US Students Struggle With Understanding of the 'Equal' Sign 1268
bickerd--- writes with news of research out of Texas A&M which found that roughly 70% of middle grades students in the US don't fully understand what the 'equal' sign means. Quoting:
"'The equal sign is pervasive and fundamentally linked to mathematics from kindergarten through upper-level calculus,' Robert M. Capraro says. 'The idea of symbols that convey relative meaning, such as the equal sign and "less than" and "greater than" signs, is complex and they serve as a precursor to ideas of variables, which also require the same level of abstract thinking.' The problem is students memorize procedures without fully understanding the mathematics, he notes. 'Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=( )+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer,' he explains. 'So the work would look like 4+3+2=(9)+2=11.'"
Well, that explains things. (Score:4, Insightful)
So I'm not being a curmudgeonly old jackass when I think this generation is stupid.
teachers (Score:4, Insightful)
Well, no one was born knowing what the equals sign represents. In fact, it's been around only for 500 years. My personal opinion is that until we start forcing graduates of US Education programs to take at least a little math beyond passing out of algebra, the cycle is doomed to repeat.
FTFA, 'Parents and teachers can help the students. The two researchers suggest using mathematics manipulatives and encourage teachers "to read professional journals, become informed about the problem and modify their instruction."'
Uh huh, see point 1 = 1 + 0 above.
Home School (Score:2, Insightful)
Calculators (Score:5, Insightful)
I blame it on calculators where the evaluate button has "=" on it.
I don't understand the example, either (Score:3, Insightful)
One cause of the problem might be the textbooks, the research shows.
Which sounds a lot like the true cause, not the students - who in my case has an honours degree in physics.
This is GREAT NEWS (Score:5, Insightful)
It means that even after China abolishes it's sweatshops there will still be a source of cheap unskilled labor in the world.
Don't know what () means (Score:4, Insightful)
RTFA, it's not that usage which he's objecting to (Score:5, Insightful)
"'Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=()+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer,' he explains. 'So the work would look like 4+3+2=(9)+2=11. This response has been called a running equal sign—similar to how a calculator might work when the numbers and equal sign are entered as they appear in the sentence,' he explains. 'However, this understanding is incorrect. The correct solution makes both sides equal. So the understanding should be 4+3+2=(7)+2. Now both sides of the equal sign equal 9.'"
4+3+2 is not equal to 9+2.
Sorry, in what context is "()" used as a variable? (Score:1, Insightful)
Re:Wrong (Score:3, Insightful)
And how about Economics, Politics, Aeronautics, and Quantum Mechanics?
Re:Well, that explains things. (Score:5, Insightful)
So I'm not being a curmudgeonly old jackass when I think this generation is stupid.
I think there's still a chance you are. Is it not more likely that rather than this generation being stupid, it is just being taught poorly by your generation? The article talks about the method students use to solve an equation. Why would a whole generation of students use a different method (and the same method) than the previous generation unless they were taught that method.
Re:How bad is it? (Score:3, Insightful)
To put it another way, he's saying that the students are treating mathematical expressions as a list of instructions to be obeyed, and not as expressions. This works fine for 1+2=? or 4/3=?, but leads to a cognative train wreck when trying to deal with even the simplest algebra. A student who works that way could never figure out what length of crossbeam they'd need to brace a 3x4 wooden frame.
Is that really the best example (Score:3, Insightful)
It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
Re:teachers (Score:3, Insightful)
Re:I guess I'm stupid, too. (Score:4, Insightful)
Thats what I gathered too, and it was a bit confusing to read. Knowing parenthesis as delimiters for so long, it was strange to see. I wonder if that is what they showed to the kids, and how it would have been different if they used something like:
4 + 3 + 2 = ? + 2
(4+3) (Score:1, Insightful)
I think (4+3) is the best answer.
Re:Wrong (Score:1, Insightful)
Me too, because I homeschooled.
Then I had Microsoft Office in junior high and Java in high school... what bullshit. Did programming suddenly get more complex, and now we can't teach it?
Re:Home School (Score:5, Insightful)
This is one reason why we home school...public school systems fail in so many ways.
A better solution is to find a better school. A better public school, or a private school, or a charter school, or something.
Yes, home schooling can be used to impart better information. You've got a much smaller class size. You've got more attachment to your pupil. You can devote as much time and effort to educating your kid as you feel necessary.
But home schooling pretty much fails to develop a kid's social skills. And I've always felt that one of the more important things that public schooling does is develop social skills.
Home schooled kids don't generally have to put up with schoolyard bullies. They don't have to make friends. They don't learn about compromises and sharing and common interests the way you do when you're surrounded by other people all day long. They don't learn to file the rough edges off their own personality, so that they can get along with others. They don't learn how to put up with other people's quirks and issues. They don't learn diplomacy and tact.
