Math illiteracy, can you believe this?

[robert Ihnot]

On a new quiz show I was just watching, "Survival Guide," a contestant is pitted against originally 100 people in booths, who also guess the answer. The contestant wins $1000 for an answer per person in a booth, if she is correct and they are not.

First question, she gains $1000 because someone did not know what claustrophobia meant. (99 contestants left.)

Second question all 99 people and contestant knew about Christ and Dec 25.

Third question: If Santa Clause parallel parks his sleigh, what is perpendicular to this position? A) The side doors B) The back of the sleigh C) The runners of the sleigh.

Before the contestant could answer, the question was graded on the 99 people in the booth. 54 OF THEM WERE WRONG. Thus she would have picked up an additional $54,000 if correct, BUT SHE WAS ALSO WRONG AND DISQUALIFIED!

Talk about a low comprehension of math, innumercy,this seems to defy belief!

 

[HallsofIvy]

And it's not just math- or contestants. I remember a game show on which the mc asked "What Shakespeare character was known as the Prince of Darkness?" Surprizingly, none of the contestants could answer so the mc read of the answer: Hamlet. (Well, maybe not so surprizingly: he had misread "What Shakespeare character was know as the Prince of Denmark"!)

 

[yenchin]

I remembered a survey done which shows that there are still people (including some high-salary executive...) who thought that the Sun revolves around the Earth... given that, I think I can believe math illiteracy

 

[arildno]

Oh, but the Sun DOES revolve around the Earth, in the Earth's rest frame..

 

[yenchin]

Oh well... You know what I meant

 

[mathwonk]

i have met people who do not know that in the infinite dimensional case, subfields of extensions fields correspond, not to all subgroups of the galois group, but only to closed subgroups, in the inverse limit topology.

 

[mbrmbrg]

You just have to know what to say to these people.
There's a gentleman who lives near me who used to hate being asked, "What do you do for a living?" because if he answers, "I'm a mathematician," he is almost guarenteed to hear, "Oh, really? I can't do math." So the guy now listens sympathetically to near-strangers take pride in their ignorance before responding, "That's all right. I can't read." Conversation stopper.
Why is it okay to be incapable of performing simple arithmetic, but it's sad and evil to be illiterate?

 

[yenchin]

And I have met people who thought that accretion disk can only form if a black hole is rotating, and not for Schwarzschild case; and people who thought a 0-dimensional sphere is a point instead of two points... BUT, I believe we are talking about *basic* math illiteracy here.

 

[Math Is Hard]

Third question: If Santa Clause parallel parks his sleigh, what is perpendicular to this position? A) The side doors B) The back of the sleigh C) The runners of the sleigh.

Do sleighs have side doors?

 

[yenchin]

You just have to know what to say to these people.
There's a gentleman who lives near me who used to hate being asked, "What do you do for a living?" because if he answers, "I'm a mathematician," he is almost guarenteed to hear, "Oh, really? I can't do math." So the guy now listens sympathetically to near-strangers take pride in their ignorance before responding, "That's all right. I can't read." Conversation stopper.
Why is it okay to be incapable of performing simple arithmetic, but it's sad and evil to be illiterate?

I have also always have people saying "I am always not good in math" or "I almost (or did) failed math" bla bla. Sometimes they seem almost proud of saying so. I guess it has something to do with the education system: most of the time people thought what they learned in schools are all the math there is in the world (hence utterly boring), and unfortunately many school lessons are about nothing but really basic calculations and simple theorems. So once they hate maths in school, it's very hard to win back their soul to like math again

Talking about math illiteracy, sometimes even students who score quite well in school mathematics also have illiteracy in one form or another. E.g. I once asked high school students and even a class of pre-university (A-level equivalent) students a simple question of what is Pi, and *NONE* of them get it correct. All they will say it's that Pi=3.14 or Pi=22/7. No one knows what is the definition of Pi after years of mathematics education! If that doesn't sound wrong to you, I don't know what does! What is happening to education

 

[robert Ihnot]

Well, I have met people who could not understand what a mathematician could be doing. Examples:

"Didn't the Greeks prove all of those things?"

Or the real killer: "That is a very practical career to undertake. Math concerns our everyday activity. We have to calculate all the time."

