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# US Students Struggle With Understanding of the 'Equal' Sign

#### Soulskill posted more than 3 years ago | from the confusing-parallel-lines dept.

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.'"

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#### Anonymous Coward 1 minute ago

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### Wrong (5, Funny)

#### dyingtolive (1393037) | more than 3 years ago | (#33238242)

That's not what = means. = is ASSIGNMENT. They're looking for ==.

Also, on a serious note, from what I recall of the US school system, frankly, the most surprising thing about this is that the problem isn't worse than reported.

### Re:Wrong (1, Interesting)

#### jez9999 (618189) | more than 3 years ago | (#33238268)

I wonder how much this has to do with programming, and the fundamentally different nature of the meaning of = in that and maths? Yeah, you heard me Americans, maths plural.

### Re:Wrong (1)

#### dyingtolive (1393037) | more than 3 years ago | (#33238348)

Unfortunately, I was joking about the first part of my statement. Middle grade levels are most certainly NOT learning programming (in the US anyway).

### Re:Wrong (1)

#### biryokumaru (822262) | more than 3 years ago | (#33238410)

My middle school had a programming class. Of course, it was logo and QBasic, but still.

### All part of their plan. (0, Informative)

#### Anonymous Coward | more than 3 years ago | (#33238528)

Middle grade levels are most certainly NOT learning programming (in the US anyway).

Warning... political rant follows

Making dumb, helpless, dependent-on-government, indoctrinated drones is exactly what the left-leaning portion of US society who have been running the education systems for decades have wanted, planned for, and are now reaping their harvest.

And we let them do it.

As a bonus, all this is next coming to a health care system near you.

### Re:Wrong (1)

#### i.r.id10t (595143) | more than 3 years ago | (#33238548)

I was doing programming in the 4th grade, and this was in the early 80s...

### Re:Wrong (1, Insightful)

#### Anonymous Coward | more than 3 years ago | (#33238646)

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:Wrong (0)

#### spiffmastercow (1001386) | more than 3 years ago | (#33238354)

Blasphemy! There is but the one true Math! Seriously though, why do you pluralize it? Do students major in Engineerings over there too? Or Literatures?

### Re:Wrong (4, Funny)

#### Raumkraut (518382) | more than 3 years ago | (#33238390)

In most of the world we study Mathematics. I didn't realise that there was only one Mathematic studied in the US.

### Re:Wrong (2, Insightful)

#### mcvos (645701) | more than 3 years ago | (#33238428)

And how about Economics, Politics, Aeronautics, and Quantum Mechanics?

### Re:Wrong (0)

#### Anonymous Coward | more than 3 years ago | (#33238580)

If you studied Quantum Mechanic you could probably build atoms and/or subatomic particles from scratch.

### Re:Wrong (0)

#### Anonymous Coward | more than 3 years ago | (#33238360)

I would say none of this has anything at all to do with programming, since it's about middle schoolers who are failing to grasp basic arithmetic, so I somehow doubt they're actually Java experts getting confused.

### Re:Wrong (1, Funny)

#### Anonymous Coward | more than 3 years ago | (#33238500)

Whoa! You Brits have more than one math?! Did Apple come out with iMath over there? lucky bastards...

### Re:Wrong (1)

#### zhong-guo (1872764) | more than 3 years ago | (#33238522)

I think you mean mathematics.

### Re:Wrong (4, Funny)

#### Kenshin (43036) | more than 3 years ago | (#33238552)

For those who don't know, the guide to school in America and England:

America - England

Math - Maths
Science - Sciences
Art - Arts
Gym - Gyms
Lunch - Lunches
Recess - Recesses
Detention - Detentions

### Re:Wrong (1, Funny)

#### dyingtolive (1393037) | more than 3 years ago | (#33238280)

Also, apparently I struggle with understanding of the "First Post".

So... frosty piss and all that.

### Re:Wrong (1)

#### oldspewey (1303305) | more than 3 years ago | (#33238282)

You are confusing mathematics with programming syntax.

### Re:Wrong (0, Flamebait)

#### snookerhog (1835110) | more than 3 years ago | (#33238380)

you can only use it to assign variables in some states. for instance in Texas, only the LORD is allowed to assign variables and he never assigns anything on sunday.

