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Old 01-22-2008, 06:24 PM   #1 (permalink)
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Math, new book

I play a game on a certain site called Joggle, its a word game, sort of like Boggle, only online. Anyway, they have a forum, and one of the other players is writing a book on how math should be taught.
I was impressed with what little I have read of it, as he added some excerpts in the forum.
this is one of them:

From: superjudge Date: October 1, 2007 Time: 2:45:54 AM [REPLY]
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This is my first draft of the preface/intro to my book, tentatively titled "X2 Files: The Secret Failure of Math Education"

The big theme of the book is the topic of a couple of keynotes that I have given, "Perspiration vs. Inspiration: Which Mathematical Road Are We On?

There will be edits of course, but this is the direction of the book

===============================================

The innocence of children is perhaps captured none better than when they

taste new food for the first time. Graces, manners, and customs are hilariously

absent when a baby rejects the offerings from a frustrated parent in no uncertain

terms. I have pictures of my son doing battle royal with pureed squash with his hands

unknowingly paying homage to Bruce Lee. His face is a portrait of pain and obstinance

that borders cartoon exaggeration—although it often seems that his head has the ability

to swivel 180 degrees away from the incoming mash of death.

The communication is unrefined, but it is highly effective. The crying, screaming and

stiff-arming not only keeps the evil root vegetable at bay, it makes me rethink my

approach to giving my son the nourishment and flavor that he deserves.

For most of us, math was the orange guck of education. And, schools worldwide

have been serving this historically unsatisfying gruel for over 50 years. The packaging

might have changed (fancier textbooks and fancier calculators), but the content and

the approach have yet to see a revolution of any significance—most people still hate

math! Finding medians of triangles might have been crucial to people during the baby

boom—a mathematical procedure having all the drama of a cheese sandwich—but today

it only qualifies as the pogo stick of mathematics. The uncontested Canon of

mathematics still must be learned by all of us. Correction. Endured by all of us.

We are still solving math problems involving digging ditches, rowing boats

upstream, calculating angles of guy wires and picking marbles out of a bag. I often

wonder why I also didn’t succumb to the cricket sounds that were produced by these

sleep-inducing topics.
In addition to a stale math curriculum, schools are frantically seeking breadth,

instead of calmly seeking depth. Deep understanding has been replaced by the popular

understudy called correctness. Calculators and teaching to the test have allowed for rave

reviews for this misguided goal of mathematics. Students, teachers, administrators and

parents can all share the blame in having math riddled with memorization tricks and

gimmicky language. Flip it and multiply is still used by many teachers to explain to

students how to divide fractions. Even Danica McKellar, who played Winnie on The

Wonder Years, advocates this kind of explanation in her book, Math Doesn’t Suck.

Actually Danica, a lot of high school math does and so does your “mathemagican”

explanation of division.

Why children still need to find the answer to something like 4⅜ ÷ 1⅔ is completely

beyond me. Oh sure, like a trained seal they can get the correct answer, but what’s the

point when they don’t really understand the question or the answer. Keep spinning that

ball on your nose, Jimmy. Mathematics education: Wasting the lives of one student at

a time.

It’s small wonder that very few people understand mathematics, never mind enjoy it.

While the carrot of assessment dangles in every subject, mathematics cannot exist

without it. The audience does not want to learn math—it has to learn math.

This might be acceptable if the knowledge that was communicated was breathtaking

or beneficial. And while there are points of brilliant light in math education, the overall

spectrum suffers from an almost immovable dullness. As a result of these factors and

many more, the actual literacy level of the average high school math student is probably

near a primary level. Yes. I said “literacy”. I don’t like “numeracy” because it sounds

like it was invented by someone who writes jingles for a living. Mathematics is a

a beautiful language that is a thousands of years old. Please don’t refer to it in a way that

implies it can be reduced to counting on your fingers and toes. And therein lies the heart

of the problem—false representation. Mathematics is one of the most stunning and

boundless parts of our existence. An inability to communicate its true measure and worth

is a tragic failure that has yet to be reported. Until now.

You and others have millions of hours of experience toiling in the mathematical mines,

excavating supposed brilliant deposits of knowledge—which unbeknownst to you, turned

out to be worthless lumps of coal. Your stories of boredom, intimidation and anxiety

have rarely been heard outside the narrow walls of academia. Any documentation on the

harm on the relevancy and stress of how and what students learn about math in school has

been far removed from public consumption.

