US Students Struggle With Understanding of the 'Equal' Sign

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.'"

Comments

Wrong

[dyingtolive]

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

[Raumkraut]

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

Re:Wrong

[mcvos]

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

Re:Wrong

[Kenshin]

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

[beelsebob]

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:Wrong

[beelsebob]

I wonder how much this has to do with programming, and the fundamentally different nature of the meaning of = in that and maths?

There's no fundamental meaning of = in programming... There's a meaning that C gave it, which happens to disagree with what most definitions of the symbol mean. Life would have been so much simpler if C had stuck with the previously used := for assignment.

Re:Wrong

[hedwards]

It's mathematics or math or math's. It's really dumb to remove the ematic and leave that trailing s. More so when you leave out the apostrophe which one is supposed to use when one leaves out letters. Plus it's much more in keeping with general rules for pronunciation of English words. Maths is just awkward.

Re:Wrong

[operagost]

Where are you from, so that I can make up a ridiculous name for your nationality?

Re:Wrong

[dyingtolive]

The country is the United States of America, so I would assume that the reason why America==US is because they drop it down to the last word. Personally I prefer to be referred to as "Coincidental Inhabitant of the United States of America", and neither American, nor USian, or even USAian.

Re:Wrong

[egamma]

Actually, people should be identified by their state--Texan, New Yorker, Floridian, etc. It's not the United State of America, it's the United States of America--indicating that each one has a level of sovereignty, and people should be identified by that smaller area. Similarly, people are Scottish or Welsh, and not United Kingdomian.

Re:Wrong

[mike2R]

Ok I'm going to display my ignorance here and ask why isn't = on its own good enough for a comparison?

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:Wrong

[phobos512]

I am so SICK of that stereotype. Having been all over Europe in the last two years, there are just as many overweight people there as in the US. Possibly more on a per capita basis from what I saw. And Scotland? Holy crap!

Re:Wrong

[bhagwad]

English is logical now? When did this happen?

Re:Wrong

[DinDaddy]

Reading your post, I got to "ematic" and thought it was some language term for a word fragment that I didn't know, until I realized it WAS the word fragment.

Slashdot reading in the early morning is hard.

Re:Wrong

[arb phd slp]

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:Wrong

[gorfie]

In third grade I wrote a BASIC program that rendered a flying saucer landing. The assignment was to draw a static picture with pixel output. That experience probably guided me to my current profession. I didn't own a computer until the 90's so I would not have gotten that experience any other way.

It would be a shame if they weren't still exposing children to programming in school.

Of course, I did get a similar "how do things work" experience by disassembling Omega Supreme and a number of other toys. :)

Re:Wrong

[somersault]

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:Wrong

[arb phd slp]

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

This is a dialectical thing about American English. We use singular verb inflections with collective nouns.
Queen's English: "Aerosmith are playing Wembley Stadium."
U.S. English: "Aerosmith is playing the Verizon Center."
This is why you hear "the data is" over here.

Re:Wrong

[Custard Horse]

Yep, obesity is a problem in Europe too, particularly the UK (where I am from).

I have to say that when going to Disney parks in Florida (not an accurate test of averages I admit) there does seem to be a large amount of *very* large people there.

However, I put this down to population density in those areas and the fact that obese people are much more visible than non-obese people. I dare say that large people may obscure the view of one or more small people too which would create the illusion of more large people. Who knows? Who cares?

I don't agree with your comment on Scotland though - heroine is an appetite suppressant.

Re:Wrong

[Mikkeles]

In a sane language, '=' would not be used for assignment.

Re:Wrong

[carlzetie]

True enough about BASIC. However one of the worst design flaws in C is the combination of using = as the assignment operator together with the liberal interpretation of what constitutes an expression. How many lifetimes have cumulatively been wasted because some tired programmer wrote "if (x = y) ..." and the compiler raised no objection? Let's be honest, C is the king of side-effects.
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

[spazdor]

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:Wrong

[Custard Horse]

Does it matter that England, Scotland, Wales and Northern Ireland are different countries and are referred to as the United Kingdom of Great Britain and Northern Ireland (the inhabitants being commonly referred to as British)?

I believe it is well established that people from the USA are American and those from the UK are British - can we leave it at that?

