When it comes to math ...

[Just thinking]

Why is it that whenever it comes to mathematics (including basic arithmetic and/or geometry) so many folks, including highly skilled individuals in their fields, fail so miserably? Just watch any game show or listen to any radio talk show (or just your average Joe).

[shadron]

Mathematics is an abstraction of life. Some people can use and manipulate abstractions; some people seeming cannot, just as some people learn linearly and some are more spatially oriented. Perhaps with another 100 or 200 years of study of the brain we will discover what happenstances lead to which abilities; maybe it all has to do with early conscious attitudes.

Why are many mathematicians seemingly ill-adept at social graces? I don't know, but I think that the answer to either will provide insight to both.

[Ziggurat]

Why is it that whenever it comes to mathematics (including basic arithmetic and/or geometry) so many folks, including highly skilled individuals in their fields, fail so miserably? Just watch any game show or listen to any radio talk show (or just your average Joe).

I suspect part of it is that it's become socially acceptable to be terrible at math, and so people who don't do well at it basically give up learning math somewhere around highschool. And after that they avoid doing math whenever possible - balancing a checkbook is about the only math many people do, and they'll usually use a calculator so they aren't really doing even that much.

[Just thinking]

Mathematics is an abstraction of life.

Abstraction? It way well be our most accurate representation of reality. But then again, it may depend on what you mean by "life".

Some people can use and manipulate abstractions; some people seeming cannot, just as some people learn linearly and some are more spatially oriented. Perhaps with another 100 or 200 years of study of the brain we will discover what happenstances lead to which abilities; maybe it all has to do with early conscious attitudes.

It's odd ... because I've seen people with highly trained skills (electricians, auto repair technicians, carpenters) seemingly avoid anything mathematic in nature like the plague.

[boooeee]

Just watch any game show or listen to any radio talk show (or just your average Joe).


It depends on the situation. I consider myself pretty good at math, but when put on the spot to do a calculation in my head, I can easily trip myself up.

[learner]

I have often noticed that when maths, of any kind, crops up in daily life, some people seem almost proud to be poor at it, and dismiss it as a geeks thing.
When one of my employees needed help with the most basic of calculations i would attempt to show her, without use of a calculator. For my troubles she would cover her ears and do the; "na,na,na,na I don't want to know how, just tell me the answer" routine. Managing to make me seem strange for knowing how to do it?

[Towlie]

Why is it that whenever it comes to mathematics (including basic arithmetic and/or geometry) so many folks, including highly skilled individuals in their fields, fail so miserably? Just watch any game show or listen to any radio talk show (or just your average Joe).

That may be true, but it bugs me a whole lot more that they can't spell.

(This comment is not directed at any individual on this forum or at any post in this thread.)

[mazyloron]

There's a definite stigma associated with being good at maths, or at least, as has been said, a certain pride taken in being bad at it (them) (the maths).

It's not just maths, though. Anything that requires even the slightest bit of work to learn seems to be looked down upon lately. Basically, a "oh you think you're better than me?" sort of attitude towards anyone who actually CAN do maths, or uses reasonably decent grammar, or anything similar. I think it's terrible.

Sure, not everyone can be great at everything, but taking pride in being BAD at something so basic, deliberately refusing to try to learn it? When did willful ignorance become a bragging right?

[jasonpatterson]

Why are many mathematicians seemingly ill-adept at social graces? I don't know, but I think that the answer to either will provide insight to both.

I wonder how much of this is confirmation bias. This falls right in with the assumption that 'smart people don't have any common sense.' Sure, we know awkward people who are good at math, but I know plenty of awkward people who aren't any good at math either. Additionally, I know lots of people who are good at math who are perfectly well adjusted. We notice those who fit our stereotypes, in short.

As far as the original question, I have to agree that it's largely because it is socially acceptable to be ignorant of math. Much the same goes for knowledge of the sciences or having a good vocabulary. If you use too many 'big words' some people get upset and assume you are trying to embarrass them. It's pretty sad.

I have a feeling that in Japan ignorance of math would not be a source of pride, for cultural reasons.

[Uncayimmy]

1) People don't like to be wrong. When it comes to math, there's only one right answer. Well, except for when there can be multiple solutions, but that's not the kinda math we're talking about.

2) Unless you do it every day, the confidence that you're doing it right goes way down. See #1.

3) Lots of people never really "get" math. They learn to follow some rules, but that doesn't mean they understand why they "carry" numbers to the next column.

Most importantly, there's no reason to suppose that all humans have an equal aptitude for math. I suppose I have a natural ability because I find it easy to do basic calculations in my head (sometimes they happen automatically). At the same time I can't draw worth a ****. It's not because I lack the fine motor skills - I'm a musician, and I'm quite handy doing delicate work like soldering. Drawing freehand is just difficult. By contrast I enjoy photography and working with elements already created.

I suppose that asking some people to divide 185 by 5 invokes reaction similar to what I would feel if asked to draw a picture of a dog sniffing a flower.

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.

[NewtonTrino]

I could care less whether or not people understand math or not. What pisses me off is the anti-intellectualism inherent in the whole idea that people would be intimidated by having to learn something new. I don't care what it is, if I need to learn it for some reason then I'll put in the sweat-work needed and learn what needs learnin'. I don't care who you are you should be able to pick up any of the basic skills needed in a variety of areas if you put some darn work into it. I've consistently found that hours doing something = getting better at it. Not exactly a big secret (BTW just sitting around and wishing is a good way to NOT accomplish anything).


Now does someone want to teach me convolution?

[Uncayimmy]

I could care less whether or not people understand math or not. What pisses me off is the anti-intellectualism inherent in the whole idea that people would be intimidated by having to learn something new. I don't care what it is, if I need to learn it for some reason then I'll put in the sweat-work needed and learn what needs learnin'. I don't care who you are you should be able to pick up any of the basic skills needed in a variety of areas if you put some darn work into it. I've consistently found that hours doing something = getting better at it. Not exactly a big secret (BTW just sitting around and wishing is a good way to NOT accomplish anything).

You're presuming that people "have" to learn it for some reason and don't. Quite frankly, I find that idea absurd. I have not encountered very many accountants who balk at doing addition and subtraction. I don't find very many statisticians going "la la la" when somebody explains how to do standard deviation. Hell, carpenters add and subtract fractions every day, but it's not often they need to calculate the total amount of the payments paid on their truck.

What I see is that sometimes in our daily lives we encounter the "need" to do something out of the ordinary. Math happens to be something that pops up more frequently than others. When I need to make an "Garage Sale" sign to hang on a telephone pole, I do it on the computer because I couldn't draw and color the letters freehand very well. Are you pissed off at me for not spending my evenings with "Drawing Freehand for Dummies" and a sketch pad?

I know I'm different. When I see two numbers, I almost always calculate the difference. If I see the year a movie was made, I automatically calculate how old I was when it came out. If I hear somebody say, "What's 12 times 13?" I just do it in my head even if I'm not asked. When I fill my gas tank, I always look at my trip odometer and calculate my MPG. Yet in my daily life I don't need to do any of that.

A friend of mine had to take remedial math in college. He was extremely bright. If you engaged him in a debate on politics, world history or current events, he'd smoke you. It was a blow to his ego that even basic math was such a struggle for him. He received plenty of ridicule about it.

Meanwhile, I know some very scientific types and plenty of software developers. They work with all sorts of abstract concepts every single day. If you try to engage them in a debate on some topic - any topic, the words escape them. They can't explain the things they understand.

But nobody seems to get all snooty about it. Artists accept that not everyone can draw. Musicians accept that some people can't even clap to the beat. Writers accept that not everyone can express themselves with words. They all accept that some people believe that even an extensive amount of effort is just not worth the paltry results.

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 (http://www.drawfluffy.com/images/cat-face.jpg). In the world of drawing, it's basic addition. Would you look down on anyone who said, "No way. I suck at drawing."

[NewtonTrino]

Again, it's not about the math. It's about the attitude. If someone truly busts ass and still doesn't get it then I'll pity them a bit but I'm not going to be mad at them. I just want to see people put the effort in. This is just because I've learned that no matter how bad you are at something putting effort in almost always pays off. If your friend really truly was unable to get it, good for them, at least they tried! I just don't like the idea that I would ask someone to do something and they would consider it "too hard" for them to the point where they were intimidated and didn't even want to try learning it.

I'm not talking about ridiculous hard core programming stuff here, but basic tasks that anyone should be able to learn if they put in the mental sweat.

Again, it's the attitude not the results that I'm looking for (the result, as I said above, tend to take of themselves when you put the work in). This is true for learning math, learning to read, learning an instrument or pretty much anything else.

[MattusMaximus]

Math is hard. Math requires work. Many people don't like the idea of getting an answer wrong. Many people need to be less lazy and work harder in school.

Can you tell I just got done grading a bunch of physics labs?

[Uncayimmy]

Math is hard. Math requires work. Many people don't like the idea of getting an answer wrong. Many people need to be less lazy and work harder in school.

Can you tell I just got done grading a bunch of physics labs?

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.

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.

[rjh01]

Maths is a skill (actually several different skills) that is different from other skills. So it is possible to be very good at one skill (like being able to repair something) and yet hopeless at another like maths.

[Aitch]

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.


What/ Nobody came up with a (very long) Select/Case statement? Amateurs! ;)

[arthwollipot]

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.I completely failed to follow your thoughts there. I can usually do simple arithmetic in my head - this does not extend to most division.

It is only quite recently that I internalised the idea that 57 + 48 = (50 + 40) + (7 + 8). Let me tell you that realisation made mental arithmetic a whole lot easier! I never picked up the similar trick for division though.

Give me a pen and paper and I'll calculate a long division in seconds. I just can't do it in my head. I never picked up the knack.

[martu]

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.