The safe and explorative environment that children start out learning math in is very

soon replaced by one that is preoccupied with constant testing, unwarranted volumes of

homework and various societal pressures—never tempered by the realities of childhood

and adolescence. Math classrooms of today are more like academic sweatshops,

producing perspiration instead of inspiration. Most math teachers roll out the

curriculum with the speed of a runaway train—often unconcerned whether or not

passengers are actually boarding. My favorite high school teacher taught us with the

calmness and relaxed demeanor that made you feel like you were sipping lemonade

with him on a breezy summer day. His name was Mr. Scott. He was a tall, somewhat

gangly fellow. His height, warmth and wisdom made me think of Gandalf from Lord of

the Rings. The only thing he ever held in his hand was a cup of coffee. No chalk. No

marker. Nothing. Whenever he took a satisfying gulp from his cup, you could be sure

a probing question or wonderful observation was going to follow.

Mr. Scott was my history teacher. While students loved the way he could talk about

bloody Assyrian battles, Napolean’s ingenious morale building techniques, or the

bravery of World War I soldiers combating mustard gas(wrapping shirts soaked in urine

around their faces), it is not why we loved Mr. Scott.

His ability to communicate history with astonishing detail was eclipsed by the elements

that are in short supply in not just math, but most subjects—passion and love.

His smile. His voice projection. His smirks and timely inflections. His purposeful eyes.

They all merged many times during his lessons to underscore how much he loved his

job, subject and students.

If love is not at the bottom of your craft/knowledge, then communicating it to strange

and detached students will be a fruitless endeavor. You might as well give them links

to Wikipedia and be done with it. So, while this book does have strong overtones of

that angry letter to the editor, it is in the end, a love letter to mathematics.

In this letter I hope you find that she is not some ugly creature pocked with blemishes

of polynomials, marked with scars of useless long division, and saddled with a

personality of a toad with its slavish devotion to the absurd demands of fraction

reduction. If this story could be told as Beauty and the Beast, then it is mathematics

which is Beauty and education which is Beast. The tragedy is that education has

rendered and distilled mathematics from a vintage bottle of wine to a commercial vat

of vinegar. The only thing which rivals the ire towards mathematics is the school’s

cafeteria serving fish sticks on a Monday.

The problem is that fish sticks only cost you 5 bucks. Receiving a poor math

education was a much steeper cost. You don’t know it, but you are still paying for

it today. Do you buy insurance? Do you buy more than one lottery ticket? Do you

buy extended warranties? Do you rely heavily on a calculator? Do you still imagine

doodled drawings of your math teachers with plus signs for eyes? If you said yes to any

of these questions, then you better take your math education to the 7th floor of Sears and

demand a refund.

In lieu of deserving reparation for your years of confusion, boredom and anxiety, I

offer you this book. You won’t get any better at calculus, but you will wish that you

could.

“Not everyone can be a mathematician, but everyone should want to be one”

R. Moore

you can read more here

http://joggle.pixelsharp.com/f_view_topic.asp?id=3499


one of the other players has totally attacked him and his writing, which seems to take away any comments directed at the writing of the book.
I can't seem to understand why some people have to be so mean. this is what he said about the book:

From: mr_bog Date: October 2, 2007 Time: 10:21:44 AM [REPLY]
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It comes off as quite pretentious and arrogant and overblown to me. If your pontifications on mathematics are anything like your sophomorisms on politics, then I think I can do without it. To quote Eulcid "There is no royal road to geometry
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in the forum there, is a site posted that is sort of an explanation of the reason the other guy is attacking him, but I just don't get it??
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Last edited by lktknow; 01-22-2008 at 06:27 PM..
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Old 01-22-2008, 06:59 PM   #2 (permalink)
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Leaving aside math for a second, education in general is geared towards training future university professors. Though it's never stated outright, and some others may disagree in some cases the truth of the matter is that the people who are rewarded the most in education are those that have the ability to become university professors.

I don't particularly care much about this, though one can find it disconcerting. Why should we teach children in such a manner when the end goal for the vast majority is not a life in academia? Maybe we shouldn't; maybe if it ain't broke don't fix it.

The pedagogy of teaching high school and pre-high school math then is clearly tied into this train of thought. If the main goal is to train future scientists and academics then by all means keep the current system. If you want to make math "fun" and enjoyable then the answers are easy in my view . Just take away all the rigor, introduce it as a historical subject and change the way in which math is graded(as in take away the x(s) and check marks, and replace them by the more ambiguous notion of grading on correct mathematical ideas and intuition).

To actually comment on the bulk of the text: It seems well written and somewhat entertaining if at times preachy. However, math education and education in general is a bloated field. Though this is not at all what I consider my subject of interest (so take my view with a grain of salt) the impression I get is that even the successful endeavors tend to have a brief flicker then fizzle out and for the most part are relegated to obscurity. I don't think that this one would be any differently received if at all.

