nospam@buzz.off> wrote in message
news:ciae44hoitn5qep8fatf9jdttsacv6gglu@4ax.com...
| Quote: |
On Wed, 04 Jun 2008 13:00:11 GMT, the following appeared in
talk.origins, posted by Cheezits <Cheezits32@hotmail.com>:
"alwaysaskingquestions" <alwaysaskingquestions@gmail.com> wrote:
[etc.]
"The UK remains one of the few advanced nations where it is socially
acceptable, fashionable even, to profess an inability to cope with
maths," it says, despite a maths A-level putting on average an extra
o10,000 a year on a salary.
I thought it was because being good at math is considered nerdy.
Could be; I've heard the comment "I don't know how much
change you should get. Oh, and did you want fries with
that?".
Sue (math nerd)
|
I'm fairly handy with numbers but I hate it when I'm with someone who has
had no maths education but can immediately mentally calculate the total odds
for an accumulator bet on several horses or when I'm asked to keep score in
darts and people are calling a finish before I've even subtracted the
previous darts. |
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Ilas
Guest
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| Posted: Thu Jun 05, 2008 11:01 am Post subject: Re: Not Just the US With Education Problems |
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"alwaysaskingquestions" <alwaysaskingquestions@gmail.com> wrote in
news:6ao1mqF38k0sfU1@mid.individual.net:
| Quote: |
IME, percentages are one of the things that confuses many people. Here
in Ireland the VAT rate is 21% added to the basic price (think Sales
Tax). We had a customer in one of our shops who was entitled to a VAT
exempt sale and simply could not grasp why we were reducing the gross
price by 17.4% instead of 21%, he argued with me for nearly an hour
and insisted I was trying to cheat him.
|
Trying to explain the odds of winning the lottery to a group of (well
educated) people I was teaching basic probability as part of a IT security
course was fun. Out of 10, only one gave me the correct answer, the others
ranged from 8.16% (or 6 chances in 49) to something like 1 chance in (I
think, can't be bothered working it out) 6 to the power of 60. The majority
came up with something like 1 chance in 300, from simply adding together 49
+48 etc, or multiplying 49 by 6. They were quite pleasingly surprised when
I showed them how easy it is to work out, because (in the words of one)
most had never bothered with maths at school because you never need it in
real life. |
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Guest
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| Posted: Fri Jun 06, 2008 10:52 am Post subject: Re: Not Just the US With Education Problems |
|
|
On Jun 6, 4:50 am, "alwaysaskingquestions"
<alwaysaskingquesti...@gmail.com> wrote:
| Quote: |
tgdenn...@earthlink.net> wrote in message
news:e4782473-3eab-4b4f-8621-7f9c1c621149@p25g2000hsf.googlegroups.com...
On Jun 5, 1:46 am, Thurisaz the Einherjer <MAILTOsecret...@carcosa.de
wrote:
tgdenn...@earthlink.net:
What are 'logarithmic maths that you do in your head'? And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they mean
by 'advanced mathematics'?
Hey I wrote that posting pretty spontaneously, okay? If my example
doesn't
make much sense, so be it. You know what I mean, don't you? :)
I really had two points: One was simply that I *don't* know what you
might mean by 'logarithmic maths' so I was curious---I didn't think
that anyone did much about logarithms anymore ( even 20 ya), and I
thought maybe this was a case of 'the other English language' at
work. ;-)
The other was the serious one which is that despite math and science
being all about precision of language, when people talk about
education in those subjects they tend to be incredibly vague. To have
a serious discussion, it really does matter what engineers need to be
able to do, and what voters need to be able to do, and so on.
This is an example of how a potentially mind numbing subject can be made
interesting; when my son was a teenager, he detested maths but he was mad
into guitars; he decided to make his own guitar for a school project and was
totally fascinated when I showed him how the spacing of the frets are a
logarithmic scale and went on to show him how all music is actually
logarithmic.
|
Excellent example. The contrast is between what I (and others
obviously) learned, which was how to employ logarithms for
calculation, even though we were never likely to use them, and a
comprehensive examination of the delights of mathematics associated
with something that is, yes, *relevant* to a young person.
The point is that we don't have people learning the 'skills' involved
in finding numbers in a table and interpolating to increase the
accuracy of the results. That doesn't contribute to understanding
anything, or if it does in some minor way, whatever that understanding
is can be developed in other ways.