Yes, you can supplement your home schooling with some good social exposures... Send your kid to the park for a good chunk of the day, or get them involved in some kind of sports or clubs... But, from what I've seen, an awful lot of folks who are doing home schooling aren't interested in exposing their kids to much of anything. They're more concerned about sheltering their kid either from harm, or from opposing viewpoints.
Some of the hardest people I've had to work with are those who've been home schooled. They're generally very smart, very well-educated, and completely unable to deal with other human beings.
Re:Don't know what () means (Score:3, Insightful)
Ah. So () is a helmet. Kids wear helmets for everything these days.
Re:Pictures (Score:5, Insightful)
So that explains the MS Office Ribbon?
Re:Well, that explains things. (Score:4, Insightful)
It's a sine of the times.
Re:Well, that explains things. (Score:3, Insightful)
Headline should read... (Score:3, Insightful)
"Researchers at Texas A&M struggle with Meaning of Parenthesis."
Re:Wrong (Score:5, Insightful)
That's not what = means. = is ASSIGNMENT. They're looking for ==.
Much as I know you're joking, I'd really love to get rid of this bane that C has brought upon us. Many previous languages used := to mean assignment, hence avoiding the clash with the mathematically well defined = symbol.
Re:Well, that explains things. (Score:5, Insightful)
So I'm not being a curmudgeonly old jackass when I think this generation is stupid.
Oh hell. Generation N has always claimed that Generation N+1 is {stupid, lazy, amoral, immoral, bound for *insert cultural analogy to Hell*}. This holds inductively for all values of N. Strangely enough, they also happen to think that Generation N+2 is cute and cuddly.
I hate to tell you, but our parents' generation thought we were idiots too, I'm sure. I know their parents thought they were.
Re:All part of their plan. (Score:3, Insightful)
Come on, you can do better than that.
First you would need to prove a left-leaning portion of US society exists.
And then explain why the "education is for he who has the money and power" right wingers should be against their evil plans to make poor people stupid.
It sounds exactly like what right wing governments all over the world have been doing since there are governments.
Left wingers actually try to make people more intelligent through public education. Their problem is that their definition of intelligent is brain-washed.
Re:Home School (Score:3, Insightful)
Yup. Take the time you are homeschooling your kid(s), or the time you take to earn the money to pay for private schooling, and instead get involved in your local public school. Don't make it better for just your kid(s), make it better for the whole class of 'em (20-25 typically).
Re:Wrong (Score:5, Insightful)
The problem (Score:4, Insightful)
The problem is students memorize procedures without fully understanding the mathematics
That sums it up quite nicely. Students learn one way of solving a problem and memorize how to crunch the numbers to get the expected answer. This always bugged me when I was in school too. As soon as something didn't fit in nicely with what they had already learned, they'd be clueless because they don't understand what each value represents or why values relate to each other in a certain way. They're not taught to think for themselves. I rarely ever did homework, but I had a good fundamental understanding of the concepts that were being taught, so I "learned" more and never once worried about staying up late to cram for a test. This applies to just about every school subject, but is most obvious in math.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Re:I guess I'm stupid, too. (Score:5, Insightful)
___, this is very ____ to do.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:4, Insightful)
Re:Home School (Score:4, Insightful)
But home schooling pretty much fails to develop a kid's social skills. And I've always felt that one of the more important things that public schooling does is develop social skills.
Oh God, I am so tired of hearing this BULLSHIT. What social skills are you talking about? Let's take the U.S. for example. Most people here have been through the public school system, correct? Yet by just about any metric, people here are a bunch of selfish assholes. Look at the divorce rate. Look at the mudslinging on any general public forum like Yahoo message boards. Look at the way people behave on the highway or on Black Friday. People's social skills unilaterally SUCK. I don't believe that homeschooling is going to produce a less socially adapted adult. Really. It's bullshit.
Re:Wrong (Score:5, Insightful)
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
Exactly.
Are you testing their knowledge of the equal sign? Or are you testing their ability to guess about the meaning of your non-standard notation? This is a common problem that teachers face. I am an ex-teacher. We worked hard (often as teams) to eliminate or rewrite questions like this from our tests and quizzes.
Re:Well, that explains things. (Score:1, Insightful)
Equality isn't being equal, it's about giving someone better treatment in the job selection process.
Fair is about how much money you make. (ie: it's not fair that you make more than me, therefore the fair thing to do is take your money and give it to me.)
And we wonder why kids are confused.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Re: Nonstandard notation (Score:5, Insightful)
Re:Wrong (Score:5, Insightful)
Re:Wrong (Score:4, Insightful)
I used various forms of BASIC as a kid, and = was fine there. I had some formal education in Pascal, = was fine there.
