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Warp wrote:
> task, they *don't want* to do that. They completely reject the notion.
> It's like they had some kind of fear or phobia, and they like to hide
> behind their "I'm not good at math" defense. Any explanations or attempts
It is - at least it's classified as a "learning disorder" in some
places. It's called math anxiety. It's probably always placed into their
heads via society (e.g. really bad math teachers and fellow students who
tend to equate intelligence with mathematical ability).
--
A Mexican newspaper reports that bored Royal Air Force pilots stationed
on the Falkland Islands have devised what they consider a marvelous new
game. Noting that the local penguins are fascinated by airplanes, the
pilots search out a beach where the birds are gathered and fly slowly
along it at the water's edge. Perhaps ten thousand penguins turn their
heads in unison watching the planes go by, and when the pilots turn
around and fly back, the birds turn their heads in the opposite
direction, like spectators at a slow-motion tennis match. Then, the
paper reports "The pilots fly out to sea and directly to the penguin
colony and overfly it. Heads go up, up, up, and ten thousand penguins
fall over gently onto their backs." -- Audobon Society Magazine
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawaz org<<<<<<
anl
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Warp wrote:
> Btw, some schools and school books in the US are taking the other extreme:
> They are dumbing down basic math to the point where nobody learns anything
> useful.
>
> For example, they don't teach the classical way of summing or multiplying
> two numbers on paper anymore *at all*. It's like it's completely censored.
>
> Instead, they give a few heuristics on how to deduce the result of a few
> easy cases, and for the rest the rule is basically "if you can't deduce it,
> use a calculator".
Do you have examples of this?
I know months ago a youtube link was posted on this newsgroup about a
Seattle woman complaining about the way they teach math these days and
comparing what she had learned with what they're teaching now.
If that's what you're talking about, I honestly can't say the "old
fashioned" way is "better". What she referred to as the new way of
teaching it weren't simply heuristics - they always work and unlike how
many of us were taught when we were young, actually force the students
to understand how multiplication and division actually work - rather
than just following an algorithm to compute the result.
For me, the only real concerns were: 1) Can kids that age be reasonably
expected to understand *how* long division works? Some always will, but
what percentage? 2) Seems if they do it the "algorithmic" way, they'll
quickly be able to divide faster, whereas with the new way, being able
to divide faster may take a lot more practice.
I didn't really understand her complaints. She seemed to just have this
opinion that the old ways were better. For me, it's best to teach both.
--
A Mexican newspaper reports that bored Royal Air Force pilots stationed
on the Falkland Islands have devised what they consider a marvelous new
game. Noting that the local penguins are fascinated by airplanes, the
pilots search out a beach where the birds are gathered and fly slowly
along it at the water's edge. Perhaps ten thousand penguins turn their
heads in unison watching the planes go by, and when the pilots turn
around and fly back, the birds turn their heads in the opposite
direction, like spectators at a slow-motion tennis match. Then, the
paper reports "The pilots fly out to sea and directly to the penguin
colony and overfly it. Heads go up, up, up, and ten thousand penguins
fall over gently onto their backs." -- Audobon Society Magazine
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Mueen Nawaz <m.n### [at] ieeeorg> wrote:
> What she referred to as the new way of
> teaching it weren't simply heuristics - they always work
I didn't claim the methods don't work. What I said that the methods
are only easily applicable to a small subset of all possible operations,
while the "classical" method can be equally easily applied to any operation
(only the length of the calculation varies, not its difficulty).
If you want to calculate "223882819200394832*4802993291324" on paper,
the "old-fashioned" way is equally easy as calculating "244*25" (it just
takes longer, which is understandable, but is in no way harder). It would
be completely hopeless to calculate that with the "new methods".
I don't disagree in teaching alternative methods for easy cases, such
as for example "25*9" (which can be thought of as, for example, "25 times
10 is 250, minus one time 25, which is 225"). However, I completely disagree
in not teaching the "mechanical" way of calculating multiplications (or
other operations), for the case when you really need to do so.
> I didn't really understand her complaints. She seemed to just have this
> opinion that the old ways were better. For me, it's best to teach both.
The old way is better in the sense that it allows you to calculate *any*
summation, multiplication and division (and even things like square roots),
regardless of the size of the operands. The "new methods" are very limited
and become very complex in many situations. Not teaching the classical way
is really stupid, IMO.
