July 28, 2011

# Why We Are Terrible At Math (And Reading Comprehension)

There are 20% more girls than boys in the class.  If there are...

You're a teacher in a public school.  You give your 3rd graders a worksheet of 50 two digit addition questions, e.g. 43+25.  The kid gets 90% of them right. Pass or fail?

II.

Now it's reading comprehension time, you give the kid this:

He gets them all right.  So?

III.

The math example, above, is real, and real(ly) scary.

4 5
+   2 4
______
6 9

So the kid had done an entire worksheet of these.  But what was hidden from view was that  the kid had absolutely no idea he was adding 2 digit numbers.  He had memorized the mechanics of the process and nothing else.  So when he was asked, "if you have 45 beads, and a friend gives you 24 beads, how many beads to you have?" he didn't know to put the numbers on top of each other like the worksheet; what he did was say the number 45 and then start counting on his fingers, 46, 47, 48, 49.... and of course he ran out of fingers and had no idea when to stop, so he guessed.

The problem is that as long as he completed the worksheet, you wouldn't know there was a problem with doing math until it was way too late.  If the kid is clever in other ways-- say, fast at finger counting-- he could easily convey the impression that he understands how to add 2 digit numbers, and what that means, and so everyone thinks he's progressing just fine; only to reach a later point when his clever shortcut is too primitive to work.  Now suddenly you have a 6th grader who appears to falling behind.  But he was never really caught up.   I suspect that this almost entirely explains Americans' universal hatred of word problems.

IV.

A second maddeningly infuriating example.  There's a summer class of 1st graders with behavioral problems who are learning to read.  Granted a unique sample set, but it's the only one I have. Ok, so one boy is reading the story of Aladdin.

I notice that he is reading the words but there's no cadence, there's no rhythm.  At times, he'll read the first words of a second sentence into the flow of the first sentence, i.e. "Aladdin took the lamp.  Jasmine polished it." becomes "Aladdin, took the lamp Jasmine polished.  It..."

However, he is reading the words correctly.  So?  So the only way you can evaluate his comprehension is to ask him questions, which he answers with little hesitation. Great, he's reading on grade level.  Except he's seen the movie.  In the story, the King of Thieves crashes the wedding and steals stuff, and you ask, "who is this guy?" and the kid says, "it's Aladdin's father."

"But Aladdin doesn't know this yet, right?  He finds that out in the end.  Who does Aladdin think it is now?"

"His father?"

The kid can't be faulted for referencing the movie, but it never occurred to the teachers (two of them) that this was going on.

It's the same problem with the manatee story, above.  A fast reader with poor comprehension can quickly re-scan the page for the answers.  "A+!" Certainly no remedial training needed here."  But that works for a paragraph, it doesn't work for 10 pages.  I accept that he may get better, but he may not;  the point here is that a lack of comprehension goes undetected because he tests well.   By the time it is detected, it's too late.

V.

Which brings me to the real point: it would require the teachers, and the parents, to be looking for these tricks and shortcuts that kids use, and to "test" the kids in specific ways.  The immediate answer you get is, "look, in a class of 20 kids, there's just no way to test kids individually like that."  That's not the problem I'm citing here.

The problem I'm citing is that the teachers and the parents don't understand math either, because they used these shortcuts when they were kids.  I'm sure adults think they have excellent reading comprehension, but I hope a survey of the universe quickly reveals that they don't.  They get the gist.

Try this:

There are 20% more girls in the class than boys.  If there are 45 boys, how many girls are there?

Some of you will be daunted by the problem, you don't know where to start.  Interestingly, people who aren't "good at math" try and start with some abstract idea of the total.  The easier way is to start with what you know, and draw it:

I don't know how applicable this method (Singapore math) is to students in general, but it worked for me and I'm already good at math.  And I'm sure there are other methods that are relevant to specific "hangups."  But how do you get parents and teachers to be aware of them, let alone use them?

I'm told that the system of the day is "Everyday Math." I have no idea what that is, but my worry is that every system of teaching is designed not to maximize learning, but to facilitate the teaching.  Standardize a process among teachers who themselves lack the deepest, intuitive sense of the material.  I have no idea what the solution is, though I am open to suggestions.

You're exactly right, sir. ... (Below threshold)

July 28, 2011 1:21 PM | Posted by : | Reply

You're exactly right, sir. It's pretty scary. I'll not present myself as any kind of expert on either math or reading, but the general population doesn't exactly make it hard to be ahead of the curve. That's unfortunate.

I recall not giving a shit in my Advanced English Comp class in college, as I was paying nearly \$400 per credit hour for remedial, high school level assignments covering comma use and parallelism. Seriously? What an insult.

And yet, our elected "representatives" are all about "creating jobs" these days (while slashing education funding). As Judge Smails so elegantly put it, "The world needs ditch-diggers too."

Thanks for the regular does of intelligence in my RSS reader, sir. Cheers.

I figured it out!T... (Below threshold)

July 28, 2011 1:42 PM | Posted by : | Reply

I figured it out!

This is a metaphor for the growing practice of cookbook-style, algorithmic health care. Am I right?

You sneaky devil.

Yup, this is why you get so... (Below threshold)

July 28, 2011 2:04 PM | Posted by : | Reply

Yup, this is why you get so many kids who are able to fake their way into college with straight A's, never having studied, only to get fucked over in college. It's not that they were smart, it's just that they knew how to take the tests they were given.

Interesting to me that my i... (Below threshold)

July 28, 2011 2:05 PM | Posted by : | Reply

Interesting to me that my initial answer to the question, while staring at the drawing and the question, was "Well it's 9..."

I has smart.

Alone, I'm an inner city el... (Below threshold)

July 28, 2011 2:13 PM | Posted by : | Reply

Alone, I'm an inner city elementary school teacher. The problem isn't that the 90% on the worksheet doesn't reflect real understanding, but that the vast majority of the students can't get past 30%. Most of my students miss weeks of school for reasons unknown, start kinder year unable to name colors, seasons and family member, let alone numbers, and when they do show up, they are completely unprepared. Every year, several children start school completely nonverbal. As a newbie, I was shocked to later see proof that they were not mentally retarded. Homework is a useless concept because nobody ever does it. Parents are usually unreachable. The majority of our energy goes to maintaining order because the kids aren't used to following directions at home. I'd say that the majority of our students should be held back at the end of each year, but politics won't allow it. So 17% mastery becomes a B- and gets passed along to the next grade level. I've taught summer classes in high school, and it's the same thing. Some of the students never even showed up, but they all received credit for the class I was teaching.
Meanwhile, I went to a public suburban school growing up, and the problem you posted above seems pretty easy to me, even though I don't consider myself to be good in math.
My point is that most children of normal intelligence will grasp basic math and reach acceptable reading comprehension levels if they are required to sit down, listen to the teacher, do actual homework, do the work in class and actually somewhat understand the material to be promoted to the next grade level. You know, like what the majority of you had to do. What can be done with children who completely refuse to apply themselves and whose parents don't care? Not as much as could be done in different circumstances.

Great post.NTLB ma... (Below threshold)

July 28, 2011 2:16 PM | Posted by : | Reply

Great post.

NTLB makes this phenomenon worse. All outcome measures are centered on a large volume of standard tests. Teachers have to teach to pass the test. In my kids' experience, this encourages algorithm-based mathematics (rather than understanding-based), and reading comprehension skills tailored toward three paragraph passages, rather than deciphering themes of significant works.

I think people also really ... (Below threshold)

July 28, 2011 2:21 PM | Posted by : | Reply

I think people also really do learn differently. For me, for example, the "draw it" suggestion would do me absolutely no good, because I have basically zero visual intuition. I always prefer a bunch of equations to a graph. But maybe that means I don't really "get it," instead am just good at following mechanical instructions, i.e., the very problem you point out? Dunno... I've succeeded with it well into things like specialized stats courses for grad students...

Bizarrely, I paused for a second on the example because of a puzzle about linguistic convention. My first thought was "20% of the number of boys, or 20% of the number of girls?" Both are legitimate interpretations of the problem, it seems to me -- the first is equivalent to the algebra problem "X+.2X=Y, X=45, solve for Y," whereas the second is equivalent to "X+.2Y=Y, X=45, solve for Y." (The second is only ruled out if you think the answer "there are 56.25 girls" involves nasty assumptions about dismemberment...) Not sure what that says about me.

Was the change from 25 to 2... (Below threshold)

July 28, 2011 2:30 PM | Posted by : | Reply

Was the change from 25 to 24 a test of my reading comprehension?

There are obviously two pop... (Below threshold)

July 28, 2011 2:57 PM | Posted, in reply to , by : | Reply

There are obviously two populations of students. I think Alone is referring to "good" students who coast through school without any real learning, but the problem you described is no small concern. I wonder if the dropout rate, or the test scores you describe might actually be higher if the issues he describes here were addressed. But we'll likely never know.

Am I the only one who simpl... (Below threshold)

July 28, 2011 3:04 PM | Posted by : | Reply

Am I the only one who simply said, "What is 1/5 of 45?"

This example fails when you... (Below threshold)

July 28, 2011 3:18 PM | Posted by : | Reply

This example fails when you have to SUBTRACT two-digit numbers. At which point you usually discover who didn't 'get' the material previously.

Replace teachers and textbooks with video games by subject. They can teach our adults to conduct fantasy military operations, they can damn sure outdo teachers for maximizing the learning potential of every student, especially on the repetitive aspects of education.

Kids are terrible at math (... (Below threshold)

July 28, 2011 3:18 PM | Posted by : | Reply

Kids are terrible at math (and other subjects) because the teaching model is fundamentally outdated. Instead of wasting everyone's time in class reciting dry material from textbooks, students should instead READ material or watch videos at home and PRACTICE homework in the traditional classroom setting.

Personally, as someone who ... (Below threshold)

July 28, 2011 3:24 PM | Posted by : | Reply

Personally, as someone who grew up 'good at math', I had no problem and didn't mind parsing information out of a word problem to express it in an equation and solve, but I always hated word problems because we were expected to write out the whole thing in words which I found irritating. In real life, if a teacher asked me how may apples I had when Jenny gave me hers, I'd answer 7 (or the appropriate number).
On a word-problem worksheet, I had to write out "when Jenny gives me her apples, I now have seven apples". As a child, that drove me nuts - not the math.

I see the point in other general though. As a teacher (of many things not including standard school), I have seen many people memorize the process without understanding the concept. People in first aid classes who lose their entire ability to process if there's a slight hitch or irregularity, for example.
I recall when taking formal logic in university (which to me was simply learning the proper symbols to use to represent obvious concepts), the people who did't *get* it at the beginning still didn't *get* it at the end - even if many of them learned how to write in the formulas to get the correct answer.