What do you find intimidating about it? You only have to hold a one number in your head to calculate this the 'traditional' way, divide 7 into 17 remember the answer and carry the remainder. No divide again and combine. Don't you picture it in your head like you were writing it down? That's how I do it anyway.

[Cuddles]

I suspect part of it is that it's become socially acceptable to be terrible at math

I think this is pretty much it. There's no point trying to come up with excuses about how some people think differently from others and that they may be good at other things. UncaYimmy's point about drawing is almost right, except that things like basic addition are the mathematical equivalent of drawing a stick man. I don't expect everyone to be able to draw a lifelike dog, but I really don't think expecting them to be able to draw a circle with a couple of lines on is too much.

Even more important is that you can easily go your whole life without ever needing to draw anything, but everyone uses numbers practically every day. If you ever buy things, drive, do your taxes, cook, watch the news, there's numbers everywhere. And a lot of the time it's quite important to be doing things with them yourself, so that you know you're not being short changed or going to be investigated by Inland Revenue, or whatever.

It's not snobbery to expect functioning adults to be able to do maths that most 6 year olds find easy, especially when they're likely to be using it throughout their whole life. And it's certainly not snobbery to find it utterly ridiculous that they're actually proud of their ignorance.

[MattusMaximus]

I have a B.S. in physics with a math minor and an M.S. in physics. I have taught math, physical science, physics, and astronomy for 10+ years at both the high-school and college level... and I still need to use paper and pencil when doing long division.

That's why our teachers taught us how to write this stuff down :)

[Just thinking]

One other thing (not 100% of the reason, but perhaps somewhat to the point), mathematics requires logical thought ... there's no getting around it. Even though many mathematical problems can be approached differently, each requires a logical method to solve them. Critical thinking, to a degree. And I believe most of us are experience learners, not think-it-through-carefully learners. My mother was head of the mortgage department in a bank for over 30 years, she could balance a checkbook with half her brain tied behind her back. But ask her how many degrees in a triangle, or try to explain why 2x + 2x = 4x ... and she just couldn't get it. I also once worked with an electrician who just couldn't understand the Metric System. I then explained to him that 1) it's much easier to work with than the clumsy English system, and 2) everything he used with his work was metric (amps, watts, etc.). Go figure.

[Tim Thompson]

A couple of ideas come to mind from my own experience.

First, I think that the natural state for the human mind is one of intellectual laziness. People don't like to think and will deliberately avoid it if possible. As an example, I have offered over the years to teach any number of people how to play chess beyond the level of making random moves. The standard response is something in the way of "oh, no, you have to think to do that". It is quite common to use the need to think as the excuse to not even try.

Second is the attitude problem already noted by others. It is not just socially acceptable, but really socially preferable to be ignorant of math, science, or anything else that requires thinking. My wife has taught math & science in middle school, and now teaches high school. It is the norm for students who are good at math & science too be ridiculed openly for it. Hence, I think this attitude is something learned, not something that comes with us for being human.

It may well be that the attitude and the laziness are related. If we change the way schooling is done from the earliest years on, to eliminate the attitude that prefers ignorance of math & science, then we may well eliminate the laziness as well.

But brains are complicated things and it may not be so simple. Witness the ability of so many people to hold powerful personal convictions about topics in science (string theory, for instance) about which they actually know next too nothing. The strength of conviction does not come from knowledge, so where does it come from? Somewhere hidden in the brain?

[Just thinking]

But brains are complicated things and it may not be so simple. Witness the ability of so many people to hold powerful personal convictions about topics in science (string theory, for instance) about which they actually know next too nothing. The strength of conviction does not come from knowledge, so where does it come from? Somewhere hidden in the brain?

Established paradigms are next to impossible to change.

Here's an experiment you might like to try, since both you and your wife are in education. Ask fellow educators (of almost any field) what is it that makes air go into a normal household vacuum cleaner ... in other words, how does it work, in very general terms. I'll bet you almost 100% will say that the somehow air gets sucked into it when in fact, there is no suction involved at all. The air inside is first PUSHED out of some volume by means of a compressor wheel creating a low pressure zone behind it. This in turn allows the higher pressure ambient air to again be PUSHED into the device, taking along with it as much nearby debris as it can. There is no pulling (suction), only pushing. See how many get that right.

[Ziggurat]

First, I think that the natural state for the human mind is one of intellectual laziness. People don't like to think and will deliberately avoid it if possible. As an example, I have offered over the years to teach any number of people how to play chess beyond the level of making random moves. The standard response is something in the way of "oh, no, you have to think to do that". It is quite common to use the need to think as the excuse to not even try.

The real reason they avoid it may be slightly different, though. The problem, I suspect, is that the enjoyment payoff from learning the activity and doing it well seems too far removed from the effort. That is, there's a perception that they will need to put in a LOT of effort before they get any enjoyment out of it. And if they aren't confident in their own intelligence, then they may also suspect that even after lessons they'll keep losing and won't enjoy the game. So the "you have to think" excuse may be exactly that: an excuse, and not the real reason.

[Ziggurat]

There is no pulling (suction), only pushing. See how many get that right.

That's a bad question to ask because of possible ambiguities about what suction means.

The basic science question I really like is where does most of the mass of a tree come from. It starts out as a seed and ends up as this huge chunk of wood, and all that mass had to come from somewhere. Common answers are the soil and water, but the real answer is that most of the mass comes from the air.

[Just thinking]

That's a bad question to ask because of possible ambiguities about what suction means.

Bottom line, though, is that nothing is pulled into the vacuum cleaner --- and it is that false paradigm that I think is commonly accepted.

[Darat]

Quite appropriate for this thread: http://news.bbc.co.uk/1/hi/magazine/8081043.stm

[Just thinking]

Nice link .... I got top marks and I use $$$$ instead of lbs.

:D

[Uncayimmy]

I completely failed to follow your thoughts there. I can usually do simple arithmetic in my head - this does not extend to most division.
I'm not sure I can explain my mental process. It's really as if my brain subconsciously "sees" an easy method based on things I already know. In this case I "automatically" know that 7*20 is less than 175 and that 7*30 is more than 175. So I know right off the bat that the answer is 20-something. So I do the first part (7*20), then do the rest (175-140=35, so what is 35/7?). I solve a few simple problems to get my answer. As I think about it, it really is like long division.

It is only quite recently that I internalised the idea that 57 + 48 = (50 + 40) + (7 + 8). Let me tell you that realisation made mental arithmetic a whole lot easier! I never picked up the similar trick for division though.
There's nothing wrong with what you do, I just do that problem differently. I use two steps. 57 + 40=97, then 97 + 8=105. If I did it the pencil and paper way in my head, it would be pain in the ass (see below).

My question, though, demonstrated my point. People have different mental processes and perhaps what you could call emotional responses to those processes. In your example, my method comes automatically and with ease. It feels good/right. Your method feels "contrived" to me, and it "bothers" me that it takes three steps instead of two. That's not a dig on you or anyone else who does it that way because it's really a great way of doing it.


What do you find intimidating about it? You only have to hold a one number in your head to calculate this the 'traditional' way, divide 7 into 17 remember the answer and carry the remainder. No divide again and combine. Don't you picture it in your head like you were writing it down? That's how I do it anyway.
That is an excellent question. No, I do not picture anything in my head at all. Zero. Nada. My ex-wife was a visual person as well as a school teacher. We had many discussions on this subject when we were much younger.

It was a startling realization for me that people actually pictured things in their head like that. Likewise she was blown away that people did not visualize things like she did. She did the math much like you describe. She couldn't fathom how I could do it without "seeing" anything.

Each year in the classroom she would discuss our dog, Buck, a black Labrador retriever. She would ask the kids by a show of hands how many automatically created a mental picture of a black Lab. It was always about half the class. The other half had no mental image unless they deliberately took the effort to create one. For them it was more like the brain automatically recalled facts about black Labs. That's how it works for me.

Even as I sit here and try to picture the long division in my head, I find it very difficult to create and hold those images. I can do it, but it takes me several times as long as my "natural" method. And I have to shut my eyes.

This is why I have empathy for people who find the process intimidating.

[casebro]

My average math scores. but exemplary language scores, and the fact that i can't 'music', makes me a believer in the guy's theory of different "intellects". Book named "The Seven Intellects" or some such. He posits that different parts of the brain are used for different intellectual functions. His theory is supposedly discredited, but not to me. Maybe they discredited it by using a mathematical system? ;)

I scored a 4 on the BBC test, but without pencil or calculator. Nor Googling pounds and euros exchange rates. Neither English monetry values. Got the chord question right, but only because the drawing was to scale. A Man has got to know how to live with his limitations.

[Uncayimmy]

Second is the attitude problem already noted by others. It is not just socially acceptable, but really socially preferable to be ignorant of math, science, or anything else that requires thinking. My wife has taught math & science in middle school, and now teaches high school. It is the norm for students who are good at math & science too be ridiculed openly for it. Hence, I think this attitude is something learned, not something that comes with us for being human.
That is such an interesting phenomenon. Here's my armchair analysis:

People, especially kids and teens, want to be accepted. People have a natural and negative reaction to those that are different. If you're outside of the meat of the bell curve, you're different. Thus, you're not accepted. Pointing this out brings the rest closer together.

If you're going to be outside the bell curve, it had better be for something admirable such as sports. It's admirable to be gifted athletically, which probably has roots in evolution (mate with the strong). Same goes for cheerleaders - mate with the attractive and athletic.

The culture in the USA at least doesn't admire intelligence the way we admire athleticism. We admire money, and we all know that intelligence and money don't always correlate. Some of the most financially successful people from my high school were not the sharpest tools in the shed. Our valedictorian is a scientist for NOAA (yawn). Meanwhile the handsome and lovable but not-so-bright "Kevin" is a highly successful real estate agent with a hot wife and gorgeous kids.

So, any ideas for making intelligence and education a goal worthy of admiration?

