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Butterfly
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09 Dec 2011, 4:46 am

Funny thing is, I can't do PSLE maths (in Singapore here), which is what I would call "common sense maths".

But I'm quite fond of Elementary Mathematics and Additional Mathematics in Secondary level here.

dy/dx, dy/dx~


I'm not sure how to answer your question, but I think it may have to do with our perception of numbers and the way we can manipulate them, as well as our own biological mechanical functions (maybe poor memory, for memorising formulas etc).



VIDEODROME
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09 Dec 2011, 6:13 am

Maybe it's difficulty with comprehension. Someone might explain to you again and again how to find the Square Root of a number through an equation, but at the end of the day you still don't follow what the hell they're talking about or what the point of it all is.

It's like trying to cross a language barrier. Often I think a popular technique of teaching a second language is merely Phrase Memorization. You might get around with that a bit but always feeling you don't really have a good proper grasp of your second language.

Otherwise there is language immersion which takes a lot longer but rewards you with superior comprehension.

I guess where I'm going with this thought is we tend to rely on the less time consuming Memorization of Equations method just to drive it into your head to pass exams. You don't know what square roots or why you would want to work them out but you can do them on paper for a test.



ruveyn
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09 Dec 2011, 10:12 am

Simonono wrote:
I just simply cannot make sense of it :shaking2:


You are in good company, or at least plentiful company. The human brain is not particularly optimized for doing abstract mathematics. We are too attached to our linguistic function. Humans are genetically evolved to be blabber mouths, singers of song and tellers of story. We are not generally well suited for proving theorems rigorously. That is why there are so few first rate creative mathematicians.

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09 Dec 2011, 11:21 pm

I've never had any trouble with math. It comes natural to me.
I guess I'm just weird.

I think many people struggle with math because it is taught poorly by people who really don't have a solid understanding of math themselves.

I also agree with the hypothesis of math & language being somewhat incomparable.
Generally those who are really good at math, are challenged with language, so they have difficulty explaining it to others. And those who are good at language aren't very good at math, so they have a tough time explaining a subject they don't understand.


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Crysisrocks
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10 Dec 2011, 9:27 pm

An interesting question, DuneyBlues. I shall attempt to give my explanation on the matter in the context below.

I assume it is due to the fact that in general, mathmatics (or math) relies dominantly on abstract, logical and cognitive processing. From a personal standpoint, I have experienced numerous individuals who have either found the subject to be very comprehensive from the start, to laboriously difficult. I would speculate that it holds some genetic correlation with how the left hemisphere of a person's brain is structured? You know, gray matter and all.

I personally indulge in math as a matter of usual practice (wherein I encounter occasions of spare time), as I am conjointly interested in subjects that to a large extent rely on it, Physics and Visual C++ scriptwriting being two notable examples, so it is, as a requirement, to have decent math skills in order to interpret the other subjects, which are in themselves not math, but rely on it predominantly (the same applies for Chemistry, as well, as it is a Science subject).

Nurture and other environmental factors are both applicable to take into hand, as well.



Last edited by Crysisrocks on 11 Dec 2011, 3:22 pm, edited 1 time in total.

LostInEmulation
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10 Dec 2011, 11:23 pm

Am I the only one who is seriously pissed off with the convention of every teacher and textbook to use either i and j or u and v or n and m as variables? For me, this visual barrier was there and it was annoying. Is it only because I am visually impaired?


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ruveyn
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11 Dec 2011, 3:23 am

LostInEmulation wrote:
Am I the only one who is seriously pissed off with the convention of every teacher and textbook to use either i and j or u and v or n and m as variables? For me, this visual barrier was there and it was annoying. Is it only because I am visually impaired?


Possibly. These letters are easily distinguishable by most sighted-readers.

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11 Dec 2011, 9:23 pm

VIDEODROME wrote:
Maybe it's difficulty with comprehension. Someone might explain to you again and again how to find the Square Root of a number through an equation, but at the end of the day you still don't follow what the hell they're talking about or what the point of it all is.

It's like trying to cross a language barrier. Often I think a popular technique of teaching a second language is merely Phrase Memorization. You might get around with that a bit but always feeling you don't really have a good proper grasp of your second language.

Otherwise there is language immersion which takes a lot longer but rewards you with superior comprehension.

I guess where I'm going with this thought is we tend to rely on the less time consuming Memorization of Equations method just to drive it into your head to pass exams. You don't know what square roots or why you would want to work them out but you can do them on paper for a test.


This.


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12 Dec 2011, 4:50 am

ruveyn wrote:
The human brain is optimized for probable reasoning, not deductive reasoning. We are born to do induction. We struggle to do deduction. That is why the principles of geometry were discovered early by induction and by trial and error. The Egyptians could build pyramids almost exactly aligned to the cardinal directions but they did not know about proving theorems. Theorems and logic were invented late in the game by the Greek philosophers. Thales was the first to prove a theorem in a deductive manner that we would recognize as such today. Aristotle was the first to work out the rules of logic and valid deduction. Even his teacher Plato did not write such a set of rules nor was his reasoning (in the dialogues) always correct. Perhaps there were others before Aristotle in lands other than Greece to work out correct logic, but Aristotle is the first that we know did the deed.

Once reasoning was made rule based, others improved and expanded the logic used by mathematicians. Even so mathematics was not rendered "logical" until mid 19 th century and logic was not expressed in a mathematical manner until late 19 th century (Boole, Frege, Russel, Whitehead, Kantor and others).

ruveyn


The Greeks made some pretty major contributions to the development of mathematics but they also inherited some mathematics from the Egyptians and Babylonians.



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12 Dec 2011, 10:08 am

The Greeks invented mathematical proofs, which outshines everything the Egyptians and Babylonians did put together.


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ruveyn
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12 Dec 2011, 11:30 am

Jono wrote:

The Greeks made some pretty major contributions to the development of mathematics but they also inherited some mathematics from the Egyptians and Babylonians.


Crude as Egyptian mathematics was, it was sufficient to use in building the great pyramids, which were the largest tallest structures on earth until the construction of the Eiffel Tower.

The Egyptians gave us tall structures. The Greeks opened the path to the Cosmos.

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12 Dec 2011, 12:09 pm

Check out http://www.khanacademy.org/ They made math into a game and its fun! :)



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13 Dec 2011, 8:52 pm

I'd think it has something to do with how intensive on working memory a lot of elementary arithmetic (which, while not synonymous with math, is still used in it) and algebraic problems can be. I know in my case that pronounced deficits in spatial working memory and nonverbal processing speed have made quite a bit of mathematics (algebra problems, geometry, etc) rather difficult and time-consuming.


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13 Dec 2011, 11:11 pm

mar00 wrote:
DuneyBlues wrote:
^
Quote:
Many 'A' graduate students have come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not
about following directions, it’s about making new direction

- Paul Lockhart , A Mathematicians Lament

Sure but then we might as well say that most people who are "good at something" are really not. Living one's life is not about following directions...oh wait, it is.


Uh, no. Life isn't just about following directions, it's also about comparing the relative advantages of different directions against one's profile of strengths and weaknesses and deciding which "to follow".


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ruveyn
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14 Dec 2011, 7:59 am

Simonono wrote:
I just simply cannot make sense of it :shaking2:


Are you able to follow a geometric proof? If you are, you can make some sense of it.

ruveyn



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02 Jan 2012, 5:24 pm

ruveyn wrote:
Simonono wrote:
I just simply cannot make sense of it :shaking2:

That is why there are so few first rate creative mathematicians.

ruveyn


Perhaps that explains why all these companies overstated their balance sheets and plunged the economy into recessions.


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