Isn't the answer 67.5? The... (Below threshold)

July 28, 2011 4:21 PM | Posted by : | Reply

Isn't the answer 67.5? The % given in the question refers to total class size. ("There are 20% more girls in the class than boys.") Boys make up 40% of the class, and girls the remaining 60%. So, the class has 112.5 students (45/.4), with 67.5 girls (112.5-45).

Isn't the answer 67.5? The... (Below threshold)

July 28, 2011 4:22 PM | Posted by : | Reply

Isn't the answer 67.5? The % given in the question refers to total class size. ("There are 20% more girls in the class than boys.") Boys make up 40% of the class, and girls the remaining 60%. So, the class has 112.5 students (45/.4), with 67.5 girls (112.5-45).

Maybe that's why everyone h... (Below threshold)

July 28, 2011 4:32 PM | Posted by : | Reply

Maybe that's why everyone hates "word problems!" Linguistic ambiguity! Since now we have at least three plausible candidate interpretations of the problem (our host's, mine, and "a little math"'s)

Maybe that's why everyone h... (Below threshold)

July 28, 2011 4:38 PM | Posted by : | Reply

Maybe that's why everyone hates "word problems!" Linguistic ambiguity! Since now we have at least three plausible candidate interpretations of the problem (our host's, mine, and "a little math"'s)

no, I got it as well.... (Below threshold)

July 28, 2011 4:49 PM | Posted, in reply to , by : | Reply

no, I got it as well.

A.L.

to those who fail at readin... (Below threshold)

July 28, 2011 4:52 PM | Posted by : | Reply

to those who fail at reading comprehension:

45 boys

45 + (45 * 1/5) == 52 girls

97 student total

A.L.

Great article. I tutor mat... (Below threshold)

July 28, 2011 5:04 PM | Posted by : | Reply

Great article. I tutor math part time and have found that the local public school classes do nothing to teach the students to understand concepts and apply them. They just want the student to be able to solve the problems in the given format. It is very possible for the students to get through the classes with a good grade and have no real grasp of what it is they are doing.

The students I had were also terrible at word problems. They couldn't even tell me what a lot of the terms meant, so that is where I started.

The best part? The classes consist of the students completing math problems on their individual computers using the state provided 'math teaching software'. Very little student-teacher interaction.

I am an engineer and think math is awesome but a word problem like the one above will destroy most 7th graders.

Oh, the answer is 'Too many students for a public school classroom'.

Autistic indeed. Check your... (Below threshold)

July 28, 2011 5:12 PM | Posted, in reply to , by : | Reply

Autistic indeed. Check your math bro-ski.

45 x 1/5 = 9

45 + 9 = 54

45 + 54 = Classroom explosion.

Re: 20% more.Isn't c... (Below threshold)

July 28, 2011 6:04 PM | Posted by : | Reply

Re: 20% more.
Isn't correct way to approach is to realize that out of 100% there 40% boys and 60% girls. So for every boy, there is 1.5 girl, for a total of 67.5.
Or, if you first mentioned girls, may be their number should be 100%, so the number of boys would be 4/5 of girls, so number of girls is 56.25.
Or, may be this is just poorly worded question.

Now, when teaching educated... (Below threshold)

July 28, 2011 6:50 PM | Posted by : | Reply

Now, when teaching educated professionals how to digest a research study, this is what thy want. I cannot figure out how to tell ppl that you need to start with common sense - not the blind heuristic reassurance that an RCT means the study conclusion is correct.

Part of problem-solving is to not over-think things.

If you read depression treatment studies, you will realize: they almost never provide info regarding whether - get this - the depression "got treated."

What do you mean by "treated?"

Me? It doesn't matter what I think "treated" means.

Who does it matter to?

[blank stare]

Who does it matter to?

"The patient?"

Great! Now, you have common sense.

We don't care whether biedermann or nemeroff believe the patient is now "treated."

We care whether the patient has gotten what they came in for: to get treated. Or, to get better.

So, how do you find out if the patient believes he or she got treated?

Use a validated questionnaire?

No.

[blank stare]

You ask them if they have gotten what they wanted. To get treated; to get better.

You ask them if they are better now.

A questionnaire could accompany that.

But the patient did not come to you asking to lose 5 HamD points.

@Pat Delancey"Or, ... (Below threshold)

July 28, 2011 7:06 PM | Posted, in reply to , by : | Reply

@Pat Delancey

"Or, may be this is just poorly worded question."

Or perhaps an interpretation that requires there to be .25 of a person is not likely to be the correct one?

e: 20% more.Isn't... (Below threshold)

July 28, 2011 7:20 PM | Posted, in reply to , by : | Reply

e: 20% more.
Isn't correct way to approach is to realize that out of 100% there 40% boys and 60% girls. So for every boy, there is 1.5 girl, for a total of 67.5.
Or, if you first mentioned girls, may be their number should be 100%, so the number of boys would be 4/5 of girls, so number of girls is 56.25.
Or, may be this is just poorly worded question.

Nope, it was worded correctly. There's 20% more girls than boys. In your example, there's 50% more girls than boys. When deconstructing word problems, look for key words such as "than", "less", "more", "out of".

I think the problem here is confusing the goal with the approach. In the manatee example, the goal is comprehension of the material, but the child is presented with "fill in the blank" type questions that beg to be answered by keyword searching the provided text, while the math problem would be best solved using a keyword style approach (what is this thing asking me to do?)

Agreed that these questions are designed to make the teacher's job easier, but like Anon said in comment #5, no form of teaching will make up for deficiencies at home, while an excellent home environment can make up for some very bad teaching.

As the Atlanta scandal shows, there are no metrics that aren't suspect, and no universal curriculum that works for every kid.

Standardize a process am... (Below threshold)

July 28, 2011 7:23 PM | Posted by : | Reply

Standardize a process among teachers who themselves lack the deepest, intuitive sense of the material.

Worse than that: Standardize a process among teachers who think they have a deep, intuitive sense of the material, but really don't.

"Oh, twenty percent of 45 a... (Below threshold)

July 28, 2011 7:28 PM | Posted by : | Reply

"Oh, twenty percent of 45 added to 45". I think the Last Psychiatrist might have been overdoing it with the rum on this one. That or he's not nearly as good at math as he thinks he is.

And what happens when the c... (Below threshold)

July 28, 2011 7:30 PM | Posted by : | Reply

And what happens when the conveyor belt moves backwards at exactly the same speed the plane moves forwards?

My reflex answer was the 67... (Below threshold)

July 28, 2011 7:31 PM | Posted by : | Reply

My reflex answer was the 67.5 that alittlemath and patdelancey came up with. But the fact that people were able to come up with three possible different answers (I'm not counting the incorrect math of autistic) does speak to a wording problem.

Here's another answer to th... (Below threshold)

July 28, 2011 7:33 PM | Posted by : | Reply

Here's another answer to the math problem, by the way: 6 girls, 4 boys. The class is 60% girls and 40% boys, therefore there are twenty percent more girls than boys.

This is wrong, but can you tell me why?

d'oh. Max already explaine... (Below threshold)

July 28, 2011 7:37 PM | Posted by : | Reply

The solution? Fire most of ... (Below threshold)

July 28, 2011 8:11 PM | Posted by : | Reply

The solution? Fire most of the teachers. Fire every teacher that can't pass a sophomore-level calculus exam. You're dead-on about "deeper understanding", and you can only have a deep understanding of thing X if you have at least a minimal understanding of the more complicated things X0,X1,X2.. that underlie it. Nowhere is that more clear than in mathematics.

So who's gonna teach the kids once we have 123 teachers left in North America? Well, first of all, there's high unemployment, so lower the barriers to entry to the profession. Then drag local tenured college professors, kicking and screaming, to teach middle school.

Speaking as somebody who us... (Below threshold)

July 28, 2011 9:40 PM | Posted by : | Reply

Speaking as somebody who used to tutor basically upper-middle-class kids ranging from grade 8 through to first year calculus, this seems to explain most of the kids I tutored.

As a side note, the method you used is basically what I used to use to tutor kids through (always the most trouble, btw) word problems. High school systems of equations, and most kids had that "don't even know where to start" thing you describe.

Also I can't take credit for this, I basically did my best to imitate the method used on me by one of the better math profs who taught me...

Also - I didn't have very many kids I tutored who's parents were "good at math". Lot more marketing and sales types and real estate salespeople than engineers or programmers or (*snort*) doctors. Upper income groups, but I didn't meet many parents who used math regularly.

What to do? What if there's nothing you can do? What if it's a fairly significant breakthrough just to understand and identify?

Alone, why don't you talk about Marshall McLuhan, btw? It seems incredible to me that you don't read McLuhan. Mcluhan seemed to be interested in Baudrillard for the same reasons you are. Asking you a direct question may be nearly as stupid as sending you a manuscript for review, but c'mon, there's a chapter of "Understanding Media" called "Narcissus Narcosis" where he points out the misunderstanding around Narcissus, in that he didn't actually know he was looking at himself... What gives?

@Rooster: you are getting i... (Below threshold)

July 28, 2011 9:50 PM | Posted, in reply to , by : | Reply

@Rooster: you are getting it upside-down. you don't need university level math to teach 3rd graders math. you just need to understand what you are teaching.
And I wouldn't want any college professor near small children. their head is in the clouds, and the children will learn nothing.

I consider making the elementary school a lunch pad for collage as the greatest mistake of western education.

If there are 20% more girls... (Below threshold)

July 28, 2011 10:49 PM | Posted by : | Reply

If there are 20% more girls than boys in the class, how many commenters are compelled to whip out their brains (dicks) to prove whose is bigger? Don't you people have anything better to do?

Wait a second... You mean t... (Below threshold)

July 28, 2011 11:22 PM | Posted by : | Reply

Wait a second... You mean the answer to a post's title question - on TLP! - is NOT "narcissism"?!?!

...hell freezes over.

I think what Alone is tryin... (Below threshold)

July 28, 2011 11:29 PM | Posted by : | Reply

I think what Alone is trying to teach us (re: the number of boys and girls) is the critical difference in evaluating absolute and relative differences.

If you buy two lottery tickets, you are twice as likely to win the jackpot.

You seem to be overlooking ... (Below threshold)

July 28, 2011 11:44 PM | Posted by : | Reply

You seem to be overlooking to fact that the purpose of compulsory education is not to teach but to socialize and sort. The system is not broken w.r.t. its actual goal.

Also, teachers can't help falling victim to Dunning-Kruger just like the rest of us.

thank you for this post. tr... (Below threshold)

July 29, 2011 1:28 AM | Posted by : | Reply

thank you for this post. truly.

almost 40 and i never learned how to calculate fractional increases (though i've never had problems with the reverse, calculating fractional decreases, strangely enough). but now, i not only now how, i will never forget. thanks too for mentioning singapore math, i googled them and have been reading about them.

the person i know who is the best at calculating anything fractional is my grandmother, the daughter of Appalachian chicken farmers, who dropped out of school at 13 to marry GI fresh from patton's army. she's a wiz with fractions because she's an avid baker.

and that highlights he main structural problem with american style compulsory education is that it is divorced of purpose and context. to understand and learn, requires purpose and context...of course the main functional problem with american style compulsory education is that it works exactly as intended...but that's another post...