Now when I occasionally do a little scripting in a modern language, I spend most of my time tearing my hair out at bugs which turn out to be the result of me using = when I should have put ==
I'm sure there are good reasons for it that make sense to proper programmers, but personally I'd like to give whoever came up with this syntax a kick in the bollocks. Why would I want to do an assignment in an if statement or a loop condition check anyway?
Re:I guess I'm stupid, too. (Score:2, Insightful)
If you have a ?, how do you write in the answer? Underneath the ? or above it or squeeze in the side?
Text books often use __, squares, and ( ) so people have a visual clue that something belongs there, before the concept of algebra sinks in.
Re:== vs = ? (Score:2, Insightful)
Of course the true nerd knows that the operator used for this depends on the language. C and C derived languages (and thanks to the pervasiveness of C, most newer languages) use == for equality and = for assignment. But not all do so. Pascal for example uses = for equality and := for assignment, and so does Ada. BASIC uses = both for equality and assignment.
Re:Wrong (Score:1, Insightful)
Re:All part of their plan. (Score:1, Insightful)
The left: Non-elites should all get the same level of education
The people: Everyone should be educated but not restrained
Yes, everyone should have the same opportunities for education. However, by lumping everyone together into the same education basket you implicitly restrain those who are capable of much more.
I am disallusioned with both parties because they BOTH support a notion of eliteness. I am more disallusioned with the left because, being a non-elite, they will lump me in with the rest of the crowd destined to become greeters at Walmart. At least the right lets me climb to the top of the non-elite crowd.
Re:Wrong (Score:3, Insightful)
I was doing programming in the 4th grade, and this was in the early 80s...
I went to a rural public school in the 80s and I learned BASIC and LOGO starting in about 4th grade. In high school, in the time between when the AP tests were and the end of the school year, we learned programming, too.
I think they still break out the Lego LOGO with the younger kids, but by the time they get into the upper elementary now, if it isn't on the standardized test, they don't bother. This is a major factor in why I'm not a teacher.
Re:Home School (Score:5, Insightful)
Are you nuts?
"Home schooled kids don't generally have to put up with schoolyard bullies. They don't have to make friends. They don't learn about compromises and sharing and common interests the way you do when you're surrounded by other people all day long."
All the homeschooled kids around where I grew up dealt with all that.
The asshole kids that bullied also bullied the home-schooled kids, granted they did not get to deal with the imported bullies from across town, but a bully is a bully. and they made friends with kids that lived near them.. Plus many were in sports programs with the public school kids. You can be home schooled and play football for your local public school at the same time. They joined lots of extra curricular activities. Many of us were jealous as they typically had a 4 hour school day plus got to take "classes" we never got. One kid was taking a class at the local motorcycle shop for learning small engine repair at 13 years old.
I know you guys love your twisted view of homeschooled kids as all living in basements and named "wolfgang" or "moon-unit-alpha" and are never let outside... but it's not reality. in fact it's pretty darn close to racism in being flat out wrong.
Re:Wrong (Score:5, Insightful)
Math sounds awkward to me, because I was brought up with Maths. This is like an essay I read ages ago about why rear wheel drive is more natural than front. I thought it was a load of crap because I'd learned to drive in FWD vehicles and my natural driving instincts in certain situations were different to what the guy said that the "natural" was.
For most things in life whatever is more "natural" for you often depends on what you were brought up with/trained on.
Re:I guess I'm stupid, too. (Score:3, Insightful)
Are you drawing that conclusion because you are a child, or because you've worked closely teaching math to young children for years? Or are you drawing that conclusion because you have a preconception about what the answer should be?
No one in my second grade class had an issue with algebra. We couldn't do division yet, but algebra was easy. The problem is not the students.
It's the calculators, you dummies! (Score:3, Insightful)
Kids nowadays have ready access to technology, and are not adequately guided in its use. You can get a calculator in a dollar shop to do your arithmetic homework.
On a calculator, what does the = mean? It means "evaluate now". So that is perhaps where the running equals comes from. It is not a misconception. The students have correctly learned "evaluate now" from their electronic buddies.
The educators are just too obtuse to identify the source.
Let's take the example from the article:
4 + 3 + 2 = (calculator produces 9)
+ 2 = (calculator produces 11)
See? If you literally put in the symbols from the homework question into a calculator, that's what you get.
Now you might be able to ban calculators from the classroom, but the kids will use them at home.
Teachers should embrace calculators and explain how the [=] button has a different meaning which means "please calculate now", whereas the = used in math is a sentence which says "the left side is the same as the right side".