Whilst we are at it, when Americans hear what they perceive to be an Australian accent, assume that the person speaking is in fact from the UK. Most Australians are drunk and wear hats with corks hanging from strings.

In return the British will listen out for an American accent with a strange twang and automatically assume the person speaking is from Canada. We will also look out for the hockey stick and racoon skin hat but will be wary of the hat without the stick as that person is likely to be Russian.

Re:Wrong

[Hognoxious]

This is why you hear "the data is" over here.

You here it in the UK too. While data is a collection of distinct and discrete ... ummm ... things, it's regarded as an uncountable noun like water, sand and (sorry, I had to) lego.

P.S. concerning your sig, shouldn't it be "sudo someone go find it"?

Re:Wrong

[CohibaVancouver]

"x = 1" is only a legal BASIC statement in the first place because interpreters have been relaxed for programmers too lazy to use "Let".

It's not really laziness. Mostly it's for historical reasons. My first computer (a TRS-80 model 1, "Level 1") had 4K of RAM. That's right, 4096 bytes. When you've got that little space for your BASIC programs, removing the requirement for "let" in your BASIC code freed up valuable bytes. (other similar shortcuts existed back in the day, such as "?" available as a replacement for "print".) ...and it wasn't just TRS-80s. Most computers of that era had similar restrictions. Today, space is virtually unlimited, but these legacy shortcuts remain.

Now get off my lawn.

Re:Wrong

[TheRaven64]

there are just as many overweight people there as in the US

Did you actually count them? As a percentage of population? Some people did and there are a lot, but not as many. The figures are around 33% for the US, 22% for the UK being classified as obese. For men, obesity in the EU ranges from 10-27% of the population, depending on the country - all of them are lower than the 33% figure for men in the USA. It's slightly different for women, where the figure for the USA is 35%, while the EU ranges from 10-38%.

So, there are a few countries in the EU where a higher percentage of he female population is obese than in the US, but no country where more men are obese.

Re:Wrong

[Hognoxious]

It would be a lot harder to type by accident when you really meant to type just one.

Re:Wrong

[maxwell demon]

Actually, originally in BASIC you had to write: "LET a=5" to set a to 5. However, BASIC implementations tried to reduce typing and allowed omitting the LET (I wonder how many people never new that LET actually existed). There were also other abbreviations like "?" for "PRINT" (that one always puzzled me: How could one get the idea to encode "PRINT" as "?", which is a sign which actually implies asking for something? The more logical way would have been to shorten "INPUT" to "?", and then maybe shorten "PRINT" to "!").

Re:Wrong

[CasperIV]

If you consider North America and South America one continent, your opinion is automatically invalid.

Re:Wrong

[commodore64_love]

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:Wrong

[squizzar]

As Franky Boyle put it: "Who else could 'Scotch' an egg. Let's take an egg, cover it in meat and batter it!" That and the deep fried mars bar may explain some of the problem..

Re:Wrong

[Sulphur]

That depends on the meaning of *is*.

Re:Wrong

[adonoman]

It's not a stereotype when it's true - yes there are fat people everywhere and thin people everywhere, but the US has more than 30% of their population obese. In the UK it's 22%. Italy, Austria and France are at around 10%. Up here in Canada we're hardly better than the US, and Mexico is nearly as bad. North America definitively holds the title for most obese continent, hands down.

Re:Wrong

[TheTrueScotsman]

Give me a break. It's nice to shout at the 80s and everything, but 90% of what C was used then for has being replaced by a language which does treat that as an error - Java. For the other 10%, modern C++ compilers will surely give a warning in this case.

Re:Wrong

[nomadic]

Most people just call them all British.

Or pasty white crumpet monkeys.

Re:Wrong

[Nursie]

That's a bit of a strong statement.

I don't want to pretend I'm some godlike C programmer, but competent coding and a simple review process catches this stuff pretty easily. And sometimes that there if(a=b) is exactly what you mean.

Can't think of any situations off hand, but I'm sure there have been some.

Re:Wrong

[painandgreed]

Actually, people should be identified by their state--Texan, New Yorker, Floridian, etc. It's not the United State of America, it's the United States of America--indicating that each one has a level of sovereignty, and people should be identified by that smaller area. Similarly, people are Scottish or Welsh, and not United Kingdomian.