The fact that people came u... (Below threshold)

July 29, 2011 1:32 AM | Posted by : | Reply

The fact that people came up with 3 different answers shows how terrible Americans are at math. There is only one right answer, and that is 54. People like Pat Deloncey probably majored in Political Science. You are part of the problem. Good luck trying to understand abstract concepts like risk...

Not going to lie: I'm kinda scared for America. We are screwed.

disclosure: SHORT America, LONG everywhere else

I was about to post the sam... (Below threshold)

July 29, 2011 2:01 AM | Posted by : | Reply

I was about to post the same thing as anonymous above me: school as we know it was not designed to teach mastery of the material. It was designed to maintain social order and produce a large pool of obedient industrial workers. This wasn't a conspiracy, it was the publicly stated goal.

Fine-tuning the pedagogical tactics won't make any different at all. The entire context is profoundly anti-educational.

Rather than rehash the argument, I'll just leave the obligatory John Taylor Gatto link: http://www.newciv.org/whole/schoolteacher.txt

people like autistic... (Below threshold)

July 29, 2011 2:02 AM | Posted by : | Reply

people like autistic lurker and elitegarbageman, who have such contempt for anyone who has a different interpretation of the problem, clearly are lacking in either logic or a sense of the ambiguity of language.

Let's break it down.

There are 20%

more girls in the class than boys.

Here's the thing. "20%" has no meaning in isolation. 20% =.2X, that is, .2 of something. But .2 of what? The problem doesn't specify.

It could be, as is the dominant (and most obvious) interpretation, 20% of boys, i.e.,

There are 20% of boys

more girls in class than boys.

Or, in symbols, where X = number of boys and Y = number of girls,

Y=X+.2x

Or it could mean 20% of girls, that is, Y=X+.2Y.

Or it could mean 20% of the entire class, that is Y=X+.2(Y+X)

Or it could mean 20% of any damn other thing. It could mean 20% of the total atomic weight of the particles in the moon. Or 20% of the average daily rainfall in Kenya in nanometers. Or 20% of the men who were with your mom last week. The question does not specify.

A term like "20% more X than Y" is inherently ambiguous. If you can't see that, then I submit that you have exactly the same problem our host is pointing out -- that is, you've been trained to interpet a phrase like "20% more X than Y" in some rote, mechanical fashion without actually having some kind of cognition about what things like percents actually mean.

Really? The question doesn... (Below threshold)

July 29, 2011 2:47 AM | Posted, in reply to , by : | Reply

Really? The question doesn't specify? How is that syntactical form ambiguous at all???

There are 20% more girls than boys.

'are' is a linking verb, which links the subject (girls) to the '20% more', which precedes a comparative word, 'than', which references boys.

Or maybe the subject not being the first word of the sentence was out of the (I quote) "rote, mechanical fashion" you are used to.

So the '20% more' is referring to girls, and that percentage is relative to the number of boys. There are multiple ways of interpreting it, but there is honestly only one correct one. 20% more than boys. boys=45. So, 20% more than 45, which is 45 plus 20%, or 45 plus 9, which is 54.

To add to that...'... (Below threshold)

July 29, 2011 2:49 AM | Posted by : | Reply

'There' is replacing 'girls'. If Alone wanted to make that sentence "less ambiguous" (i.e. more conforming to mechanical translation) he could have said:

girls are 20% more than boys.

which sounds sort of odd when spoken, but spells out the math problem pretty clearly.

But the comparative "than" ... (Below threshold)

July 29, 2011 2:56 AM | Posted by : | Reply

But the comparative "than" doesn't specify a referent for the "20%," it simply specifies that the comparative relationship is between girls and boys, that is, the number of girls are 20% (of something) more than the number of boys, as opposed to being 20% (of something) more than the number of teachers, or Russian admirals of the 19th century.

This comment thread is a hi... (Below threshold)

July 29, 2011 2:58 AM | Posted by : | Reply

This comment thread is a hilarious illustration of the original thesis.

What the "oh, oh, oh, every... (Below threshold)

July 29, 2011 3:12 AM | Posted by : | Reply

What the "oh, oh, oh, everyone sucks at word problems and reading comprehension" crowd, including the original post, is missing is that we use symbolic representations of things like quantity just because by doing so we can strip away most of the ambiguity of ordinary language.

That's why, for example, economists express their hypotheses with formal models -- not because they're brainwashed into solving problems by rote and hence unable to understand their claims expressed in words, but because the words yield less precise, more ambiguous, and hence less testable, predictions.

(And this is leaving aside things like quantum physics in which there is no non-symbolic intuition. Or profoundly counterintuitive mathematical and logical theorems which it's impossible to "get," except insofar as one just follows the steps of the proof.)

Are you kidding? TLP makes ... (Below threshold)

July 29, 2011 3:27 AM | Posted, in reply to , by : | Reply

Are you kidding? TLP makes up fake McLuhan quotes left and right like he's Oscar Wilde. "I may have been born yesterday, but I still went shopping." --Marshall McLuhan

"A term like "20% more X th... (Below threshold)

July 29, 2011 3:36 AM | Posted by : | Reply

"A term like "20% more X than Y" is inherently ambiguous. If you can't see that, then I submit that you have exactly the same problem our host is pointing out -- that is, you've been trained to interpet a phrase like "20% more X than Y" in some rote, mechanical fashion without actually having some kind of cognition about what things like percents actually mean."

you're an idiot, if this trips you up- how will you ever prove the central limit theorem or understand quantum mechanics?

Indeed, symbolic representa... (Below threshold)

July 29, 2011 3:44 AM | Posted, in reply to , by : | Reply

Indeed, symbolic representations of logic are non-ambiguous, but still must be derived from ambiguous human language (or human thought, which is pretty dependent on human language).

Don't glorify logic in place of intuition, though. Logic, although powerful, more than often fails to solve the problem, and notably is pretty much the only missing link between human intelligence and computer intelligence (it's easy to represent logic with 1's and 0's, not so easy to represent intuition).

Regressing for a moment, I still don't see the ambiguity in Alone's statement. As a note, the original statement said 20% more girls in the class than boys. I failed to include that specifier, but with that, I cannot personally spot any ambiguity.

That might just be illuminating the difference between intuition and logic, though. (deductive) logic, when suited for a problem, cannot be wrong. Intuition, albeit much more robust and powerful, can be wrong.

Elitegarbage man: I'm done ... (Below threshold)

July 29, 2011 4:14 AM | Posted by : | Reply

Elitegarbage man: I'm done with you after this, but just to briefly point out a couple things: 1) being able to attend to the ambiguity in a problem =/= being "tripped up" by said problem. 2) were you not able to read the bit where I pointed out that quantum mechanics doesn't have intuitions accurately expressible in ordinary language?

Rambling fool -- I think what I'm saying, in attempt to be charitable to all sides, is that what we're working with when we work with these word problems is multilayered conventions. First, there's the convention of standard english -- the meanings that we collectively assign to words and arrangements of words. In that convention, "20% more X than Y" is ambiguous, because the referent of the 20% is unspecified.

However, I accept that there might be a secondary convention layered on top of that original convention. That is, it might be part of standard mathematical english that when you say "N% more X than Y," the referent of the N% is the quantity following the "than." But that's not something we get from ordinary English (i.e., not knowing it is not a failure of reading comprehension). Nor is it a matter of having a conceptual/intuitive understanding of what a percentage is or how it works -- you can fully understand a percentage without being able to pick out, in a sentence, to which quantity the writer means to apply the percentage.

Instead, knowing and applying the "N% more X than Y means N% of Y more X than Y" convention is itself a mechanical rule -- it's exactly the same sort of mechanical rule as lining up the two-digit numbers on the worksheet, and can be learned as a rule and mechanically applied just as anything else.

So (and this is my ultimate point) the people who insisted on a different interpretation of the problem (which, for elitegarbageman's edification, I note did not include me -- I simply pointed out that there were other permissible interpretations, without suggesting that the main interpretation was non-preferrable) simply were not aware of the secondary convention giving a nonstandard meaning to that particular arrangement of words and numbers, not failing to understand mathematical concepts or failing to understand standard english. Nor was it a failing of intuition.

(That being said, there is a possible argument for the impermissibility of the alternate interpretations insofar as each requires fractional students. But you could easily write versions of the problem that don't require fractional students on alternate interpretations, and then this argument would go away.)

(I think I should unsubscribe from this thread, it's a little stressful -- but thanks for engaging like a reasonable person, rambling fool.)

@Paul GowderIs Engli... (Below threshold)

July 29, 2011 4:58 AM | Posted by : | Reply

@Paul Gowder

I only ask because your interpretation of the question is astonishingly contrived.

""20% of the number of boys, or 20% of the number of girls?" Both are legitimate interpretations of the problem, it seems to me."

100% wrong.

To make it blindingly obvious, substitute 100% for 20%.

You have ably illustrated the point of the post.
Simply because you found the question hard it doesn't mean that the wrong answer is right.

Jim: NTLB makes this phe... (Below threshold)

July 29, 2011 5:05 AM | Posted by : | Reply

Jim: NTLB makes this phenomenon worse. All outcome measures are centered on a large volume of standard tests. Teachers have to teach to pass the test. In my kids' experience, this encourages algorithm-based mathematics.

Ugh! What you're saying doesn't make sense. Mathematics is, intrinsically, algorithm-based. Given a set of inputs, you transform them according to a logic set into a set of outputs. Humans learn this by rote memorization, I'm sorry to burst your bubble.

I'm sick of these so-called 'constructionists' who go around and try to dumb down math education; lets make it colorful and fun and hope the kids discover Fermat's theorem themselves since we're too busy fighting for a guaranteed job with inflation +4%. Fucking Ramanujan had to sit there as a kid and learn the basic operations via rote memorization.

We should be lucky enough that our brains, devised for advanced hunting and communication strategies, is even able to comprehend mathematics as we do. Yet, here we sit, mad that it takes effort and unfun work.... if only we could teach a kid how to count by naively exposing them to the number of bullets left in a clip in Call-of-Duty. Oh snap, lightbulb, call a constructionist!!

As Benjamin Bloom discovered in his 1984 metastudy on the topic, 1-on-1 education results in a two standard deviation improvement in performance. The closer we can approximate this, the better. Somehow we've been regressing since the day of a single nun with a class of 50 kids, sans air-conditioner, internet and calculators. IMHO because the problem, as Alone articulated, is that most teachers today are functionally retarded. A downstream effect of this is that they aren't able to comprehend the material themselves and are unable to infer and mentally retain where each student's relative progress is.

