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Why do some people find mathematics difficult? math
Old 09-13-2011, 01:38 PM   #1
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Mathematics is quite simple. I'm not saying this because I'm good at it, on the contrary; I'm one of those "some people." But as stated on Wikipedia:

  Originally Posted by Wikipedia
David Hilbert defined mathematics as follows: We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise.

Any given number has a set of attributes that can be recognized and proven as long as the person doing mathematics is in the possession of the necessary knowledge. A 5 year old will know how to visualize 3, and what 3 apples look like, but he may not know that it is the square root of 9.

Due to its
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the number of possible interpretations are not as loose as they are in the case of art, where individual imagination allows a limitless number of interpretations.

Understanding high level of mathematics evidently requires plenty of education, as it is required to learn its "language," so it's not simple in the sense that it's easily understandable, it's simple in the sense that it states what is with clarity.

"Clarity" is a neat little word. It's probably my favourite word, even. No ambiguity, no confusion, no bad choices. Clarity is something to strive for in life, but hard to achieve.

Mathematics is the language through which clarity can be obtained, as far as I can tell. So why is it such a dreaded subject? Why do some many people struggle with it?

How does IQ tie in the picture? Simply saying "they are not smart enough" is insufficient here - elaborate.

How can it be taught efficiently?

Why are Japanese and Chinese students supposedly so much better at mathematics than Western students? What are they doing differently?

What's the neuroscientific explanation for being good or bad at math?

What are your general insights about understanding mathematics?

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Old 09-13-2011, 02:24 PM   #2
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Im not 100% sure. It's something that was posted on a forum ages back. Don't Japanese students at an early age take a few classes. Then the classes that they have shown to exceed at, they take more advanced classes of said particular subject. While they let the other subjects stay at average levels?


I dont even know anymore. But i do know is that math is easy for some people and hard for others. Personally I always loved math but had terrible and boring teachers. Often times i would correct the teacher themselves just because they are reading off of a course syllabus. It was worst when I moved to Texas and they were JUST STARTING algebra in the 10th grade. It amazed me how slow some of the other people were. Even in advanced classes (where all the Asians were at), It felt slow and boring. Finally college came along and the challenge came but largely easy.


Aside from my life story up above, I personally think that the reason why math is so easy for some people is because that they try their hardest to think logically. You can explain 99.9% of everything with math and science.
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Old 09-13-2011, 03:00 PM   #3
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If two apples plus two apples gives four apples, then what does two oranges plus two oranges give?

How the heck should I know? You have not said anything about oranges, it was all about apples.
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Old 09-13-2011, 03:10 PM   #4
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  Originally Posted by thod
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If two apples plus two apples gives four apples, then what does two oranges plus two oranges give?

How the heck should I know? You have not said anything about oranges, it was all about apples.

So we won't know the answer until we know more about oranges. Until then, we can assume it'll be four oranges, unless proven that the oranges possess attributes which would somehow change the result to something else. No?

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Old 09-13-2011, 03:20 PM   #5
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If a car travels 50 miles in one hour and a motorbike travels 30 miles in half an hour, how long would it take a bicycle to travel a mile?
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Old 09-13-2011, 03:26 PM   #6
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I think it might have something to do with objective measures and concepts actually being pretty unconvincing to people, who are of course subjective. Objectivity that isn't convincing on the human/subjective level is, in effect, the same as arbitrariness. That's why so many people get pissed off at things like math, quantum physics, and the NCAA Bowl Championship Series. They're all systems that do in fact have some amount of arguable logic behind them, but if you can't explain it in a way that makes sense to people, any claims about it being objective is more likely to goad people into further feelings of hostility towards the subject.

To look at it another way, think of a school district with five individual schools in it, none of which are performing well. There are two improvement scenarios, but suppose that in both cases, the aggregate number of graduates (or whatever is serving as the measure of success) is exactly the same. In the first scenario, each individual school sees a 10 percent improvement in its graduation rate. In the second scenario, the worst school is completely turned around into one of the region's best. According to the objective standard, both results are the same. But which one sounds like a better outcome? Which is a better rallying point if you're asking for more funding? If you were the district superintendent, which accomplishment would you rather have on your resume?