[casebro]

So, any ideas for making intelligence and education a goal worthy of admiration?

Use a not-high-school judgment system?

I guess if you are going to start breeding right out of high school, your judgment may be valid. But I'll bet other NOAA scientist are in love with your valedictorian.

Personally, I'm not concerned with "the meat of the bell curve". I'm not in advertising.

[Uncayimmy]

Use a not-high-school judgment system?

I guess if you are going to start breeding right out of high school, your judgment may be valid. But I'll bet other NOAA scientist are in love with your valedictorian.
My judgment is valid whether you breed or not because I am not using it to justify anything. I am giving an armchair explanation for something we all observe. Many of us here value intellectual pursuits and quite frankly, look down on people who do not. We call them intellectually lazy. What we need to do is understand why some people don't value it the way we do and look for a way to change their value system or at least accept it.

BTW, I dated that valedictorian for a while, not that her love life was essential at all to my point.

Personally, I'm not concerned with "the meat of the bell curve". I'm not in advertising.
That comes across as intellectual snobbery. For the longest time it was thought that women were not equal to men intellectually. The culture had to change for it to be acceptable for a woman to become a lawyer, doctor, or crane operator as well as or instead of a mother. It took time and effort and a lot of what you refer to as "advertising" to get to make it socially acceptable.

My question was a sincere one. How do you change a culture to value intellectual pursuits considering what is currently valued socially?

[I Ratant]

I do all kinds of things with numbers all the time.
I'm an engineer, I live with and by numbers.
There's so many ways to look at them and play with them.
What bothers me more than innumeracy, is illiteracy!
This is a solely visual media, and accuracy in language is vital to getting one's ideas across.
Having to interpret what passes for communications nowadays on many forums is quite off-putting!
(And a surprising number of engineers are barely literate!)

[shadron]

My question was a sincere one. How do you change a culture to value intellectual pursuits considering what is currently valued socially?
If we knew how to do that, atheism probably wouldn't be the most hated class in America either. Tough question.

[Towlie]

Let me give you an example:

175/7=?

How do you approach it?I got the answer immediately when I recognized that seven quarters are worth $1.75.

[dahduh]

Maybe people don't like maths because it is so easy to be proven to be unequivocably wrong.

[Uncayimmy]

I got the answer immediately when I recognized that seven quarters are worth $1.75.
Wow. That never entered my mind. It's amazing how differently people approach the same problem.

[Towlie]

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 = ?

[borealys]

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 (http://www.drawfluffy.com/images/cat-face.jpg). In the world of drawing, it's basic addition. Would you look down on anyone who said, "No way. I suck at drawing."

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.

[rjh01]

Quite appropriate for this thread: http://news.bbc.co.uk/1/hi/magazine/8081043.stm
I got 6 / 7 right. I got the one with the circle and lines wrong. I started off without a calculator, but when I got to the one about the largest area I got the calculator out. The first few problems I could see short cuts in the arithmetic.

[Just thinking]

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.

[Ziggurat]

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 = ?

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.

[Uncayimmy]

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.

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]

Cute.

You know what really hurts ... the fact that I used to know that trick, and used it often. And have since over time totally forgotten about it.

:(

[Just thinking]

By my count that's at least four different ways of solving the same rather simple problem.

Amazing how the mind can work.

(BTW ... nice shot of EvZ in your avitar.)

[arthwollipot]

By my count that's at least four different ways of solving the same rather simple problem.Not a single one of which occurred to me. I'd have used repeated doubling and taken four times as long.

[Uncayimmy]

Amazing how the mind can work.

(BTW ... nice shot of EvZ in your avitar.)

<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>

[Modified]

Wow. That never entered my mind. It's amazing how differently people approach the same problem.

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.

[Modified]

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).

Tangrams

[arthwollipot]

I suppose this might not work in countries that don't use coins with a value of 25.You suppose correctly.

[Uncayimmy]

Tangrams

Exactly! Thanks!
For those who want to play on-line:
http://tangrams.ca/inner/play.htm

[nathan]

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.

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.

[arthwollipot]

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.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.

[SezMe]

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.

[Cuddles]

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.

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.

[mazyloron]

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.

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.

[mazyloron]

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.

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.

[mazyloron]

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.
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.

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).

What/ Nobody came up with a (very long) Select/Case statement? Amateurs! ;)

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.

[Molinaro]

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.

I do much the same for things like 63 x 91

= (60+3) x (90+1)
= (6x9x100) + (60) + (3x90) + 3
= 5400+60+270+3
= 5733

[Uncayimmy]

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).
When are you told to use the fewest lines of code?

[I Ratant]

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.
.
Yes.
I encounter many situations where combinations such as the quarters and 1.75 have been solved so frequently that similar problems are easily solved, while more complicated situations can require some fingering out.
I even played around with doing long division a while ago, as I hadn't done any in years relying on the calculator.

[I Ratant]

I do much the same for things like 63 x 91

= (60+3) x (90+1)
= (6x9x100) + (60) + (3x90) + 3
= 5400+60+270+3
= 5733
.
It would be interesting watching that being done in 1520! :)

[mazyloron]

When are you told to use the fewest lines of code?

My former company was weird. Most of us learned to code on the job, so sometimes things like that were requests from management (who also learned coding and such on the job and knew little about how an IT company should really be run). And, given that a loop that simple wouldn't take any time at all to run, so there's no worry about bogging down the system. So, yeah...coding the lazy way using five lines instead of, say 30 or so doing it the right way was actually something that was quite common.

[Ladewig]

Established paradigms are next to impossible to change.

Here's an experiment you might like to try, since both you and your wife are in education. Ask fellow educators (of almost any field) what is it that makes air go into a normal household vacuum cleaner ... in other words, how does it work, in very general terms. I'll bet you almost 100% will say that the somehow air gets sucked into it when in fact, there is no suction involved at all. The air inside is first PUSHED out of some volume by means of a compressor wheel creating a low pressure zone behind it. This in turn allows the higher pressure ambient air to again be PUSHED into the device, taking along with it as much nearby debris as it can. There is no pulling (suction), only pushing. See how many get that right.

Can you give me a reliable citation for that? When I use the hose attachment, there is definitely sucking and no pushing. Perhaps I am misunderstanding your description.

[I Ratant]

It's just semantics.
Air moves from high pressure to low pressure.
Something has to create the low pressure.

[mazyloron]

Can you give me a reliable citation for that? When I use the hose attachment, there is definitely sucking and no pushing. Perhaps I am misunderstanding your description.

I'm guessing that this is like the "there is no such thing as cold" semantics argument. It's a perception vs. physics thing.

Technically, the air going into the vacuum is not being sucked in, but pushed in by the higher pressure of the air in the room around the vacuum cleaner - it's trying to equalize pressure, and doing so through a small opening causes a big rush of air. Debris in the vicinity gets pushed along for the ride.

[Ladewig]

Thanks for the responses.

[Uncayimmy]

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.

If you think that, then I guess I am failing to make my point. I saw a couple of examples of "shortcuts" that I know to be occasionally taught. My ex-wife showed me a bunch of "shortcuts" she learned in a college course she took on teaching math. They were new to her as well. She only taught a few when she was a teacher. Other examples in this thread were not shortcuts but rather examples of different mental processes for attacking the problem. These are not taught - it's just how people think.

My point is that natural aptitude in math runs the gamut from those who will never grasp basic math no matter what to the Human Computer Guy (Danny T). Some people can visually do math the "long way" in their heads; others cannot. Some learn shortcuts. Some of us attack problems in our own ways that are efficient and comfortable for us.

I believe that answers the OP, which asked why "so many folks, including highly skilled individuals in their fields, fail so miserably." There's no reason to expect everyone to be good or even comfortable with math just as there is no reason to expect everyone to be able to draw a cat's face, which is literally child's play - hang out in art class for first graders to see what I mean.

I believe that many with a natural aptitude for math don't realize that they even have such an aptitude. They think it's like that for everybody. It's not. And while you can teach certain rote methods, for many people those rote methods are just that. They never "get it" so they are never comfortable with it.

Consider this example given earlier:
47 X 53 = ?
92 X 88 = ?
76 X 84 = ?

I looked at that for a few seconds and quickly realized the "shortcut" that was implied. I had never heard of it before. Anybody could be taught to recognize such a problem and to use the shortcut, but I argue that if you don't realize it yourself without being told, you'll never "own" it.

People without the right aptitude have to look at each problem and run through a mental checklist of available shortcuts they have been taught. It's like a toddler using a shape shorter - the child will try the shape in each hole until it fits. A developmental milestone is met when the child recognizes the shape in his hand and associates it with the corresponding hole. Some people never make the connections that come naturally to others.

Everyone's aptitude has its limits. I remember in junior high school geometry we did proofs. I found them incredibly easy and enjoyable. Other very bright students were stumped, which I found puzzling. I also remember learning about parabolas and such. It wasn't too long before I could see in my head what it would look like without having to make the graph. As I recall, very few of us could do that. Even students who got better grades than me (I was lazy and didn't check my work) couldn't do it and commented that it was "weird" that I did.

My education and career path never required calculus, but my ex-wife's did. I remember helping her with it. I never actually did any of the math, but I could I explain to her in principle what was happening and what needed to be done. She got good grades, but I don't think she ever "owned" it.

In fact she was one of those people who hated being asked to do math in her head. She didn't really like doing it on paper. She worked hard in school and graduated college with some level of cum laude that I forget now. She was one of a handful of teachers offered an "open contract" before graduation, which in effect means, "We want you to work for us. Sign this and we'll find a spot." She was a successful student who put in lots of effort.

And yet I think some would consider her a "math averse" type of person because she would balk at having to do simple math in her head. Meanwhile, someone like myself with much less training in math and who really put very little effort into it would be considered the opposite.

