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bladerunner060
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10/3/2015 7:52:52 AM
Posted: 1 year ago
So, I'm taking math. Because I am a stupid, stupid man, I signed up for the class that I tested into, as opposed to ones below where I tested into. But my poor life decisions are not the point of this post.

I'm curious about what makes someone good at math. I mean, obviously, people are good at math. I'm pretty good at simple algebra and basic functions. Those seem to be simple applications of principles. But once we get into the devil's math--i.e., Calculus--it feels like it's more about memorization. And maybe that's what the elementary stuff is, too--memorization and then application of the rules. But the rules of basic algebra and basic functions are more intuitive. It's easier to re-figure them out, if you forget them. That's what I do, on occasion, when I do forget a rule.

If I can't remember whether when you multiply two variables with an exponent you ADD the exponent or MULTIPLY the exponent, I can just plug in a few example ones, and rediscover something that I'm supposed to remember out of hand.

Once we get into Calculus, though, there doesn't seem to be a quick way to get to the principles. Same thing, really, with the "hard" parts of Trig.

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?
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Fkkize
Posts: 2,149
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10/3/2015 8:02:36 AM
Posted: 1 year ago
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:
So, I'm taking math. Because I am a stupid, stupid man, I signed up for the class that I tested into, as opposed to ones below where I tested into. But my poor life decisions are not the point of this post.

I'm curious about what makes someone good at math. I mean, obviously, people are good at math. I'm pretty good at simple algebra and basic functions. Those seem to be simple applications of principles. But once we get into the devil's math--i.e., Calculus--it feels like it's more about memorization. And maybe that's what the elementary stuff is, too--memorization and then application of the rules. But the rules of basic algebra and basic functions are more intuitive. It's easier to re-figure them out, if you forget them. That's what I do, on occasion, when I do forget a rule.

If I can't remember whether when you multiply two variables with an exponent you ADD the exponent or MULTIPLY the exponent, I can just plug in a few example ones, and rediscover something that I'm supposed to remember out of hand.

Once we get into Calculus, though, there doesn't seem to be a quick way to get to the principles. Same thing, really, with the "hard" parts of Trig.

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

Practice.
Sounds stupid, but I'm serious. Find the most basic explanation online and practice its application.
: At 7/2/2016 3:05:07 PM, Rational_Thinker9119 wrote:
:
: space contradicts logic
bladerunner060
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10/3/2015 8:04:53 AM
Posted: 1 year ago
At 10/3/2015 8:02:36 AM, Fkkize wrote:
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:
So, I'm taking math. Because I am a stupid, stupid man, I signed up for the class that I tested into, as opposed to ones below where I tested into. But my poor life decisions are not the point of this post.

I'm curious about what makes someone good at math. I mean, obviously, people are good at math. I'm pretty good at simple algebra and basic functions. Those seem to be simple applications of principles. But once we get into the devil's math--i.e., Calculus--it feels like it's more about memorization. And maybe that's what the elementary stuff is, too--memorization and then application of the rules. But the rules of basic algebra and basic functions are more intuitive. It's easier to re-figure them out, if you forget them. That's what I do, on occasion, when I do forget a rule.

If I can't remember whether when you multiply two variables with an exponent you ADD the exponent or MULTIPLY the exponent, I can just plug in a few example ones, and rediscover something that I'm supposed to remember out of hand.

Once we get into Calculus, though, there doesn't seem to be a quick way to get to the principles. Same thing, really, with the "hard" parts of Trig.

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

Practice.
Sounds stupid, but I'm serious. Find the most basic explanation online and practice its application.

Well, yes, practice is good. But what are you practicing? A thought process, or mere memory application?
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Fkkize
Posts: 2,149
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10/3/2015 8:08:13 AM
Posted: 1 year ago
At 10/3/2015 8:04:53 AM, bladerunner060 wrote:
At 10/3/2015 8:02:36 AM, Fkkize wrote:
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:
So, I'm taking math. Because I am a stupid, stupid man, I signed up for the class that I tested into, as opposed to ones below where I tested into. But my poor life decisions are not the point of this post.

I'm curious about what makes someone good at math. I mean, obviously, people are good at math. I'm pretty good at simple algebra and basic functions. Those seem to be simple applications of principles. But once we get into the devil's math--i.e., Calculus--it feels like it's more about memorization. And maybe that's what the elementary stuff is, too--memorization and then application of the rules. But the rules of basic algebra and basic functions are more intuitive. It's easier to re-figure them out, if you forget them. That's what I do, on occasion, when I do forget a rule.

If I can't remember whether when you multiply two variables with an exponent you ADD the exponent or MULTIPLY the exponent, I can just plug in a few example ones, and rediscover something that I'm supposed to remember out of hand.

