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Author Topic: I Don't *Do* Math!  (Read 7355 times)

UnReconstructed

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« Reply #15 on: June 16, 2005, 09:21:47 pm »

I suppose that *was* my point.....although I rambled about....

that is part of the reason they are teachers....they have no aptitude for math.

It is very sad that the person in the article compounds upon this non-aptitude by refusing to see the utility for it, when, in fact nearly everything around her has been designed and built and distributed by people who *do* know math.

And yet another group of students is turned off to math by teachers who cannot teach......
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Roy J. Tellason

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« Reply #16 on: June 17, 2005, 12:11:13 am »

I sat here and read through that whole thread,  and it's about the most depressing damn thing I've read in a LONG time...

We're really seriously screwed.  Way worse than what I'd thought before,  even.  :-(
 
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« Reply #17 on: June 17, 2005, 09:27:16 am »

Arithmetic is one of the fundamentals of understanding. If you don't have a good grasp of basic arithmetic, you don't have a good understanding of how numbers relate to each other.

The relationships between things (relative sizes, multiples, sets, etc.) is very important in dealing with the world.

You can't manage money without an understanding of arithmetic and if you can't handle money effectively, it's hard to be anything other than a peon living paycheck-to-paycheck.

If you don't appreciate the value of things (converting the monetary cost of something into the time it takes to earn that money if necessary) then it's easy to get seduced into frittering your life away on trivia.


 
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UnReconstructed

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« Reply #18 on: June 17, 2005, 10:38:52 am »

Roy,

I suspect that it is far far worse than either you or I think....and this really does explain a lot.

Have you read 'An Underground History of American Education' by John Gatto?

John Gatto Website

It is an outstanding read....and it goes quite a long ways to explaining exactly what is wrong with public education today....

His main thesis, (which he backs up with lots of evidence) is that the public schools are not broken.....they are working splendidly....churning out a uniformly dumbed down product that cannot think critically..........

And on another note.....

Here in PA we get quite a lot of the 'teachers need more pay'...routine.

And I reply (at least in my mind.....) Why? The teachers degree is among the easiest to obtain. Why *should* they make top dollar? Because they have all day custody of your kids?

That is another problem entirely....

I do agree that a truly skilled teacher should get major money....but then again....most truly skilled teachers will not be happy working for a gubbmint skool......
« Last Edit: June 17, 2005, 10:41:20 am by UnReconstructed »
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mi6a2lm

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« Reply #19 on: June 17, 2005, 12:01:36 pm »

Quote
Arithmetic is one of the fundamentals of understanding. If you don't have a good grasp of basic arithmetic, you don't have a good understanding of how numbers relate to each other.

I suppose I have a good grasp, but I appreciate Kronecker's view:

God made the integers, all else is the work of man.

It can be argued that all one needs is the binary operation of addition, the numbers 0 and 1, and the resulting arithmetic is just tedious. :P

Quote

The relationships between things (relative sizes, multiples, sets, etc.) is very important in dealing with the world.

You can't manage money without an understanding of arithmetic and if you can't handle money effectively, it's hard to be anything other than a peon living paycheck-to-paycheck.

Which is why I own about 8 calculators.  Three HP's (a business model, 48G and a 49G), two TI's (solar financial, another financial) and some Casio's laying about.  When civilization collapses I'll still be able to multiply 5292645 X 6832473 by hand but for now I'll let my trusty BA-35 solar take care of that.

Quote

If you don't appreciate the value of things (converting the monetary cost of something into the time it takes to earn that money if necessary) then it's easy to get seduced into frittering your life away on trivia.

« Last Edit: June 17, 2005, 12:02:41 pm by mi6a2lm »
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« Reply #20 on: June 17, 2005, 04:15:23 pm »

Maybe I shouldn't comment on education, since I don't have any kids. I think I was a kid, a while back, so I'll just rant on that basis.

Every kid needs to learn how to add, subtract, multipy, and divide without a calculator, and needs to practice it enough that he/she will never forget how to do it.

But after that point is reached, it is time to move on! Calculators exist, they have existed for years, and there is no reason to inflict hundreds of mind-numbing arithmetic exercises on the young brain. Much better to spend the time on useful, practical stuff.

For example, there is rarely any real-world situation where you will need to multiply 989 by .0955 by hand.  But there are lots of situations where you will want an approximate answer fast -- for example, "how much will the 9.55% sales tax cost me on this $989 purchase?" Everyone should be able to do this in their heads. "Well, that's just under 1000 times just under 1/10, so it'll be below $100, somewhere around $95-ish."

(In some ways I miss the slide rule. A slide rule only tells you the digits in the answer, but doesn't tell you where the decimal point goes, so you are always forced to do a rough estimate in your head. This provides a "sanity check" on the results. With a calculator, it's easy to press the wrong button and blindly accept an obviously-wrong answer. But I'm digressing.)