### Re:Wrong (0)

#### Anonymous Coward | more than 3 years ago | (#33238482)

The problem is not worse than expected, and no one should expect it to be. Math is properly the work that Americans will not do. That's what the rest of the world is for. Can these kids use iPods? Do they appreciate the featureless contours of Macs? Well then, leave them be; once they muddle through school, they will get a law or MBA degree and soil the world. IOW, they're getting all the skills they need.

### It should be: 4+3+2=x+2 (Solve for x) (5, Insightful)

#### Knertified (756718) | more than 3 years ago | (#33238530)

It should be: 4+3+2=x+2 (Solve for x) I don't see the point in substituting parenthesis for a variable. It just makes it more confusing for everyone.

### Well, that explains things. (4, Insightful)

#### dr_strang (32799) | more than 3 years ago | (#33238246)

So I'm not being a curmudgeonly old jackass when I think this generation is stupid.

### I guess I'm stupid, too. (5, Funny)

#### maillemaker (924053) | more than 3 years ago | (#33238352)

Because I can't figure out how you are supposed to solve such a problem, and I have a BS in Computer Science.

Let's look at the problem:

4+3+2=( )+2

4+3+2 = 9

( ) + 2 = 2

So we have a false equality 9 = 2

Since this is not true, I can easily see how lots of kids would go through contortions to try and make it true.

But unless this is a trick question, why are the setting up false equalities like this for grade school kids?

### Re:I guess I'm stupid, too. (2, Funny)

#### Issarlk (1429361) | more than 3 years ago | (#33238382)

9 = 2 is neither true nor false, it yield an error because 9 is not a variable.

### Re:I guess I'm stupid, too. (4, Informative)

#### dyingtolive (1393037) | more than 3 years ago | (#33238434)

I think that the () is supposed to be an unknown variable? 4+3+2=x+2; 4+3+2-2=x; 4+3=x; 7=x.

### Re:I guess I'm stupid, too. (4, Insightful)

#### surgen (1145449) | more than 3 years ago | (#33238588)

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

### Re:I guess I'm stupid, too. (0)

#### Anonymous Coward | more than 3 years ago | (#33238618)

So why the hell wouldn't you use x or something?

4+3+2=()+2

4+3+2-2=()+2-2

() = 4 + 3 = 7

### Re:I guess I'm stupid, too. (0)

#### Anonymous Coward | more than 3 years ago | (#33238452)

You're joking, right? Or are you that obtuse?

### Re:I guess I'm stupid, too. (4, Informative)

#### skids (119237) | more than 3 years ago | (#33238570)

I had to read it twice to get what they wanted done. An empty set of parens in proper mathematical expressions is valid and equivalent to (0).

"4+3+2=x+2 solve for x" is the correct way to state that problem.

### Re:I guess I'm stupid, too. (1)

#### Dienyddio (161154) | more than 3 years ago | (#33238504)

solve x in:

4+3+2 = x+2

Use of braces to signify a missing number is alien to me too.

### Re:I guess I'm stupid, too. (0)

#### Anonymous Coward | more than 3 years ago | (#33238554)

That's how it works in all pre-algebra textbooks I've read.

### Re:I guess I'm stupid, too. (1, Funny)

#### Anonymous Coward | more than 3 years ago | (#33238636)

The students are supposed to solve for the number in the parenthesis. Replace the ( ) with an x, then solve for x.

4 + 3 + 2 = x + 2

Since the students aren't familiar with algebra, they're expected to rewrite the LHS in the same form as the RHS.

4 + 3 + 2 = 9 = 7 + 2

Therefore:

7 + 2 = x + 2

So x = 2.

### Re:Well, that explains things. (5, Interesting)

#### oldspewey (1303305) | more than 3 years ago | (#33238378)

I have a friend who's a high school teacher. He's been predicting the downfall of society for a few years now, based on the fact the kids he teaches are - for the most part - useless twats. What makes it even worse is they also carry a strong sense of entitlement, as in "even though I can't be bothered to do the work properly or learn a single fucking thing while I'm here, I deserve an A grade from you, and when I graduate I am going to deserve an \$80K starting salary somewhere just for showing up and playing FarmVille all day."

### Re:Well, that explains things. (3, Informative)

#### Zeek40 (1017978) | more than 3 years ago | (#33238384)

Not just stupid, defiantly and proudly stupid. We've devolved into a culture that celebrates its own ignorance

### Re:Well, that explains things. (5, Funny)

#### fahrbot-bot (874524) | more than 3 years ago | (#33238402)

So I'm not being a curmudgeonly old jackass when I think this generation is stupid.