If you want to "judge" us on our dedication, she would win hands down. Only nobody ever judges me because it comes easy to me. Those who judge her would come to the wrong conclusions unless they knew her like I did.

[Uncayimmy]

I'm guessing that this is like the "there is no such thing as cold" semantics argument. It's a perception vs. physics thing.

Technically, the air going into the vacuum is not being sucked in, but pushed in by the higher pressure of the air in the room around the vacuum cleaner - it's trying to equalize pressure, and doing so through a small opening causes a big rush of air. Debris in the vicinity gets pushed along for the ride.

I would also point out that the fan inside is pushing air out - it's a blower after all. This is what creates the low pressure area, and the other explanations pick it up from there.

You can look at it another way. Suppose you have an ordinary room fan with a protective wire cover. You put a piece of paper on the back. What's holding it in place? It's the air behind the paper pushing it against the fan cage. The air on the other side of the paper isn't applying some force to pull the paper.

Another visual is a rubber suction up. Push one against the wall on the inside of a sealed box. What holds it in place? Is the suction "pulling" or is the air in the box pushing? To answer that question, "suck" all the air out of the box. What happens?

[mazyloron]

I would also point out that the fan inside is pushing air out - it's a blower after all. This is what creates the low pressure area, and the other explanations pick it up from there.

You can look at it another way. Suppose you have an ordinary room fan with a protective wire cover. You put a piece of paper on the back. What's holding it in place? It's the air behind the paper pushing it against the fan cage. The air on the other side of the paper isn't applying some force to pull the paper.

Another visual is a rubber suction up. Push one against the wall on the inside of a sealed box. What holds it in place? Is the suction "pulling" or is the air in the box pushing? To answer that question, "suck" all the air out of the box. What happens?

Exactly. It's physics vs. perception, with a touch of semantics thrown in. In common terms and intuitive observation, one thing appears to be happening, whereas the actual driving forces behind the phenomena are doing the exact opposite. Nothing's sucking air into the vacuum, it's being pushed in. The paper isn't being sucked against the fan, it's being pushed against it. The suction cup isn't being pulled against the wall, external air pressure pins it there. And hypothermia isn't being too cold, it's being not warm enough.

Even so, the end result tends to be the same, whether using the colloquial or technical. Not always, though. Which is why it does pay to understand what's really causing these things, even if you don't think about them like that every day.

[Uncayimmy]

Even so, the end result tends to be the same, whether using the colloquial or technical. Not always, though. Which is why it does pay to understand what's really causing these things, even if you don't think about them like that every day.
I hate to extend this derail too much further, but I just want to say that the best part of pointing out that my Hoover doesn't suck is that it does get people to think about it. If somebody accepted everything that has been explained but said, "Right. That's what sucking is," I would be fine with it. They could call it hooveristics for all I care.

[SezMe]

If you think that, then I guess I am failing to make my point.

No, I think you have been clear. I suspect our differences arise out of simple definition of "math". For example, consider this snippet.

I believe that many with a natural aptitude for math don't realize that they even have such an aptitude. They think it's like that for everybody. It's not. And while you can teach certain rote methods, for many people those rote methods are just that. They never "get it" so they are never comfortable with it.

Consider this example given earlier:
47 X 53 = ?
92 X 88 = ?
76 X 84 = ?

You used the word "math" then gave these examples. But I would NOT call those examples of math but examples of arithmetic.

That minor quibble out of the way, I agree with your point that there is a wide range of math aptitude out there and some people might be pretty good at it but for social stigma or fear of being wrong.


Finally, I think the real interesting part of the OP is the "pride of ignorance", so to speak, that many of us have seen around us. It's a real shame.

[Uncayimmy]

You used the word "math" then gave these examples. But I would NOT call those examples of math but examples of arithmetic.
Fair enough.

Finally, I think the real interesting part of the OP is the "pride of ignorance", so to speak, that many of us have seen around us. It's a real shame.
It *is* a shame. I also think it's also a defense mechanism to some degree with many people. Just because there's no shame in not having an aptitude for something is no reason to take pride in the fact. But then again, boys don't make passes at girls who wear glasses.

[Mark6]

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 (http://www.drawfluffy.com/images/cat-face.jpg). In the world of drawing, it's basic addition. Would you look down on anyone who said, "No way. I suck at drawing."
The difference is, nobody is ever proud of sucking at drawing.

[Mark6]

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.
You teach that very easily -- in fact it is called "binary search" and is part of every first year Computer Science course. I taught it by telling my students that I can tell their Social Security number with 30 yes/no questions. "Is it bigger than 500,000,000?" That cuts the range in half. Then I keep halving it.

I bet every programmer who DID NOT come up with last solution was self-taught.

[Edited]On the second thought, if I had tp dp this particular problem -- find unknown number amount 100, -- I would use solution #1 because it takes fewest lines to write, and savings in computational time are infinitesimal. But if I had to write a program which finds one number among a billion, or one out of 100 a billion times, I would definitely use solution #4. Knowing when to use wasteful but simple algorithms, and when to use complicated but efficient ones is also something taught in Computer Science. A lot.

[Uncayimmy]

You teach that very easily -- in fact it is called "binary search" and is part of every first year Computer Science course. I taught it by telling my students that I can tell their Social Security number with 30 yes/no questions. "Is it bigger than 500,000,000?" That cuts the range in half. Then I keep halving it.

I bet every programmer who DID NOT come up with last solution was self-taught.
By definition, if you taught them, they did not come up with it. You did. I was self-taught, and I came up with that.

[Edited]On the second thought, if I had tp dp this particular problem -- find unknown number amount 100, -- I would use solution #1 because it takes fewest lines to write, and savings in computational time are infinitesimal. But if I had to write a program which finds one number among a billion, or one out of 100 a billion times, I would definitely use solution #4. Knowing when to use wasteful but simple algorithms, and when to use complicated but efficient ones is also something taught in Computer Science. A lot.
If you're gonna play the "real world" game then you would use solution #5: output X. There's no need to do any processing because you already have the value being passed in. It was an exercise in efficient code. How anyone could think otherwise is beyond me.

I hate to derail this thread, but the attitude you describe is the reason so much software today runs slower than it should. We have a crop of programmers who look at each little piece of inefficient code as not being a big deal. So what happens when somebody uses that horribly inefficient function inside of another loop? And the next guy uses that loop inside another loop? And then users use that program to process millions of records instead of a few dozen like during testing?

Typing is the least expensive thing a programmer does. When a programmer knows of multiple solutions and decides to save a few minutes of typing by choosing an inefficient method, he wouldn't be working for me very long. I have investigated far too many "why is this so slow?" areas of programs and said, "what lazy idiot wrote this?"

The time it takes to type out the code is really the thing that should be ignored, not the processing requirements. Of course, this is not to say that you spend a full day trying to shave a few clock cycles if the payoff is not worth it. There's always a cost-benefit analysis, but a few minutes of typing is not a factor. I can't recall ever having two options where the number of lines of code was so significant that it would set a project behind schedule.

By contrast I have seen countless routines rewritten because they were too slow due to "save some typing" programmers who didn't think about the big picture and all the possible future ramifications. This is expensive to the company. First, you have clients (usually multiple ones) complaining to service reps. Dissatisfied clients don't give referrals and sometimes speak out against you or switch vendors. The problem moves up the chain. Somebody ends up having to root around in the code to find the problem. So then it gets rewritten. That change has to be documented. It needs to go through QA again.

Just one little blip like that can cost literally hours if not days of company time (and untold amounts of revenue). It's just not worth it.

For example, one of my peeves is programmers using SELECT * to get all the fields from a table instead of just the one(s) they need. The excuse is that they don't want to type out the field names, yet tools exist to do it for you. If not, it only takes a minute type.

Meanwhile, if you have every programmer doing SELECT * for every hit on the database, it will slow things down. And when somebody modifies that table to include something like a memo field, which in many DBMS is stored in a different physical location on the disk, things slow down even more. It all adds up.

Okay, my rant is done.

[mazyloron]

I hate to extend this derail too much further, but I just want to say that the best part of pointing out that my Hoover doesn't suck is that it does get people to think about it. If somebody accepted everything that has been explained but said, "Right. That's what sucking is," I would be fine with it. They could call it hooveristics for all I care.

Agreed. Getting people to think about it is the key, really.

And I don't think it's too much of a derail, as it's very closely related to the point made in the OP, though yes, it's not exactly what was mentioned.

:)

[mazyloron]

By definition, if you taught them, they did not come up with it. You did. I was self-taught, and I came up with that.


If you're gonna play the "real world" game then you would use solution #5: output X. There's no need to do any processing because you already have the value being passed in. It was an exercise in efficient code. How anyone could think otherwise is beyond me.

I hate to derail this thread, but the attitude you describe is the reason so much software today runs slower than it should. We have a crop of programmers who look at each little piece of inefficient code as not being a big deal. So what happens when somebody uses that horribly inefficient function inside of another loop? And the next guy uses that loop inside another loop? And then users use that program to process millions of records instead of a few dozen like during testing?

Typing is the least expensive thing a programmer does. When a programmer knows of multiple solutions and decides to save a few minutes of typing by choosing an inefficient method, he wouldn't be working for me very long. I have investigated far too many "why is this so slow?" areas of programs and said, "what lazy idiot wrote this?"

The time it takes to type out the code is really the thing that should be ignored, not the processing requirements. Of course, this is not to say that you spend a full day trying to shave a few clock cycles if the payoff is not worth it. There's always a cost-benefit analysis, but a few minutes of typing is not a factor. I can't recall ever having two options where the number of lines of code was so significant that it would set a project behind schedule.