Our only hope is Khan Academy and turning it over to the computers. Lets face it, the teacher's are too busy on facebook.

V, how many students have y... (Below threshold)

July 29, 2011 6:35 AM | Posted by : | Reply

V, how many students have you taught Euler's identity? If none of them responded with some combination of "No way, that's crazy" and "Holy crap, that's amazing!" then the answer is zero. And if all of them did, then congratulations, you're a constructionist.

I'm not saying schools shou... (Below threshold)

July 29, 2011 7:45 AM | Posted, in reply to , by : | Reply

I'm not saying schools should be a launch pad for college. What I'm saying is that it takes some knowledge in abstract algebra to be truly aware of the underlying structures in middle school algebra, the differential calculus for being truly aware of what is going to high school physics and so on.

I mentioned drafting college professors because if you truly set the bar high enough for middle school (where the problem seems to come from) teachers, you're going to fire too much of them. And I hear this argument often: "we can't set the bar this high: our teacher pool is inadequate and we know it, but who's going to teach the kids?". Drafting tenured professors (and hiring unemployed engineers and scientists who got bumped off the tenure track and are sitting on their hands) is a temporary solution.

I homeschool my son and fou... (Below threshold)

July 29, 2011 8:03 AM | Posted by : | Reply

I homeschool my son and found the same problem when using standard curriculum. Now he can do both, but there is still a disconnect when having to put the words to paper. He actually does better on verbal word problems where he finds the answer intuitively. We are working on this, but my student:teacher ration is 1:1. I don't see how he would be able to get it in a standard classroom; I'm sure his actual ability to do verbal math would've been missed.

Not saying he has the answe... (Below threshold)

July 29, 2011 9:33 AM | Posted by : | Reply

Not saying he has the answer right now, but i'd put money on Sal Khan of khanacademy.org eventually figuring out how best to simultaneously teach millions of kids how to do math.

@PaulIf you were t... (Below threshold)

July 29, 2011 9:59 AM | Posted, in reply to , by : | Reply

@Paul

If you were to hear an advertisement for a car on the radio that said "now with 50 percent more horsepower" would you understand what the "50 percent more" was reffering to?

"I think Alone is referring... (Below threshold)

July 29, 2011 10:30 AM | Posted, in reply to , by : | Reply

"I think Alone is referring to "good" students who coast through school without any real learning..."

Agreed, but he could have made that fact much clearer.

If this is true, it's frightening. I was a history major in college. I was in the special class for math in high school. And I still figured out the math problem in seconds.

But how much of what Alone describes is down to lack of interest and/or confidence? One of the first challenges I had in elementary school was calming myself down enough to actually try the tests, and working up any interest in them.

I'm fairly certain most people could do it if they tried, but many people blank out when they see math, or just lose interest when they see the old word problems, or worry about making fools of themselves.

"There are 20% more girls t... (Below threshold)

July 29, 2011 11:27 AM | Posted by : | Reply

"There are 20% more girls than (there are) boys."

Someone's way overthinking this. Why would 20% refer to anything but what's in the problem? Which is boys and girls, not freaking Russian admirals. But let's say that we throw linguistic convention out the door, and make the 20% refer to girls. If were 100 girls, and (100 minus 20%=) 80 boys, there would be 25% more girls than boys. So that doesn't work. And even if the 20% did refer to girls, then there would be no way for the student to solve the problem. Not very instructive, that.

I think part of the problem is self-identified "intellectuals" trying to justify their existence by constructing complicated arguments for why simple problems have multiple answers depending on dubious reinterpretations they've concocted to make themselves feel smarter than they are.

Wow, TLP was right. You pe... (Below threshold)

July 29, 2011 11:29 AM | Posted by : | Reply

Wow, TLP was right. You people really do suck at math.

20% more girls than boys implies that the number of girls, y, is dependent on the number of boys, x.

So, y = 0.2x + x makes sense since that sets up a solvable equation where is y is a variable totally dependent on x.

y = 0.2y + x implies a different meaning. 0.8y = x, which implies that x is 80% of y. If this equation were the case, the problem might read "The number of boys is 80% of the number of girls. There are 45 boys."

That means that "there are 20% more girls than boys" doesn't imply that "the number of boys is 80% the number of girls."

People forget that you can't just add and subtract percentages when the percentages of what change.

If I increase the number of boys in the class by 20% then decrease it by 20%, I don't wind up with the same number of boys. If I start with 45, then 45 + 0.2 (45) = 54. Then 54 - 54(0.2) = 43.2.

To me, the phrase "20% more Y than X" implies that there is more Y and than X and that the extra amount of Y is 20% of what X is. That what I learned in math, the name way I learned what metaphor was in reading.

The system may be a little at fault with how we teach math anyway. We teach kids increasing complex calculations without any real world connection to them. The we finally introduce a couple simple "world problems" (real world applications, NOOOO!!!) and they flunk miserably, and we just shunt them along since "nobody likes world problems."

That's like a doctor that learns all the anatomy and physiology, biochemistry, pharmacology, etc, but then refuses to try to solve a patient care scenario.

Maybe the math systems is backwards, maybe we should START with real life scenarios and show kids simple mathematical ways to go about solving them.

If it makes you feel any be... (Below threshold)

July 29, 2011 11:42 AM | Posted, in reply to , by : | Reply

If it makes you feel any better, I have a degree in math and my first response to the question was exactly the same. It's not phrased as clearly as it might be. But that's because the person who phrased it WAS ONE OF THE PEOPLE TLP IS TALKING ABOUT.

No.Does the car on... (Below threshold)

July 29, 2011 12:07 PM | Posted, in reply to , by : | Reply

No.

Does the car only come with one power train configuration? Do they compare it to any competitor's products in the ad, especially right before the assertion of the larger horsepower? Shall I go on?

Of course in this instance I'm immediately suspicious not because the assertion is ambiguous on its face (which it is) but because when I hear even *potential* ambiguity in an advertisement I assume somebody is trying to get me to make an unwarranted assumption.

I've never thought a so sim... (Below threshold)

July 29, 2011 1:55 PM | Posted by : | Reply

I've never thought a so simple math problem could generate so much bad language (from adults? Or the bad language guys still in kindergarten?)

I don't have any suggestion, Alone, but

Keep up
the good work

Be honest with yourselves. ... (Below threshold)

July 29, 2011 2:24 PM | Posted by : | Reply

Be honest with yourselves. If you got the question wrong, then your math is lacking. There are no excuses. Behind every squiggly line and strange symbol is some intuition in math. The sooner you understand that, the sooner you will be able to solve 3rd grade math problems.

STOP LYING TO YOURSELF.

http://www.mathematicallycorrect.com/

actual sat problem:<p... (Below threshold)

July 29, 2011 2:31 PM | Posted by : | Reply

actual sat problem:

A store charges \$28 for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store employees can purchase any remaining sweaters at 30 percent off the store's cost. How much would it cost an employee to purchase a sweater of this type at this sale?

* \$ 8.40
* \$14.00
* \$19.60
* \$ 20.00
* \$ 25.20

hint: there is only one correct answer. the college board will not will give you points for your multicultural, philosophical, postmodernist interpretations

are you starting to see what i am saying now? QED bitches

Seems pretty obvious that f... (Below threshold)

July 29, 2011 3:27 PM | Posted by : | Reply

Seems pretty obvious that factory schools, which treat students as products, create people fit only for working in factories. That's their purpose, after all. You don't need to understand what calculus is in order to algorithmically produce answers, just like you don't need to understand how a Corvette works in order to screw Nut A onto Bolt B.

One obvious solution would ... (Below threshold)

July 29, 2011 3:30 PM | Posted by : | Reply

One obvious solution would be to treat education as a priority. Spend resources to attract young, innovative teachers and give them a mandate to improve the educational process from the students' perspective.

Maybe this is simplistic, but teachers should be the skilled facilitators of learning, not just standardized babysitters. Raise the prestige of teachers, pay them more and give them more money for supplies, and provide enough money for the school boards to properly evaluate their performance (not just review how their students do on standardized tests).

Hire the passionate young ones that are inspired learners themselves and make them read your essay is my suggestion.

Store is buying th... (Below threshold)

July 29, 2011 5:11 PM | Posted, in reply to , by : | Reply

Store is buying them for \$20.00 each. \$28.00 = x + 0.4x, so x = \$20.00.

I'm unclear on whether "30 percent off the store's cost" refers to their buying or selling price. But either way:

If you mean the employees are taking an additional 30% of the store's original buying price (\$20.00), then they're getting them for \$14.00/each.

If you mean the employees are getting them for 30% of the store's selling price (\$28.00), then it's \$19.60 each. I'm assuming you meant the former, since the whole mess about the 40% increase in this case would then be extraneous information that doesn't add to solving the problem.

Not rocket science, people. That's what high school was for.

On another note, someone post more problems like this. I'm always up for shallowly validating my ego via showcasing high school math skills on anonymous websites

Nah, the problem is that we... (Below threshold)

July 29, 2011 5:30 PM | Posted by : | Reply

Nah, the problem is that we started reaching the point of diminishing returns. Almost all the data I've seen over the years is that when you institute a K-12 education program you increase average IQs from the 60s or 70s that are common in semiliterate and illiterate societies to about 100. So beginning in the 1950's, flush with our success in turning European peasants into the most productive workforce in history, we begin investing ever more into education. Educators and policy makers eagerly awaited the results, which were... nada, nothing , zilch. So in the 1970's we started disinvesting from education. Hell, we were already harvesting more than enough doctors, lawyers and engineers. The rest is all theater. The less productive students get sent off to "studies" programs to raise their self esteem. Your ability to solve TLP's word problem tells you which group you belong to.

For all the people struggli... (Below threshold)

July 29, 2011 6:04 PM | Posted by : | Reply

For all the people struggling with the percentages.

Jesus christ. "X is 20% more than Y" = "X is 120% of Y". Clear now?

Phoenix Online GEDs for eve... (Below threshold)

July 29, 2011 6:12 PM | Posted by : | Reply

Phoenix Online GEDs for everyone!!

Let C = the store's cost.<b... (Below threshold)

July 29, 2011 6:37 PM | Posted, in reply to , by : | Reply

Let C = the store's cost.
Let S = end-of-season clearance price.

Then \$28.00 = 140% of C = 1.4C
S = (100% - 30%) of C = 0.7C

Oh wow! S = half of that original \$28.00 price, because 0.7C is half of 1.4C!

Therefore S = \$14.00.

Perhaps I'm being pedantic ... (Below threshold)

July 29, 2011 7:31 PM | Posted by : | Reply

Perhaps I'm being pedantic here but let's see if I can use some math to prove a point.