Now, now. Just because these youngsters need pictures of the food on their cash-register buttons in order to do their job doesn't mean they're stupid. :-)

### Re:Well, that explains things. (1)

#### The Grim Reefer2 (1195989) | more than 3 years ago | (#33238442)

So I'm not being a curmudgeonly old jackass when I think this generation is stupid.

Well actually you are, but it doesn't = being incorrect either. ;-)

### Re:Well, that explains things. (5, Insightful)

#### KnownIssues (1612961) | more than 3 years ago | (#33238464)

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:Well, that explains things. (1)

#### The Moof (859402) | more than 3 years ago | (#33238466)

At first I had the same reaction. Then I sat and tried to remember when we get exposure to pre-algebra in a standard public school education. It's 8th grade, with some advanced courses for 7th and 6th. However, most kids won't see it until 8th. Since middle school grades typically consist of 6-8, this comes as no surprise that kids who have never had pre-algebra wouldn't know how to solve a basic algebra question.

### Extra Credit (1)

#### TreyGeek (1391679) | more than 3 years ago | (#33238252)

Maybe the students figured they would get extra credit for going the extra step?

### How bad is it? (1)

#### Haedrian (1676506) | more than 3 years ago | (#33238264)

This is a bit weird. I mean how bad is the lack of understanding? Bit hard to follow the article to be honest, is it just because of the 'everything in one line equal to each other' ? Or does it also include more complicated stuff like "1 = Number" ?

### Re:How bad is it? (1)

#### biryokumaru (822262) | more than 3 years ago | (#33238326)

Ya, I've never understood why 1 + 2 = 3 = 4 - 1 isn't okay. Maybe it's his understanding of mathematics that's flawed, since to convey the same thing he'd need 1 + 2 = 3, 3 = 4 - 1 and 4 - 1 = 1 + 2, which is stupid.

### Re:How bad is it? (2, Informative)

#### Haedrian (1676506) | more than 3 years ago | (#33238392)

Its because you're shoving them into one equation. The scope of your 'working out' is to solve whatever is in that equation so the correct answer to
1+2 = 3
is
3 = 3
true.

### Re:How bad is it? (1)

#### biryokumaru (822262) | more than 3 years ago | (#33238494)

3 = 3 = 3

A rose is a rose is a rose.

But, actually, it seems that their math is wrong [slashdot.org] . I still stand by my rose statement, though.

### RTFA, it's not that usage which he's objecting to (4, Insightful)

#### Sockatume (732728) | more than 3 years ago | (#33238398)

"'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.

### Re:RTFA, it's not that usage which he's objecting (1)

#### biryokumaru (822262) | more than 3 years ago | (#33238456)

Wow. I can't read. Heh. Thanks!

### Re:RTFA, it's not that usage which he's objecting (1)

#### Haedrian (1676506) | more than 3 years ago | (#33238490)

And NOW I finally understand it. To add an example of my own [1+2+3+4+5]

1 + 2
= 3 + 3
= 6 + 4
= 10 + 5
= 15

I blame overuse of calculators if that's the case.

### Re:RTFA, it's not that usage which he's objecting (1)

#### biryokumaru (822262) | more than 3 years ago | (#33238594)

Ya, what's up with that? We were never allowed calculators in university, why do they give them to kids?

### Re:How bad is it? (0)

#### Anonymous Coward | more than 3 years ago | (#33238430)

But you can't do it the 2 + 2 = 4 - 1 = 3 + 10 = 13 style. I guess you know why.

### Re:How bad is it? (2, Insightful)

#### Sockatume (732728) | more than 3 years ago | (#33238474)

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.

### Re:How bad is it? (0)

#### biryokumaru (822262) | more than 3 years ago | (#33238568)

Yes, I see that now. I am a fool who cannot read. Perhaps if I hadn't wasted such much time in middle school learning what '=' meant...

### Re:How bad is it? (3, Informative)

#### Buggz (1187173) | more than 3 years ago | (#33238578)

Ya, I've never understood why 1 + 2 = 3 = 4 - 1 isn't okay.

Technically it is as okay as it gets, both sides of each equality operator is equal which is exactly how the symbol works. TFA is about how people don't actually "get" that, if you look at the example in the summary it essentially says 9 = 11 which of course is plain wrong.
The reason "double equalities" might be wrong is if you're solving an equation while showing each step.