By contrast I have seen countless routines rewritten because they were too slow due to "save some typing" programmers who didn't think about the big picture and all the possible future ramifications. This is expensive to the company. First, you have clients (usually multiple ones) complaining to service reps. Dissatisfied clients don't give referrals and sometimes speak out against you or switch vendors. The problem moves up the chain. Somebody ends up having to root around in the code to find the problem. So then it gets rewritten. That change has to be documented. It needs to go through QA again.

Just one little blip like that can cost literally hours if not days of company time (and untold amounts of revenue). It's just not worth it.

For example, one of my peeves is programmers using SELECT * to get all the fields from a table instead of just the one(s) they need. The excuse is that they don't want to type out the field names, yet tools exist to do it for you. If not, it only takes a minute type.

Meanwhile, if you have every programmer doing SELECT * for every hit on the database, it will slow things down. And when somebody modifies that table to include something like a memo field, which in many DBMS is stored in a different physical location on the disk, things slow down even more. It all adds up.

Okay, my rant is done.

See, this is the same thing I was referencing when I said I'd choose 1 or 4 depending on what I was asked to do. My old company was full of managers who didn't think like this, and when this was explained to them (by us self-taught programmers no less), the typical response was a combination of "yeah but computers are faster now so that doesn't matter" and "just get it done quickly, I don't care." Which of course left us with not enough time to do it the right way in many situations. And we were often editing code already full of the "wrong way" - which doesn't excuse doing it the wrong way again, but the software was already so clunky and outdated as to not matter anyway.

The funny part? (OK, funny to only me.) Now I work for another company who's a client of my old company. So, that nonsense with the inefficient coding isn't flying with me anymore. I know what's wrong with the software we've bought from them, I know how it can be better, I know what it can do that it's not doing, and I know how much we're overpaying for it...

There's another reason for you to code the right way...it can come back to bite ya in more ways than just inefficiency.

OK...now that's enough derailing from me. :)

To sort of bring it back to the thread topic: these things I tried to point out to management were things I picked up on my own, or learned from coworkers who knew what they were doing. My managers had the same opportunities to be exposed to this information as I did, and yet they couldn't understand why it was important, and didn't want to listen when it was explained to them; they knew enough and didn't need to listen to us programmers whine about unimportant stuff like this. And so they allowed the software, and thus the company, to suffer for it.

That's a halfway decent real-world example of why the willfully-ignorant mindset can be a very bad thing.

[Modified]

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).

I once gave a cashier a 50 and she gave me change for a twenty. She insisted I give her the change back so she could rescind the transaction and start over. I said "Why don't you just give me thirty dollars more?" and got a blank stare.

[Towlie]

I once gave a cashier a 50 and she gave me change for a twenty. She insisted I give her the change back so she could rescind the transaction and start over. I said "Why don't you just give me thirty dollars more?" and got a blank stare.Nowadays cashiers let their terminals figure everything out for them. I once ordered a sandwich, fries, and a drink at McDonalds. The clerk clumsily punched the order in and said "that'll be $54.95" without even blinking.

[Amapola]

The difference is, nobody is ever proud of sucking at drawing.

They are, actually... I can't tell you how many times someone has said to me, "I can't even draw a straight line!" (pronounced with smug satisfaction). (And you thought drawing a cat face was easy!)

Well, I can draw. For evidence I offer this. (http://www.beautiful-horses.com/jewelry.htm) In high school I experienced the same things that have been talked about here - social awkwardness, not being "cool" etc.

Now, no question math is more applicable to daily life than the ability to draw. But I think this is more the way people treat an outlier (as has been mentioned before, someone not in the center of the bell curve) than math particularly being singled out. I think people like to feel part of a group. To change that, well, most would have to be good at whatever - math, drawing etc. Then that would be what people desired, because that would be the norm for the group. Right now, it is not the norm for most to be good at math.

I suck at math. I suck at basic arithmetic. And I have to use it in my work, constantly... therefore I have struggled my whole life with it, and forced myself to do it all the time. I still suck at it... I *always* check my answers with a calculator when I am finished figuring it, because I make mistakes, and I can not afford to do that. If you are working out how many grams of gold need to be cast, and a gram of gold is going to cost you $X, you have to get it right. For me it never mattered if being good at math was cool or not cool, it's just a chore I have to get through - like washing dishes, or laundry.

[Uncayimmy]

They are, actually... I can't tell you how many times someone has said to me, "I can't even draw a straight line!" (pronounced with smug satisfaction). (And you thought drawing a cat face was easy!)
I have said that very line on many occasions. Never once have I felt smug doing so. It's a way of saying, "I find what you do amazing, especially considering that for me even something as simple as a straight line is difficult!"

[fuelair]

Math is hard. Math requires work. Many people don't like the idea of getting an answer wrong. Many people need to be less lazy and work harder in school.

Can you tell I just got done grading a bunch of physics labs?Just curious: any of them get the math answer(s) wrong because they didn't have the concept down?

[fuelair]

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.

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.For me, the long division in my head for 175/7 is just as easy and as quick- but I understand your point.

[Amapola]

I have said that very line on many occasions. Never once have I felt smug doing so. It's a way of saying, "I find what you do amazing, especially considering that for me even something as simple as a straight line is difficult!"

I went out to breakfast with some friends this morning and brought up the topic of this thread because I thought it was pretty interesting. They felt it had somewhat to do with the age of the person involved. Both my friends told me that they were bad at math, but had absolutely no pride in it. In fact they regretted it and had taken steps to improve because it made them feel a little guilty to be so bad at math. (This is similar to the way I feel about it.) So I think at least the three of us would say, although we are all bad at math, we are amazed and appreciative of those who are good at it.

My friends felt however that kids in high school don't have this same type of attitude. They work with the local 4-H kids, and one of them teaches riding lessons to children in the summer and skiing to kids in the winter. Their feeling was that "kids these days" actually *do* think it is not cool to be good at math. That may just apply to the kids they have worked with, in this area. I surmise from reading this thread the phenomenon is more wide-spread.

So what about that? Is age a factor? Is there some age - over 40, say, where you don't tend to find the idea of being bad at math cool?

[borealys]

I have said that very line on many occasions. Never once have I felt smug doing so. It's a way of saying, "I find what you do amazing, especially considering that for me even something as simple as a straight line is difficult!"

The same way I don't feel smug when I say that I suck at mental arithmetic. Most people I talk to get that, though a few haven't, and have gotten snotty with me. There's a bit of oversensitivity to it in some circles, a tendency to assume that when certain kinds of people (say, linguistics majors) claim to be bad at math, that they're proud of it, rather than merely stating a fact.

Of course, often when I say it, I'm usually not just stating a fact. What I'm really saying is "please don't ask me to do that calculation in my head ... it'll be painful for both of us, and chances are I'll get it wrong."

Similarly, I have a coworker who often comments in my presence that she can barely draw a straight line. What she really means most of the time is that she'd like me to draw whatever it is that needs drawing, because I can draw moderately well.

[borealys]

My friends felt however that kids in high school don't have this same type of attitude. They work with the local 4-H kids, and one of them teaches riding lessons to children in the summer and skiing to kids in the winter. Their feeling was that "kids these days" actually *do* think it is not cool to be good at math. That may just apply to the kids they have worked with, in this area. I surmise from reading this thread the phenomenon is more wide-spread.

So what about that? Is age a factor? Is there some age - over 40, say, where you don't tend to find the idea of being bad at math cool?

Kids who are good at school in general (maybe especially math, I don't know) are often bullied, and called names like "brainer" that, really, in a culture that valued intelligence, ought not to be insults at all.

I have it on good authority (from a friend of a friend who happened to have been the girl who bullied me the most mercilessly in grade school) that that sort of bullying is often done out of feeling threatened by kids who seem to be smarter than you.

There were times as a kid that I would be tempted to throw a math test, just to make myself less of a target. I didn't, partly because I didn't really believe it would help (though if K was telling the truth, it just might have), and partly because I just couldn't bring myself to give a wrong answer when I knew the right one.

It wasn't so much that being bad at math was cool as that being good at math was uncool. A fine distinction, but possibly an important one.

[Terry]

I hate to derail this thread, but the attitude you describe is the reason so much software today runs slower than it should. We have a crop of programmers who look at each little piece of inefficient code as not being a big deal.

Premature optimization is the root of all evil (or at least most of it) in programming.

If the final program is too slow, it should be profiled, and the problematic area fixed.

[Amapola]

Kids who are good at school in general (maybe especially math, I don't know) are often bullied, and called names like "brainer" that, really, in a culture that valued intelligence, ought not to be insults at all.

I have it on good authority (from a friend of a friend who happened to have been the girl who bullied me the most mercilessly in grade school) that that sort of bullying is often done out of feeling threatened by kids who seem to be smarter than you.

There were times as a kid that I would be tempted to throw a math test, just to make myself less of a target. I didn't, partly because I didn't really believe it would help (though if K was telling the truth, it just might have), and partly because I just couldn't bring myself to give a wrong answer when I knew the right one.

It wasn't so much that being bad at math was cool as that being good at math was uncool. A fine distinction, but possibly an important one.

Maybe along the lines of, "Don't listen to them, they're just jealous!" sort of thing? That makes sense, in a weird sort of way.

[Uncayimmy]

If the final program is too slow, it should be profiled, and the problematic area fixed.

Just to be clear, we were talking about typing time being a factor in the decision about which method to use. That's different than "premature optimization," something I acknowledged regarding getting the bang for your buck in time spent on optimization.

I will say this in response to what you wrote: If you're discovering and dealing with the problem in the final program, it's too late in the game. It's far more expensive at that point. There's a difference between being casual about wasting processing power and RAM versus being incredibly stingy with it. I've met far more of the former, and found the latter easier to manage.

[Uncayimmy]

My friends felt however that kids in high school don't have this same type of attitude. They work with the local 4-H kids, and one of them teaches riding lessons to children in the summer and skiing to kids in the winter. Their feeling was that "kids these days" actually *do* think it is not cool to be good at math. That may just apply to the kids they have worked with, in this area. I surmise from reading this thread the phenomenon is more wide-spread.