Re:Headline should read... (Score:4, Insightful)
Re:Confusing symbols (Score:4, Insightful)
Yes, and no doubt the teacher worked a few problems on the board so that everyone could see how they were done.
And since everyone daydreamed through the class, the homework got done with the calculator.
4
+
3
+ (calculator displays 7)
2
= (calculator displays 9; write it down)
+
2
Now to finish the problem? Well, = of course, and write down “= 11”. That’s what the calculator said.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:4, Insightful)
Well, it's sort of that confusing.
For the most part, my math skills are about that of a competent sophomore or maybe junior in high school, which isn't so bad for an adult American these days. I have never seen anyone present an equation like "4 + 3 + 2 = () + 2". To me, that's either a syntax error, or somebody saying "9 = 2", which is just wrong. I've never seen empty parentheses treated as a variable, and I'd be shocked if it's commonly-taught in American schools.
That said, I would never come up with putting 4+3+2 in the parentheses. That's just a WTF.
Social problem. (Score:3, Insightful)
This is what we get when we have a society that values the celebrity and athlete more highly than anything else. This is what we get when parents think socializing is more important than good academics. And ultimately a lot of the blame falls on the teachers as well, for not doing their job properly.
Americans seem to think throwing money at our schools will fix everything. They also seem obsessed with small class sizes. That's something I've always found utterly ridiculous considering in Asia you'll routinely find classes with 30+ students and they are better educated than American students in a class half the size. Too much of our educational system has gotten too obsessed catering to the slowest kid in the class and making things fun. So instead of trying to bring the slow kids up to speed we're instead slowing the rest of the class down.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
Why? The world doesn't format problems neatly for you. That's the job of the person approaching it. Simply identifying the mapping to known math formalisms is 90% of the challenge, if not more! If you can't convert a "put more apples on the table and find how many are on it now" into an addition problem, the world won't hold your hand and do it for you.
If the students genuinely understand (or even notice) what they're being taught, they won't be thrown off by stuff like this.
I mean, I'm a little sympathetic, but still, students shouldn't be taught some narrow skill that works *only* for your class. The skills you teach need to be grounded to the rest of the world so they know how it fits in and can adapt to novel situations as necessary.
If their understanding is so brittle that it requires this careful handling before it's a "fair" test, they haven't learned anything, except how to pass tests. Worse, tests presented by *that* teacher.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:4, Insightful)
It's very confusing. Only after continuing reading the "wrong" solution by students, I realized that he used parentheses for variable names.
FWIW, parentheses usually group statements. In the example there's nothing to group, so I would say that this "non-standard" use is simply wrong.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
In general, brackets serve to contain elements of the equation and signify the order in they are treated - empty brackets should therefore logically denote zero
Logically denote zero? Nope. 0 = 0. Empty brackets clearly are just empty - that is, they contain no value. There's a difference between zero and a lack of value - namely, zero is a value of zero, and no value isn't. The empty brackets are a space where value can logically be inserted -- a zero is a zero.
This stuff isn't rocket science. Nearly 100% of foreign students figured it out easily, compared to only about 30% of American students. The excuses don't work; there is something fundamentally flawed at play.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:2, Insightful)
4 + 3 + 2 = ( ) + 2
=> 4 + 3 + 2 = (x) + 2 (solve for x)
=> 9 = (x) + 2
=> 9 = (-7) + 2
=> 9 = 7 + 2
=> 9 = 9
I can't wait for my daughter to argue math with me because the schools are teaching her in a confusing manner. I agree with the "solve for x" guy - why reinvent the standard for equation formatting.
Re:Wrong (Score:2, Insightful)
In a sane language, = would not be used as an operator at all, neither for assignment nor equality test. Neither is what the symbol means in a mathematical equation, and allowing it for either is asking for trouble.
Re:Wrong (Score:4, Insightful)
BASIC is perfectly sane. There are clean, contextual rules which disambiguate between = the assignment operator and = the equality test.
Let's take a moment to remember that "x = 1" is only a legal BASIC statement in the first place because interpreters have been relaxed for programmers too lazy to use "Let".
Re:Home School (Score:4, Insightful)
Are you nuts?
Not as far as I know...
"Home schooled kids don't generally have to put up with schoolyard bullies. They don't have to make friends. They don't learn about compromises and sharing and common interests the way you do when you're surrounded by other people all day long."
All the homeschooled kids around where I grew up dealt with all that.
The asshole kids that bullied also bullied the home-schooled kids, granted they did not get to deal with the imported bullies from across town, but a bully is a bully. and they made friends with kids that lived near them..
So, you're saying that my anecdotal experience is not the same as your anecdotal experience?
