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#1 2006-12-13 06:34:05

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Mental arithmetic making you look bad?

John E. Franklin's "Subtraction for kids" thread brough this to my mind. But I thought its a good topic in its own right.

Has anyone else had the annoying problem that just because your an A math student, people think you can do lightening fast arithmetic in your head? And when you can't they think your a fraud?

I once worked in a grocery store where the owner couldn't find the zeros of y = -3x^2 + 2x + 7, but his arithmetic was razor sharp as he did it all the time, every day. Me on the otherhand, who could tell you the area under  y = -3x^2 + 2x + 7, was not so quick with arithmetic as I rarely practice it anymore. He thought I was mathematically illiterate and often laughed at my slowness. My other skills were of no use as all we ever did was add subtract and multiply. You don't need much else to run a grocery store.

People seem to think slow or poor mental arithmetic proves you are not good at math and your just making it up if you say you are.

Another time I was adding prices on a reciept where we had to multiply the price times the quantity bought. There was a box with the quantity number,  and beside it a box with the price.
In some spots, there was a price written in for an item (in pen) but no quantity listed. Now naturally I figured the absense of a coefficient is a coefficient of 1. x = 1*x so I marked each of those items once. But appearently not. No quanity meant 0. My boss laughed at me for being an idiot!

Another time in english class my teacher asked me to calculate a percentage for him, and I said  "umm..about 30,000"Some people in the room murmered and I realized it was incorrect.

It drives you crazy!

Moved to Dark Discussions folder - Ricky (You're wish is my command, Mikau)

Last edited by mikau (2006-12-13 06:46:05)


A logarithm is just a misspelled algorithm.

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#2 2006-12-13 06:39:18

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

Oops.... I meant to post this in dark discussion, silly me..


A logarithm is just a misspelled algorithm.

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#3 2006-12-13 09:31:53

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: Mental arithmetic making you look bad?

Well, I wouldn't say I'm bad at arithmics. However, I totally get what you mean. Somehow, a lot of people can't understand you can be good at math, even if you're not very sharp at arithmetics.


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#4 2006-12-13 14:16:08

mikau
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Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

Me personally I have a very bad short term memory, I need a number of sentance down on paper, otherwise I forget it quickly. However, short term memory is not required to understand the analytical side of math.

My arithmetic is fine with pencil and paper, its neither slow nor inaccurate. But when I do things in my head, I find I loose track of things quickly.


A logarithm is just a misspelled algorithm.

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#5 2006-12-13 21:27:10

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Mental arithmetic making you look bad?

I understand it well .... and you see those people on TV who can do huge sums in seconds. Or people who can calculate poker odds on the fly. Amazing skills, but won't get you a degree.

However, you could train yourself to be fast ... that was why I made "Speed Math" (with the dice), and "Money Master" ... but I think I could make something better for the person who really wants to be good at mental math. Anyone interested?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2006-12-14 04:04:42

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

I'm interested. But I think it demends on whether or not it is possible to "train your memory".

I'd like to see what you've got in mind.


A logarithm is just a misspelled algorithm.

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#7 2006-12-14 11:02:12

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Mental arithmetic making you look bad?

Dr Kawashima's Brain Training is quite good for training yourself in speed maths.

You get given a simple addition, subtraction or multiplication question and you have to write down the answer as fast as you can. There's also the option to add division questions in there, but they're all really simple, mostly single digit numbers.

You get either 20 or 100 questions depending on what mode you're on, and you get given the overall time that it took you to answer them all. And there's also an option so that you can say the answers instead of writing them, but I don't usually get as good times on that one because the voice recognition takes a while to verify that I got the right answer.

Still, quite good and quite fun. Especially for everyone else if you're doing the voice mode in a crowded place. wink


Why did the vector cross the road?
It wanted to be normal.

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#8 2006-12-14 11:49:29

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Mental arithmetic making you look bad?

Well ... Speed Math must be pretty close to an arithmetic trainer, how should it be changed?

Maybe the "answer" boxes could stay fixed (they would have to be smaller and lots more of them) ... maybe in a 10x10 grid for ten times table.

And instead of dice just "6x8="

And for harder problems like "1.25 x 1.2 =" there could be multiple choice.

What would you like to see?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#9 2006-12-14 13:08:21

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

I'd definitly say the answer box should stay fixed. I also think dice may not be the best option.

That game seems fine for kids but for good practice maybe numeric digits and typable answers.


A logarithm is just a misspelled algorithm.

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#10 2006-12-14 13:09:56

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Mental arithmetic making you look bad?

Mmm, the answer boxes being fixed would definitely be better, as it would be more about speed maths and less about speed searching.

But then it would weight it more towards speed mouse-precision...

So maybe another possible option would be a box to type the numbers in. I don't know about other people, but I think that I'd be a lot faster if I could type answer rather than clicking on them. If both options were left in, then there'd be a choice and people could just pick the one that they can do faster.

I think removing the dice is a good idea as well. They're very good and could be used very well somewhere else, but I think just having the numbers would be better here. That way, you can get into the 'Speed Zone' without having to keep waiting for the dice to stop rolling.


Why did the vector cross the road?
It wanted to be normal.

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#11 2006-12-14 13:56:29

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

Pretty much exactly what I just said, Mathsy! :-)  So thats two votes!


A logarithm is just a misspelled algorithm.

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#12 2006-12-15 03:09:56

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: Mental arithmetic making you look bad?