There are 20% more girls in the class than boys. What percentage of the class are boys?

Let x=% of boys
Let y=% of girls

As all the members of the classes are either boys or girls
x+y=100

As there are 20% more girls in the class than boys.
y=x+20

x+x+20=100
2x=80
x=40

Therefore
y=60

40% of the class is boys and 60% is girls (ie 20% more than boys). If there are 45 boys, how many girls are there? 67.5

BUT

Isn't 20% of 45 equal to 9? Obviously yes, so why are there two different answers? The answers differ because one is 20% of the total number of people in classroom and the other is 20% of the total number of boys. The question is ambiguous because every student in the classroom is presumably either a girl or a boy and therefore the total percentage necessarily equals 100%. Reference point is always an issue in math when it comes to percentages. Make sense?

For those of you still pond... (Below threshold)

July 29, 2011 7:56 PM | Posted, in reply to , by : | Reply

For those of you still pondering the 20% issue: in the phrase "20% more girls than boys" the 20% references the number of boys, not the total class, and implies multiplication. A 60/40 split in the class is not a difference of 20% that refers to subtraction. Percentage difference between two numbers requires multiplication, always. You can have a difference of twenty students, which implies subtraction, but percentage necessitates multiplication.

Easy, It takes off. ... (Below threshold)

July 29, 2011 7:56 PM | Posted, in reply to , by : | Reply

Easy, It takes off.
See it here:

what i'm trying to say is:<... (Below threshold)

July 29, 2011 8:38 PM | Posted by : | Reply

what i'm trying to say is:

just cuz the neurons in your brain are fried from all the wellbutrin and seroquel and find the problem ambiguous- that fact alone doesn't make the problem ambiguous...

"to be or not to be is true" -Bool

stop trying to fool yourself into thinking you are smart...
YOU THINK INDIAN KIDS STUDING FOR THE 'JEE' EXAM FIND THESE PROBLEMS AMBIGUOUS?

we are like so screwed bro...

I'm a homeschooling mother.... (Below threshold)

July 29, 2011 9:19 PM | Posted by : | Reply

I'm a homeschooling mother.

I want a motherfucking pension, a parade, and a pony.

That 20% is referring to an... (Below threshold)

July 29, 2011 9:33 PM | Posted, in reply to , by : | Reply

That 20% is referring to an increase in relation to the number of boys in the classroom. Period. If it were referring to the 60/40 type of split that you and others have mentioned, it would have said "The percentage of girls in the classroom is 20% more than the percentage of boys".

I'm pretty sure that everybody who finds the question ambiguous, even after all of this discussion, is a.) arguing for the sake of argument or b.) didn't get it right initially, and they want to justify their mistake.

"The math question was wrong, not me!"

I am a computer programmer, and we so often create programs that fail to run and after hours upon hours of unsuccessful debugging, we conclude "My program is correct. The compiler is clearly wrong."

In my experience of writing code that didn't work, the only time my code was EVER not the problem, there was a SERVER SETTING that caused the problem. Still human error, though, because I should have been looking at server settings to begin with. Yet, I am just as guilty as any other... After hours of fruitless debugging, I convince myself that my compiler is broken.

unless you're developing on... (Below threshold)

July 29, 2011 9:49 PM | Posted by : | Reply

unless you're developing on .NET, then the compiler is wrong :-)

OMFG, some of you really ar... (Below threshold)

July 29, 2011 9:58 PM | Posted, in reply to , by : | Reply

OMFG, some of you really are braindead.

To summarize the idiocy since my last post:

"There are 20% more girls than boys so there must be 60% girls and 40% boys" WRONG. 54 is 20% more than 45, but 54/45 DOESN'T EQUAL a ratio of 60/40. It's more like a ratio of 54.5/45.5.

This is because there are total of 99 kids.
% girls is 54/99 = 54.5%
% boys is 45/99 = 45.5%
This is not 60% and 40%.

Such is the beauty of math/science--it's objectivity weeds out the stupid.

A knowledge, a growth, a go... (Below threshold)

July 29, 2011 10:48 PM | Posted by : | Reply

A knowledge, a growth, a good article can make a person to enhance the taste, thank you for sharing, I will carefully read the product to make themselves rich!
cheap chi flat iron

I will freely admit that I ... (Below threshold)

July 29, 2011 10:51 PM | Posted by : | Reply

I will freely admit that I have a deep resentment for the beautiful people that didn't have to learn math. Go into any computer/engineering/hard science class at a decent university. Why do you only see Asians and autistic people? If I could have made a living as an insurance salesman, believe me- I would trade this life for that one in a heartbeat. But I am not beautiful, and I am socially awkward. I didn't choose this life- it chose me.

So when people wonder why we math-literate find people's stupidity offensive, it's most likely rooted in jealousy of your no-talent-ass-clown-mba lifestyle. No amount money writing code at a hedge fund can fill the complex you have because you couldn't look the opposite sex in the eye for two decades.

Without question, I am a narcissist. Maybe that can be fixed?
But you sirs, suck at math. If you're over 25y/o, that can't be fixed. :-)

There are 20% more girls in... (Below threshold)

July 29, 2011 11:03 PM | Posted by : | Reply

There are 20% more girls in the class than boys. If there are 45 boys, how many girls are there?

IS WHY YOU DON'T UNDERSTAND:
Congress just passed a 20% tax hike. If you paid 4500 in taxes before, how much will you pay now?

"a lunch pad for collage" -... (Below threshold)

July 29, 2011 11:28 PM | Posted by : | Reply

"a lunch pad for collage" --- Awesome. An all-timer.

Ummm... really?Tho... (Below threshold)

July 30, 2011 12:23 AM | Posted, in reply to , by : | Reply

Ummm... really?

Those who things aren't always mutually exclusive. There are plenty of people out there who are intellectually and mathematically inclined that are also very socially savvy.

You may just not realize it because those who also maintain good social awareness know how to verbally showcase their intelligence through wit, charm, etc instead of fumbling through clueless, dorky ramblings.

It's much easier to close yourself off on a little narcissistic island when you've never really been socially keyed in to begin with.

Sadly, you seem to be worse... (Below threshold)

July 30, 2011 12:40 AM | Posted, in reply to , by : | Reply

Sadly, you seem to be worse off than the 'beautiful anti-mathematicians' you hate. Life is subjective, as are the priorities, values and joys thereof. Consider this. Those people have a system of priorities that is also their way of life (although I assure you, some are living a lie).

You got fucked, though (or fucked yourself). You have wound up with a perceived importance on the very same things as those people, while your life has taken you to a much different place. Those people find your way of life silly and inconsequential to them, because well, it is. Why can't they be the same to you? It'd make you happier, or at least help you feel less like a high school goth kid.

Find joy in what defines your life, forget about that lifestyle you were conditioned to envy but were denied. I'll let you in on the secret... that lifestyle, at least the way it is presented, it doesn't actually exist. Certain people just want you to think it does. It's how *they* feel good about themselves.

I remember being a child in... (Below threshold)

July 30, 2011 12:53 AM | Posted by : | Reply

I remember being a child in school and this is simply not true.

When we learned addition and subtraction, we were taught the "big picture" - adding and subtracting represent changes in the amount of something. It is not some game where if a 5 and a 4 are lined up that equals a 9.

This is why children first are introduced to arithmetic by using pictures depicting numerical amounts of items. A very young child will be shown a picture of 3 bananas, and then one of 5 apples, and then an equal sign which shows 3 bananas + 5 apples = 8 fruit in total. Children absolutely are encouraged to learn the "point" of all of this.

If some children are incapable of seeing the larger point of a thing, in spite of ample encouragement (pictorial depictions of items being added or reduced), that is probably some kind of focused learning disability or developmental disability on behalf of that specific child. The overwhelming majority of american children can easily answer that question "45 beads plus 24 more from a friend".

Not all americans hate word problems. I loved word problems, but then again I also like puzzles (I'm an INTP ...meh). It depends on the personality of the individual human you are dealing with. Not all humans are mental and enjoy puzzles - not all people enjoy the process of teasing out a problem . There's nothing wrong with that. Not everyone can sit around thinking , arguing, contemplating, wondering all day. If so, who would get anything done? Who would apply that which we know?
Some people are more practical and just want the facts plainly spelled out, and they have other interets/abilities/talents.

Regarding your example of reading comprehension (a child can scan the paragraph and come up with the answers), then what we are dealing with a is a problem of attention. If the child can pass the manatee test, their comprehension is fine. If they fail a 10 page example, the problem is their attention is poor, it does not mean that their comprehension is poor. Most children have a poor attention span. Children with attention spans long enough to sit through 10 pages of a story and read it closely enough to answer specific questions are very rare, assuming they are young children.
They make word problems short on purpose - they are not testing attention, they are testing comprehension. Reading the paragraph quickly and getting every question right means your comprehension is on the mark. Young children can be expected to have crap for close attention.

Regarding your 20% of 45 + 45 example... this was so simple I thought it was a trick and I was reading it wrong. Are people really unable to instantly work this problem out? Srsly? That's sad. Nah, most people are smart enough to figure that out instantly , I think.

I agree with anon @ 7/28 2:... (Below threshold)

July 30, 2011 1:24 AM | Posted by : | Reply

I agree with anon @ 7/28 2:13

I was thinking the same thing.
The problem is not our school system. The problem is that a whole lot of kids do not give a shit at all about anything, least of all learning.

Their parents are ignorant morons who set no expectations for them, and so they go to school merely because they have to, and make no effort while they are there. They are not naturally curious and there is no external encouragement to achieve anything.
This is the life of a ghetto dweller, and so much of america is rapidly becoming a giant ghetto.

We are returning to the feudal system. We have broken down the smallest social structures, left people isolated fragments with nothing, meanwhile a very few privileged people manipulate and lie their way to security and control using the media and government. The main difference is that in feudal england power was handed down by birth ... here it's handed down by how efficient you are at lying manipulating and presenting the reverse of a thing as true (since the key for this social structure to work is that the broken down slave american must believe he is free, matrix style... if he knows he is a slave, he will rebel. The key to keeping the slave american ignorant of his status is to plow him down with lots of sugar and starch so he is fat and dead in the mind, lots of porn so he has no drive to compete or achieve anything, and the myth of endless choices and possibilities for himself. Let him believe if he really WANTED TO he could be the president. He simply CHOOSES to be a fat world of warcraft playing pepsi drinking porn addicted nothing.)

We are eternal children constantly expecting handouts, satiation, like mothers milk which just arrives in our mouth from a nipple. A disturbingly small amount of people have the energy to think about things, evaluate them, and determine what is right or best for themselves, the world.

The ones who try are presented as crackpots - e.g. the norway crazyman.
"See what happens when you go about trying to think about the world and dare to have thoughts of changing it? It means you are crazy. So don't think. Just follow."