So what about that? Is age a factor? Is there some age - over 40, say, where you don't tend to find the idea of being bad at math cool?

Note: My reaction to the generational stuff almost always starts from the position that the current generation is not fundamentally much different from the prior but that neither generation realizes it. With that confession out of the way...

I'm 43. I believe art reflects life. The movies from when I was coming up seem to reflect intelligence as a less than desirable trait: The Breakfast Club, Fast Times at Ridgemont High, Revenge of the Nerds. The stereotype of the brainy nerd has been around as long as I can remember. In my school system I was part of the first wave of gifted and talented programs. Trust me, it was not something you bragged about or which brought you respect.

YMMV.

[Modified]

If the final program is too slow, it should be profiled, and the problematic area fixed.

Optimization in the small at the cost of clarity is rarely worth it, but a good portion of real world speed issues involve the choice of algorithms or high-level design problems. Not to mention that a ten second execution time for some process may be considered acceptable when it could take one millisecond.

[GreyICE]

Why is it that whenever it comes to mathematics (including basic arithmetic and/or geometry) so many folks, including highly skilled individuals in their fields, fail so miserably? Just watch any game show or listen to any radio talk show (or just your average Joe).
Theory: Game shows are, in fact, designed to be stressful and difficult. This is how you get Elephant/Moon answers - bad reactions to stress.

[arthwollipot]

You used the word "math" then gave these examples. But I would NOT call those examples of math but examples of arithmetic.Where does arithmetic end and math begin?

[GreyICE]

Where does arithmetic end and math begin?
Math doesn't have numbers. If it uses numbers, it's basically arithmetic.

[borealys]

Maybe along the lines of, "Don't listen to them, they're just jealous!" sort of thing? That makes sense, in a weird sort of way.

I heard that line so very, very many times when I was in grade school. I never once believed it. It was astonishing to learn that, in this one case at least, it was true.

But it does fit in with a general observation that, when you're a certain age, the coolest thing to be is just like everyone else. The worst bullying I experienced happened in the 10-13 age range, which happened to be the age where wearing the "right" clothing brand, listening to the "right" music, and watching the "right" TV shows was the most important (YMMV on the age group that's the worst for this. I found high school much better than middle school). Being different was uncool. Being different in a way that made you in any way "better" than anyone else was uncool and threatening. Some kids were able to compensate thanks to above-average social skills, and got to be both brainy and popular. The rest of us weren't so lucky.

For adults to think being bad at math is somehow "cool" is probably a sign that they've never really matured socially past that middle school worldview. Either that, or they're still intimidated by the brainers of the world, and are clinging to an old defense mechanism.

[drkitten]

Here's an experiment you might like to try, since both you and your wife are in education. Ask fellow educators (of almost any field) what is it that makes air go into a normal household vacuum cleaner ... in other words, how does it work, in very general terms. I'll bet you almost 100% will say that the somehow air gets sucked into it when in fact, there is no suction involved at all.

So what? You specifically asked for an answer "in very general terms" and now you're complaining when "very general terms" involves oversimplification?

See how many get that right.

Almost all of them will get it right. Applying an unfair grading standard will not change that.

Similarly, "sucking water up a straw" is a completely legitimate colloquialism, even though what actually happens is the water being pushed up by atmospheric pressure. Unless you are a hydraulic engineer and need to move water up more than about 30 feet, the difference isn't really that important.

[Uncayimmy]

Similarly, "sucking water up a straw" is a completely legitimate colloquialism, even though what actually happens is the water being pushed up by atmospheric pressure. Unless you are a hydraulic engineer and need to move water up more than about 30 feet, the difference isn't really that important.

A creative science teacher could take that one question and have it fill an hour of informative discussion. It can lead to discussions about barometers, suction cups, boiling points, why Hamburger Helper has a different directions for higher elevations, SCUBA diving, and countless other topics. It's not about fooling people; it's about getting them to think about wonder of the ordinary things around them.

[drkitten]

A creative science teacher could take that one question and have it fill an hour of informative discussion.

Absolutely.

Which is exactly why it should be left in science class. Because if I just want little Jimmy to stop making those annoying noises with his straw, I don't have an hour before the manager of Burger Hut comes over and throws us out.

There is a time and a place for illuminating science discussions. There is also a time and a place for sharp pointed comments just before I turn little Jimmy over my knee. And when Just thinking has explicitly told people that he's not talking about a situation involving informative discussions, it's really unfair for him to complain about Jimmy getting spanked....

[borealys]

Here's an experiment you might like to try, since both you and your wife are in education. Ask fellow educators (of almost any field) what is it that makes air go into a normal household vacuum cleaner ... in other words, how does it work, in very general terms. I'll bet you almost 100% will say that the somehow air gets sucked into it when in fact, there is no suction involved at all. The air inside is first PUSHED out of some volume by means of a compressor wheel creating a low pressure zone behind it. This in turn allows the higher pressure ambient air to again be PUSHED into the device, taking along with it as much nearby debris as it can. There is no pulling (suction), only pushing. See how many get that right.

I'm confused by this discussion. Isn't that what suction is?

To someone without a background in physics, it'd be easy to confuse exactly where the force is coming from, but it was my understanding that suction is a pushing force that most people misinterpret as a pulling force.

It's been a few years since OAC physics, so please correct me if I have that wrong...

[Uncayimmy]

Absolutely.

Which is exactly why it should be left in science class. Because if I just want little Jimmy to stop making those annoying noises with his straw, I don't have an hour before the manager of Burger Hut comes over and throws us out.

There is a time and a place for illuminating science discussions. There is also a time and a place for sharp pointed comments just before I turn little Jimmy over my knee. And when Just thinking has explicitly told people that he's not talking about a situation involving informative discussions, it's really unfair for him to complain about Jimmy getting spanked....

Where the heck did "little Jimmy" in Burger King come from? The whole discussion started with, "Ask fellow educators (of almost any field) what is it that makes air go into a normal household vacuum cleaner..."

A vacuum cleaner does use suction. While you can get all "colloquial" on us, the fact is that far too many people misunderstand suction to be an attractive force when it's not. So, if I use the right word but misunderstand what that word means, is that a good thing?

[drkitten]

Where the heck did "little Jimmy" in Burger King come from?

The fact that he specifically asked for an explanation "in very general terms," and specifically excluded the sort of technical accuracy you'd expect in a science classroom.

[Uncayimmy]

The fact that he specifically asked for an explanation "in very general terms," and specifically excluded the sort of technical accuracy you'd expect in a science classroom.

So you consider "pull" to be general and "push" to be specific and technical? I consider that nonsense. Furthermore, the question was asked of educators. Using general terms is great, but only so far as they are accurate. It's not a pulling force; it's a pushing force. The fact that it is a pushing force is related to countless other examples including Bernoulli. Any educator who refers to it as pulling is simply wrong. Any educator who thinks it "somehow gets sucked into it" isn't grasping a very basic concept.

You might think this pedantic. It's not. Suppose you have a stack of Oreo cookies and are asked to remove the one from the bottom. You pick up a ruler and lay it flat on the table so that the cookies are between you and the ruler. You then move the ruler and knock out the bottom cookie. I would completely agree that one could just as easily state that as either pushing or pulling. It's a "push" from the point of view of your hand but a "pull" from the point of view of your body. To argue one over the other would be picking nits.

It's a vacuum cleaner. Any accurate explanation must touch on the fact that a vacuum cleaner is trying to create a vacuum.

[Aitch]

Where the heck did "little Jimmy" in Burger King come from?

Well, some time ago, Jimmy's Mummy and Daddy had a special cuddle and nine months later the stork left baby Jimmy under a gooseberry bush for them to find him. :covereyes

Does that help? :cool:

[SezMe]

Math doesn't have numbers. If it uses numbers, it's basically arithmetic.
Good answer. Using equations is math. When it comes down to "plug and chug" it's arithmetic.

[Just thinking]

So what? You specifically asked for an answer "in very general terms" and now you're complaining when "very general terms" involves oversimplification?

Almost all of them will get it right. Applying an unfair grading standard will not change that.

Similarly, "sucking water up a straw" is a completely legitimate colloquialism, even though what actually happens is the water being pushed up by atmospheric pressure. Unless you are a hydraulic engineer and need to move water up more than about 30 feet, the difference isn't really that important.

Wow ... did you ever miss the target on this one. I was noting how difficult it can be to change or alter established paradigms, and that once thought of as being correct, they remain so pretty much throughout life, even by those whose profession it is to illuminate and inform others. The vacuum cleaner is a good example as it is thought of by many as being able to pull debris into it, when if fact there is no pulling being done by the device at all. If you took one to the moon and got it to operate on the surface, nothing would happen, except for the motor turning (a bit faster than here on Earth, as there is no atmosphere for the device to push out). Not one speck of lunar dust would get drawn in even though it would be working just fine. Besides, a vacuum cleaner is a device everyone can easily relate to as it's a common household item used frequently by everyone.

Absolutely.

Which is exactly why it should be left in science class. Because if I just want little Jimmy to stop making those annoying noises with his straw, I don't have an hour before the manager of Burger Hut comes over and throws us out.

There is a time and a place for illuminating science discussions. There is also a time and a place for sharp pointed comments just before I turn little Jimmy over my knee. And when Just thinking has explicitly told people that he's not talking about a situation involving informative discussions, it's really unfair for him to complain about Jimmy getting spanked....

And now you have me spanking kids ... I had better not strike a match with all this straw about. There is absolutely no reason why science must remain in the science class, especially since scientific principles get used everywhere. If your car breaks down on the road, are you not going to think of what might be an easy fix because you're not in auto-shop class? Or because you're not a certified mechanic?

[Just thinking]

I'm confused by this discussion. Isn't that what suction is?