Once we get into Calculus, though, there doesn't seem to be a quick way to get to the principles. Same thing, really, with the "hard" parts of Trig.

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

Practice.
Sounds stupid, but I'm serious. Find the most basic explanation online and practice its application.

Well, yes, practice is good. But what are you practicing? A thought process, or mere memory application?
If you struggle with Calculus, then I'd practice that.
: At 7/2/2016 3:05:07 PM, Rational_Thinker9119 wrote:
:
: space contradicts logic
bladerunner060
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10/3/2015 8:14:23 AM
Posted: 1 year ago
At 10/3/2015 8:08:13 AM, Fkkize wrote:

Practice.
Sounds stupid, but I'm serious. Find the most basic explanation online and practice its application.

Well, yes, practice is good. But what are you practicing? A thought process, or mere memory application?
If you struggle with Calculus, then I'd practice that.

Doesn't really answer the underlying question.
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WAM
Posts: 139
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10/3/2015 2:45:32 PM
Posted: 1 year ago
You need to understand the essence of your calculation. I'm not too sure how I can explain this well, but you need to know what you are doing, why you are doing it and what you want to achieve with it. In fact, this is applicable to everything you want to learn/be good at. Basically Action - Reason - Result.

As a somewhat unrelated example, lets take calculation with pi. While the majority of individuals may know how to calculate with pi, they do not know what pi actually is, thus they do not understand what they are doing.

If you understand exactly what you are doing and why you are doing it and what your result actually is, it is way easier to retain the knowledge. Practice itself is useless. You can practice a calculation or in fact any skill as long as you want to, if you do not understand it, the practice is useless.

Hope this helped..
bsh1
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10/3/2015 7:40:37 PM
Posted: 1 year ago
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.
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Fkkize
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10/3/2015 7:42:43 PM
Posted: 1 year ago
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

I guess so, but I am not good at explaining these things.
: At 7/2/2016 3:05:07 PM, Rational_Thinker9119 wrote:
:
: space contradicts logic
bsh1
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10/3/2015 7:44:30 PM
Posted: 1 year ago
At 10/3/2015 7:42:43 PM, Fkkize wrote:
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

I guess so, but I am not good at explaining these things.

Okay.
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ESocialBookworm
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10/3/2015 7:50:39 PM
Posted: 1 year ago
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:

If you know how to work something and what you'll get from it, you can apply it to other scenarios.
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WAM
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10/3/2015 7:54:57 PM
Posted: 1 year ago
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

At 10/3/2015 7:52:52 AM, bladerunner060 wrote:

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

This is not about a specific study of maths, as far as I understand calculus was simply used as an example.
bsh1
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10/3/2015 7:58:33 PM
Posted: 1 year ago
At 10/3/2015 7:54:57 PM, WAM wrote:
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

At 10/3/2015 7:52:52 AM, bladerunner060 wrote:

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

This is not about a specific study of maths, as far as I understand calculus was simply used as an example.

I know that. Calculus was merely a convenient example.
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UtherPenguin
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10/3/2015 8:18:45 PM
Posted: 1 year ago
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

One does not do Calculus, Calculus does you.
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WAM
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10/3/2015 8:18:45 PM
Posted: 1 year ago
At 10/3/2015 7:58:33 PM, bsh1 wrote:

I know that. Calculus was merely a convenient example.

Somebody on here ought to know... My Dad is a Phd astrophysicist, I'd assume he'd know, but its like 4 am here so I can't really ask him...

Besides, I have nearly 100% on maths at Uni, I simply relate it and try to calculate it myself first and then see how others do it... Normally it's a huge mess and I always argue with my family, my tutor and the other students, but the result (and thus the calculation) is always correct... But I wouldn't really recommend that if you don't have a pretty good understanding of numbers and calculations..
bsh1
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10/3/2015 8:22:02 PM
Posted: 1 year ago
At 10/3/2015 8:18:45 PM, UtherPenguin wrote:
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

One does not do Calculus, Calculus does you.

I didn't know calculus was a top.
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Varrack
Posts: 2,410
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10/3/2015 10:34:29 PM
Posted: 1 year ago
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:
So, I'm taking math. Because I am a stupid, stupid man, I signed up for the class that I tested into, as opposed to ones below where I tested into. But my poor life decisions are not the point of this post.

I'm curious about what makes someone good at math. I mean, obviously, people are good at math. I'm pretty good at simple algebra and basic functions. Those seem to be simple applications of principles. But once we get into the devil's math--i.e., Calculus--it feels like it's more about memorization. And maybe that's what the elementary stuff is, too--memorization and then application of the rules. But the rules of basic algebra and basic functions are more intuitive. It's easier to re-figure them out, if you forget them. That's what I do, on occasion, when I do forget a rule.

