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When it comes to math ...

UncaYimmy said:
But it seems like the mathematically inclined tend to get snobby with those who prefer to avoid math. Suppose there's a room full of people and somebody says, "If 9 people donated a total of 72 dollars, what was the average donation?" It seems like you'd expect everyone to give the answer.

Well, what if in that same room someone said, "Who would like to come draw a cat's face on the blackboard?" Do you think everyone should volunteer? It's really easy. In the world of drawing, it's basic addition. Would you look down on anyone who said, "No way. I suck at drawing."
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I've always been terribly slow at mental arithmetic. I'm fairly good (given my minimal post-secondary math education) at reasoning my way through mathematical concepts -- put a calculator in my hand and I can solve some pretty complicated stuff. But simple multiplication tables have never really stuck in my head. It isn't that I can't do it at all, it just takes me longer than it "should," and I need a pen and paper at least. I'm sure if I had a need to do calculations in my daily life, I'd pick it up with the practice. (I did improve quite a lot when I started using pen and paper to track my word counts for some daily creative writing challenges I was doing.) I suppose I would say that I "can't be bothered" to master that particular skill. I've just never needed mental arithmetic the way I need other skills -- typing, for instance, or phonetic transcription, or even drawing.

And yes, I've been judged for it. I remember, in my undergrad days, admitting how bad I was at mental math in the presence of a chemistry grad student, who promptly informed me that I was "innumerate" and therefore "uneducated."

He probably thought exactly the same thing of me that has been expressed by some people in this thread -- that I was lazy and anti-intellectual and thought people good at math were geeks and was flaunting that I wasn't a geek like him. The fact that I was the token arts student in a group of friends composed mostly of scientists and engineers probably didn't help my case in his mind.

I can only laugh at how very poorly he read me.
 
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I wonder if there's a connection (or analogy) to drawing anything, even a simple house frame, in 3D as opposed to a single side frontal view. When I taught, many students thought I was an artist just because I could draw a cube (or other basic diagrams) in 3-dimensions on a 2D chalkboard. Then I showed them how easily they could do it.
 
Towlie said:
Try these. They're all easy to do in your head once you know the secret:

47 X 53 = ?

92 X 88 = ?

76 X 84 = ?
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Cute.


47x53 = 50x50 - 3x3 = 2491
92x88 = 90x90 - 2x2 = 8096
76x84 = 80x80 - 4x4 = 6384

It's just a difference of squares problem. I'm used to that in a more analytic context, haven't really thought much before about using it for straight arithmetic.
 
Just thinking said:
I wonder if there's a connection (or analogy) to drawing anything, even a simple house frame, in 3D as opposed to a single side frontal view. When I taught, many students thought I was an artist just because I could draw a cube (or other basic diagrams) in 3-dimensions on a 2D chalkboard. Then I showed them how easily they could do it.
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I hope the following is acceptable thread drift because what you wrote made me recall a story I think I have shared before.

Many years ago my ex-wife and I received a small gift from one of her students. Imagine a rectangular piece of black plastic. Now using the whole thing cut it up into various shapes (triangles, squares, rectangles). Put together correctly these shapes form the rectangle (obviously).

The game included cards that had black shapes drawn on them. The goal was to use some or all of the pieces to create that shape. My wife and I approached it very differently. She "saw" little lines on the drawing that told her where the pieces go. By contrast I reasoned out how to do it. I always solved the puzzles, but at times she would just get stuck.

So I attempted to visualize it the same way she did. It took some effort, but I actually began to "see" where the pieces would go. I was absolutely amazed. It was quite a revelation to learn that this is how she and other people think.

And getting back to my math problem example, I asked my current wife, a programmer, to solve 175/7. The way she did it was in effect to look for a multiple of 7 that ended in 5. Well, 7*5=35. So she subtracted that from 175 and saw she had 140. That's easy enough to solve. Thus the answer is 25.

By my count that's at least four different ways of solving the same rather simple problem.
 
Just thinking said:
Amazing how the mind can work.

(BTW ... nice shot of EvZ in your avitar.)
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<off topic>
Nobody ever caught the significance of my avatar or if they did, they didn't mention it. For a while there were some people accusing me of leading a "gang" of followers in picking on the fair maiden, VisionFromFeeling, whereas we thought we were doing good. Eric von Zipper and The Rats immediately came to mind. I love that guy!
</off topic>
 
UncaYimmy said:
Wow. That never entered my mind. It's amazing how differently people approach the same problem.
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Most people can do math with "money" in their heads much better than they can with "numbers". Ask someone how much 25 x 9 is, then after they sit and think for a few seconds without answering ask them how much money nine quarters is. I suppose this might not work in countries that don't use coins with a value of 25.
 