### Re:How bad is it? (0)

#### Anonymous Coward | more than 3 years ago | (#33238372)

It's baloney. My 1st grader had been doing this type of fill in the blank(s) problem all year. I doubt any of his GP or regular classmates have been making this mistake. What age where the study "student"? Pre-K?

### And it's official! (0)

#### Anonymous Coward | more than 3 years ago | (#33238274)

I'm now completely ashamed of being from the US...

### Re:And it's official! (0)

#### Anonymous Coward | more than 3 years ago | (#33238318)

You should have been as soon as GWB took office. At this point the entire country is a joke.

### teachers (3, Insightful)

#### flynt (248848) | more than 3 years ago | (#33238284)

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.

### Re:teachers (3, Insightful)

#### NEDHead (1651195) | more than 3 years ago | (#33238544)

Since I doubt you can produce someone older than 500 years, so far as everyone is concerned the = symbol has been around forever. If anyone beyond 3rd grade cannot understand the problem and solve that equation for the unknown value placeheld by the ( ) symbol then the teachers' unions should take the blame.

### Home School (2, Insightful)

#### glittermage (650813) | more than 3 years ago | (#33238290)

This is one reason why we home school...public school systems fail in so many ways.

### Um, what? (0)

#### Anonymous Coward | more than 3 years ago | (#33238292)

Is the equal sign new or something? Or do today's students have more problems than all the previous generations? Do students in other countries understand it better? TFA is a little sparse.

### Calculators (5, Insightful)

#### Anonymous Coward | more than 3 years ago | (#33238296)

I blame it on calculators where the evaluate button has "=" on it.

### I am terrible at math..but (1)

#### lupinstel (792700) | more than 3 years ago | (#33238302)

I am terrible at math; I had to take the most basic math course twice in college. However I can not begin to comprehend how fucking stupid you have to be to not be able to properly answer 4+3+2=( )+2. I guess they can always become philosophy majors like I did.

### Re:I am terrible at math..but (1)

#### ACS Solver (1068112) | more than 3 years ago | (#33238526)

Pretty mind boggling indeed. Sure I've seen my share of kids really bad at maths but this is hard to believe. 90% of what I know about American schools is from reading Slashdot but this sounds like a problem with teachers to me. Seriously, I'd expect everyone who does not border on metal retardation to be able to understand the equal sign. Hell, if the students add the numbers on the left side and write that in the parenthesis, it shows they're capable of some thinking.

And out of curiosity, do your schools really offer tasks written as 4+3+2 = ( )+2 past the first 2-3 grades? TFA mentions "middle grades", which in my country would typically refer to grades 5-9, therefore ages 12-16 approximately, I assume US isn't much different. I remember that in the second grade, equations were presented with an empty box for the unknown variable, so it'd be like 5+3 = [ ] + 6. But already in the third grade they were introducing the concept of letters in equations, so they'd offer it in the form of 5+3 = x+6.

### Re:I am terrible at math..but (1)

#### ivan_w (1115485) | more than 3 years ago | (#33238592)

It's cognitively not that obvious.

Parsing "4+3+2=()+2" is actually not a trivial process. It may become trivial after some time, but it's not intuitive.

This could easily be parsed as (4+3+2=x)+2 and therefore, as ((4+3+2=9)+2)=11 because () is usually meant to change the precedence of a statement.

Now this could easily be read as :

"There are four red apples, three green apples and two yellow apples in a (nice little red basket) and two brown apples".. How many apples ?

### == vs = ? (0)

#### Anonymous Coward | more than 3 years ago | (#33238308)

The nerd in me wants to point out that == is what they are looking for, but that concept isn't taught until later in school anyways so I'll leave that alone :)

I'd say its a failure on the teaching system, not making them explain things to be sure they understand it. Teachers now are more focused on making sure they pass tests so that they don't get fired (which is another broken part of the system). I'd say we need an overhaul on the education system in the USA as well, in addition to many other things!

### Well DUH! (1)

#### Anonymous Coward | more than 3 years ago | (#33238312)

Schools in america do not reward understanding of the mathmatics behind the symbol.

They reward memorization.

Don't blame the players when the game is retarded...

### I don't understand the example, either (2, Insightful)

#### petes_PoV (912422) | more than 3 years ago | (#33238316)

Are they saying the quantity denoted by the braces () is an unknown and we should solve for it. Are they saying it's some sort of sub-total of evaluating the LHS of the expression? from the rest of the text:

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.