Plus many were in sports programs with the public school kids. You can be home schooled and play football for your local public school at the same time. They joined lots of extra curricular activities. Many of us were jealous as they typically had a 4 hour school day plus got to take "classes" we never got. One kid was taking a class at the local motorcycle shop for learning small engine repair at 13 years old.
You did read the full text of my post, didn't you?
Specifically, the bit where I said:
Yes, you can supplement your home schooling with some good social exposures... Send your kid to the park for a good chunk of the day, or get them involved in some kind of sports or clubs... But, from what I've seen, an awful lot of folks who are doing home schooling aren't interested in exposing their kids to much of anything. They're more concerned about sheltering their kid either from harm, or from opposing viewpoints.
Like it or not, the folks who were home schooled when I was growing up did not turn out to be well-rounded individuals.
Like it or not, most of the folks that I've found very difficult to work with have turned out to be home schooled.
And since I'm not omniscient, I can only speak from my own relatively small chunk of life experiences.
RPN! (Score:3, Insightful)
Perhaps kids should be taught to use RPN calculators.
On an RPN calculator, the keys which perform operations are labeled with symbols that represent mathematical operations. There's no misuse of '=' to mean 'perform calculation'.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
understanding of equality.
I'm sure they understand equality just fine, it's just that after punching everything into a calculator for all their lives, they don't understand that = means equality instead of "what do the things I just entered equal?"
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Re:Wrong (Score:1, Insightful)
but...but...I'm not an Indianaian, I'm a Hoosier!
Re:Wrong (Score:4, Insightful)
Back then (80s) programming was the only way to use the TRS-80s and Apple IIs the schools gave us. Today? You just need to learn how to turn them on and click an icon, and so programming is no longer considered necessary unless you're going into a CSE major.
BTW:
I see a problem with the problem in the summary: 4+3+2=( )+2 is not the way math questions are typically phrased. In my experiences these problems usually looked like this: "4+3+2 = __+2 ; Fill in the blank." The instructions were explicit so students did not need to guess the teacher's desired result.
I don't like teachers that think writing confusing tests (aka trick questions) is any test of student ability. It's more a demonstration of the test-writer's lack of communication skills.
Re:Who ever came up with this should be fired. (Score:5, Insightful)
The students are the one who made up the =11 part. Try punching it the question "4+3+2= +2" into a calculator and you'll see why. To the students raised on calculators, "equals" doesn't mean equality anymore, it means "what do the numbers up to here add up to?" So they get to " = ( ) " and perform the "what do the numbers up to here add up to" operation, and write the answer in the blank provided. Then they're left with the +2 bit, so they add it again.
Left to right order of operations, for all operations.
Re:Voting test (Score:3, Insightful)
You know, that's exactly the kind of thing used to deny blacks the right to vote after the Civil War.
Re:Who ever came up with this should be fired. (Score:4, Insightful)
The problem here is not the use of the equal sign, it is their completely asstarded implementation of the parenthesis that is some how intended to imply one variable twice, with a line break in the middle.
The parenthesis weren’t what triggered that interpretation; the equals sign was. Exactly like a calculator: you calculate, you push “equals”, you get an answer. You calculate some more, you get a new answer.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:4, Insightful)
Why? The world doesn't format problems neatly for you. That's the job of the person approaching it. Simply identifying the mapping to known math formalisms is 90% of the challenge, if not more! If you can't convert a "put more apples on the table and find how many are on it now" into an addition problem, the world won't hold your hand and do it for you.
OK, how about this one then ...
4#3#2@[]#2
Now I just wrote it and know which arbibrary symbols I replaced the more common ones with, but I still have trouble looking at it and working out what it means! The standardisation of mathematical symbols, and their common use, is what makes it even vaguely teachable. Using "()" as an indicator of a missing term in an equation is madness because everyone I've ever known would use them to indicate a change to the default order of calculation (BODMAS [easymaths.com]). If kids are being taught this way what the hell do the do if they see an equation with braces in it? Ignore the contents and just replace everything in it perhaps?
Re:Home School (Score:4, Insightful)
That's because the homeschooled adults with bad social skills are the ones he notices; he's never realized that the homeschooled adults with good social skills exist, because it never occurs to him to ask adults with good social skills how they were schooled.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
The equation noted lacked the precision of mathematics, and is therefore inappropriate without an instruction to the effect of "Solve for the number in () that makes this a true statement."
I'm just an engineer and all, but I had to look at it twice to understand what they were looking for.
Re:Well, that explains things. (Score:5, Insightful)
Bad research: it is a operator precedence problem (Score:2, Insightful)
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
Equals always equals equals.
In English - four plus three plus two equals something plus two. That's exactly how I read it, and how everybody I know would read it. Educated in Canada, for clarification.
