How did the visual thinkers learn math?

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pete1061
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16 Dec 2011, 1:08 pm

I think my extreme visual mind had helped much more than hindered my math skills, which are really good.
In my head I see everything in terms of geometry, which is the purest way to express numbers.
for basic arithmetic, I usually use rectangles which are sized proportional to the number they express, then I split up or put together those rectangles depending on the operation being performed.
For more complex math, I will see the graphs in my head.

The actual linguistic numerals like 1,2,3 are more of a hindrance for me.


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16 Dec 2011, 2:21 pm

When I first learned addition, it was with scratch marks. I would put them on paper when I count while looking at the problem and writing down the answer. My teacher called those sticks. Then one day she decided I was going to use my fingers by counting on them. Then when I learned addition I also used my hands. I have to hold up my hands and take away a certain amount of fingers and whatever fingers were left, that was the answer.



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16 Dec 2011, 2:51 pm

I know this post doesnt really help.

I'm a visual learner but I happen to be lucky where I'm also a patterned thinker too so Im good at math. Neither talented in either realms, I'm more visual though. I never had problems with math. My weakness is verbal, I have learning disorders affecting for word acquisition, grammar, and spelling.


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SammichEater
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16 Dec 2011, 4:02 pm

Without a calculator, I do basic math by estimation. For example, this is how I would solve 195 * 43:

I would first break it down into 200 * 40. To calculate this, I first count how many times it takes for 200 to go into 1,000. Obviously, the answer is 5. Since 5 goes into 40 8 times, the answer is 8,000.

Then I calculate what 200 * 43 would be. I can now easily conclude that the answer is 8,600.

But 200 * 43 isn't the question. I need to find 195 * 43. Since 195 is only 5 less than 200, the final answer will be 8,600 minus the product of 5 and 43. Once again, 5 times 40 is 200, and 5 times 3 is 15. By adding the two together, 5 times 43 is 215. I can now subtract 215 from 8,600 to get my final answer of 8,385.

Think of this method like drawing a circle. First, you start with a triangle, and work your way up to a square, then a pentagon, hexagon, etc. Eventually, you'll end up with something that looks very similar to a circle. I taught myself this method. As far as I know, nobody else does this.


For other sorts of problems, use dimensional analysis. Here's a nice hint: every time you hear the word "per," that means to divide. For example, to find speed, in miles per hour, you take the distance (miles), and divide it by the time (hours). Same for Miles per gallon, parts per million, etc.


Another thing that bothers me is that nobody actually teaches what percent is. If you have 100% of something, you have 1 of it, not 100. If you have 75%, that's really 0.75. If you have 155.67%, you really have 1.5567. Yet, in all the science classes and what not, they always tell you to multiply whatever by 100 to get the percent. No, that is WRONG, and that's not the way to think about it.


I first struggled with algebra. It's actually really easy, once you get past this one basic concept. Suppose, for example, you have x - 5.

Don't think of it as x minus 5. Think of it as two separate entities: x, and negative 5. Every time you see a plus or minus sign, visualize it as a sea. The x is on one island, and the negative 5 is on another. Whatever you do to one island, you have to do to the other.

When you get into more complex stuff, such as 5x^4 - 3x^2 + 71, it really helps to think this way. 5x^4 is it's own little island, and totally different from the -3x^2 and 71.


The whole concept of graphs and such came naturally to me. Once I understood what an x axis, y axis, and slope were, it all just made sense to me.


Geometry, I can't really help with that. I mean, I get the concepts. But I failed almost every proof I did, and I never knew why. What makes sense to me doesn't make sense to other people, I guess.


Calculus, like most of the graphing stuff, is easy for me. The derivative is the rate of change (slope) and the integral is the opposite (area under a curve). What is so hard to understand about that?


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slovaksiren
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16 Dec 2011, 4:56 pm

How did I learn? Practice, practice, practice...