Or as a third (and even simpler) example, there's that case where you offer a kid one of two glasses of juice. They both contain the exact same amount, but one glass is tall and thin and the other is wide and short. Most kids take the tall one, even if you explain to them that they're the same, just because it looks like more.

Bringing it back to the subject of math in general, I think some part of the problem is that no amount of telling people that it's easy and simple and objective and methodical is going to make them feel like it actually is easy and simple and objective and methodical. A related issue might be that the people who naturally do pick up math with ease are often the worst at explaining it to people who have a hard time with it. I'm sure most of us know a genius who can't teach worth a damn, just because he expects his area of expertise to be as instantly-understandable to everyone else as it is to him.

.............


My other guess for why some people aren't good at math is that it's socially acceptable. "I'm not a math person" isn't really going to raise any eyebrows, outside of math-dependent occupations. For comparison's sake, consider "I'm not really a math person" to similarly statements, like "I'm not really a hygiene person" or "I'm not really a 'don't molest children' person." In those cases, the fact that something doesn't come naturally and easily to you isn't a justifiable reason to avoid doing it.

Of course, I'm using exaggerated examples, but I do think that being less-than-great at math isn't seen as being an impediment or prohibition to being a smart person in our society in the same way that being functionally illiterate it. And on the same token, being really good at math is more likely to confer instant smart-person status on you than being really good at reading is. Compare someone with a bachelor's in math to someone with a bachelor's in literature or art.
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Old 09-13-2011, 03:38 PM   #7
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Because those who are supposed to teach it make a mystery out of it.

It takes a decade of studying hard until you realize why the concept of mathematics is actually considered "beautiful".

(If you're lucky, your maths and physics teacher are the same person - that's either double trouble or a lucky integration of a theory and its application.)
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Old 09-13-2011, 04:00 PM   #8
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A baseline would be to say we're not analytical machines but emotional animals.

  Originally Posted by ElstonGunn
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Of course, I'm using exaggerated examples, but I do think that being less-than-great at math isn't seen as being an impediment or prohibition to being a smart person in our society in the same way that being functionally illiterate it. And on the same token, being really good at math is more likely to confer instant smart-person status on you than being really good at reading is. Compare someone with a bachelor's in math to someone with a bachelor's in literature or art.

I think you're on to something here. A documentary on IQ I saw (which names escapes me at the moment) mentioned that the reason why there are more Asians on the upper echelon of IQ, grades, and schools that are hard to get into in America is because studying is so ingrained in their culture. They cited some Chinese philosopher who emphasized that knowledge has value and who presumably started the whole shebang.

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Old 09-13-2011, 04:35 PM   #9
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  Originally Posted by thod
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If a car travels 50 miles in one hour and a motorbike travels 30 miles in half an hour, how long would it take a bicycle to travel a mile?

no glasses on missread question

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Old 09-13-2011, 04:35 PM   #10
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The way math was taught to me did not fit with my learning style. I also have never had a real math teacher (someone with a background in math). Often we were given a formula and told to fill it with numbers and churn out an answer... this does not tell me WHY I should do it, WHAT I get from doing it, WHERE in life I'd use it, etc. I don't really understand math, and thus, have not learnt it and do poorly in it.

Health, I understand health, I understand it so well I can apply it elsewhere and can speak the language of health. I imagine if I were taught math as well as I'd been taught health I could toy and play with it but for now it is a jumble of letters and numbers that I can't picture in my mind or see in real application.
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Old 09-13-2011, 05:59 PM   #11
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  Originally Posted by Silverity
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The way math was taught to me did not fit with my learning style. I also have never had a real math teacher (someone with a background in math). Often we were given a formula and told to fill it with numbers and churn out an answer... this does not tell me WHY I should do it, WHAT I get from doing it, WHERE in life I'd use it, etc. I don't really understand math, and thus, have not learnt it and do poorly in it.

Health, I understand health, I understand it so well I can apply it elsewhere and can speak the language of health. I imagine if I were taught math as well as I'd been taught health I could toy and play with it but for now it is a jumble of letters and numbers that I can't picture in my mind or see in real application.

This is part of my problem, as well. I was OK with math until about the 5th grade, and then I failed miserably at it from then until the present.