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

[gmuslera]

There is a lot of United States of ..., and usually the country is known as the last part (i.e the official full name of Mexico is basically United States of Mexico). Could be discussed if there is right to "own" the continents with that pick of a name, but by the time the name was picked there was the only "united states" of the continent. There are more geographic related country names, i.e. Uruguay (first example that came to my mind because i live there :), South Africa and a lot more, that seem to claim ownership over something that they don't own.

Re:Wrong

[oldmac31310]

Maths is awkward? Math's is just plain bonkers. How did you arrive at that abomination?

Re:Wrong

[orgelspieler]

Similarly, people are Scottish or Welsh, and not United Kingdomian.

Most people just call them all British.

Just don't call a Scot "English," or you'll likely start a fight.

Re:Wrong

[gfreeman]

One or two people have noted that us Brits tend to understate things a wee bit.

Re:Wrong

[Tassach]

That's a bit of a strong statement.

I don't want to pretend I'm some godlike C programmer, but competent coding and a simple review process catches this stuff pretty easily.

I wouldn't say I'm a godlike programmer either, but I've been doing it for a living for 22 years. I've learned a thing or two in that time and seen many times what happens when programmers don't follow best practices.

In my experience competent programmers use all the automated tools at their disposal; exceptional ones find more things to automate.

Running a static code checker a 10,000 line program takes less than a second and catches 100% of stupid errors. Reviewing the same program by hand takes hours and is significantly less than 100% effective. Wasting hours of your time doing something the computer could do better in under a second is extremely foolish and unprofessional -- in other words, it's a sign of incompetence. That time could be better spend checking things that automated tools CAN'T easily catch, like critiquing the high-level design, writing automated test cases, etc.

If you don't consistently follow best practices, you're not a competent programmer. Considering that I've made a very lucrative career out of cleaning up other people's messes, I can say there's definitely no shortage of incompetent programmers working in the field.

And sometimes that there if(a=b) is exactly what you mean.

Can't think of any situations off hand, but I'm sure there have been some.

If you had bothered to read the splint output, you'd have seen this:

If an assignment is intended, add an extra parentheses nesting (e.g., if ((a = b)) ...) to suppress this message

Reading is fundamental.

Re:Wrong

[mattack2]

We're #1! We're #1!

Re:Wrong

[JWSmythe]

    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:Wrong

[shutdown -p now]

The story goes that K&R did a statistical analysis of some existing code, and found that assignment was 30% more frequent than comparison, so they went with the shorter version for assignment. But := and = are more historically correct in that they match mathematical operators.

I kinda like the assignment in ML language family, though:

x <- 456;

Re:Wrong

[Nursie]

Hey, I thought about my comment and you're right - there's really no reason not to use the automated tools that are available. It is manifestly possible to produce rock solid, enterprise grade software without them, but from an efficiency perspective you're spot on.

Well, that explains things.

[dr_strang]

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

Re:Well, that explains things.

[oldspewey]

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.

[Zeek40]

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

Re:Well, that explains things.

[fahrbot-bot]

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.

[KnownIssues]

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.

[theskipper]

It's a sine of the times.

Re:Well, that explains things.

[caramelcarrot]

The thing is every time someone talks about new ways of teaching math to fix problems in understanding like the one in the article, such as one way I saw of encouraging children to realize that e.g. '4', '2+2', '3+1', '1+3' are all the same thing, they're derided as some sort of wacko modern maths that makes no sense. Make your mind up, children aren't in general stupid, but their teaching certainly can be.

Re:Well, that explains things.

[Mr. Underbridge]

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:Well, that explains things.

[KarrdeSW]

Yeah, from what I've seen here in DC, playing farmville all day is worth only $40K max. That's with at least 2 years of FarmVille experience.

Re:Well, that explains things.

[TapeCutter]

"Our youth now love luxury. They have bad manners, contempt for authority, they show disrespect for their elders and love chatter in place of exercise; they no longer rise when elders enter the room; they contradict their parents, chatter before company, gobble up their food and tyrannize their teachers." - Socrates, (circa 400BC)

Re:Well, that explains things.

[Mr. Underbridge]

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:Well, that explains things.

[arose]

Your friend should not be teaching...