If I can't remember whether when you multiply two variables with an exponent you ADD the exponent or MULTIPLY the exponent, I can just plug in a few example ones, and rediscover something that I'm supposed to remember out of hand.

Once we get into Calculus, though, there doesn't seem to be a quick way to get to the principles. Same thing, really, with the "hard" parts of Trig.

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

I'm taking Calculus right now and actually had this thought recently. The tests so far have been based off of how good one is at memorizing formulas or methods to complete problems. Of course there is some memorization involved, but a lot of it has to do with how good you are at figuring out how to find the solution.

For example, a lesson may require the memorization of a certain method in order to solve problems. Someone who is not good at math may have no problem memorizing the method, but they'll struggle trying to apply it in order to find the solution of a problem. Someone who is good at math would be skilled at applying past rules to a problem in order to ring out a solution.
UtherPenguin
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10/3/2015 11:25:47 PM
Posted: 1 year ago
At 10/3/2015 10:34:29 PM, Varrack wrote:
I'm taking Calculus right now

God have mercy on your soul.
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Varrack
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10/3/2015 11:57:37 PM
Posted: 1 year ago
At 10/3/2015 11:25:47 PM, UtherPenguin wrote:
At 10/3/2015 10:34:29 PM, Varrack wrote:
I'm taking Calculus right now

God have mercy on your soul.

I'm sure you're dying to learn about derivatives, sigma, functions, and all that wonderful stuff deep down inside :)
SolonKR
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10/4/2015 12:26:47 AM
Posted: 1 year ago
At 10/3/2015 8:14:23 AM, bladerunner060 wrote:
Doesn't really answer the underlying question.

Go with the thought process as much as you can; only use normal memorization for specific formulas that can't be retrieved any other way (for example, derivatives of incredibly useless/obscure quantities like f(x) = arcsec(x)). Find a thought process that works for you, and practice that. It's easy enough to learn the "shortcut" method for derivatives, and it works extremely well, but learning about limits that could take the slope at a point (and then, later, the derivative) is what I needed to actually understand the concept.
Usually, when it comes to formulas, looking at the proofs is best.
For derivatives with division, I know that the derivative's low d-high minus high d-low all over low squared thanks to a mnemonic device, but seeing the proof makes the reason why it works more clear.

When all else failed, I was able to approximate based on what I knew, and then I worked backwards to see where that might have come from / what quantity it looked roughly equal to.
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Sapphique
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10/4/2015 2:24:43 AM
Posted: 1 year ago
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:

Once we get into Calculus, though, there doesn't seem to be a quick way to get to the principles. Same thing, really, with the "hard" parts of Trig.

So, it's a long way round the mountain to get to wondering: is being good at high-level math really just being good at remembering the rules? Or is there a way of thinking that makes one more math-y, and if so, what is it?

I took Calc BC last year, and most of it wasn't that bad (except optimization and series). There are a lot of rules, i.e. derivatives and integrals, and if you want to understand where they came from I guess proofs are a good place to start. The thing is that they're so long sometimes that you just don't have time to re-derive the formulas when you're taking a test. In that sense it's faster to use memorization. But I think there's a difference between being "good" at math (being good at applying formulas) and understanding what you're doing with them. Ex. if you know how to calculate an integral then you can get the answer, but if you don't understand that you're actually adding up area under a curve then you haven't understood the concept. So I guess just knowing why you're doing something should help a lot.
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Lee001
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10/5/2015 10:47:41 PM
Posted: 1 year ago
At 10/3/2015 7:52:52 AM, bladerunner060 wrote:

When I took the placement test for college, I got placed into Trigonometry. There sure was ALLOT of stuff to remember, and if you have to take Pre-Cal and Calculus, you must remember all the Trig functions etc.. Calculus is like Trigonometry on steroids.

SOHCAHTOA was very helpful for Trig.

SOHCAHTOA

A way of remembering how to compute the sine, cosine, and tangent of an angle.

SOH stands for Sine equals Opposite over Hypotenuse.

CAH stands for Cosine equals Adjacent over Hypotenuse.

TOA stands for Tangent equals Opposite over Adjacent.

You also need to memorize the Trigonometry table. This will definitely help you understand equations. Once you remember the table, you wont have to constantly look at it in order to solve an equation. Come up with silly or easy abbreviations to remember steps etc..
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triangle.128k
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10/8/2015 1:43:10 AM
Posted: 1 year ago
At 10/3/2015 8:18:45 PM, UtherPenguin wrote:
At 10/3/2015 7:40:37 PM, bsh1 wrote:
At 10/3/2015 8:08:13 AM, Fkkize wrote:

I think Blade is asking "how do you calculus." Do you memorize and apply formulas, or is there a specific mental approach, a way of thinking, that one ought to adopt.

One does not do Calculus, Calculus does you.

In Corporatist America, you do Calculus. In Soviet Russia, Calculus does you.