This is the subtle message we are all given when we hear yet another story about some crazy fuck with a a manifesto. Thinking about how things are and trying to change them has become synonymous with mental illness. There are no positive examples of people who attempt to change the status quo. We are purposely fed a steady diet of subliminal propaganda which vaccinates us against the practice of thinking, evaluating, and trying to make changes.

It's so contrived to say so but really, we truly are just cattle who are to be manipulated for the benefit of a very few people. This is how humans are designed by evolution. This is how our genetics shape our nervous systems. We are incapable of doing what's right or valid, we only can do what we are told to do. We're like dogs... a pack is just like human society. Very few of us can think about things and make those kind of judgment calls and the ones who try are rapidly shot down as psychopaths by our media.

The key to avoiding a change of power is to keep the cattle placated. More sugar and high calorie food and porn and alcohol, no one will throw a fit. Its only when we cant have corn syrup or anal porn or budweiser that we need to worry about shit changing. When people's chemical haze is ripped from under them, those who would naturally be crazy fucks starting uprising and terror attacks suddenly find the motivating push to act.

The people presently in power have studied history, they have learned their lessons. When you tell people to eat cake its not long until someone else is at the top of society and youve been ripped apart by an angry mob.

At the end of the day, all we want is the very bottom of the maslow pyramid. Successful control of a society is oriented around giving us this.

I have to wonder if maslow specifically chose a pyramid to represent his ideas because of its implications to masonry and social control. Bottom layer of the pyramid fuckers, food and sleep and shitting.

But I have already been rambling too much too long, much like a crazy norway bomber so feel free to ridicule me and make a mental note that "people who criticize society are crazy and don't make sense".

Healthcare has always been ... (Below threshold)

July 30, 2011 1:41 AM | Posted, in reply to , by : | Reply

Healthcare has always been algorithmic.

Diseases, once identified, have a common pathology. Or at least they should. Therefore, treatment between patients can follow an algorithm as the pathology is similar.
If your patient presents with symptom x, you ask these questions, order these basic tests. If the tests have certain results, then you do more specific y test. If y test is positive, you have a diagnosis.
Once you have a diagnosis, you start with initial treatment protocol, and then tailor it to specifics of the patient (e.g. kidney labs high; lower drug dose. Body weight high; increase loading drug dose. Pt not making improvement after a certain timeframe; add on a new drug or try a different drug depending on which intervention is more appropriate).

The only thing different today vs lone door to door physician days, is now it is "frowned upon" If a doctor dunks you in water for no good fucking reason, or hooks electrodes up to your brain because he is a doctor and can do that and you have no choice but to listen, regardless of whether or not his idea is insane and random and not based in any evidence what so ever. You can't just drill a hole in someone's head and pour some strange mixture of herbs in there anymore.

Now we have routes for treating diseases, which have (supposedly) been tested established by the scientific method.

It is no longer appropriate for a physician to do whatever crazy shit he wants and he will face repercussions for it.

The only problem is not the algorithmic nature of healthcare - the problem is the established algorithms are often very shitty and the result of corporate interests.

Don't tell diabetics to go on a low carbohydrate diet, the absolutely most effective intervention for the majority of cases of diabetes. NOOOO! Not at all! Tell them to do their OGT combos and that they can eat all the carbs they want, just buy Dannon brand (r) diabetic yogurt or Glucerna (r) shakes instead.

Don't follow the scent of bullshit which rapidly reveals most diseases of civiliation are, not so surprisingly, caused by our diet and lifestyle. Just make more drugs and minimize patient education as the new treatment protocol.

Our epidemic levels of mental illness, depression, surely have no relation to SEVERE omega 3 fatty acid deficiency... in spite of AMPLE scientific evidence the brain is made of fat and a lack of omega 3 fatty acid causes profound dysfunction. Just half heartedly tell your patient to take 1 gram fishoil (sort of like spitting in a rainstomrm) and to continue their Cymbalta (r) as prescribed.

And surely, some random dude can see a person for 5 minutes and know exactly that they have bipolar II disorder and are presently in the manic phase of illness.
And, they can know if they see a random lady in 5 minutes and know her problem is she is a borderline. Nothing more worth investigating.

Psychiatrists are conditioned to BELIEVE they can magically halleluja style faith detect the illness of their patient just by looking at them. No one gets any false positives because of the biases of the doctor - when he is wrong, he doesn't care, the patient just stops coming or never gets better. When he is right, oh look what a smart fuck I am I"m the smartest fuck in this whole practice / building / city.

They are taught to believe this power because the insurance companies and other corporate interests have brainwashed them since they were little doctors that they can do this.

The ones who realize they actually can't, realize they can't change the system anyway, and so they just go with this revolving patient door model. Mental illness is not like physical ones. We have no tests which can instantly tell you what the problem is. It takes TIME to figure it out. This is why rapid patient treatment in psychiatry is such a problem - you can only sorta maybe know if you have actually spent some time with the patient, more than your reflexive human judgment.

I could rant on but why bother.

The problem isn't the algorithmic nature of healthcare.

The problem is the algorithms are horse shit

They are shit because of the aforementioned problem in my previous rant - corporate interests and a few powerful people literally control the world. And you. Especially you.

<a href="http://mathnotatio... (Below threshold) There is an ambiguity in ho... (Below threshold)

July 30, 2011 4:01 AM | Posted, in reply to , by : | Reply

There is an ambiguity in how it's worded, but it's not so big: when somebody says "there's 20% more Y than X" it almost always means "X=Y*1.20". Like when McDonalds said "now 80% more meat" you didn't assume it was less than 20% meat before (well, I did, but I was about ten and pretty suspicious of McD). It still meant it could only be slightly more than 50%.

When there is no interest o... (Below threshold)

July 30, 2011 5:26 AM | Posted by : | Reply

When there is no interest of deeper exploring reality (this is what education offers), there is no way to push it in the brain.

This is a fairly interestin... (Below threshold)

July 30, 2011 12:28 PM | Posted by : | Reply

This is a fairly interesting topic but I want to start out that as an English speaking human being, I've already handicapped myself. English is actually a fairly difficult language to learn math with - it's clumsy. I'm not saying it's isn't a strong language but an incredibly difficult one to start out with.

It all starts out with basics. Read these numbers out loud 4, 8, 5, 3, 9, 7, 6. Without looking at them, spend the next twenty seconds memorizing these numbers and write them down. If you're English, you have a 50/50 chance of remembering the entire string. If you're Chinese, you're almost certain to get it right. We human beings have memory loops that only last for about two seconds; within that two seconds, you can easily memorize whatever you want. Chinese language allows them to memorize these numbers because they can fit those seven numbers within the two second memory loop.

Now, I'm pulling some text off of Malcolm Gladwells Outliers and out of Stanislas Dehaene's book The Number Sense.

Dehaene wrote:
Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is "si" and 7 is "qi"). Their English equivalents are - "four", "seven" - are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of it's speakers. In this domain, the prize for efficacy goes to te Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about ten digits.

For example, we say fourteen, sixteen, seventeen and nineteen; but one could logically expect us to say oneteen, twoteen or fiveteen but we do not. Past twenty, we start changing convention to decade-number; ie: twenty two. Each number in our language has a different form, our numbering system is highly irregular. The Chinese has a very logical numbering system. Eleven is ten-one (obviously not the actual language but we will represent the Chinese numbering system this way), twelve is ten-two and Twenty-four is two-tens-four, ect. By learning how to count quicker, using a logical numbering pattern they're learning the numbering system faster than we can.

There is also another bonus; if you ask an English seven-year old to add 37 + 22, they have to convert the words into numbers first. 2 plus 7 is 9; 30 and 20 is 50; which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence: five-tens-nine. There is a reason why kids become disenchanted with math at an early age; conceptually, it's a very difficult system to learn in English because of how clumsy our mathematical system truly is. Asian kids can learn to hold more numbers in their heads because it's quite simple and logical, which leads them to less frustration and will likely lead them to enjoying math more - they have a built in advantage to their system.

Interesting points Primer. ... (Below threshold)

July 30, 2011 2:36 PM | Posted, in reply to , by : | Reply

Interesting points Primer. Have you read any of Daniel Tammet's writing about math and his experience as someone who is synaesthetic? Or about the common colour/number language that synaesthetic people seem to have?

http://en.wikipedia.org/wiki/Daniel_Tammet

http://www.optimnem.co.uk/

And a Ted Talk by Tammet...... (Below threshold)

July 30, 2011 2:50 PM | Posted, in reply to , by : | Reply

And a Ted Talk by Tammet...

http://www.ted.com/talks/daniel_tammet_different_ways_of_knowing.html

can't you just train your b... (Below threshold)

July 30, 2011 3:58 PM | Posted, in reply to , by : | Reply

can't you just train your brain to not read the numbers out loud with your voice in your mind? Ie just memorizing the "image" 3, the "image" 4 and so on.

Does anyone else add then t... (Below threshold)

July 30, 2011 11:23 PM | Posted, in reply to , by : | Reply

Does anyone else add then tens place first then the ones? I'm not sure why I do this as it slows me down and causes errors but I always do it.

Oh, crap, this is the absol... (Below threshold)

July 31, 2011 1:14 AM | Posted by : | Reply

Oh, crap, this is the absolute worst (and by that I mean best) thing for me to read right before launching into psychology graduate school.

For a number of the studies that I have been reading, overall cognitive function is generally measured by problems not too far off from the things you've posted above. Which now begs the question (and it irritates me that it's taken me this long to ask this question) WHAT THE HELL ARE WE ACTUALLY MEASURING WITH THIS STUFF?

We have to hold the idea that the tests that we are administering are proxies for these constructs that we are trying to get at. When, actually, congratulations, in any survey-based study, you've just correlated the number of circles bubbled in on one piece of paper with the number that got circled on another piece of paper. Is it too late to go join that project on cortisol? Oh, wait, that's another proxy for another vague psychological construct, because we hold that changes in the natural cycle of cortisol are caused by "stress response" and, again, what does that even mean?

July 31, 2011 2:18 AM | Posted, in reply to , by : | Reply

Non-trivial incorrect use of:
'begs the question' and 'correlated'

but whatever- it's not what words mean, it's how you feel about them and how you interpret them...

If 90% of math teachers wer... (Below threshold)

July 31, 2011 2:21 PM | Posted by : | Reply

If 90% of math teachers were liberal arts majors in college, and are 80% more interested in getting home to watch Jersey Shore than they are in the welfare of their students, of the 78% of students who aren't getting proper support at home, how many will end up owing money on a credit card with a 24% APR?