To someone without a background in physics, it'd be easy to confuse exactly where the force is coming from, but it was my understanding that suction is a pushing force that most people misinterpret as a pulling force.

It's been a few years since OAC physics, so please correct me if I have that wrong...

You're most certainly not confused at all. Take a look at a very basic explanation here (http://en.wikipedia.org/wiki/Suction).

Suction is the flow of a fluid into a partial vacuum, or region of low pressure. The pressure gradient between this region and the ambient pressure will propel matter toward the low pressure area. Suction is popularly thought of as an attractive effect, which is incorrect since vacuums do not innately attract matter. Dust being "sucked" into a vacuum cleaner is actually being pushed in by the higher pressure air on the outside of the cleaner.

The higher pressure of the surrounding fluid can push matter into a vacuum but a vacuum cannot attract matter.

I assure you, I did not make that entry, even though it mimics my previous comments very closely. The bolding is mine in that it illustrates the common paradigm that most people make. I could have chosen many others, but that is the one that came to my little mind first.

[Cuddles]

Where does arithmetic end and math begin?

Math doesn't have numbers. If it uses numbers, it's basically arithmetic.

Arithmetic is maths. And a very important part of it, given that by far the most common use of maths is to get some kind of number out at the end. Sure, it's not all of maths, but claiming that numbers aren't maths is, quite frankly, bizarre.

This obsession with dividing maths up into separate parts and trying to classify and teach them all separately is really quite weird. It seems to be more of an American thing as well. You don't teach arithmetic, geometry, algebra, calculus and so on, you just teach maths. Every part is related to every other part, at least at school, and you simply can't separate them all if you actually want to understand any of it.

[lightfire22000]

I watch the Daily Show, I confess. Jon Stewart, who is a friend of skeptics everywhere imo, was talking about military enlistment's relation to the GI Bill. He showed one article that claimed a particularly enhanced GI Bill would cause re-enlistments to decline by 10%. He then pointed to another source that stated the new GI Bill would increase enlistments by 10%. So far so good. He then tried to put it into his own words saying something to the effect of, "If you have a 10% decrease, and then you have a 10% increase, doesn't that mean there's no loss?" I just mildly chuckled because Jon Stewart did his fourth grade math wrong. If you lose 10% and then gain 10% you still have a net loss.

[lightfire22000]

SezMe,
What would you consider Geometry? I always describe it as using equations and numbers to describe and measure space, but people don't tend to like that definition.

[drkitten]

This obsession with dividing maths up into separate parts and trying to classify and teach them all separately is really quite weird. It seems to be more of an American thing as well.

Not in my experience. The UK uses more or less the same breakdown as the USA, although sometimes the separate parts are called "modules" (for example, at Imperial). But here's a partial list of some of the "modules" at Imperial:


Analysis
Algebra
Probability and statistics
Complex Analysis
Differential Equations
Multivariable Calculus
Metric Spaces and Topology
Algebraic topology
Galois theory
Algebraic number theory


None of which would be out of place as courses at a US mathematics department.

You may be confusing the university treatment of math, which is generally modular no matter where you study, with the secondary school treatment, which is generally not modular unless you have enough students to do tracking.

[lightfire22000]

I don't know much about UK education, but I know a few kids from Bermuda who studied over there. They said there high school or "college" is more specialized.

[Cuddles]

You may be confusing the university treatment of math, which is generally modular no matter where you study, with the secondary school treatment, which is generally not modular unless you have enough students to do tracking.

I'm not confusing anything. I specifically said I was talking about school. Feel free to read posts before arguing with them.:rolleyes:

Edit: And given that we've been talking about the general public, game shows and the like, why the hell would you think university maths courses would be at all relevant?

[Jeff Corey]

Does anyone recall Asimov's short story about the scientists who were so dependent upon calculators that no one knew how to do simple math? One scientist figures out how to multiply (I recall) with a pencil and paper and the other scientists are initially skeptical.
The reason this may be appropriate here is that when I ask Psych 1 students to give the mode, median and mean of 5 one digit numbers they insist they need a calculator.

[Cainkane1]

before I could go to college I had to go to adult school and take two remedial math courses, two algebra course and a trigonometry class. I graduated from a not that well though of University after six years but at least I have a nice liberal arts diploma on my wall.

[lightfire22000]

You know what's a lost art? Newton's method for approximating square roots. Lets see the percentage of university math majors could derive it.

Congratulations Cainkane1!

[Just thinking]

Does anyone recall Asimov's short story about the scientists who were so dependent upon calculators that no one knew how to do simple math? One scientist figures out how to multiply (I recall) with a pencil and paper and the other scientists are initially skeptical.
The reason this may be appropriate here is that when I ask Psych 1 students to give the mode, median and mean of 5 one digit numbers they insist they need a calculator.

I recall a study that was done (too many years ago for me to recall exactly) where college students were given calculators by the instructor for an exam (guised to instill a sense of fairness) ... the caveat being that they were programed to give false answers. The real exam was to see how many students realized this was going on. The degree of error varied from operation to operation, but if I recall correctly, few if any realized it. No matter what the calculators spewed out it was accepted as gospel.

[mazyloron]

I recall a study that was done (too many years ago for me to recall exactly) where college students were given calculators by the instructor for an exam (guised to instill a sense of fairness) ... the caveat being that they were programed to give false answers. The real exam was to see how many students realized this was going on. The degree of error varied from operation to operation, but if I recall correctly, few if any realized it. No matter what the calculators spewed out it was accepted as gospel.

That's amusing. And depressing. But mostly amusing.

[GreyICE]

I recall a study that was done (too many years ago for me to recall exactly) where college students were given calculators by the instructor for an exam (guised to instill a sense of fairness) ... the caveat being that they were programed to give false answers. The real exam was to see how many students realized this was going on. The degree of error varied from operation to operation, but if I recall correctly, few if any realized it. No matter what the calculators spewed out it was accepted as gospel.

You know that I did basic math operations in my head, right, as did most students? Add 15, multiple by 8, that sort of thing. If I'm multiplying 0.8762*723.9 I honestly don't have a clue what I'll get. Beyond a basic sanity check (it better be less than 700, and more than 560) I don't really have a clue. And if I have something like 0.8762*(155.3+543.2)^(1.024/1.008)/4.3755 beyond a small sanity check, yes, I'm trusting the calculator.

No really, solve that problem without a calculator. I dare you.

[Just thinking]

You did fine ... you realized that the answer should be somewhere below 700; and you would likely think something was awry if the answer came out 1500 or so, right? Now, it's true that I can't directly solve the above problem to the nearest decimal --- but it looks like it's going to be the fourth root of 600 or so, which is the square root of a number somewhere from 25 to 30 ... so I'm guessing around 5.2.

Am I close?

(Using a calculator I got 4.4)

[SezMe]

Arithmetic is maths. And a very important part of it, given that by far the most common use of maths is to get some kind of number out at the end. Sure, it's not all of maths, but claiming that numbers aren't maths is, quite frankly, bizarre.

Well, I'd say arithmetic is a subset of math. Look, I brought up the distinction only to quibble with the idea early in the thread which seemed to conflate the ability to use various arithmetical shortcuts to quickly get a numerical result with being able to do math. I stand by my disagreement with that point. That said, it does not make any sense to try to define a sharp boundary between the two.

SezMe,What would you consider Geometry? I always describe it as using equations and numbers to describe and measure space, but people don't tend to like that definition.

And this is a good example. Geometry and math and arithmetic are overlapping categories with fuzzy boundaries and no small overlap. I think trying to draw sharp definitions is a waste of time which can have no useful outcome.

[GreyICE]

You did fine ... you realized that the answer should be somewhere below 700; and you would likely think something was awry if the answer came out 1500 or so, right? Now, it's true that I can't directly solve the above problem to the nearest decimal --- but it looks like it's going to be the fourth root of 600 or so, which is the square root of a number somewhere from 25 to 30 ... so I'm guessing around 5.2.

Am I close?

(Using a calculator I got 4.4) Well, I'd certainly smack the calculator and type it in again. If the number I got the second time was wrong I'd type it in a third time. If that number sanity checked I'd blame my bad typing (which hey, I've known my number typing to screw up before, so YMMV). Of course if the error is random and not especially large (i.e. it won't give me -1 million or something) then chances are I'd get one that sanity checks, accept it and move on.

Second the divide thing was supposed to be after the power, it's kind of hard to type here (if I typed it in my graphing calculator that way with the ^(...) it would recognize what I meant, but I forgot that other people aren't used to weird power things, so whatever) but with that one I'd be much more likely to type it in several times before concluding instrumentation rather than human fault (geometrically increasing the likelihood of getting an answer that sanity checks).

Of course given that I have a friend who is not only a genius but dyslexic, this test could only be described as cruel and unusual punishment for that person, thinking about it. So, chances are my reaction, when I realized what the teacher had done would be to rip the test in half, drop it on his desk along with the calculator, and walk over to student services to drop the class and file a complaint. I didn't take that sort of crap lightly back then (I've mellowed a bit).

P.S. Arithmetic (this includes all of algebra, etc.) is not math. I've had this very convincingly explained to me, and I believe it. In general you can define as arithmetic any problem with a discrete form and a single answer. I'd say math really starts around geometry (that's when the concept of a 'proof' which is basically what math is) shows up. Only proofs are math.

[Just thinking]

Second the divide thing was supposed to be after the power, it's kind of hard to type here (if I typed it in my graphing calculator that way with the ^(...) it would recognize what I meant, but I forgot that other people aren't used to weird power things, so whatever) but with that one I'd be much more likely to type it in several times before concluding instrumentation rather than human fault (geometrically increasing the likelihood of getting an answer that sanity checks).