UncaYimmy said:
Many years ago my ex-wife and I received a small gift from one of her students. Imagine a rectangular piece of black plastic. Now using the whole thing cut it up into various shapes (triangles, squares, rectangles). Put together correctly these shapes form the rectangle (obviously).
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Tangrams
 
Modified said:
Most people can do math with "money" in their heads much better than they can with "numbers". Ask someone how much 25 x 9 is, then after they sit and think for a few seconds without answering ask them how much money nine quarters is. I suppose this might not work in countries that don't use coins with a value of 25.
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Yes on two counts.

a) There is no 25 value coin or note in the UK. My mental process on the 175/7 was, 17/7->2, 35->5, oh 25. ohh! that's obviously right 175 is 25 * 8 - 25. (multiplying by 25 is easy, it's 100/4, regardless of whether you have quarters)

b) My mother-in-law is a primary school (now head) teacher, and relates this story about a remedial maths class. The teacher asked the children 'what problem do you find hardest with maths', and one child said 'what's 3 plus 5?' Teacher thinks, oh wow, that remedial, and proceeds to say, 'well, if you have 3 apples and 5 apples ...'. Kid interjects with, 'yes, I know 3 apples plus 5 apples is 8 apples, but what's 3 plus 5? What's 5?'

Stick a unit on a number and it becomes something tangible.
 
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Modified said:
Most people can do math with "money" in their heads much better than they can with "numbers". Ask someone how much 25 x 9 is, then after they sit and think for a few seconds without answering ask them how much money nine quarters is. I suppose this might not work in countries that don't use coins with a value of 25.
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I'd have to say that 20 x 9 = 180 (I work that out by multiplying 9 by 2 and then by 10) and then 5 x 9 = 45, so 180 + 45 = 200 + 25 = 225 (that last step exchanges 20 from the right to the left). I don't have a more intuituve method - I have to plod along by using base arithmetic.
 
This thread seems to confuse knowing how to use various shortcuts to do arithmetic with the ability to be proficient at math. To me they are totally different.
 
SezMe said:
This thread seems to confuse knowing how to use various shortcuts to do arithmetic with the ability to be proficient at math. To me they are totally different.
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I agree. Knowing shortcuts to do doing mental arithmetic is a nice party trick and can be useful in saving a few seconds here and there, but all the problems mentioned should be solvable by anyone, even if they have to take a bit longer. I have absolutely no problem with people who take a minute or two to work out 9*25 just because I can do it faster. It's the people who apparently can't work it out at all and worse, are actually proud of that fact, that are the problem.

Seriously, I've seen people on quiz shows that can't subtract one two digit number from another given 5 minutes and a piece of paper. You'd think they'd be embarrassed about that, but instead they actually boast about it on national TV.
 
UncaYimmy said:
As for the comment about spelling, that's yet another skill. Some people can read and comprehend as well as converse on a high level, but there's something different that keeps them from spelling properly. Most good spellers don't consciously memorize words - they just know if it "looks right" or not. Also, some people who can speak quite intelligently cannot write even basic sentences. Just ask elementary school teachers who will sit with a kid for 15 minutes trying to get one sentence written. The kid can talk a mile a minute and read fluently, but when it comes to writing, something just isn't right. Strange.
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This is how I am with English. It's just an intuitive thing for me. I couldn't tell you all the parts of speech or break down a sentence structure or any of that. But I always got top grades in English class, always took pride in my vocabulary and grammar in school, and would help proofread friends' papers who had memorized all of the little parts of speech and whatnot, but needed guidance putting together a decent sentence.

Math is about the same. I just do it in my head most of the time. Sometimes it bothers me when I have to grab a piece of paper or a calculator, depending on the problem. And I know I do it weird...I've never been able to explain my thought process to other people, though it's generally some combination of two approaches: 175/7 = (140/7) + (35/7) OR 175/7 = 7x $0.25 I do find myself using the money shortcut a lot. Likewise, I've always been baffled by how hard it is for some people to make change - or, when I get "the look" from a cashier when paying, say, $5.25 for something that costs $4.04.

When I worked retail, this was usually a sure sign to me of which of my fellow cashiers would last, and which wouldn't: how easily they made change, or how easily they counted their drawer down. Some would lose their minds if the customer offered up a few coins after they'd typed in $20.00 as the payment, because the register didn't say the right change anymore, and they couldn't figure out what the new change was (a couple had to be, um, relieved, when they yelled at customers for doing that). Likewise, if their drawer was out of balance by $10, they didn't understand why there wasn't really a need to count the loose change all over again.