In a sense, yes, I suppose ... (Below threshold)

July 31, 2011 2:57 PM | Posted, in reply to , by : | Reply

In a sense, yes, I suppose you could train your brain into associating numbers with images. Your brain does it all the time with words, if you misspell a word but use all the same letter, ie: dalring, you still read it as darling. Your brain is quite adaptable when it comes to associative processes.

Another interesting point, I was taking about this subject with a friend recently and he mentioned that he created his own numbering language in pre-school. He felt at that age that the English language was too bulky and needed to be shortened to words that are only one syllable long. Ie 1 = on, 5 = ei. When asked, he would just say these numbers he made up, his teachers all thought he had a learning disability until they had him do long division and was getting the correct answer. And quicker than his peers, I might add. They then took the next two years retraining him to learn standard English math.

I teach high school math an... (Below threshold)

July 31, 2011 5:11 PM | Posted by : | Reply

I teach high school math and science at a private school. I started teaching math in public school. This is what I can tell you:

Public schools have a variable quality of teacher. Many of them have the best of intentions, many of them are hard workers, but none of that matters if you're inexperienced. If you are inexperienced, you can usually go to a more experienced person, say "what should I do?" and copy them until you have enough experience to work on your own. But the public schools I've encountered are suffering from two problems for that: one, they train people with "education" degrees that are absolute garbage, and the people with "education" degrees come in lacking the humility to recognize that their degrees are absolute garbage and they know nothing. They have the illusion of competence, and the absolute worst person to bullshit about your competence is yourself, because you can't correct it. And you won't go ask for help.
The second problem is that administrative staff fires experienced teachers because they have a pay schedule to stick to, with standard raises based on years experience, and their budgets are being cut. So instead of reducing the bloated admin salaries (sometimes superintendents pay themselves \$500k and up per year) they fire the experienced teachers and hire new ones lower on the pay schedule. This means they save money. And this means kids have shittier teachers.

This doesn't even necessarily mean that the rookie teachers are incorrigible. They could be taught, they could improve, but in the situation they're in, they have incompetents in authority above them firing the competent people they should be learning from, and setting up more incompetents as the arbiters of wisdom. This means that they go to teaching workshops, listen to teaching "experts," and all in all have a theater of expertise which makes everyone be able to bullshit each other that they know how to teach. Meanwhile, they do not.

The solution? Reduce admin, reduce oversight, make schools teacher-run and a local concern. Hell, let the parents use vouchers so they can go to a private school. As a science teacher, as an atheist, I've thought for years that the voucher program was a thin cover for creationism. Now I see creationism taught to a few dopes as being less threatening than entire generations being ineptly taught as a part of a big stupid Education Theater that nobody cares about.

Hell, I went to Catholic school and it didn't stop me from getting into science.

As a Singaporean, I've grow... (Below threshold)

August 2, 2011 12:58 PM | Posted by : | Reply

As a Singaporean, I've grown up with these sort of model methods before progressing to algebraic equations and such in secondary school (13 yo)

I've been pretty good at math, so I'm lucky. What I do appreciate is that the model method does work for a few weaker students. It might be a bit more long winded, when it comes to solving problems with simultaneous equations, or anything with >1 variable. You end up having to draw all kind of funny models, to make it 1 variable. And believe me, our questions in the final exams of primary school, is tough. It can even leave some of the senior math professions stumped. They do come up with complicated methods to reach the answer, which can be explained in a somewhat clearer manner using the model method.

What I'm amazed at, is at the comments wrt to the math problem. Granted that "comprehension" of the English expression in math problems can be tricky, and we have our occasional linguistic gaffes in the exams, I dare say that most (if not all) of students put through the Singapore system, would be able to solve that, regardless of the language issue. Ans: 54

Solving simple math is one thing, and I see it more as a neutral statement. After you get the kid of solve it, so what? Teaching, should involve learning.. as well as applying, which is what I feel lacks in Singapore.

P.s TLP, my model method would be slightly different. For the "boys", I'd split the model into 5 segments, and draw the girls as 6 segments. (that takes away the 20% which tends to confuse most kids)Or if they're younger, you draw 10 segments and shade 2 etc.

As an educator, I believe t... (Below threshold)

August 2, 2011 3:03 PM | Posted by : | Reply

As an educator, I believe two of the biggest challenges in education are first that teachers are not well-versed in content knowledge and how to assess student learning both summatively and formatively. Secondly, high-stakes testing have left teachers with little wiggle-room to actually teach. As a result, problem-solving and logic, along with general reasoning skills are all taking a back seat to test-taking skills that focus on filling in the correct bubbles on annual tests. Couple this with a culture that is increasingly obsessed with games and entertainment and it is no wonder students are unable to comprehend math concepts or read well.

Schools employ an appro... (Below threshold)

August 3, 2011 8:46 AM | Posted by : | Reply

Schools employ an approach that they justify as "deeper than rote memorization"; it's "critical analysis." Jonathan Kozol attacked conventional learning as "drill and kill."

The problem, which the post, I think, punctuates, is that it's as possible to memorize simple processes as it is basic facts.

Ask a kid what his favorite video game: "Ultimate Warrior II is better than Night ranger because NR's graphics are wack and you only have two possible routes; UWII has twelve."

That's critical analysis. Comparing estates.

The issue with these students is not the inability to perform simple processes, it's issues of "mental stamina", which is the big thing in educational testing today.

Fatigue. Attention. That's the issue

The math problem is easy. I... (Below threshold)

August 3, 2011 10:23 PM | Posted, in reply to , by : | Reply

The math problem is easy. I don't believe TLP was making a reading comprehension point, but the comments thread sure confirmed that either people don't know math or people are trying to sound smart by making an easy question hard. Either way y'all done come off soundin stupid.

To those of you arguing that the answer is something other than 45+(45*.2)=54 as the number of girls in the class, I'd like pass along some advice my Mom told me a thousand times and has served me well, better to keep your mouth shut and thought the fool than open it and remove all doubt.

I wouldn't want a college p... (Below threshold)

August 3, 2011 10:29 PM | Posted, in reply to , by : | Reply

I wouldn't want a college professor teaching my kids because his name might be David Epstein

Seriously? "A lunch pad for... (Below threshold)

August 4, 2011 10:19 PM | Posted by : | Reply

Seriously? "A lunch pad for collage..."? No love?

Really interesting post. On... (Below threshold)

August 8, 2011 11:53 AM | Posted by : | Reply

Really interesting post. One bit sticked out to me more than the others did "...I suspect that this almost entirely explains Americans' universal hatred of word problems...".

As a Hungarian from Europe, I found this quite interesting, as here, we never had a hatred this serious towards problems like those. Of course there were problems which proved to be frustrating than others, but such a categorical distinction was practically non-existing. Interesting.

For what it's worth, Cathol... (Below threshold)

August 10, 2011 12:46 PM | Posted, in reply to , by : | Reply

For what it's worth, Catholic schools actually teach science and don't try to teach creationist pseudoscience (which is why many a kid's science education at a Catholic school has led them to becoming an atheist). From what I understand, Catholic schools in the US are historically better schools than the general public schools. The Fundamentalists/creationists pushing for the voucher system don't want to teach religion and science as separate subjects and give kids the kind of education you got, they want to teach kids religions AS science (quite the opposite of what you were taught in Catholic school and quite the opposite of teaching kids critical thinking in the way that you were). Catholic schools tend to be highly focused on producing high achieving students, they're generally highly focused on academic success (which means learning how to think critically). "Teaching the controversy" is kind of the opposite of what Catholic schools do (though I didn't go to a Catholic school many of my friends did, granted boys' and girls' schools may be different) - but then the Catholic church has a much more profound historical relationship with academia/knowledge, science and society than modern Fundamentalists (that seems to have mainly emerged out of TV evangelicism on the Protestant Holy Roller side of things). It may take the Catholic church a couple of hundred years but Catholic dogma can and does change and the Catholic church is not as hostile to science in general as Fundamentalists who want to "teach the controversy" are.

Interesting observation. Ba... (Below threshold)

August 10, 2011 3:01 PM | Posted by : | Reply

Interesting observation. Based on your friends' stories, do you know whether there is a friction among the teachers of that Catholic school concerning evolution?

These two posts explain why... (Below threshold)

August 20, 2011 8:07 PM | Posted by : | Reply

These two posts explain why my 40 year old marketing manager has no idea how (or even precisely where) he has lost market share year after year, much less how to improve his businesses: he never crunches numbers on a spreadsheet.

Now it's clear to me why he doesn't do that: he can't.

And neither can or do any of my fellow product managers that are age 40 or younger...And that means about 75%. No wonder the company is in trouble.

The only people who INSIST at modeling and testing hypotheses are 45 and up. The younger colleagues basically guess, or jump to conclusions on a tiny bit of data that they are given from the finance department.

When I respond to question from a 30 year old product manager with "I don't know, I would have to run the numbers", he is frustrated that I don't deliver an answer on the spot for what to change and why in a \$250 million dollar per year product line! When I tell him it would also be helpful if he looked at the numbers (and even supply him the raw data), he says he will ask someone else to do it) (huh?)

I've been frustrated with the idiocy because this is not how I learned and know to run a business or product line.

Now I understand WHY they are such idiots: grade inflation, narcicism and complete lack of math skills.

Thanks for lifting the veil of ignorance from my eyes on this matter. I was just thinking they didn't take the time for the spreadsheet work - but this explains both why none of boss boy's argumentation is ever grounded in math and why I've never seen him crunch any numbers in 3 years. He can't do either of the two.

Poli Science Major in sales and marketing who kept taking math classes through freshman college calculus in 1981.

The graphical answer to one... (Below threshold)

August 25, 2011 5:22 PM | Posted by : | Reply

The graphical answer to one of the examples is false. If there are 20% MORE girls than boys the right part representing the girls should be much wider.

And 43 to 45.... (Below threshold)

September 3, 2011 3:25 AM | Posted, in reply to , by : | Reply

And 43 to 45.

What is 10 percent of 45, t... (Below threshold)

September 3, 2011 3:28 AM | Posted by : | Reply

What is 10 percent of 45, times 2?

This is what you get when f... (Below threshold)

September 8, 2011 5:25 PM | Posted by : | Reply

This is what you get when from the universities elites and not-for-profit foundations take care of education from a for-profit-enterprise point of view. And they make a huge profit.

Add to that schools were taken from the locals and impinged with federal regulations and very funny tests given to children. Depending the way they answer the test, the teacher has no other thing to do than to comply with the guidelines coming from capital city, and pass on the information regarding how the parents behave towards the children. Among many other useful information on the families.

The Rockfellers started as snake oil sales people. They were selling "medicine" that was nothing but salt mixed with water, in the good cases. After a while doing that they figured that if they can dictate what people will learn (or be allowed to learn), soon or later, even if it takes decades to accomplish, ministering a poor education is highly profitable, as the wheel always turn toward profits. Education is not an exception.