I did better with word problems than with anything else, because I could visualize the problem. I cannot visualize a bunch of x's and y's meaning a bunch of #s that have just as little relevance to me as the x's and y's.

Plus, dyscalculia. I didn't know it existed, and everyone just thought I sucked at math, so that's how it was addressed. Fractions and decimals were about to the point I could handle, because those are things I could visualize. I failed at long division because I had to show my work, and couldn't just put the answer down even when I knew it, so sometimes even when I knew the answer, I'd get it wrong because I had to 'math it out'.

I simply can't understand numbers. I can memorize them alright, but as far as understanding and manipulating go... lost.

I am, however, pretty good at things like spelling and grammar. Always 'exceeding expectations'. When I was starting to fail math, I was reading and writing things far ahead of my peers. I've noticed that people who tend to specialize in either words or numbers tend to do more poorly on the other.

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Old 09-13-2011, 07:11 PM   #12
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Since it's found to be the least heritable skill, they find it difficult because they haven't learned it. One can be incredibly smart but craptacular in maths or have poor nutrition or sleep. I can attest since I'm both been super good at math and bad at it. I recently saw a once student of math state that he's now terrible at math as he's gotten rusty with lack of practice.
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Old 09-13-2011, 10:14 PM   #13
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My thoughts on the matter are this: Mathematics is a language. One specifically developed to express facets of physical reality. Language, yes, but it is very different from language originating in communications. What the symbols represent and how they are manipulated is wholly different. Everyone's mind works in different ways. We should expect different people to have different strengths. Why do some people find math difficult? They just weren't built that way. They don't jive well with the behavior of the symbols. I have absolutely no idea and it really doesn't matter. I'm certain they have plenty other strengths to carry them happily thru life.

It is unfortunate the gauge for intelligence favors those of us who excel in mathematics.
True capacity is not measured by IQ. Put Mozart, Einstein and Frank Lloyd Wright in the same room... Who is the smart one? Intelligence cannot be linearly measured.
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Old 09-13-2011, 10:22 PM   #14
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I find mathematics fascinating, but my mind doesn't always make connections or computations quickly. Plus, I'm big into meaning. Why is something the way it is?

I've had algebra teachers who explained how formulas and equations were discovered and applied, and other teachers who skipped all the meaning and just stated the rules. I learned best from the former.

Sometimes, it's all in the delivery, because we don't all process information the same.
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Old 09-13-2011, 10:39 PM   #15
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For the same reason I don't call a person other than myself 'me' or 'I'.
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Old 09-13-2011, 11:37 PM   #16
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I'm an engineering major, but I can't memorize song lyrics / movie quotes. I have a friend who is a history major, is terrible at math, but can listen to a song once and have it memorized.

Peoples' brains just work differently.
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Old 09-13-2011, 11:41 PM   #17
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I'm good at applied math, but I can't do proofs worth a shit.
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Old 09-13-2011, 11:48 PM   #18
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Mathematics is difficult for most people because most people don't like to think. They like to memorize an answer and spit it back. You'll be surprised how many people don't have a clue what the idea behind sine and cosine are. They just plug the value into their calculators (or look them up on a table) and go on their merry way. Never once wondering what the hell it means.

It annoys me how many teachers pander to this. No one ever learns math by memorizing arbitrary things. They just learn to pretend that they know math.
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Old 09-14-2011, 12:13 AM   #19
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You seem pretty angry about math
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Teachers pandering to certain types of students is a whole different problem. The average new teacher only stays in the profession for 4-5 years now because of how bad the system is currently. Teachers are judged almost completely by standardized test scores, and are at the whim of their students and/or students' parents. Teachers are being forced to teach to an increasingly constraining syllabus, and are also becoming less adept at the subjects they are teaching because of said constraints and schools' difficulties in recruiting the best and brightest teachers out of college. It's a self-perpetuating cycle (in the US at least) and will continue down this path unless something huge happens. What that thing is? Idk.
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Old 09-14-2011, 01:45 AM   #20
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  Originally Posted by Phenom
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You seem pretty angry about math
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Teachers pandering to certain types of students is a whole different problem. The average new teacher only stays in the profession for 4-5 years now because of how bad the system is currently. Teachers are judged almost completely by standardized test scores, and are at the whim of their students and/or students' parents. Teachers are being forced to teach to an increasingly constraining syllabus, and are also becoming less adept at the subjects they are teaching because of said constraints and schools' difficulties in recruiting the best and brightest teachers out of college. It's a self-perpetuating cycle (in the US at least) and will continue down this path unless something huge happens. What that thing is? Idk.