Yes ... I wasn't sure of that either, which is why I went the harder route. Basically, you have 600 to the 1st power --- which is 600. Divide by 4.3 and you're somewhere around 135 or so. If the calculator kept yielding 80 as my answer, I'd become suspect. But how many students would?

[GreyICE]

Yes ... I wasn't sure of that either, which is why I went the harder route. Basically, you have 600 to the 1st power --- which is 600. Divide by 4.3 and you're somewhere around 135 or so. If the calculator kept yielding 80 as my answer, I'd become suspect. But how many students would?

It's between 500-1000 over a little over 4, I'd accept anything in the 100-220 range. ~125 and ~185 both sanity check on a cursory glance.

You ignored how this basically involves cruel and unusual punishment on people with dyslexia, nice 'test.'

[Just thinking]

????

[Molinaro]

You know that I did basic math operations in my head, right, as did most students? Add 15, multiple by 8, that sort of thing. If I'm multiplying 0.8762*723.9 I honestly don't have a clue what I'll get. Beyond a basic sanity check (it better be less than 700, and more than 560) I don't really have a clue. And if I have something like 0.8762*(155.3+543.2)^(1.024/1.008)/4.3755 beyond a small sanity check, yes, I'm trusting the calculator.

No really, solve that problem without a calculator. I dare you.


Bolding mine.

I look at that and think that I need to take away 1 tenth and a tenth of a quarter. Both calculations are pretty simple in my head.

My estimate would be:

(724/10) = 72.4
(724/10/4) = 18.1
I would add these as I calculated them to get 90.5

Take that from 724 to get 633.5

[GreyICE]

Bolding mine.

I look at that and think that I need to take away 1 tenth and a tenth of a quarter. Both calculations are pretty simple in my head.

My estimate would be:

(724/10) = 72.4
(724/10/4) = 18.1
I would add these as I calculated them to get 90.5

Take that from 724 to get 633.5
Not a bad sanity check, but a little long. I'm going to ballpark 600-675 every time.

[Uncayimmy]

You know that I did basic math operations in my head, right, as did most students? Add 15, multiple by 8, that sort of thing. If I'm multiplying 0.8762*723.9 I honestly don't have a clue what I'll get.

My quick check is what's 90% of 700? That's easy (9 * 7 = 63, shift the decimal point). So I figure it's about 630. Real answer is 634.28118.

[GreyICE]

My quick check is what's 90% of 700? That's easy (9 * 7 = 63, shift the decimal point). So I figure it's about 630. Real answer is 634.28118.

Please put it back in context now. Okay? Do you see how what you did was excessively wrong, to the point of deception?

[Molinaro]

Not a bad sanity check, but a little long. I'm going to ballpark 600-675 every time.

It's not long at all. Typing it out is much longer than actualy doing it in my head.

The sequence of thoughts would be roughly:

- I have to add 724 to 1/4 of that and it's obviously divisible by 4 since 72 is 8 under 80. Which means 2 under 20 which is 18. (This thought hapens in under 2 seconds. It's just recognized as a property of the number)

- So add 724 and the result of dividing it by 4 that is 181

7+1 = 8
2+8 = 10 so actualy 90x
4+1 = 5 so 905 and the decimal is over 1 so 90.5

Subtracting that is simply -100 + 10 - 0.5 and can be done to 724 very quickly.

The whole process took under 10 seconds in my head when I first saw the question.

[Uncayimmy]

Please put it back in context now. Okay? Do you see how what you did was excessively wrong, to the point of deception?

What are you talking about? Are you referring to the study that JustThinking referenced but didn't actually perform himself?
http://forums.randi.org/showthread.php?postid=4791853#post4791853

I'll give you a real life story. In an old cell phone the display was getting hinky. I used the calculator for something and noticed that the answer was not near what I expected. I tried it again. Same wrong answer. Tried other calculations. Some were right, others were wrong. And then I realized it was a garbled display. The whole process took about 30 seconds, but it was an odd 30 seconds indeed.

[GreyICE]

What are you talking about? Are you referring to the study that JustThinking referenced but didn't actually perform himself?
http://forums.randi.org/showthread.php?postid=4791853#post4791853

I'll give you a real life story. In an old cell phone the display was getting hinky. I used the calculator for something and noticed that the answer was not near what I expected. I tried it again. Same wrong answer. Tried other calculations. Some were right, others were wrong. And then I realized it was a garbled display. The whole process took about 30 seconds, but it was an odd 30 seconds indeed.

Unca, I then went on to describe the basic procedure of a sanity check.

You took my sentence out of context, and then proceeded to show me... how to do a sanity check.

What does this add to the discussion? The point is that the test is not remotely fair beyond any basic level of math, as a random number generator programmed to produce non-insane results (sign switches, massive order of magnitude jumps, etc.) will simply by random chance, pass any non-paranoid sanity checks thrown at it for at least one student in the class.

Not to mention the poor dyslexic guy. I don't even understand how you can defend a procedure that seems to, by definition, screw the guy that has difficulty telling what a number is AND what he typed into the calculator.

[Uncayimmy]

Unca, I then went on to describe the basic procedure of a sanity check.

You took my sentence out of context, and then proceeded to show me... how to do a sanity check.
I showed how *I* would do it. You described one "sanity check" and I described another one. So did at least one other person.

What does this add to the discussion?
It adds quite a bit to those who followed it from the start. Many of us have given examples of different ways we approach arithmetic in our heads.

The point is that the test is not remotely fair beyond any basic level of math, as a random number generator programmed to produce non-insane results (sign switches, massive order of magnitude jumps, etc.) will simply by random chance, pass any non-paranoid sanity checks thrown at it for at least one student in the class.
Nobody knows the specifics of how the calculators were programmed or the types of problems the test contained. Except you, apparently.

Not to mention the poor dyslexic guy. I don't even understand how you can defend a procedure that seems to, by definition, screw the guy that has difficulty telling what a number is AND what he typed into the calculator.
First off, I never defended anything. That's all in your mind, much like your knowledge of how the calculators were programmed.

Second, my understanding based on what JustThinking said is that the goal of the test (he called it a study) was to see how blindly, if at all, people rely on calculators. If you can figure out a way to do that and still allow the subjects to know the true purpose of the test, I'm all ears. You're acting like this was some real math test where the students were set up for failure.

I like the idea of the study. I won't bitch about the particulars at least until after I know them.

[Cuddles]

Not to mention the poor dyslexic guy.

You keep bringing up dyslexia as if it is at all relevant. This:
the guy that has difficulty telling what a number is AND what he typed into the calculator.
is not dyslexia.

[GreyICE]

You keep bringing up dyslexia as if it is at all relevant. This:

is not dyslexia.

...

Yes it is. I mean I don't even know how to respond to that. It is, and you're wrong, it's not something you can really have an opinion on.

[Cuddles]

...

Yes it is. I mean I don't even know how to respond to that. It is, and you're wrong, it's not something you can really have an opinion on.

No, it's not something you can have an opinion on, it's a simple matter of fact.
http://en.wikipedia.org/wiki/Dyslexia
You're really not good at this are you?

What you describe would be closer to dyscalculia, but it doesn't quite fit with that either.

[GreyICE]

No, it's not something you can have an opinion on, it's a simple matter of fact.
http://en.wikipedia.org/wiki/Dyslexia
You're really not good at this are you?

What you describe would be closer to dyscalculia, but it doesn't quite fit with that either.

I'm sorry, I had my friend hand me his calculator several times to read off the numbers he entered and the result. I watched him miscopy numbers like 565 as 556, etc.

This is very clearly dyslexia, and this is just not really something you can debate.

I don't know what I'm not good at, explaining dyslexia to people who don't understand what it is maybe, but whatever I'm so poor at, you remain quite wrong.

[Uncayimmy]

I still don't get what dyslexia has to do with this anyway. Fine, suppose one of the students has some sort of disability that makes it extremely difficult for him to detect that the calculators are inaccurate. So what? Do we know if this actually happened in the study? Do we know how this affected the results?

What's the big deal?

[Cuddles]

I'm sorry,

The rest of your post suggests otherwise.

I had my friend hand me his calculator several times to read off the numbers he entered and the result. I watched him miscopy numbers like 565 as 556, etc.

This is very clearly dyslexia, and this is just not really something you can debate.

As I said in my last post, I agree it's not something you can debate, so I'm really not sure why you're trying to. I just provided you with link that gave a very clear description of dyslexia. What you describe is simply not dyslexia, and it will not magically become such just because you keep repeating it.

I don't know what I'm not good at, explaining dyslexia to people who don't understand what it is maybe,

As demonstrated by the actual definitions of dyslexia, you are the one who does not understand it. Your friend may well have some kind of disability involving numbers, but that is not dyslexia.

but whatever I'm so poor at, you remain quite wrong.

The evidence clearly demonstrates otherwise.

I still don't get what dyslexia has to do with this anyway. Fine, suppose one of the students has some sort of disability that makes it extremely difficult for him to detect that the calculators are inaccurate. So what? Do we know if this actually happened in the study? Do we know how this affected the results?

What's the big deal?

As far as I can tell, the only reason GreyICE keeps mentioning dyslexia is to try to distract from the actual topic at hand. Obviously a person who cannot recognise numbers has far more problems than could be caused by a single study testing if people actually apply common sense to check the answers their calculators give. In fact, I don't see how such a study would cause that person problems at all. If they can't copy the correct number off the calculator in the first place, what difference would it make if the number shown on the calculator is wrong?

[GreyICE]

The rest of your post suggests otherwise.

You're right. You're pretty sorry. Please learn what Dyslexia is.

http://www.dyslexia-parent.com/mag43.html

Problems in math/s can arise from a dyslexic child's difficulties with sequencing. Getting numbers in the correct order, and being able to reverse that order is a challenge for the student.

Seeequeeencing and nuuuuuumbersssssss....

Goddamn it, tired of arguing what are plain facts with plainly stupid people. This is a waste of time.