Re:Well, that explains things.

[Mr. Underbridge]

I can't speak for other families, but I know my mom, my dad, my wife's mom, and wife's dad all "respect their elders" and look/looked up to them. Our parents are in their early-mid 50s. I know my grandparents, in my family, didn't think my parents' generation was a bunch of slobs, mostly: while they thought some were bad apples, they didn't think the generation was a wash.

That may have been a great family, but it doesn't necessarily generalize. You know what their elders' generation also gave us? The Klan. Jim Crow. I'm just saying, in every generation, there are good people, and there are bad people. Every generation has a tendency to glamorize their own, and gloss over the bad parts. Hell, same with high school graduating classes. I mean, everybody I talk to thinks their class was the really special one. The kids under them? Turds.

Yet, if over a lifetime a person is taught poorly - or worse and seemingly more likely, taught incorrectly - he or she is going to be a bit of a simpleton by the time they reach adulthood.

I disagree. They might lack skills, but general logic and the ability to think independently isn't something that has to be learned. Indeed, too often formal education removes that characteristic. My family had a whole lot of sharp people who, by growing up in poverty had no access to education beyond the 5th grade. Oddly enough, they weren't droolers.

Re:Well, that explains things.

[Proteus]

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. :-)

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.

1. McDonald's (for example) is an international company, and they serve their core menu in dozens of languages. It's much easier and less error-prone for them to produce a picture-based keypad than to translate everything without error
2. Fast food companies did research indicating that it's faster -- even for highly-literate people -- to find an item by image rather than by name. Faster means better service with fewer staff, which means more profit.
3. Many fast food chains, and McDonald's in particular, hire people with disabilities. This is a huge win for such people -- real, productive work that can help make them at least partly independent. Many with cognitive or developmental disabilities have written-language challenges, and the picture "menus" are much easier for them to use efficiently. It doesn't make sense to have two versions of something if one works for everyone, does it?

And those are just the three reasons that are most obvious to me. Now get off your high horse!

Re:Well, that explains things.

[natehoy]

I drank WHAT?
  Socrates, (399BC)

teachers

[flynt]

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

[NEDHead]

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

[glittermage]

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

Re:Home School

[Ephemeriis]

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:Home School

[i.r.id10t]

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:Home School

[Anonymous Coward]

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:Home School

[operagost]

Many, if not most public schools actively DISCOURAGE parents from "interfering" with their children's "education". Mostly, if you disagree with their policies or methods, you're kindly asked to SHUT UP. If you teach your child to read and count before kindergarten, you're yelled at. Essentially, you're supposed to just be a cheerleader and shout, "RAH RAH" while the school produces a herd of ignorant do-nothings with a ingrained sense of entitlement.

Re:Home School

[glittermage]

I feel vouchers will address many issues with the public school system. I vote for people who support putting in a voucher system. Other than voting my energy will primarily be focused on my children's upbringing and not "the public" upbringing. My wife is the alpha educator in our house.

We can't agree on healthcare or retirement policies how on Earth would I convince others to adopt a specific learning methodology?

For those interested a great read on our public education system: http://www.amazon.com/Weapons-Mass-Instruction-Schoolteachers-Compulsory/dp/0865716315

Re:Home School

[Lumpy]

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:Home School

[Anonymous Coward]

I'm going to guess you're home-schooled, both because of your defensiveness and because of your lack of analytical skills (as opposed to memorization).

And you would be incorrect. Which means that I am a social paragon. Actually, just put me under the column of counter-example.

They made a comparison between two subject groups, which you did not address.

They didn't address it either except with some anecdotal evidence. Most of the socially maladjusted people I have met are products of the public school system. So, there is my anecdotal evidence. It cancels out. Care to bring any actual research to the discussion?

In fact, the existence of bullies undermines the argument, since those folks are by definition not socially well-adapted, and furthermore, they tend not to be "cured" by graduation.

In fact, let's roll with their thesis. Fire all the teachers, principals, etc. and just send the kids into a locked building with no adults for 6 hours a day. Of course, we shall expect them to not only master the social graces, but be experts in automobile engineering, medicine, mathematics, literature, composition, business, and pretty much everything else. Why not? They can learn all that stuff on their own, just like they can learn social skills in an unsupervised setting.