--
- Warp
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Invisible wrote:
> Seems pretty solid logic to me.
It always seemed to me it was because I messed up the curve. I wasn't
hated for being good at math when I was in AP Calculus where everyone
was good at math. I was hated for being good at physics because I didn't
have to do more than one homework problem from each set to know I
understood what was going on well enough to ace the tests.
Everyone can play football at some level or another. (And yes, you can
be disliked for not playing football too well, if someone is required to
put you on their team. :-)
The thing is, the people who are good at football don't compete with the
people who are bad at football. But they have to compete with the people
who are good at math and science, or they don't graduate grade school.
Think about college (university?) - did anyone dislike you if you aced
all your math tests? No, because at that level, they weren't required to
take the advanced math classes you were taking.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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Invisible wrote:
> realistically have no significant impact.
How do you know? There's *some* reason that Japan moved up to one of the
world's superpowers (economically at least) over the course of 50 years.
Maybe obsessing over details *is* important.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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Warp wrote:
> Is it really so that in the US, the UK and other places everybody has
> to explicitly fill out tax forms each year, specifying all their income,
> tax reductions, etc?
Yeah. I saw recently someone calculated that 60% of everyone could get
away with just filling out on the tax form that which had already been
reported to the government.
> (Of course for employers it's a completely different matter, but normal
> people don't have to worry about that.)
I'm always amazed how much overhead there is for employers to pay taxes.
Call it 10x the paperwork for each employee as the employee ever sees.
Even if you're the only employee of the company. Try to start a 3-person
company and you have practically no choice but to hire some outside
company to do the employment paperwork in the USA.
>> [Why do they make them so complicated? Is it a conspiracy to ensure you
>> get them wrong and hand over more money than you're supposed to??]
>
> You mean there are no tax returns where you live? That would be odd.
It's complicated so the legislature can favor particular people and
companies and behaviors over others. And then when the rules interact
poorly and let some subset of people get away with having lots of money
and no taxes, they put together a second set of rules to deal with that.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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scott wrote:
> able to do at least the basics very quickly in your head.
It also helps if you can do some common sense. If you look at sample
apartments in a half-dozen neighborhoods to figure out how much rent you
might have to spend to get there, and you have $1200/month, $1400/month,
$900/month, and your average comes out to $30,000/month, you better know
you've done something wrong.
> took a long time and a lot of effort - not sure if that was a profitable
> use of my time though!
I was actually pleasantly surprised with the tax authority last year.
They sent me a letter telling me I hadn't paid tax on some income I
made. I called them up and told them I'd reported it on the consulting
company's tax return, even tho the employer had filled out my personal
name on the paperwork they sent to the government. Took about 15
minutes to get audited, over the phone, and I got a letter a week or two
later saying "nevermind."
I expected it to be way more of a PITA. But then, I'd never heard of
anyone honest getting audited before, so that might play into it.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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scott wrote:
> That really is crazy.
Yes.
> How do they justify taxing you when you are not even living there?
Because they can.
> Does that mean that anyone born in USA must
> (potentially) pay USA taxes for the rest of their life no matter in
> which country they live? What a hassle!
I believe it's five years, last I remember hearing about it. Possibly
longer if you remain a citizen of the USA.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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Invisible wrote:
> Hell, I can't even multiply numbers in my head!
>
> I'm good at understanding principles and elligant mathematical theories.
> I'm not good at memorising vast amounts of unstructured data.
If you think multiplication tables are "unstructured data"... ;-)
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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Warp wrote:
> The "new methods" are very limited
You may be speaking about different "new methods".
In the USA, there's "new math", introduced a few decades ago. It gets
rid of "three apples plus two apples is five apples", and instead tries
to teach arithmetic based on formalism instead of "common sense".
This has the benefit that you actually learn the math instead of just
the algorithms, and the drawback that it's harder to understand how to
apply it to every-day situations.
It sounds like Warp is talking about a system of shortcuts rather than
something more comprehensive.
(And the running joke here is the parent's can't help the children with
the "new math" because they don't understand it. That is, they know the
arithmetic, but not the math behind it that makes it work.)
I know that I was in graduate school before anyone actually explained
what a formal system really is and how it works and why it matters. I
did years of calculus and statistics and such, without ever being taught
the fundamentals of anything like proof theory, rewrite rules, lambda
calculus, etc. I personally think those latter are much more useful to
learn than (say) partial integrals or some such.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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