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16 Dec 2011, 5:10 pm

Valoyossa wrote:
I'm visual thinker and I learned basic math many years ago, but I remember this. I imagined dots and I... oooh, I'm visual, so I have to draw it :lol:

Image

I saw blurred somethings in my mind, like on the picture. Later I could imagine the numbers.


That's how I started learning multiplication in first grade.

3x3 means 3 columns and 3 rows of dots. How many dots are there?

* * *
* * *
* * *

9! Once I understood what muliplication meant, it was just a matter of memorizing the multiplication tables and learning the various rules for more advanced math techniques. But, almost everything in elementary math (All the way before you get to calculus) can be represented graphically somehow which is basically how I 'understand math'.



pensieve
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16 Dec 2011, 5:21 pm

I used dots too, or my fingers.

Now I use basic addition and try to add together bigger numbers so I can just remember them.
The only time I can do addition like people in the thread are explaining is when I'm on medication.

Math applications help. Do you have a smart phone or iPad?


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marshall
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16 Dec 2011, 5:52 pm

SammichEater wrote:
Without a calculator, I do basic math by estimation. For example, this is how I would solve 195 * 43:

I would first break it down into 200 * 40. To calculate this, I first count how many times it takes for 200 to go into 1,000. Obviously, the answer is 5. Since 5 goes into 40 8 times, the answer is 8,000.

Then I calculate what 200 * 43 would be. I can now easily conclude that the answer is 8,600.

But 200 * 43 isn't the question. I need to find 195 * 43. Since 195 is only 5 less than 200, the final answer will be 8,600 minus the product of 5 and 43. Once again, 5 times 40 is 200, and 5 times 3 is 15. By adding the two together, 5 times 43 is 215. I can now subtract 215 from 8,600 to get my final answer of 8,385.


That's exactly how I do arithmetic when I don't have access to a calculator. I might have to write down the 200 * 43 = 8600 though so I don't forget.

I picture money and/or clocks when doing arithmetic that involves factors or multiples of 4, 5, 6, 12, 15, 20, 24, 25, or 60. And being familiar with binary helps with various powers of 2, i.e. 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc... Then there's angles that involve 15, 30, 45, 90, 180, 360, etc...

Example:

What's 750 divided by 12?

I easily remember that 5 * 12 = 60 by looking at a clock

So write 750 = 600 + 150.

I know 600 / 12 = (60 / 12) * 10 = 5 * 10 = 50.

Now 150 / 12 = (120 + 30) / 12
= 10 + 30 / 12
= 10 + 1/2 * (60 / 12)
= 10 + 1/2 * 5
= 12.5

So... 750 / 12 = 50 + 12.5 = 62.5.



SammichEater
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16 Dec 2011, 6:35 pm

I would have done that differently. :P

12 * 10 = 120

120 * 6 = 720

Therefore, 12 * 60 is 720.

With the other 30, that can be broken down into 24 and 6, which is 12 times 2 and 0.5.

So, the answer is 60 + 2 + 0.5, which is 62.5. I think that's kinda easier.


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matt
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17 Dec 2011, 3:03 am

I imagine dots.

It works for addition, subtraction, multiplication and division. It also works better when understanding the terms "squared" and "cubed" because I imagine actual squares or cubes with that many dots across each side.



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17 Dec 2011, 3:42 am

SammichEater wrote:
Without a calculator, I do basic math by estimation. For example, this is how I would solve 195 * 43:

I would first break it down into 200 * 40. To calculate this, I first count how many times it takes for 200 to go into 1,000. Obviously, the answer is 5. Since 5 goes into 40 8 times, the answer is 8,000.

Then I calculate what 200 * 43 would be. I can now easily conclude that the answer is 8,600.

But 200 * 43 isn't the question. I need to find 195 * 43. Since 195 is only 5 less than 200, the final answer will be 8,600 minus the product of 5 and 43. Once again, 5 times 40 is 200, and 5 times 3 is 15. By adding the two together, 5 times 43 is 215. I can now subtract 215 from 8,600 to get my final answer of 8,385.