I'm not angry, just annoyed that teachers pander to the "just give me an algorithm so I can pass the test" mentality. OP thinks he's asking why people are bad at math, but OP is actually asking why people are so averse to mental exploration and prolonged thought.

When I say people are averse, I'm not insulting them. We've all been too lazy to think at one point or another. We all know what it feels like. Why people often feel this way is a much deeper question (I have a few theories). In any case, almost anyone can be good at math if they feel like thinking about it. Which is to say, almost anyone can be good at math if they have enough dopamine in their system. Which is to say, almost anyone can be good at math if they take dextroamphetamine. Which is to say, mathematicians are generally people with a certain neurochemical disposition which endows them with an inherent affinity for thought. Which is to say, most people need medication to get to that same mental state.

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Old 09-14-2011, 06:39 AM   #21
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  Originally Posted by thod
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If a car travels 50 miles in one hour and a motorbike travels 30 miles in half an hour, how long would it take a bicycle to travel a mile?

If you are trying to point out an underlying truth of mathematics that I seem to have missed by guiding me toward it with your questions, I'm afraid I won't be able to pierce what you're getting at - otherwise, I probably wouldn't have made this thread.

  Originally Posted by ElstonGunn
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I think it might have something to do with objective measures and concepts actually being pretty unconvincing to people, who are of course subjective. Objectivity that isn't convincing on the human/subjective level is, in effect, the same as arbitrariness. That's why so many people get pissed off at things like math, quantum physics, and the NCAA Bowl Championship Series. They're all systems that do in fact have some amount of arguable logic behind them, but if you can't explain it in a way that makes sense to people, any claims about it being objective is more likely to goad people into further feelings of hostility towards the subject.

To look at it another way, think of a school district with five individual schools in it, none of which are performing well. There are two improvement scenarios, but suppose that in both cases, the aggregate number of graduates (or whatever is serving as the measure of success) is exactly the same. In the first scenario, each individual school sees a 10 percent improvement in its graduation rate. In the second scenario, the worst school is completely turned around into one of the region's best. According to the objective standard, both results are the same. But which one sounds like a better outcome? Which is a better rallying point if you're asking for more funding? If you were the district superintendent, which accomplishment would you rather have on your resume?

Or as a third (and even simpler) example, there's that case where you offer a kid one of two glasses of juice. They both contain the exact same amount, but one glass is tall and thin and the other is wide and short. Most kids take the tall one, even if you explain to them that they're the same, just because it looks like more.

Bringing it back to the subject of math in general, I think some part of the problem is that no amount of telling people that it's easy and simple and objective and methodical is going to make them feel like it actually is easy and simple and objective and methodical. A related issue might be that the people who naturally do pick up math with ease are often the worst at explaining it to people who have a hard time with it. I'm sure most of us know a genius who can't teach worth a damn, just because he expects his area of expertise to be as instantly-understandable to everyone else as it is to him.

.............


My other guess for why some people aren't good at math is that it's socially acceptable. "I'm not a math person" isn't really going to raise any eyebrows, outside of math-dependent occupations. For comparison's sake, consider "I'm not really a math person" to similarly statements, like "I'm not really a hygiene person" or "I'm not really a 'don't molest children' person." In those cases, the fact that something doesn't come naturally and easily to you isn't a justifiable reason to avoid doing it.

Of course, I'm using exaggerated examples, but I do think that being less-than-great at math isn't seen as being an impediment or prohibition to being a smart person in our society in the same way that being functionally illiterate it. And on the same token, being really good at math is more likely to confer instant smart-person status on you than being really good at reading is. Compare someone with a bachelor's in math to someone with a bachelor's in literature or art.

Interesting points. I haven't thought of it like that before.