 

[Gokul43201]

I recently was reminded of this state of innumeracy while watching the Late Show. It was a segment titled "Stupid Pet Tricks", and one of the pets invited was Dave, the Math Dog. This dog seemingly produces correct answers to simple numerical problems (addition, subtraction, multiplication, division, squares, cubes, square roots) and it was quite amazing to watch. However, what I found more amazing (though, by now, I shouldn't) was Mr. Letterman's complete ignorance of how the integers worked. He struggled to come up with a pair of numbers whose difference (first minus second) was positive. Then he fumbled with providing number a, b such that b|a (the dog could only answer questions which had whole number answers). After this, he completely failed with the incredibly difficult task of producing a square of an integer (so the dog could compute the square root). When someone eventually came up with 36 and the dog answered with 6 taps with its paw, Letterman didn't know if that was correct! Later in the show, he was given a calculator to confirm this.

http://www.jg-tc.com/articles/2006/11/22/news/news003.txt
http://rrochat.com/davethemathdog/images/elmwood_il.html

 

[morphism]

I recently was reminded of this state of innumeracy while watching the Late Show. It was a segment titled "Stupid Pet Tricks", and one of the pets invited was Dave, the Math Dog. This dog seemingly produces correct answers to simple numerical problems (addition, subtraction, multiplication, division, squares, cubes, square roots) and it was quite amazing to watch. However, what I found more amazing (though, by now, I shouldn't) was Mr. Letterman's complete ignorance of how the integers worked. He struggled to come up with a pair of numbers whose difference (first minus second) was positive. Then he fumbled with providing number a, b such that b|a (the dog could only answer questions which had whole number answers). After this, he completely failed with the incredibly difficult task of producing a square of an integer (so the dog could compute the square root). When someone eventually came up with 36 and the dog answered with 6 taps with its paw, Letterman didn't know if that was correct! Later in the show, he was given a calculator to confirm this.

That's unbelievable - both the dog and Letterman's idiocy!

 

[yenchin]

The dog beats a human

 

[uart]

It reminds me of a so called "National IO test" that one of the TV stations ran here last year. One of the questions was :

"What is ten divided by one half?"

Almost everyone doing the challenge answered 5 instead of the correct answer of 20.

 

[matt grime]

One I like to get off my chest occasionally:

last year, whilst helping someone with A-level maths preparation, I found the textbook (yes, the textbook) asserting that sqrt(2)=1.4. Mathematical illiteracy is ingrained by the very tools that are supposed to educate. No wonder I struggle make students understand the difference between equal and isomorphic when they haven't learned the difference between equal and not equal.

 

[arildno]

Or the ubiquitous \pi=3.14

 

[uart]

Or the ubiquitous \pi=3.14

Actually that (and Matts post) reminds me of something that I’ve often noticed. Have you ever had the situation where you received some information at a very young age from a trusted source, like a parent or teacher, and either the information was wrong or you just grossly misinterpreted it and as a result you ended up with something really erroneous stuck in your brain. It's almost like this obviously fallacious "fact" gets filed away in a part of the brain that is reserved for "things that are correct without question" and it can be quite funny/embarrassing when this "unquestioned" information comes out many years later when you really should know better.

This is something that has happened to me and speaking to various other people it seems quite common. Lots of people can recount some really dumb childhood learned thing they held to be true for a very long time, I mean long after that same information would have been rejected as false if it had been presented to them at this later age.

My example is actually the Pi one. At a young age my father was teaching me to use a slide-rule. Now my dad was never a mathematician, so he told me "If you have to do calculations involving circles then there's this thing marked Pi on the slide-rule that is very useful. Some slide-rules don’t have Pi marked so you can just use 3.1, but if you want the exact value use 22/7".

So at this young age I learned that 3.1 was only an approximation for Pi (so far so good), but that 22/7 was it's exact value . Now this little piece of misinformation sat dormant in my brain for many years until one day in a university maths course out it came. The Lecturer was discussing Pi and he said something along the lines of how the “Pi button” on our calculators was necessarily only an approximation of the true value of Pi. At this point I blurted out something like “yeah but if you use 22/7 it’s exact”. Ouch, I nearly got laughed out of the lecture theatre.

Actually my example is pretty tame, some people’s accounts are really laughable. Ones involving gross misunderstanding of physical phenomenon can be quite funny. Like the student in a 3rd year astrophysics course who stated that “the phases of the Moon are caused by the Earths shadow falling on the Moon”.

Has this type of thing ever happened to anyone else here?

 

[Gokul43201]

Has this type of thing ever happened to anyone else here?

Until recently, I'd been pronouncing 'timbre' the same way I pronounce 'timber'!

Naturally, I blame my 9th grade physics teacher!

 

[matt grime]

Now this little piece of misinformation sat dormant in my brain for many years until one day in a university maths course out it came. The Lecturer was discussing Pi and he said something along the lines of how the “Pi button” on our calculators was necessarily only an approximation of the true value of Pi

A university course teaches what the pi button does? I feel faint. Nurse, my tablets, please.