### Re:I don't understand the example, either (2)

#### ihatejobs (1765190) | more than 3 years ago | (#33238406)

Upon seeing the problem, it was immediately obvious to me that they wanted us to insert whatever number should be in the parentheses to make the statement true.

4+3+2=(7)+2 would be the correct answer.

If there is a statement with an equals sign in the middle, that means that the left needs to be equal to the right. If there is a blank space, and the two sides clearly aren't equal yet, they want you to make the statement true. Pretty obvious to me.

### Confusing symbols (5, Interesting)

#### M_Hulot (859406) | more than 3 years ago | (#33238330)

Didn't they just fool the students with odd / non-standard use of symbols?
I presume that 4+3+2=( )+2 is supposed to mean the same as 4+3+2=x+2.
If they had presented the equation with x, surely (almost) everyone would have solved it?
I'm from the UK, is 4+3+2=( )+2 a commonly used / commonly understood way of presenting the problem in the US?

### Re:Confusing symbols (4, Informative)

#### flynt (248848) | more than 3 years ago | (#33238422)

No, we use 'x' over here, too.

### Re:Confusing symbols (4, Informative)

#### TheGratefulNet (143330) | more than 3 years ago | (#33238644)

we used BOTH an x and a 'box' (as per my other post).

starting out, they taught us to fill in the missing value in the 'box' (square symbol). then, over time, when it was the right time to introduce letters as 'box symbols' they put an 'x' there.

made sense to me. a progression to get the kid up to that level of thinking. a box is empty and can be filled. makes good concrete sense. then later, we 'upgrade' the box to an x. same concept but more steps to get the kid there.

### Re:Confusing symbols (0)

#### Anonymous Coward | more than 3 years ago | (#33238460)

Admittedly I'm not in the maths, but this is the first time I've seen it presented that way, as a 29-yo American.

### Mod parent up. (1)

#### khasim (1285) | more than 3 years ago | (#33238556)

That's what I was trying to understand. Why not use the traditional "x" for the unknown instead of the non-tradition open and closing parentheses "()"?

This doesn't show that kids do not understand the equals sign.

This seems to show that kids do not understand the what they are supposed to solve for in that example. They do not understand the meaning of empty parentheses.

And frankly, I wouldn't be sure that I had solved it THE WAY THE PERSON WHO WROTE IT THOUGHT IT SHOULD BE SOLVED if I had just substituted x for () and gone from there.

### Re:Confusing symbols (4, Interesting)

#### R.Mo_Robert (737913) | more than 3 years ago | (#33238560)

I'm from the UK, is 4+3+2=( )+2 a commonly used / commonly understood way of presenting the problem in the US?

It sure isn't. I wonder if notational trickery isn't part of the problem, not a lack of understanding. (TFA doesn't say if there were directions, like "Solve for the missing quantity in parentheses" or something like that.) I bet more people would have understood if they used something like x. Maybe they were trying to avoid "scary" variables for middle schoolers, but that's actually exactly when I remember learning what they were--if not, the year before.

### Maths is all about clarity - this FAILs (1)

#### petes_PoV (912422) | more than 3 years ago | (#33238566)

The point of using symbols in maths texts is to convey clarity. The use of "()" does exactly the opposite here. For a lot of people the expression in the example evaluates to FALSE, or maybe SYNTAX ERROR, or if your eyesight isn't too good - or the teacher's writing is poor, the () could look like a zero, which would really screw up people's understanding.

The more I think about this topic, the more I see the fault as being in the way the problem is presented, not in any lack of understanding in the students.

### Re:Confusing symbols (1)

#### Mini-Geek (915324) | more than 3 years ago | (#33238584)

I'm from the UK, is 4+3+2=( )+2 a commonly used / commonly understood way of presenting the problem in the US?

No, that's not standard usage in the US or anywhere else that I'm aware of.
It's always possible the report was not properly representing what he was trying to convey, but the report definitely shows usage that isn't clear for anyone, unless it was explained on the test. No wonder people are confused.

### Re:Confusing symbols (1)

#### spleen_blender (949762) | more than 3 years ago | (#33238596)

I modded you insightful, then thought about it. The entire premise is an understanding of the equals sign. And even if they were confused by the () 4+3+2 NEVER EQUALS (9)+2

I think they chose a nonstandard notation for that fact so they would have to rely on the contextual meaning of what an equals sign DOES mean to understand what the intent of () was.