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Old 09-14-2011, 08:23 AM   #22
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  Originally Posted by rufsketch1
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I'm not angry, just annoyed that teachers pander to the "just give me an algorithm so I can pass the test" mentality. OP thinks he's asking why people are bad at math, but OP is actually asking why people are so averse to mental exploration and prolonged thought.

When I say people are averse, I'm not insulting them. We've all been too lazy to think at one point or another. We all know what it feels like. Why people often feel this way is a much deeper question (I have a few theories). In any case, almost anyone can be good at math if they feel like thinking about it. Which is to say, almost anyone can be good at math if they have enough dopamine in their system. Which is to say, almost anyone can be good at math if they take dextroamphetamine. Which is to say, mathematicians are generally people with a certain neurochemical disposition which endows them with an inherent affinity for thought. Which is to say, most people need medication to get to that same mental state.

I share your frustrations.

I am trying to actually learn mathematics now, the entire history of everything, etc...

Any book recommendations?

I think I am going to go and try and get a script for dextroamphetamine as soon as possible.

There is nothing as great as mathematics it seems, and this is said after a life of hating math...or what I thought math was.

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Old 09-14-2011, 09:07 AM   #23
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  Originally Posted by MrFreakaficial
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Mathematics is the language through which clarity can be obtained, as far as I can tell. So why is it such a dreaded subject? Why do some many people struggle with it?

How does IQ tie in the picture? Simply saying "they are not smart enough" is insufficient here - elaborate.


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may answer some of these questions.

 
How can it be taught efficiently?

The teacher first of all must understand the subject. Then, true understanding render the ability to explain high mathematical concepts in layman language, thus the ideal as hoped by Einstein that "Relativity can be explained to five-year-olds".

 
Why are Japanese and Chinese students supposedly so much better at mathematics than Western students? What are they doing differently?


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Well, define "mathematics" under this context. If I remember correctly, such research is conducted with primary school or secondary school students, while "mathematics" at that stage hardly touch the easiest theory and foundations of mathematics at all. Japanese and Chinese students, as I observed (I am a Chinese), are very good at calculation, i.e. they are very good at memorising a particular route to perform a particular type of calculation. Regarding logic and proofs, meh, a lot of them are lame. Those who can really master and become a real mathematician remains a minority, and the population, my two cents, is way smaller than the professional mathematicians in Western countries.

 
What's the neuroscientific explanation for being good or bad at math?

As suggested in the book I mentioned before, the ability of abstraction is the key to master higher level mathematics. Abstraction is possibly the ability to recognise pattern and organise. I think the prefrontal cortex has to be fully developed for that. Also, it is possible that a more diffused network of neural connection, which leads to the connection of seemingly unrelated ideas, is beneficial to studying mathematics.

 
What are your general insights about understanding mathematics?

I'm not sure what you are asking for here. I personally think that to understand mathematics, the ability to visualise and interpret is very important.

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Old 09-14-2011, 12:28 PM   #24
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^ very true.
I've only had a taste of math above calculus and all I can say is that it's a lot different.
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Old 09-14-2011, 12:30 PM   #25
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  Originally Posted by MrFreakaficial
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What are your general insights about understanding mathematics?

I would have to say the only reason I'm any good at it is because I understand the relationships math intends to describe. Abstract thought is helpful in being able to manipulate information but the true intent of mathematics is to express real relationships in our universe. Some of us are more aware of the properties and relationships that exist throughout the universe. For these people, mathematics give them a language to express these properties and look onto how they might relate to another. If I were less aware of what the symbols represented, I would have a rather hard time with math. It might as well be working with the Kingon Language, if that were the case... I'm certain I could learn all the rules of how to properly arrange all the symbols and eventually I might be able form a complete thought or two -in Klingon. The problem is: If I have no idea what those symbols represent, it would be a realm of complete abstraction and nonsensical relationships. Sure I could say something, but it would be utterly meaningless to me. In the same way, math students could be trained to manipulate equations and still have no idea what the equation means. I've tutored math and I've watched it happen many times. Getting better in math amounts to better understanding the underlying principals then how to apply the symbolism. For those really good at math, knowing the underlying principals and relationships comes easy and things like memorizing equations becomes unneccessary; when you understand the relationships, you can generate the equations.

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