In the face of this, that our kids do not learn, and that "new" ways to reverse that must be found, it keeps the problem unsolved as all eyes are in the effects of the problems, and talk about it as if the effects are the problem, instead of asking what is the origin for the problem.

If you think that America is ignoramus today, you have no idea how much more it will be in 40 or 50 years. I am glad I will be dead by then.

OMG, I'm a self proclaimed ... (Below threshold)

October 20, 2011 12:16 PM | Posted by : | Reply

OMG, I'm a self proclaimed "math moron" and even I got it right. I think tipping service workers must be a real struggle for some of you.

Wow what a bunch of hot air... (Below threshold)

January 10, 2012 7:19 AM | Posted by : | Reply

Wow what a bunch of hot air about basic math. If you think the question is ambiguous or you get the answer wrong then you are too dumb to vote. And you are basically proving the blog writer right. Schools are horrible at teaching people reading comprehension. Majority of people can solve a simple equation, but they can't create one based on problem description because they have 0 reading comprehension and 0 analytical ability. And then they enroll into philosophy, psychology, medical, anthropology etc... causing these fields to be populated almost entirely by people with no analytical ability.

I'm twenty-three. I ... (Below threshold)

May 24, 2013 12:21 PM | Posted by : | Reply

I'm twenty-three.
I have no idea how to add a percentage. (What is twenty-three percent of fifty: No idea. How do you determine a percentage?)

The other thing is that I did not know that memorization is the same as comprehension.

When I read your manatee description, I was intrigued when I read that they can weigh up to 3,000 pounds, then when I read the question, I re-scanned the information because I had almost immediately forgotten that information.

Is that a problem in reading comprehension, or a problem retaining information?

If you're 23 years old, and... (Below threshold)

May 24, 2013 1:19 PM | Posted, in reply to , by : | Reply

If you're 23 years old, and can't figure out "twenty-three percent of fifty" (hint: .23 x 50 = 11.5), you have much bigger problems than "retaining information."

I think the problem of our ... (Below threshold)

May 24, 2013 1:30 PM | Posted by : | Reply

I think the problem of our time is that we (the first world/middle-upper class) have so much luxury that we, especially the younger generations, are taking it for granted & believing that they can afford being intellectually lazy, which many probably can, but at a large scale, at the population level we can't afford it. Hard times lie ahead, I'm afraid.

I disagree. I think the pr... (Below threshold)

May 24, 2013 5:23 PM | Posted, in reply to , by : | Reply

I disagree. I think the problem is the divorce of education from the rest of the human universe. Kids today don't know what they don't know because they're 16 or older before they interact with the business world. It's easy to snow people into thinking that they know what's going on if their idea of what they're supposed to know comes from TV. And that's kinda how our system works.

A kid doesn't necessarily know something is wrong if he can't do algebra. Ask them, they have no idea what kinds of things algebra is used for. The fourth grader who's doing page after page of fractions and getting good grades for it has no idea what kinds of things fractions are good for. Go down the list. They don't really learn how to read critically because they never read a report to figure out why something isn't working.

My solution is more or less getting kids to solve more real-world problems. Have them solve a basic business problem of figuring out how much of item X to order for a store based on last week's sales and the projection that this week's sales will be 10% lower. Have them figure out how to get a 4% margin on a product that costs \$5 for labor and \$2 for materials. This is what happened in the early part of America -- kids learned to do adult skills by working on the farm or in the family store. By the time they hit adulthood, they'd already been doing the skills of their future careers for years, decades even.

The other thing is that they were given more or less the classical education. Grammar logic, rhetoric. They were doing more thinking in 8th grade than most of our adults do.

We have exactly the amount ... (Below threshold)

May 24, 2013 10:00 PM | Posted, in reply to , by : | Reply

We have exactly the amount of people being intellectually active (whatever is the opposite word of lazy) as we need. Perhaps more than we need. The problem that you are experiencing is that we have exactly the amount of people that are intellectually lazy as we need, and we also need to be able to whine that percentage. TLP has a good explanation of why this is; read more of it.

Essay can be defined as a p... (Below threshold)

June 5, 2013 6:54 AM | Posted by : | Reply

Essay can be defined as a piece of writing, which is written according to personal views and opinion of the author about a particular topic. The essay is all about discussion of every aspect related with any topic on which essay is written.

Daaaaaammmmnnn, America is ... (Below threshold)

November 15, 2013 11:38 AM | Posted by : | Reply

Daaaaaammmmnnn, America is fucked!

What a pity I stumble upon this thread 2 years late.

It's AMAZING how many stubborn dumbfucks there are in the comments, who fail on level1 of comprehending word sequences and then fail again on level2 of adding and substracting numbers, but are fully committed to go to war with anyone disagreeing with their conclusions. Plus, they can't even logically structure arguments and debate without getting personal. A Culture of hating, wound children.

I'm aware of hating as well here, but this is just toooo hilarious! I can't believe people like Paul Gowder really exist and weren't trolling. Wow, is that guy's logic twisted and wow ishe full of anger and spite. Good luck, America!

Herman the German, your con... (Below threshold)

November 15, 2013 11:45 AM | Posted by : | Reply

Herman the German, your contribution was insightful.

Most interesting is the nat... (Below threshold)

November 16, 2013 1:41 PM | Posted by : | Reply

Most interesting is the nature of the most of the comments seen here. All except a few address the issue on its face without comprehending what the author is trying to communicate,so congratulations to the few of you who actually saw a deeper meaning in the article, e.g. Algorithmic Health care. But Algorithmic thinking is the symptom, not the cause! Try this perspective......When we read the simple word problem, we have been trained not to think critically about it, either in terms of reading comprehension, or in computational aspects. Chances are, if we were to get this question on a 4th grade math quiz, we would be choosing a, b, c, or d, not filling in the blank. the Singapore method as well serves to retard critical thinking. With the Manatee example, we as a reader have little retention due to the fact that is is purposefully written to bore the hell out of us!! Language comprehension is proficient amongst the younger generations. We comprehend language very well. Reading comprehension however is meager at best. This is because we have been taught to believe that reading is boring as hell. Example: We can parrot Ezekiel 25:17 via Pulp Fiction, but we don't even know who Othello is. What we as a younger generation (15-45) lack are imagination and critical thinking. The public education system of the last 30 tears taught us this....taught us to abhor imagination and critical thinking, and to abhor the few whom still embark on such ventures. Taken in this context, the article becomes a metaphor symbolizing the complete lack of "education." The complete lack of independent thinking. Education meaning the teaching of not how to solve a simple problem, but HOW to think about, cognitively process, that problem so a unique, independent, novel, and logical solution becomes possible!

"Yup, this is why you get s... (Below threshold)

November 18, 2013 3:03 PM | Posted, in reply to , by : | Reply

"Yup, this is why you get so many kids who are able to fake their way into college with straight A's, never having studied, only to get fucked over in college. It's not that they were smart, it's just that they knew how to take the tests they were given."

No. You don't get it. You are completely missing the point.

This is why you get so many kids who are able to fake their way THROUGH college with straight B's, never having studied, only to get fucked over in LIFE. It's not that they WEREN'T smart, it's that they were never TAUGHT.

wat the hell... (Below threshold)

January 28, 2014 4:44 PM | Posted by : | Reply

wat the hell

The problem with our math e... (Below threshold)

April 12, 2014 5:53 PM | Posted by : | Reply

The problem with our math education is that it focuses on form rather than function. Basically useless arithmetic equations that are divorced from reality or any practical uses, rather than the most practical and efficient way to do math. The East Asians have a efficient way to count, do math, and their education system is more efficient at teaching people useful, but rather than attributing that to properly educating their children we rather resort to some racist mystical Asian Culture that orientalist seem to think Asians have.

I remember a fellow 5th grader outsmarted my horrible, know-nothing,blowhart, incompetent 5th grade teacher by doing a efficient math problem that was short and to the point. The teacher was the typical blue collar teacher who was down on his students, expected you to fail because you didn't have enough money or were non-white, was dead set on rote memorization as the only way to learn, and arithmetic equations. He was set in his ways, and didn't like being questioned.

The problem with our educat... (Below threshold)

April 12, 2014 8:39 PM | Posted by : | Reply

The problem with our education system is that it has always been terrible. It's that the world has changed much and other nations are catching up with us, the old model of education isn't working.

The public education system was created a hundred years ago to make sure the sons of factory workers and farmers and laborers are at least literate. Higher Education was only for the rich.
It was serviceable for it's time.

Fast forward to the 1970s, structural adjustment occurs, blue collar jobs are out white collar jobs are in. But do we change the education system to suite the needs of a competitive global job market?

Not surprising public school education focuses on useless forms and shapes rather the content and nature of learning. Because the type of people education was made for were never going to use it, so it didn't matter. But now in 2014 it does matter, and the average student is wholefully unprepared for the real world.

The average high school student doesn't need to study, all they need to do is barely read this book, regurgitate facts from said book, remember this complicated but useless equation, and they are set for college. In college they will avoid the classes that takes abstract reasoning or mental stamina, and focuses on the classes that are necessary for their major, no math, no science, no arts, no humanities. Than they are set for life, they never have to read a book anymore, never read a news magazine,never do anything, and best of all they never had to remember anything.

It also doesn't help that the people that are teaching us grew up in that environment, so they don't know any better. Students learn early that critical thinking and developing mental stamina doesn't matter, who cares if what you are learning is useless, your teacher holds life or death over your future, so you do what the teacher tells you too. So it's a self-reinforcing system.

And the education system replicates class divides. The preppy kids get the best education money can buy and are virtually not allowed to fail. They are attended to, any problem they have. And they can get away with smoking,drinking,drunk driving, and very stupid things. The blue collar and non-white kids are told they are born failures, and that they will never amount to anything and if they are caught doing things the rich kids do, they are screwed.

If math was taught in the most efficient way and you paid attention to people with learning disabilities, and taught how math can be used in your day to day life, and that goes for every subject in school, we might be able to salvage the education system. I don't see that happening...

And I can't believe I need to do this after so many people got it wrong.

45*20%

45*.20=9

45+9=54

I was never really good at math do to learning disability I have, and even I got this right. The education system is as broken as Alone says it is.

Nearly half of the people proceeded to do what Alone was talking about. This is sad.

F- for you - 50% grade. Yo... (Below threshold)

October 3, 2014 1:03 PM | Posted, in reply to , by : | Reply

F- for you - 50% grade. You also missed that the 45 became a 43. :-)

Some people are good at Mat... (Below threshold)

July 20, 2015 2:01 AM | Posted by : | Reply

Some people are good at Math and some are at literature. There is another category of people who are good at both Math as well as literature. But, those who are poor in writing essays and other genre of writing surely depend on some external supports like college paper writing service in order to improve their writing style and vocabulary.