 

[uart]

A university course teaches what the pi button does? I feel faint. Nurse, my tablets, please.

Haha. No he wasn't teaching us how to use buttons on the calculator. It was a very long time ago so I can’t remember the exact details. I believe he was merely using it as an example of the limitation of decimal representations when it comes to irrational numbers. Or it may have even been something he was saying in response to a question asked by a student. Anyway you can put the tablets away Matt, I can assure you that at no time in my university course did any lecturer ever give us a "buttons on a calculator" lesson. :)

 

[mathwonk]

well i traditionally talk about what the numbers on the calculator mean.

many of m y calcuklus students believe the answers their calcuklators give are exact.

others seem to think all real numbers are integers, and interpret the rules

(af)' = af' for derivatioves accordingly, asonly true for integers a.i have often thought about how to persuade my students that there are more real numbers than just the integers, or finite decimals, or fractions.

it is not easy when you do not treat real numbers correctly. i have settled on emphasizing the purpose of real numbers is to emasure lengths, and explaining how this leads to representing them as infinite decimals.this does not suffice, as so many students have in grained false ideas, like the pi = 22/7.

i try to explain how "numbers" should have various properties, like their physical interpretation or application, their symbolic representation, their convenience for calculation, their axiomatic properties,...

i.e. isa "number" somthing such that a+b = b+a, or something that represents a length, or somehting that can be approximated by a decimal, or something that can easily be added and multiplied?

we think of them by their axioms, but students think of them by their names.

 

[mathwonk]

uart, when i was in high school, my algebra book defined a function roughly as " two quantities so related that a change in one of them brings about a corresponding change in the other".

I dutifully memorized this and repeated it when i interviewed for admission to the honors calculus course in college at harvard.

that one answer almost got me diismissed immediately from consideration for the course. fortunately the prof gave me one more chance, and i recovered by proving the real numbers are uncountable, by cantors "second diagonal method", which i had learned by independent reading.

 

[Gib Z]

LOL I remember that! Do you live in Australia? It was on channel seven or sumthing, as the tests made me want to laugh. They probably designed it so people felt better about themselves :). About that contestant who could have had 54k, i want to him him.

 

[uart]

LOL I remember that! Do you live in Australia?

Yes that was it. I really was pretty laughable wasn't it.

 

[Daverz]

I was wondering the other day how many times I'd miscalculated the derterminant of things like

<br /> \frac{1}{2}\begin{pmatrix}a &amp; b \\ c &amp; d\end{pmatrix}<br />

as \frac{ad-bc}{2}

 

[murshid_islam]

and there's of course the famous example of the confusion about 0.999... = 1.

 

[mbrmbrg]

and there's of course the famous example of the confusion about 0.999... = 1.

Doesn't it? The same way that 0.333...=1/3 ?

 

[Worzo]

and there's of course the famous example of the confusion about 0.999... = 1.

Uh oh...don't start that one off!

 

[Gib Z]

Lol maybe your abit confused mbrmbrg, he was stating it was correct and that far, far, FAR too many people either think it isn't, or think their really smart being able to prove it is equal.

As to my example of math illiteracy, I was trying to teach someone Differentiation by First Principles, which involves using Newtons Difference Quotient. Anyway, while I derived it, it basically doesn't even need to be derived..the denominator required x+h-x . Now..what can i say to someone who can not figure that out...

 

[Doodle Bob]

Third question: If Santa Clause parallel parks his sleigh, what is perpendicular to this position? A) The side doors B) The back of the sleigh C) The runners of the sleigh.

actually, this is a rather ill-posed question. what exactly is meant by "this position"? There is an unspoken assumption of orientation here that confuses things a bit. All of the given answers are parts of the sleigh itself (and one of the answers -- the side doors -- can change their position), so anyone of them could be considered perpendicular to something else on the sleigh.

Furthermore, whatever does the "parallel parking" aspect have to do with things? A better form of the question would be:

If Santa Claus parallel parks his sleigh, which of the following is perpendicular to the curb? A) The side doors (when closed) B) The back of the sleigh C) The runners of the sleigh.

 

[mattmns]

actually, this is a rather ill-posed question. what exactly is meant by "this position"? There is an unspoken assumption of orientation here that confuses things a bit. All of the given answers are parts of the sleigh itself (and one of the answers -- the side doors -- can change their position), so anyone of them could be considered perpendicular to something else on the sleigh.

Furthermore, whatever does the "parallel parking" aspect have to do with things? A better form of the question would be:

If Santa Claus parallel parks his sleigh, which of the following is perpendicular to the curb? A) The side doors (when closed) B) The back of the sleigh C) The runners of the sleigh.

I completely agree. I would have missed the original question.