If anything, the comments on this article really drive home its point. Why are people throwing out the rules when they come upon an unknown? If they understood clearly, concretely, what "equals" meant, there wouldn't be the sort of confusion that's been going on. I think another poster had a good theory, that nowadays "=" is seen as "solve it" due to its use on calculators.
Re:The problem (Score:3, Insightful)
Re:Well, that explains things. (Score:5, Insightful)
While it's true that just because they thought it doesn't mean it's true, the opposite is likewise valid: just because many previous generations thought it, does not make it false.
It provides a burden for uniqueness that needs to be met, though.
It used to be that wisdom of age was respected and revered, even taken to heart.
When? When in living memory did the majority of young people actually respect their elders? Again, you're repeating things that have been said since the beginning of time. Hell, I've seen almost the exact same thing written in the bible. Kids were assholes then too. They still are. Time goes on.
We're talking about basic, first grade mathematics concepts here. How is this "not getting stupid"?
No, you're actually talking about pre-algebra if you look more closely at the example. Which kids have always generally sucked at.
The last couple generations, however, have been increasingly "stupid" in the "can't solve for x" sense. Test scores clearly prove this.
If there's a problem, it's not with the gene pool of the kids or their abilities. It's caused by well-meaning but catastrophically stupid policies that prevent the removal of problem students from classes, and the elimination of ability-based tracking. This means that normal kids are surrounded by juvenile delinquents and children who don't even speak English. If you remove those students (who would have not taken the test in prior generations) from the scoring, I wonder how the stats would play out.
In other words - it's not that the kids are getting stupid. It's that our schools are completely failing them.
Re:Math education in America is pathetic (Score:3, Insightful)
It's too bad I already posted in this thread and can't mod this up. You're precisely right. The government education system abandoned learning a long time ago. Today it far more akin to another government make-work welfare program.
Granted, there is something to be said for a well-designed, visually appealing text book, as long as it has actual material in it. I have some of my Dad's old Schaum's outlines from the 60's and 70's, and it's damn near impossible to learn anything from them because of the sheer density of material.
Re:Wrong (Score:1, Insightful)
The problem is that
America is a continent
Except... It isn't. At least not on any globe I've ever seen. Not anymore than "Dakota" or "Carolina" is a state.
Of course, you Europeans love playing games with the names of large land masses to further your own ends. It was you racist honky bastards that decided "Europe" was a continent instead of what it actually is, a part of Asia. But, you couldn't bear your pure white homeland to be infringed by the dirty dark skinned peoples could you you racist piece of detritus? You cracker motherfuckers have something coming and when Islam takes over, we're going to be coming to give it to you.
Captcha: tribute
Imagine that.
Re:I guess I'm stupid, too. (Score:4, Insightful)
___, this is very ____ to do.
I can find at least two solutions :
Re:Calculators (Score:2, Insightful)
123
+456
-------
579
- 54
-------
525
which reads (out loud) very similarly to "123+456=579-54=525", which is, as the article points out, incorrect. Don't be too quick to blame calculators when longhand methods introduce similar errors.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
I'm pretty sure it's supposed to be an ASCII drawing of a circle, just like [ ] is supposed to be a box, and ( o Y o ) is supposed to be boobs. Lots of primary/middle school textbooks use circles or boxes for the spot you put the answer. So what happens is, a student sees "4 + 3 + 2 = circle" and writes 9 in the circle. They do that all of the time, tests, assignments, that's how it works. You add the numbers and put them in the circle. So, they see "4 + 3 + 2 = circle + 2" and they put 9 in the circle like always, they do the math left to right like they're supposed to, and after they have done that, there is another + 2 after they are done, so they add 9 and 2, since they have "9 + 2" still, now it's 11. It's reasonable, because they were never taught what = means, exactly, just to put the answer in the circle, and to do things left to right. The problem is, they haven't learned algebra yet. So, chuckling about how they couldn't derive it from first principles is just stupid. Show it to them once they've seen algebra. Saying that 70% of americans in grade X got it wrong, but 0% of chinese of the same age were wrong, is meaningless if they teach algebra there sooner. You might say "100% of Chinese who have learned algebra understood algebra, but 'only' 30% of Americans who have never seen algebra, picked it up on the spot".
When I was in grade 9 or 10, I missed like a week of school with a bad case of the flu. I guess we learned algebra that week. When I came back it was test time, and the teacher said I could do it later since I missed the whole section. I said "Naw I'll be fine" and wrote it. I guess I'm in the 30% because after going "Wut" over and over I figured out what it meant. But I can totally see how they could be totally confused by it, circle or x or whatever other placeholder you like. 70% sounds about right for how many wouldn't get algebra if you threw it in their faces with no warning. Obviously, in hindsight everybody on Slashdot would say "OMG SO FUCKING EASY JUST ALGEBRA WHAT RETARDS", but it's not obvious until you have your "ah ha!" moment.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
The world doesn't format problems neatly for you.