As soon as possible, kids ought to get real-world math problems. I don't mean the stupid contrived "word problems" from the textbooks, I mean stuff from real life. How many rolls of insulation do we need to buy for the shed? If we buy a car with better gas mileage, how much money will we save per year? How much is the aquarium going to weigh after it's full? These sorts of problems will naturally go along with learning geometry and simple algebra. And they ought to make it obvious why everyone needs to be able to "do math".
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Roy J. Tellason

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« Reply #21 on: June 17, 2005, 07:02:33 pm »

Quote
 
Quote
Roy,

I suspect that it is far far worse than either you or I think....and this really does explain a lot.

Thanks,  I really needed to hear that...   :-|

Quote
Have you read 'An Underground History of American Education' by John Gatto?

John Gatto Website

It is an outstanding read....and it goes quite a long ways to explaining exactly what is wrong with public education today....

Hell yeah!  I also recommend that site when it seems like a good idea...

Quote
His main thesis, (which he backs up with lots of evidence) is that the public schools are not broken.....they are working splendidly....churning out a uniformly dumbed down product that cannot think critically..........

Hence my comments about "those bastards that are doing this to us",  may they rot...

Quote
And on another note.....

Here in PA we get quite a lot of the 'teachers need more pay'...routine.

You're in PA?  PM me if you would.  Yeah,  I hear that nonsense from time to time.

Quote
And I reply (at least in my mind.....) Why? The teachers degree is among the easiest to obtain. Why *should* they make top dollar? Because they have all day custody of your kids?

They have to make *more* because some other teachers in some other school district are making more,  never mind that costs of living may be different,  or that other district may have more money,  or...

Quote
That is another problem entirely....

I do agree that a truly skilled teacher should get major money....but then again....most truly skilled teachers will not be happy working for a gubbmint skool......

Perhaps not.

I read an interesting article in Nuts&Volts of all places about a distinction between "teaching" and "training".  Well worth it.
 
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mi6a2lm

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« Reply #22 on: June 18, 2005, 12:31:15 pm »

Practical application!  (only pencils and non-graphing calculators and one sheet of paper are allowed - you have 10 minutes to complete this problem, when you are done please stay seated until time is up)

------------------------------

Problem:  The news media reports that notebooks containing 36,000 entries were found in the arrest of a convicted child molester.  The San Jose police department says this man may have molested 36,000 children over a 40 year period as a result of finding these notebooks.  Disregarding the fact that the man has spent some of those 40 years in prison, how many children would the man have had to molested
i) per year
ii) per month
iii) per day.

Extra credit:  Is this is in any way plausible and do you think the news media and the San Jose police department can do arithmetic?


------------------------------
« Last Edit: June 18, 2005, 12:44:23 pm by mi6a2lm »
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« Reply #23 on: June 18, 2005, 03:28:26 pm »

Quote
Practical application! ... how many children would the man have had to molested
i) per year
ii) per month
iii) per day.
This is, actually, brilliant.

There must be all sorts of math problems lurking in the daily news. Great idea, mi6a2lm!
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RagnarDanneskjold

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« Reply #24 on: June 19, 2005, 09:08:12 am »

Quote
Extra credit:  Is this is in any way plausible and do you think the news media and the San Jose police department can do arithmetic?


------------------------------
No and No. Similar to that story about how many women Wilt Chamberlain had s  e  x  with. It was also an arithmetical impossibility, although I don't remember what the claim was.
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UnReconstructed

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« Reply #25 on: June 20, 2005, 12:20:33 pm »

This seemed terribly relevant.....it was in todays online Wall Street Journal:


Ethnomathematics

By DIANE RAVITCH
June 20, 2005; Page A14

It seems our math educators no longer believe in the beauty and
power of the principles of mathematics. They are continually in
search of a fix that will make it easy, relevant, fun, and even
politically relevant. In the early 1990s, the National Council of
Teachers of Mathematics issued standards that disparaged basic
skills like addition, subtraction, multiplication and division,
since all of these could be easily performed on a calculator. The
council preferred real life problem solving, using everyday
situations. Attempts to solve problems without basic skills caused
some critics, especially professional mathematicians, to deride
the "new, new math" as "rainforest algebra."

In a comparison of a 1973 algebra textbook and a 1998 "contemporary
mathematics" textbook, Williamson Evers and Paul Clopton found a
dramatic change in topics. In the 1973 book, for example, the index
for the letter "F" included "factors, factoring, fallacies, finite
decimal, finite set, formulas, fractions, and functions." In the
1998 book, the index listed "families (in poverty data), fast food
nutrition data, fat in fast food, feasibility study, feeding tours,
ferris wheel, fish, fishing, flags, flight, floor plan, flower beds,
food, football, Ford Mustang, franchises, and fund-raising carnival."

Those were the days of innocent dumbing-down. Now mathematics is
being nudged into a specifically political direction by educators
who call themselves "critical theorists." They advocate using
mathematics as a tool to advance social justice. Social justice math
relies on political and cultural relevance to guide math
instruction. One of its precepts is "ethnomathematics," that is, the
belief that different cultures have evolved different ways of using
mathematics, and that students will learn best if taught in the ways
that relate to their ancestral culture. From this perspective,
traditional mathematics -- the mathematics taught in universities
around the world -- is the property of Western Civilization and is
inexorably linked with the values of the oppressors and conquerors.
The culturally attuned teacher will learn about the counting system
of the ancient Mayans, ancient Africans, Papua New Guineans, and
other "non-mainstream" cultures.