-tg |
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Thurisaz the Einherjer
Guest
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| Posted: Fri Jun 06, 2008 11:01 am Post subject: Re: Not Just the US With Education Problems |
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|
Bob Casanova:
| Quote: |
Any EE uses logs; ever heard the term "decibel"?
|
True. But the average joe rarely has to do any _calculations_ about
decibels, does he? :)
--
Romans 2:24 revised:
"For the name of God is blasphemed among the Gentiles through you
cretinists, as it is written on aig."
My personal judgment of monotheism: http://www.carcosa.de/nojebus |
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alwaysaskingquestions
Guest
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| Posted: Fri Jun 06, 2008 11:01 am Post subject: Re: Not Just the US With Education Problems |
|
|
<tgdenning@earthlink.net> wrote in message
news:e4782473-3eab-4b4f-8621-7f9c1c621149@p25g2000hsf.googlegroups.com...
| Quote: |
On Jun 5, 1:46 am, Thurisaz the Einherjer <MAILTOsecret...@carcosa.de
wrote:
tgdenn...@earthlink.net:
What are 'logarithmic maths that you do in your head'? And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they mean
by 'advanced mathematics'?
Hey I wrote that posting pretty spontaneously, okay? If my example
doesn't
make much sense, so be it. You know what I mean, don't you? :)
I really had two points: One was simply that I *don't* know what you
might mean by 'logarithmic maths' so I was curious---I didn't think
that anyone did much about logarithms anymore ( even 20 ya), and I
thought maybe this was a case of 'the other English language' at
work. ;-)
The other was the serious one which is that despite math and science
being all about precision of language, when people talk about
education in those subjects they tend to be incredibly vague. To have
a serious discussion, it really does matter what engineers need to be
able to do, and what voters need to be able to do, and so on.
|
This is an example of how a potentially mind numbing subject can be made
interesting; when my son was a teenager, he detested maths but he was mad
into guitars; he decided to make his own guitar for a school project and was
totally fascinated when I showed him how the spacing of the frets are a
logarithmic scale and went on to show him how all music is actually
logarithmic. |
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Tim Norfolk
Guest
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| Posted: Fri Jun 06, 2008 11:17 pm Post subject: Re: Not Just the US With Education Problems |
|
|
On Jun 6, 7:38�am, tgdenn...@earthlink.net wrote:
| Quote: |
On Jun 6, 7:10�am, "alwaysaskingquestions"
alwaysaskingquesti...@gmail.com> wrote:
tgdenn...@earthlink.net> wrote in message
news:c2998cc9-3166-4b7f-9472-0ee59c142e05@x41g2000hsb.googlegroups.com...
On Jun 6, 4:50 am, "alwaysaskingquestions"
alwaysaskingquesti...@gmail.com> wrote:
tgdenn...@earthlink.net> wrote in message
news:e4782473-3eab-4b4f-8621-7f9c1c621149@p25g2000hsf.googlegroups.com...
On Jun 5, 1:46 am, Thurisaz the Einherjer <MAILTOsecret...@carcosa.de
wrote:
tgdenn...@earthlink.net:
What are 'logarithmic maths that you do in your head'? And what
engineers use such skills?
Why is is so difficult for people to be explicit about what they
mean
by 'advanced mathematics'?
Hey I wrote that posting pretty spontaneously, okay? If my example
doesn't
make much sense, so be it. You know what I mean, don't you? :)
I really had two points: One was simply that I *don't* know what you
might mean by 'logarithmic maths' so I was curious---I didn't think
that anyone did much about logarithms anymore ( even 20 ya), and I
thought maybe this was a case of 'the other English language' at
work. ;-)
The other was the serious one which is that despite math and science
being all about precision of language, when people talk about
education in those subjects they tend to be incredibly vague. To have
a serious discussion, it really does matter what engineers need to be
able to do, and what voters need to be able to do, and so on.
This is an example of how a potentially mind numbing subject can be made
interesting; when my son was a teenager, he detested maths but he was mad
into guitars; he decided to make his own guitar for a school project and
was
totally fascinated when I showed him how the spacing of the frets are a
logarithmic scale and went on to show him how all music is actually
logarithmic.
Excellent example. The contrast is between what I (and others
obviously) learned, which was how to employ logarithms for
calculation, even though we were never likely to use them, and a
comprehensive examination of the delights of mathematics associated
with something that is, yes, *relevant* to a young person.