It also does not require a strict answer. If the constraints for the answer are manufactured (as they are here) then the constraints for the question must be as well. This evaluation is poorly constructed and should not be defended.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:1, Insightful)
Not in pure mathematics, which is the subject under discussion.
Testing people's ability to understand symbols by using non-standard symbols is deeply flawed.
Re:Well, that explains things. (Score:3, Insightful)
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:2, Insightful)
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Really? So ( )*9=72, you think the difference between treating ( ) as x vs. 0 is "pretty inconsequential"? Remember, this study is about the development of the students' understanding...that is, the ability to move on to other kinds of more complicated math than in the problem presented...like multiplication.
By the way, can I posit that this is actually not a problem with US students so much as a problem with US teachers? Most people, including teachers, seem to think that knowing a subject marginally better than the students is all there is to teaching. TFA closes with: Parents and teachers can help the students. The two researchers suggest using mathematics manipulatives and encourage teachers "to read professional journals, become informed about the problem and modify their instruction." How many people reading this that grew up in the US can honestly say that they can imagine their grade school teachers reading a professional journal and keeping up with the latest in their field? (I can say a small sampling of my teachers were committed in this way, but my public school was in the top 4% in the country and they represented the exception, not the rule.)
Re:Wrong (Score:3, Insightful)
This used to be the norm, but I think our civil war put pat to that idea as the nation become more important than the individual states. Even then, which one would it be? My state of birth? The one I grew up and was socialized in. And if more than one, which? The current state of residence? The last one I paid taxes in? I'd bet most people move from state to state at least once in their life and often more due to schooling and work. I suppose mine would be Washingtonian as that's where I live, although I prefer the term Okie as I grew up in Oklahoma and left never to return (where people who still live there are Oklahomans).
Re:Wrong (Score:2, Insightful)
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:1, Insightful)
Throughout this thread people are posting about how this bit of notation totally negates their research and makes them all jack-asses. First off, let's show a little faith in the researchers that, perhaps, as professionals, they considered how their notation could confuse children. I know it makes us all feel better to see some bit of new research and immediately find it's fundamental flaw, but seriously. I mean any study of mathematics education will include _countless_ hours of discussion and debate over notational practices.
If you watched the video in the article, you'd see a question formed with _____ instead of empty parenthesis. Also, you'd see references to children and hear a man talking about students' _preparation_ for algebra. Hence, placing an 'x' in the equation, will only confuse these little kids who are, as we can gather from the difficulty of the question stated, still learning basic arithmetic. In response to the OP, the variable would only confuse the test subjects even more! As a teacher who presents students with their first exposure to variables, I can tell you that this is a _huge_ jump in abstraction for most students. It's one that many struggling, failing students never grasp. Switch the letters back to blanks or boxes and it clicks for them.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Why? The world doesn't format problems neatly for you. That's the job of the person approaching it.
If you are trying to quantify a student's ability remember and use the addition property of equality (as in this case) then introducing a brand new notation is a really bad idea. If you are trying to test their ability to adapt to a new notation based on knowledge they have already proven they know, then this could be a good question.
Try and test both at once and you cannot be sure where the student stumbled. Subsequently, there is no way to determine what needs remediation.
It appears you have a problem with what is being taught. A distraction from the issue at hand.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Why did you have to parse it like that. I parsed it as "four plus three plus two something two". Sure, I recognized the equal sign, and the plus sign, but I also recognized the parentheses. The other way of parsing it for me was "four plus three plus two equals quantity zero end-quantity plus two"... a false statement. I'm used to seeing operators written out as the conjunction of other, sometimes unrelated, operators. I'm not familiar with "()" written out to mean "unknown quantity". In that case I'm used to "x".
I'm not. There are many unknowns there... mainly what the parentheses mean. I applied my best guess. Or, as someone else once said, communicating badly and then acting smug when you are misunderstood is not cleverness [xkcd.com].
If they understood clearly, concretely, what "equals" meant, there wouldn't be the sort of confusion that's been going on
That symbol was not understandable, unambiguously, as equals. That's the major source of confusion. The equals sign can be used to represent causation "=>", a test returning the truth value of an equality "==", a declarative statement about equality "=", a test of identity "===", and others. What does it represent in "=()+"? How do you know?
That's an interesting hypothesis, and I would love to see a test of that. Unfortunately, this study was flawed do to its non-conventional usage of "()" as "unknown quantity".