I did it like this: (195 x 10)4 + (195 x 3). In my brain. Came up with 8385 too.



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17 Dec 2011, 7:48 am

swbluto wrote:
Valoyossa wrote:
I'm visual thinker and I learned basic math many years ago, but I remember this. I imagined dots and I... oooh, I'm visual, so I have to draw it :lol:

Image

I saw blurred somethings in my mind, like on the picture. Later I could imagine the numbers.


That's how I started learning multiplication in first grade.

3x3 means 3 columns and 3 rows of dots. How many dots are there?

* * *
* * *
* * *

9! Once I understood what muliplication meant, it was just a matter of memorizing the multiplication tables and learning the various rules for more advanced math techniques. But, almost everything in elementary math (All the way before you get to calculus) can be represented graphically somehow which is basically how I 'understand math'.

This is quite a good description of what happens in my mind too, when doing basic arithmetic calculations.


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17 Dec 2011, 8:42 am

I actually remember learning how to add and subtract by trial and error using a kids calculator that tested you on it. I'm also a visual thinker.

Counting: I remember seeing a set of dots or objects next to numbers and that was a good visual picture.

Addition and subtraction: With the more basic numbers, i just did it instinctively, i don't remember whether I "saw" a picture in my head. Later on, I used to imagine in my head more complex addition and subtraction as I would write it out (including carrying of numbers). I liked the repetition and certainty in maths, it's a recurring special interest of mine so I guess I did a lot of work to understand it all.

Multiplication: I remember seeing a visual diagram of multiplication where you had for, say, 2*3 a rectangle with unit dots with a width of 2 dots and a length of 3 dots. I used repeated addition to derive the products until I had my times tables locked in my head (I don't recommend it).

Unfortunately I don't have much recollection of my childhood before I was 9 so I can't really say much else about math stuff at primary/elementary level.



pete1061
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17 Dec 2011, 8:42 am

SammichEater wrote:
Without a calculator, I do basic math by estimation. For example, this is how I would solve 195 * 43:

I would first break it down into 200 * 40. To calculate this, I first count how many times it takes for 200 to go into 1,000. Obviously, the answer is 5. Since 5 goes into 40 8 times, the answer is 8,000.

Then I calculate what 200 * 43 would be. I can now easily conclude that the answer is 8,600.

But 200 * 43 isn't the question. I need to find 195 * 43. Since 195 is only 5 less than 200, the final answer will be 8,600 minus the product of 5 and 43. Once again, 5 times 40 is 200, and 5 times 3 is 15. By adding the two together, 5 times 43 is 215. I can now subtract 215 from 8,600 to get my final answer of 8,385.

Think of this method like drawing a circle. First, you start with a triangle, and work your way up to a square, then a pentagon, hexagon, etc. Eventually, you'll end up with something that looks very similar to a circle. I taught myself this method. As far as I know, nobody else does this.


...snip...


I use the same method for arithmetic. It's essentially breaking the problem up into pieces.


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17 Dec 2011, 11:41 am

I got yelled at all the time for using my fingers, but I needed a visual representive of how many there were of something. If I couldn't use my fingers, I would just use objects in the room. When I got older I just used a Calculator. I also did geomotry for a while before I felt comfortable doing algebra. I find algebra much easier than basic math and trying to remember a bunch of things. I also needed examples of how math was appiled to real life and how I would use math in being a vet. I was always told math has applications in other areas and in real life, but was never told how.


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byakuugan
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17 Dec 2011, 1:19 pm

Also I forgot to add that when a person (I'm not sure how different it is for visual thinkers) sees an image, and is then asked to describe that image in words once they are no longer seeing the image, their visual recollection of that image later will actually be worse than if they had never been asked to describe the image in words.