 

[morphism]

I completely agree. I would have missed the original question.

It took me a good five minutes to even understand what it was asking.

 

[robert Ihnot]

I am not exactly sure how the question was put. In fact, I think Answer C was The Raindeer; I did not really remember that.

I thought, however, that the use of the term "parallel park," which is common in America, or was in my day, and tests the driver at the motor bureau, indicated something. The driver is expected to park close to the curb so that the front and back wheels of the passenger side of the car are within something like 1 foot from the curb. The examiner then grades this.

 

[Doodle Bob]

I thought, however, that the use of the term "parallel park," which is common in America and is frequently tested to get a license, indicated something. The driver is expected to park close to the curb so that the front and back wheels of the passenger side of the car are within something like 1 foot from the curb.

I completely understood the parallel parking aspect of it. In fact, you'll notice that I incorporated it into my own version of the question.

My point, however, was that the contestants may not have gotten the question wrong more to having not understood the question and just guessing rather than math illiteracy.

 

[Gokul43201]

My point, however, was that the contestants may not have gotten the question wrong more to having not understood the question and just guessing rather than math illiteracy.

Much faith, hast thou!

As to the original anecdote (whose accuracy is not necessary for the main point in the OP to be true)...

http://www.fullcontactpoker.com/poker-forum/index.php?showtopic=83507
(not original source)

Santa just parallel parked his sleigh. Which part of the car is perpendicular to the curb?
a. the driver's side door
b. the passenger's side door
c. the back end

From another recollection... http://boards.sonypictures.com/boards/showthread.php?p=607381

Santa just successfully parallel parked his sleigh! Which part of it is now perpendicular to the curb?

54 were wrong including Annie Duke (she ended up with 35 correct) and Patridge in a pear tree for the Christmas theme - Danny Bonaduce.

The choices:
Passengerside Door
Driverside Door
Back End

 

[robert Ihnot]

Doodle Bob: My point, however, was that the contestants may not have gotten the question wrong more to having not understood the question and just guessing rather than math illiteracy.

I suppose. There was not much time given to that question. The main contestant seemed to at first have mumbled something to suggest she knew the correct answer, but then all that Santa and sleigh part confused her, and she must have thought it a trick question.

As for a previous question on "claustrophobia," all but one seemed able to get that.

 

[HallsofIvy]

It's not only math. I remember a game show in which the question was "Namd this nation directly east of Germany". Answer: " Uhh--- Germany?"

I'm going to be generous and attribute this as well as other silly answers to nervousness. No telling how I would answer if I had television cameras pointing at me!

 

[Doodle Bob]

From Gokul: "Santa just parallel parked his sleigh. Which part of the car is perpendicular to the curb?
a. the driver's side door
b. the passenger's side door
c. the back end"

This is a bit better than RI's recollection of the problem. But, again, we run into the problem of how to interpret the relative positions of the doors: they can be opened after all so as to be perpendicular to the curb.

Incidentally, these are not trivial matters. I have been on several committees involved with the Achievement Exams for the Ohio Department of Education. And one of the truly difficult parts of writing these exams is generating problems whose forms will minimize semantic and set-up difficulties and actually assess the test-takers knowledge of the mathematical content. For high-stakes tests like these, the amount of overthinking and stress can often cause the most mathematically literate people stumble over problems that are poorly worded or ill-posed.

A poignant example was a problem that referred to a child's "backyard." A great deal of students, living in urban apartment buildings, didn't have a clue as to what a backyard was and found the problem inordinately difficult. Granted the word "backyard" should be in most people's vocabulary, but nevertheless it was a math exam not a vocabulary exam.

 

[murshid_islam]

G. H. Hardy's sister Gertrude Edith Hardy once wrote the following about "the self-satisfied ignorance she found among some students":

There is a girl I can't abide.
Her name? I'll be discreet.
I feel I'd need some savoir dire
Should I her parents meet!

...

She says "I never could do Maths.
When Daddy was at school
He could not add!" I'd love to say
"Then Daddy was a fool!"

"In dictee I got minus two;
There's not a verb I know;
I always write the future tense
Of 'rego', 'regebo'

"But then my Mother cannot write
Or speak a foreign tongue."
Sweet maid, how much the world had gained
If they had both died young!


(this is taken from the book "The Man Who Knew Infinity" by Robert Kanigel)

 

[SticksandStones]

It's not only math. I remember a game show in which the question was "Namd this nation directly east of Germany". Answer: " Uhh--- Germany?"

I'm going to be generous and attribute this as well as other silly answers to nervousness. No telling how I would answer if I had television cameras pointing at me!

Were there any more clues? That alone could make it either the Czech Republic or Poland.