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:1, Insightful)
Math is a language. I agree students should learn to be flexible (after they've learned the basics), but saying you can throw any syntax together and it's the same as proper syntax is like saying slang is proper english.
I would say the answer to the summary problem is "False". 4+3+2=()+2 -> 9=(0)+2 -> 9=2 -> False
Re:Confusing symbols (Score:3, Insightful)
If you teach and expect kids to be stupid, they will be.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
Re:Well, that explains things. (Score:5, Insightful)
You're absolutely correct, it doesn't. And, in fact, they don't need them at all. Comments like this just show your ignorance of how organizations work at large scale. The pictures are there because they are universal.
And those are just the three reasons that are most obvious to me. Now get off your high horse!
Re:All part of their plan. (Score:3, Insightful)
Actually I observed more people in CS/college to have more left leaning socially supportive views than any other class.
By contrast, the poorly-educated-blue-collar work force, I've found more Rush Limbaugh listening imbeciles with completely socially deviant views, absolutely ignorant of the reality about them
To me, this clearly indicates how we can have a government for 10 years that ass rapes it's citizens, especially their low income supporter base (Rush Limbaugh & Fox news viewers), whereas when a change in command comes in and wants to support the less privileged, these same people dig their nails in for a fight to the death, instead of change for a better life and opportunities.
Completely mind boggling. America is reviving the dark ages that Europe went through during the middle ages. Lead by the conservative christian right and religious superstitions of men.
I am not from the US... (Score:2, Insightful)
...and I had a very hard time understanding why one would put anything other than a 7 inside the parentheses.
Then it dawned on me that, apparently, some US students interpret the "equals" sign as a "write the result of the preceding arithmetic operations" sign, which the students promptly do. Then, they see the "+2" following the parentheses, and are completely dumbfounded by it, so they assume there is a missing "write the result of the preceding arithmetic operations" sign, which they add, so that they can enter the result of "9+2" after it. Presumably, "+" does not mean just "plus", but “add these numbers and write the result after the "write the result of the preceding arithmetic operations" sign”.
Wow!
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:5, Insightful)
But just as in a grammar problem you have to choose the right word to put in the blank to make the sentence correct, in a mathematical problem you have to choose a number that results in a correct formula, and that's where they failed. They didn't understand that a formula with an equal sign (an equation) is correct if and only if the two sides have the same value. This is what TFA means by "the meaning of the equal sign".
Re:Home School (Score:4, Insightful)
Re:Wrong (Score:3, Insightful)
That all depends on the school, and the classes the school assigns a student to.
I was introduced to programming in the early 1980's. The school bought a TRS-80 Model III, and it was given to the gifted class. That was when I was in primary school. No one had a clue of what to do with it. I got my hands on some programming books (the good ol' printouts of basic programs) and started learning. We didn't have any software to run, so that was the limit of what we could do, and most people had no interest in it at all. Heck, most kids couldn't even type then.
Later on, still in the early days of computers for students, weren't taught how to write programs, we were simply instructed on how to run programs. "insert disk, type this, follow the prompts". As we started getting computers at home too, some of us started programming.
I would strongly suspect that it is different now, but I could be mistaken.
I think the article is misunderstanding the confusion. Children are being taught "1 + 1 = ". the equals sign means that they take the formula on the left, and calculate it to put on the right. It would seem to be a logical extension of that to use the equals sign to indicate a calculation should be done, not that both sides are equal. It's not a problem with their ability, it's that the idea hasn't been explained to them. It wasn't until I was in Algebra that the idea that the equals sign really showed that both sides were to be equal, and that you should solve the problem accordingly.
Re:It should be: 4+3+2=x+2 (Solve for x) (Score:3, Insightful)
I'm just an engineer and all, but I had to look at it twice to understand what they were looking for.
Yeah, me to, except I have math and comp sci degrees. I didn't even understand that that bizarre expression that's not a well-formed expression was a question to be answered, until I read the discussion and found a bunch of jerks ridiculing people who don't automatically grok nonstandard (and ill-formed) expressions such as that one.
I'm tempted to rephrase the question using traditional Chinese or Sanskrit or Arabic notation, and see how many of those jerks instantly understand what I'm writing. But luckily for them, slashdot doesn't permit non-Latin1 notation, so my rephrasings can't be posted here.
Presenting obscure or idiosyncratic notation, and then ridiculing people for not understanding it, is merely being a jerk. It says nothing about the intelligence or education of your victims. If it did, I could easily "prove" that 99% of Americans are totally ignorant of mathematics, by simply presenting them with a set of problems in classical Greek or Arabic or Chinese, and observing that they fail to answer any of the problems.
OTOH, I've learned some new notation from this discussion, so it's not a total loss. ;-)