### Math education (1)

#### rennerik (1256370) | more than 3 years ago | (#33238332)

I think the U.S. math curriculum could use some equality with the Chinese system.

### Below Average (1)

#### snookerhog (1835110) | more than 3 years ago | (#33238340)

So if half of all students are of below average intelligence, then this means that 40% of the above average students still get this wrong.

sheeeeshhh

### This is GREAT NEWS (4, Insightful)

#### lxs (131946) | more than 3 years ago | (#33238356)

It means that even after China abolishes it's sweatshops there will still be a source of cheap unskilled labor in the world.

#### Anonymous Coward | more than 3 years ago | (#33238358)

Back in first grade I recall a problem just like the demonstration. The goal WAS to have "9" in the parenthesis. We were also taught 7-9= "impossible" till later grades to avoid confusing our young minds. Thank god I had calculators at home capable of negatives to prove the teacher wrong.

### Texas? (0, Troll)

#### Issarlk (1429361) | more than 3 years ago | (#33238362)

These researchers might be wrong and the students right. What does the bible say about the equal sign?

### 4+3+2=( )+2 (5, Funny)

#### batquux (323697) | more than 3 years ago | (#33238370)

Let's see here.. I'm going to go with:
4+3+2=(21/3*981727612785316256514034236^0)+2

### Don't know what () means (4, Insightful)

#### Neil Watson (60859) | more than 3 years ago | (#33238376)

I have college diplomas in the fields of mechanical and electronic engineering (technologist and technician for the Canadians). I also took all advanced math, physics and chemistry classes in high school. I don't remember ever seeing the notation "4+3+2=( )+2" before.

### Re:Don't know what () means (0)

#### Anonymous Coward | more than 3 years ago | (#33238498)

you're supposed to solve for ( ). children who haven't been exposed to algebra are afraid of variables, so textbooks put a safe pair of parentheses instead.

### Re:Don't know what () means (1)

#### PatrickThomson (712694) | more than 3 years ago | (#33238532)

This is the US education system. I recall seeing the notation when I was in primary school (ages 5-11). It may have been too long ago for you to remember. The problem is only written like that because they haven't been introduced to the concept of adding all 3 numbers together at once!

### Re:Don't know what () means (1)

#### TheGratefulNet (143330) | more than 3 years ago | (#33238586)

instead of a pair of empty parens, when I grew up they used a square box. it was extremely clear (to everyone!) that you put the 'solve for' value in the box.

sorry you could not see that a pair of parens was a virtual 'fill-in box' of sorts.

### A bit shocked (1)

#### TheCarp (96830) | more than 3 years ago | (#33238412)

I mean, I guess I just never thought of it that way.

I was aware that people solve math problems differently, mostly from discussing methods of figuring the tip at restaurants (I just round off to the nearest 5 and divide by 5 to get about 20%) however I never considered that someone might not learn the meaning of the symbols that they use.

I would like to know more because, I understand the equals sign, but I still use that a + b = 1 + 2 = 3 notation when I am just calculating something for a quick note, since I don't care about formality, I just want to have the result and the values used to calculate it so that I can check my work later if need be.

-Steve

### Sorry, in what context is "()" used as a variable? (2, Insightful)

#### Tuan121 (1715852) | more than 3 years ago | (#33238416)

Kind of baffled to see "( )" instead of say.. x? I have never seen parentheses used like that, at least not that I can remember. In what region/mathematical area is this commonplace? You would think an article discussing not understanding basic symbols would actually attempt to use the most commonly used symbols in the argument..

### uhhhh? (0)

#### Anonymous Coward | more than 3 years ago | (#33238420)

you can put pretty much ANYTHING in the brackets, as long as it comes to"7", so
you could put sqrt(49) in there?

### This is obviously liberals' fault (1, Funny)

#### roman_mir (125474) | more than 3 years ago | (#33238424)

Obviously the US students are now totally confused about what equality means, everything is equal to everything else, your work effort is equal to anybody else's work effort because based on liberal agenda the outcomes are supposed to be equal.

So clearly, women=men, black=white, all humans have equal rights, this inevitably leads to everything else being equal to everything else.

so 11=9, 0=1, Islam=Terrorism, America=Fuck Yeah=One Nation Under God=Obama=God Bless America=And No Place Else=Nuke The Whales=There Is No God=Gay Is Good=Gay Is Bad=Government Is Going To Fix Everything=Large Corporations That Are Monopolies Because Government Made Them Monopolies Are Going To Fix Everything

So you see, these students maybe confused, or maybe they are right and everybody else is stupid for not getting with the times.