The point is that we don't have people learning the 'skills' involved
in finding numbers in a table and interpolating �to increase the
accuracy of the results. That doesn't contribute to understanding
anything, or if it does in some minor way, whatever that understanding
is can be developed in other ways.
Some of it may have to do with personal inclination - I have always been
fascinated with both puzzles in general and with knowing how things work; in
my first job - just before the introduction of desktop calculators - I had
to learn how to use a slide rule and was thought it was a fantastic
invention.
Yes, I earned my nerd status with a little plastic slide rule that was
always in my shirt pocket, I think even before high school. (No pocket-
protector though.) �But again a great example---a good slide rule
could 'do logarithms' to 3-4 decimal places sometimes, which was more
than enough. A current parallel might be students learning 4 ways to
'solve' quadratic equations or find trigonometric solutions when their
$12 calculator can do it in an instant.
-tg- Hide quoted text -
- Show quoted text -
|
A minor quibble, but I don't know of a $12 calculator that will solve
quadratic and trig equations. The TI-series that most of our students
have used are in the $80 range. If you are talking about simply
plugging in the values into the quadratic equation, too many students
still group terms incorrectly, and get reasonable-looking, but
completely incorrect results.
The major point is that I can think of at least 5 different ways that
one teaches solution of quadratics, depending on the level of the
student and course, each of which is intended, like scales in music,
to re-inforce mastery of a basic skill:
1. Factoring, which leads to higher-order polynomial equations, and
others of polynomial type, re-inforcing some of the basic algebra
skills.
2. Completing the square, which is how the quadratic equation is
derived. This is used later in the analysis of conic sections, thence
quadric surfaces in multi-variate calculus, necessary for the analysis
of solutions to optimization problems.
3. The quadratic formula itself, which is a handy tool, inasmuch the
most common types of equations encountered by undergraduates in
science and engineering are second-order, linear, constant-coefficient
ordinary differential equations, or linear systems of first-order
ones. This takes care of a lot of statics, dynamics and even control
theory, as well as stability analysis for many numerical methods,
where the eigenvalues of the operator involved correspond to the zeros
of a polynomial equation (frequently quadratic), and should lie in the
left half of the complex plane for appropriate stability or control.
The quadratic equation is also the basis for the third-order
Laguerre's method for non-linear equations, an extension of Newton's
method.
4. Graphical solutions, for those students who are less symbol- and
more visually-oriented, a valuable skill for those students doing
mathematical modelling.
5. Numerical methods, to show how such things as Newton's method work.
If you want to argue that most students will not do most of these
things later, and so don't need these ideas, I would agree, if you
want to have an extremely elitist scheme in which only the most
motivated and capable students are taught technical subjects after age
13 or so.
As in our previous discussion, I would point out that I have tried to
teach many students who have been taught mathematics exactly by the
automated tools that you espouse. Thier learning of other material is
much more difficult, including things which are conceptual. |
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Bob Casanova
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| Posted: Sat Jun 07, 2008 3:24 am Post subject: Re: Not Just the US With Education Problems |
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On Thu, 5 Jun 2008 18:12:46 -0700 (PDT), the following
appeared in talk.origins, posted by Tim Norfolk
<timsn274@aol.com>:
| Quote: |
On Jun 5, 5:22?pm, Bob Casanova <nos...@buzz.off> wrote:
On Thu, 05 Jun 2008 19:40:04 +0200, the following appeared
in talk.origins, posted by Thurisaz the Einherjer
MAILTOsecret...@carcosa.de>:
tgdenn...@earthlink.net:
...despite math and science
being all about precision of language, when people talk about
education in those subjects they tend to be incredibly vague. To have
a serious discussion, it really does matter what engineers need to be
able to do, and what voters need to be able to do, and so on.
Hmmm. I plead guilty. :)
Yes I was quite vague. I openly confess that I haven't used logarithms for
so long that I just have a very vague idea left on how to do it, if I ever
have to again. Sad, I admit.
I guess that's why logarithms were the first thing that crossed my mind when
I thought "I should perhaps state an example of something that not everyone
needs in everyday life" :)
Any EE uses logs; ever heard the term "decibel"?
or Richter scale, for the geologists and newsmen.
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Point; thanks.
--
Bob C.
"Evidence confirming an observation is
evidence that the observation is wrong."
- McNameless |
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