As a fun little game, the dices are fine. However, if you really want to compete, against yourself or others, numbers and an input-box would be preferable though.


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#13 2006-12-15 06:25:45

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Mental arithmetic making you look bad?

Yeah, perhaps a scoreboard or something of the like could be implemented or an entire server could be created (I expect it shouldn't be too hard) so people can race against each other and stuff. It could have lots of people if it's good enough, it would be fantastic.
I also support an input box so you can type your answers.

Oh, and I was wondering:
For multiplication with numbers of 2 digits or more, do you actually run through the whole algorithmic working in your head, do you do multiplication by parts (e.g 12*15=10*15+2*15), or do you use your own top-secret formula what?

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#14 2006-12-15 07:09:02

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Mental arithmetic making you look bad?

mikau wrote:

Pretty much exactly what I just said, Mathsy! :-)  So thats two votes!

Three votes. ;D

It would be better to enter the numbers on your keyboard, takes too long to find the number in my opinion. wink

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#15 2006-12-15 07:46:17

rida
Real Member
Registered: 2006-09-25
Posts: 839

Re: Mental arithmetic making you look bad?

Devanté wrote:
mikau wrote:

Pretty much exactly what I just said, Mathsy! :-)  So thats two votes!

Three votes. ;D

It would be better to enter the numbers on your keyboard, takes too long to find the number in my opinion. wink

I Agree as well so thats 4 votes


Dreams don't come true, you gotta make them come true.

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#16 2006-12-15 08:51:25

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

w00t! Can I vote again? :-P


A logarithm is just a misspelled algorithm.

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#17 2006-12-15 11:37:00

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Mental arithmetic making you look bad?

So ... problems like "12x9=" and answers in a box. Got it. Give me a few days.

Call it "Speed Math II" ??


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#18 2006-12-15 12:00:42

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

Seeing as this is for slighlty more advanced peoples, who don't need colorfull dice to entertain them, I'd say we should call it "The Integral of Acceleration Math"


A logarithm is just a misspelled algorithm.

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#19 2006-12-15 15:38:17

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Mental arithmetic making you look bad?

rida wrote:
Devanté wrote:
mikau wrote:

Pretty much exactly what I just said, Mathsy! :-)  So thats two votes!

Three votes. ;D

It would be better to enter the numbers on your keyboard, takes too long to find the number in my opinion. wink

I Agree as well so thats 4 votes

Hey, i voted yes too!

So that's 5 then!

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#20 2006-12-15 20:18:21

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Mental arithmetic making you look bad?

Mmmm, I share the same problem with Mikau. My long term memory is not good, either. Actually the partial reason why I love maths is that it is the subject that requires the least memorizing!! Literature is always the last subject I want...

Last edited by George,Y (2006-12-15 20:21:26)


X'(y-Xβ)=0

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#21 2006-12-15 21:02:27

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Mental arithmetic making you look bad?

George,Y wrote:

Actually the partial reason why I love maths is that it is the subject that requires the least memorizing!!

apart from the thousands of identities you have to learn tongue


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The End Of All Things To Come.

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#22 2006-12-16 02:42:55

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Mental arithmetic making you look bad?

Toast wrote:

Oh, and I was wondering:
For multiplication with numbers of 2 digits or more, do you actually run through the whole algorithmic working in your head, do you do multiplication by parts (e.g 12*15=10*15+2*15), or do you use your own top-secret formula what?

The speed math thing doesn't ever ask you to do that, does it? In the most complicated mode, it asks you to add two dice together, then multiply that by what you get when you add another two dice together. So you'd very rarely be asked to multiplt two 2-digit numbers together, and when you were, the numbers would never be above 12.

Anyway, to answer you question, I usually split it up like you have. So, 12*15 would be 10*15 + 2*15. For more complicated stuff, I sometimes split both numbers up to get, for example,  10*10+2*10+10*5+2*5.

However, for that particular question, I'd divide 12 by 2 and multiply that to the 15. So now I have 12*15 = 6*30, which is a lot easier because it's just two single-digit numbers multiplied together, with an extra 0 on the end.

Another way that is sometimes helpful is to use the difference of two squares: (a+b)(a-b) = a² - b².
If, for example, I had the question 15*25, then I could recognise that that was (20+5)(20-5) and so use the difference of two squares to change that into 20² - 5² = 375, which would be slightly quicker than working out the original sum.

In general, I think the best way to do stuff like that quickly is to know as many methods as possible, and be able to choose the best one for the situation.


mikau wrote:

Seeing as this is for slighlty more advanced peoples, who don't need colorfull dice to entertain them, I'd say we should call it "The Integral of Acceleration Math"

But that's "Velocity Math Plus c". If anything, "The Derivative of Distance Math" would work better. Or, you know, perhaps just "Speed Math II" tongue


Why did the vector cross the road?
It wanted to be normal.

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#23 2006-12-16 04:16:57

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

Velocity Math plus C! HAHAHA!! :-P

But I think Velocity math sounds pretty cool!


A logarithm is just a misspelled algorithm.

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#24 2006-12-16 10:41:22

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Mental arithmetic making you look bad?

"Velocity Math" is cool ... or maybe "Reaction Math"?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#25 2006-12-16 13:11:24

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Mental arithmetic making you look bad?

How about mathletics? :-)


A logarithm is just a misspelled algorithm.

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