Obviously.

### Re:This is obviously liberals' fault (2, Funny)

#### bsDaemon (87307) | more than 3 years ago | (#33238470)

Additionally, as you can see, our President wants to KILL SMURFS!

### Calculator math (0)

#### Anonymous Coward | more than 3 years ago | (#33238440)

They are too used to calculators. Type 4+3+2=+2= into one and indeed the answer is 11.

### Look at both sides of the issue (1)

#### roystgnr (4015) | more than 3 years ago | (#33238446)

Sure, inability to understand basic arithmetic leaves students unprepared for work in science... or engineering... or operating a cash register... or keeping society from crashing and leaving behind a postapocalyptic wasteland. But *in* that postapocalyptic wasteland, the cannibal hordes will find innumerates to be just as delicious as anyone else, so learning math would have been a waste of time anyway!

### Maybe they just haven't learned algebra yet (1)

#### Lije Baley (88936) | more than 3 years ago | (#33238468)

In my (very) small town school in the 70's and 80's, we didn't really learn algebra until 9th grade. Up to that point, the equals sign was pretty much used only as the "answer symbol", meaning "here is the result of all the stuff on the left".

### Oh, if only it were RPN (and gozinta) (1)

#### shoppa (464619) | more than 3 years ago | (#33238478)

I note that the example cited in the lead article, is simply what you would get if you hit those keys on a calculator.

If only we all used RPN, and there was no equals sign!

I am also extremely frustrated that all calculators have a divide button, but very few have the "gozinta" button. "Gozinta" is a way more useful concept than "divide" most of the time.

e.g. "7 gozinta 42" has the answer "6 times". I can do that rather painlessly on most RPM calcs with xy but on most other calculators it's more like "7, I already typed that in, I'll hit 1/x, then multiply by 42 and hit equals".

### Is that really the best example (2, Insightful)

#### VisiX (765225) | more than 3 years ago | (#33238524)

I have a hard time believing algebra students would do something similar if you replaced the parenthesis with a single character (like an x) in 4+3+2=( )+2. I am not surprised that students are confused when presented with equations using unfamiliar symbols rather than conventional single character variables. I am also not surprised that pre-algebra math students don't understand algebra. Judging from the summary it looks like this research was setup with the specific intent to prove their preformulated conclusion.

### Petkovsek, Wilf, Zeilberger A=B (2, Interesting)

#### bo-eric (263735) | more than 3 years ago | (#33238576)

For an expanded explanation of what the equals sign means, check out Petkovsek, Wilf and Zeilberger's A=B [rutgers.edu] . I remember it as a very enjoyable read from university, in parallel with Concrete Mathematics [wikipedia.org] ... (btw, why won't &scaron; show in comments?)

### (4+3) (1, Insightful)

#### Anonymous Coward | more than 3 years ago | (#33238606)

I think (4+3) is the best answer.

### What a stupid article... use a square box (1)

#### DustCollector (903185) | more than 3 years ago | (#33238628)

Did they try to use something else besides parens? Growing up, to solve math problems, I had to fill in a square box, or place the answer above an underscore. Parens actually have meaning in mathematical notation, so perhaps that is the real source of confusion, and not the equal sign.

### transitive property (0)

#### Anonymous Coward | more than 3 years ago | (#33238632)

Sounds to me like kids who answer a question like that migigh have less of a problem with the equals sign and more of a problem with the transitive property - if a=b and b=c, then a=c.

### Absolutely (1)

#### dcollins (135727) | more than 3 years ago | (#33238642)

I've noticed and written about this previously. I don't even blame the students that much; I don't think I was ever explicitly told what the symbol meant either. In standard curriculum you either have to pick it up inductively or you're crippled. Quoting myself:

But here's another way of looking at it: Each line of math is, effectively, a sentence. (A highly condensed sentence in specialized notation, but the same nonetheless. It can be re-hydrated back into normal English at any time.) And the equals sign is the verb "to be". It's the most important verb in any language! What if someone were in a writing class and submitted a paper without any verbs? What if they were entirely unable to say "you are", "I am", "he is" anything at all? Would an English teacher totally flip out? You bet they would.

http://angrymath.blogspot.com/2010/03/equals-signs.html [blogspot.com]

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