Partisans of social justice mathematics advocate an explicitly
political agenda in the classroom. A new textbook, "Rethinking
Mathematics: Teaching Social Justice by the Numbers," shows how
problem solving, ethnomathematics and political action can be
merged. Among its topics are: "Sweatshop Accounting," with units on
poverty, globalization, and the unequal distribution of wealth.
Another topic, drawn directly from ethnomathematics, is "Chicanos
Have Math in Their Blood." Others include "The Transnational Capital
Auction," "Multicultural Math," and "Home Buying While Brown or
Black." Units of study include racial profiling, the war in Iraq,
corporate control of the media, and environmental racism. The theory
behind the book is that "teaching math in a neutral manner is not
possible." Teachers are supposed to vary the teaching of mathematics
in relation to their students' race, gender, ethnicity, and
community.

This fusion of political correctness and relevance may be the next
big thing to rock mathematics education, appealing as it does to
political activists and to ethnic chauvinists.

It seems terribly old-fashioned to point out that the countries that
regularly beat our students in international tests of mathematics do
not use the subject to steer students into political action. They
teach them instead that mathematics is a universal language that is
as relevant and meaningful in Tokyo as it is in Paris, Nairobi and
Chicago. The students who learn this universal language well will be
the builders and shapers of technology in the 21st century. The
students in American classes who fall prey to the political designs
of their teachers and professors will not.

Ms. Ravitch is a historian of education at New York University, a
senior fellow at the Brookings Institution, and a member of the
Koret Task Force at the Hoover Institution.  
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mi6a2lm

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« Reply #26 on: June 21, 2005, 01:27:03 am »

Translating the below statement so you can impress others:



The bold a, b, c are vectors.  The easiest way to envision a vector is a three-dimensional one with an x, y and z axis.  Just look a corner of the room you are in and choose that to be the origin.  Say, let a be one meter to the right, one meter towards you and one meter up.  Hence, a would be (1,1,1).  The Greek letters (alpha, beta and gamma) would then correspond to scalars - just numbers with no physical units.  So for the vector a = (1 ,1 ,1) a scalar of beta = 2 multiplied by a would be simply (beta) x a = (2, 2, 2).  The upside down 'A' means 'for all', the curvy 'E' means there exists', the weird-looking C means the set of complex numbers and the weird-looking R means the set of numbers (everything from the number 1 to pi to the square root of 2).  So, in words:

There is a vector a when multiplied by (parenthesis) betab plus gammac equals betaab plus gammaac, for all a, b, c which are elements of A, and for all beta, gamma being elements of the complex numbers, C (or the real numbers, R).

 ;)

----------------------------

Oh, yeah, in refence to an above post, 'Abelian' = 'commutative'.  For example, 1+ 2 = 2 + 1.  Here, 1 and 2 commute.  And you're thinking, "Duh".  However, there are many situations where a set of things might not commute, such as in matrix multiplication, quantum mechanics etc.  The famous example in quantum mechanics is that the position and momentum of an object do not commute.  In other words, 1 + 2 does not equal 2 + 1.  For further explanation you'll just have to buy my former professor's book referenced higher in this thread (the first one I linked to).   :)
« Last Edit: June 21, 2005, 01:34:53 am by mi6a2lm »
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billy-jay

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« Reply #27 on: June 21, 2005, 03:59:13 am »

Thanks to the kind mod who fixed the title of this thread.
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Mostly Harmless

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« Reply #28 on: June 21, 2005, 11:17:40 am »

Quote
Practical application!  (only pencils and non-graphing calculators and one sheet of paper are allowed - you have 10 minutes to complete this problem, when you are done please stay seated until time is up)

------------------------------

Problem:  The news media reports that notebooks containing 36,000 entries were found in the arrest of a convicted child molester.  The San Jose police department says this man may have molested 36,000 children over a 40 year period as a result of finding these notebooks.  Disregarding the fact that the man has spent some of those 40 years in prison, how many children would the man have had to molested
i) per year
ii) per month
iii) per day.

Extra credit:  Is this is in any way plausible and do you think the news media and the San Jose police department can do arithmetic?


------------------------------
i) 900
ii) 75
iii) 2.46

That's assuming no leap years and no taking a day off now and again.

Extra credit: No, it's not plausible. I can't decide whether it's lack of math skills or a desire to intimidate the sheeple by demonizing the molesters.
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mi6a2lm

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« Reply #29 on: June 21, 2005, 11:44:55 pm »

Sorry, I wrote above that the capital "E" that looked curvy meant "there exists".  Actually, the curvy "E" means "is (or are) elements of".  To confuse things further, "E" (the capital letter as you see it), when it is flipped 180 degrees in the plane of the paper (the arms are pointing left) means "there exists" or "there exist".
-------------------

Edit: Here is a big list of mathematical notation.
http://mathworld.wolfram.com/topics/Notation.html
« Last Edit: June 21, 2005, 11:50:32 pm by mi6a2lm »
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