Last edited by albania; 01-22-2008 at 07:11 PM.. Reason: Automerged Doublepost
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Old 01-22-2008, 10:27 PM   #3 (permalink)
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Having studied math in both the French and American education systems, I do think the American one(described here) is flawed, and needs a revamp. The French one isn't perfect, but it did spark my interest a lot more than the tired US system.
I really think I would buy that book. He should write a series about the different fields of mathematics, putting them each into a perspective that is interesting and easy to understand. When taught well, math really is a cool/wonderful world.
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Old 01-23-2008, 04:17 AM   #4 (permalink)
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Quote:
Originally Posted by albania
If you want to make math "fun" and enjoyable then the answers are easy in my view . Just take away all the rigor, introduce it as a historical subject and change the way in which math is graded(as in take away the x(s) and check marks, and replace them by the more ambiguous notion of grading on correct mathematical ideas and intuition).
That might work on math at a higher level, but there is still always a right and a wrong answer. There is no ambiguity to 2+2=4. I'm also not so sure that teaching it as a historical subject would work any better as history is right up there with math as one of the more loathed subjects in school.

Quote:
Originally Posted by albania
To actually comment on the bulk of the text: It seems well written and somewhat entertaining if at times preachy. However, math education and education in general is a bloated field. Though this is not at all what I consider my subject of interest (so take my view with a grain of salt) the impression I get is that even the successful endeavors tend to have a brief flicker then fizzle out and for the most part are relegated to obscurity. I don't think that this one would be any differently received if at all.
This I'm not sure I could have said any better though. Math is just one subject out of many that could be taught very differently, but ultimately I'm not sure just how much good would come of it. Our education system is so ingrained into society that changing it would almost be like changing the US to the Metric system.
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Old 01-23-2008, 04:51 AM   #5 (permalink)
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While I would read this book just to see what ideas this guy has, the same thing can be said about any subject. I dislike history and language because I am a visual thinker- I remember pictures before anything else. The only difference is as children we are immersed in our language and events, so language and history are relatively easy subjects to teach. Mathematics is more difficult to demonstrate, especially when you start off with the counting, adding, multiplying, dividing, subtracting, etcetera, because we do not think it as often as speaking a language or reflecting upon memories. If schools were to start off with something like basic geometry, get the kids interested in pictures, shapes, and then relate it to the numerical part, then it would be interesting. All you need are good, wacky cartoons demonstrating the basic ideas of math (think Donald Duck in Math-Magic Land) and you will have the kids' attention. Yet, when I was a child, things like School House Rock annoyed me without end.
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Old 01-23-2008, 05:55 AM   #6 (permalink)
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I have to say I agree with some of the commentary here, but disagree with the preferable outcome.

Mathematics is, for all intent and purpose, a hard science. Like other hard sciences such as chemistry and physics, mathematics is a practice of truths and a building block to more advanced topics.

While many students may "hate" math or "hate" science, it does not move me to believe that the system is flawed. A lot of students hate gym class, too. Perhaps we should relegate it to the ages and replace it with nothing but games of tag and hide and seek. Sounds a bit lame, no? If the purpose of gym is to promote physical well being, the purpose of math and science is to promote mental well being and logical comprehension.

I do agree that the American public educational system is flawed, but I believe that flaw to be the fact that it is already entirely too simplistic. Education isn't about fun and games, it's about learning, gaining knowledge to some greater point. Sure, not every kid is going to be a physicist or engineer. But then, not every kid is going to be an athlete or musician. Should we get rid of or lessen those endeavors? Not every kid will grow up to be a writer or editor, so do we really need to teach them grammar? Proper punctuation? Not every kid will be a historian. Not every kid will be anything. *shrug* You still have to learn as much as you can in different fields to help you determine what you WILL be when you grow up. The country is already on the educational fast track to a society of burger flippers with the education we have now. Why make it worse?

Teaching kids how to solve "4⅜ ÷ 1⅔" as mentioned in the above excerpt isn't about turning them into a human calculator or making them do tricks akin to a seal balancing a ball. It's about teaching them toe process so that it may be applied to other things. Something as simple as fractions are important on a mainstream level. Hell, just shopping I overhear people trying to figure out what 25% off an item will come out to. If people can't even learn to do that, we're pretty damned hopeless.
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Old 01-23-2008, 11:55 AM   #7 (permalink)
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We have the opposite problem here in the UK, where education is going the route of becoming the lowest common denominator, and soon a basic secondary education will not equip kids for anything useful, academic or otherwise.
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Old 01-25-2008, 05:46 PM   #8 (permalink)
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Quote:
Originally Posted by Randle2I
That might work on math at a higher level, but there is still always a right and a wrong answer. There is no ambiguity to 2+2=4. I'm also not so sure that teaching it as a historical subject would work any better as history is right up there with math as one of the more loathed subjects in school.
Well I said it was my view; as in it would have made math enjoyable to me. As for it working only in higher levels of math my intuition tells me otherwise, but I have no first hand experience in trying to teach children so it might be as you say.

An aside: your second sentence is false, specifically if dealing in mod 2, mod 3 and mod 4.

Last edited by albania; 01-25-2008 at 05:48 PM..
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