But, like other people have said, it's not about the shortcut, or being able to do it quickly in your head. It's about being afraid of math, or being proud that you can't do it. I don't care if you can't do it in your head, or HOW you do it in your head, as long as you can do it somehow, or are willing to give it a decent try. If you grab a pencil and paper and go at it, that's fine. If you say "Oh I'm no good at that" and don't even try, that's the problem.
 
borealys said:
I've always been terribly slow at mental arithmetic. I'm fairly good (given my minimal post-secondary math education) at reasoning my way through mathematical concepts -- put a calculator in my hand and I can solve some pretty complicated stuff. But simple multiplication tables have never really stuck in my head. It isn't that I can't do it at all, it just takes me longer than it "should," and I need a pen and paper at least. I'm sure if I had a need to do calculations in my daily life, I'd pick it up with the practice. (I did improve quite a lot when I started using pen and paper to track my word counts for some daily creative writing challenges I was doing.) I suppose I would say that I "can't be bothered" to master that particular skill. I've just never needed mental arithmetic the way I need other skills -- typing, for instance, or phonetic transcription, or even drawing.

And yes, I've been judged for it. I remember, in my undergrad days, admitting how bad I was at mental math in the presence of a chemistry grad student, who promptly informed me that I was "innumerate" and therefore "uneducated."

He probably thought exactly the same thing of me that has been expressed by some people in this thread -- that I was lazy and anti-intellectual and thought people good at math were geeks and was flaunting that I wasn't a geek like him. The fact that I was the token arts student in a group of friends composed mostly of scientists and engineers probably didn't help my case in his mind.

I can only laugh at how very poorly he read me.
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See, I don't have a problem at all with your story. I don't expect other people to do things in their head the way I do, or memorize multiplaction tables, or anything like that. As long as you don't need a calculator to solve 2 + 2, that is :p

My issue here is more the pride in not knowing, or the fear of attempting. You sound like you're willing to do it when it's needed, which is all I would expect of anyone.
 
UncaYimmy said:
LOL!

Have you ever (I mean this as a genuine "have you ever" not a snotty "have you ever") talked with the less mathematically inclined about how they approach relatively simple math problems? Let me give you an example:

175/7=?

How do you approach it? In my mind I just know 7*20=140. I then subtract 140 from 175 (actually, I don't - mind just automatically says "35" without any effort). What is 35/7? It's 5, of course. Thus my answer is 25. It's easy for me to hold those numbers in my head.

If I did it the long division (as taught in elementary school) way in my head, I would find it frustrating and, quite frankly, intimidating without a piece of paper and a pencil.
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I used to get into trouble on homework assignments in maths class for exactly this reason. I could look at simple problems and just "know" the answer, and I'd get marked down for not showing my work. I could never understand what "work" was involved in something like 63/9...

I spent many years in software development. My last boss, a man in his 70s who taught college as well as programmed computers for many moons, and I discussed how to teach programmers to think creatively. We both agreed that either your mind works a certain way or it doesn't. Nobody taught me how to solve the above problem like I did. Likewise, even though you could show programmers all sorts of clever ways to approach problems, some never come up with them on their own. To use a metaphor, they always use the long division method because that's a solid formula that always yields the right answer with a predictable number of steps.

Example: Suppose you had to write a program to determine the value of X given that X was an integer from 0 to 100.

* One guy loops a counter called i from 0 to 100 checking if x=i each time around. When they match, he quits and gives the answer.

* Another guy, who thinks he's being clever because he just read about a function that returns a random integer within a range, sets up an infinite loop generating a random number i and checking if x=1. Yech.

* Still another guy sees the above code and thinks, "Well, since the random number generator might repeat a number, I'm going to keep track of the numbers I've already checked so I don't check them again! I'm so smart!" This is a double-yech.

* The smart programmer writes a program that starts with the number 50 (1/2 of the range). He then checks if x>50. If not, he divides his starting number in half and checks if x>25. With just a few iterations he'll find the value of x.

How do you teach that? I never taught programming, but I did supervise and train a number of programmers. In my experience programmers either came up with that last solution or they didn't.
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Guess that would depend on if I was told to do it using the least lines of code (first solution), or the least number of calculations (fourth solution).

Aitch said:
What/ Nobody came up with a (very long) Select/Case statement? Amateurs! ;)
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I nearly fell out of my chair laughing at this. Then I remembered that I've seen something similar in code that my former coworkers had written.

Though, you could certainly use a select...case with the fourth solution, just not with 100 cases.
 
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