Who is lacking the analytical skills? Really?

Re:Home School

[Ephemeriis]

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.

Re:Home School

[IICV]

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:Home School

[Just Some Guy]

[citation needed]

Here I am. Cite me: I'm an original source.

My kids go to the public Montessori school in my city. It only goes to 3rd grade, though, and after that they have to transfer. We'd heard good things about another local public school and enrolled my daughter there. It was a fucking disaster.

Examples:

In 3rd grade, she was doing square roots. Her new 4th grade class was starting to learn 2-column addition.

The class had one hour to do math problems 1 through 20 (out of 100). She finished in about 10 minutes because it was remedial to her. For want of something to do, she went ahead and finished problems 21-100. Her teacher called her out in front of the entire class: "The assignment was 1-20, not 1-100. You didn't pay attention."

Since she wasn't allowed to work ahead, she pulled out a book to read. Again, from the teacher: "This is math, not reading. Put that away!" She was literally required to sit quietly in her desk for the remaining time.

Her weekly list of words to memorize for the spelling test on Fridays included "off" and "zoo". In 4th grade. I swear to God that I'm not exaggerating.

She'd cry in the mornings. "Please don't make me go to school today! I hate it there! Can't you tell them I'm sick and work from home and let me stay here with you?" I'd be sad if she was saying those things 6 years from now. Coming from my 4th grader, it broke my heart.

So I went to talk to the principal. He was a nice guy, and I'm a nice guy. We had a great visit and he said he'd work with the teacher to find more challenging work for my daughter to keep her busy and interested. We shook hands and I left.

Within the week, my daughter got detention for "looking bored in class". Shortly after that, she got a 96% on a test. Her teacher asked her (yet again, in front of the class) why she doesn't "get perfect scores on all her tests if [she's] so smart."

That afternoon, I enrolled her in a different local private school. They were doing cubes and long division in math class, and learning Latin and Greek word components in language class.

Sometimes it's not enough to talk to the teachers and administration.

Re:Home School

[PitaBred]

If you could get rid of all the religious wackos who use homeschooling as a way to indoctrinate their kids without having them exposed to the outside world, there would be a lot less stigma on the homeschooled crowd.

Re:Home School

[Shin-LaC]

You're a good dad.

Calculators

[Anonymous Coward]

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

Re:Calculators

[dtremenak]

Or it could be a holdover from being taught to do longhand addition and subtraction chained vertically, like so:
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.

I don't understand the example, either

[petes_PoV]

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

[ihatejobs]

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

[M_Hulot]

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

[flynt]

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

Re:Confusing symbols

[R.Mo_Robert]

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.

Re:Confusing symbols

[TheGratefulNet]

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

[blueg3]

If you watch the video, they have pictures of the math questions, which makes things a lot clearer. The parentheses are TFA's way of trying to draw a blank space. In the original questions, it's an underlined blank space (so ___ would have been a better choice) -- the same sort of underlined blank space provided in grade school where they want you to fill in the answer. In mathematics classes before algebra, when they're trying to introduce you to algebraic concepts, it's common to use blank spaces for "figure out what goes in this space and write it", rather than writing an "x" and saying "solve for x", which would use a concept the students haven't yet been taught.

Re:Confusing symbols

[clone53421]

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:Confusing symbols

[PitaBred]

If you teach and expect kids to be stupid, they will be.

I guess I'm stupid, too.

[maillemaker]

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.

[Issarlk]

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

Re:I guess I'm stupid, too.

[dyingtolive]

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.

[skids]

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.

[surgen]

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.

[blueg3]

The actual notation used in math questions and textbooks is a blank space (e.g., an underlined blank space). The parenthesis are a poor attempt and rendering that in text.

Re:I guess I'm stupid, too.

[hjf]

___, this is very ____ to do.

Re:I guess I'm stupid, too.

[nschubach]

If_only_there_was_a_symbol_for_placing_an_underscore_in_a_blank_space.__Someone_should_get_on_that.

Re:I guess I'm stupid, too.

[arekusu_ou]

It's not a trick question. I've seen it before, and I understood it the first time I saw it.

The problem isn't the fact they used odd notions that others assume incorrectly. Instead of ( ), I've also seen the use of an empty box, underline as someone else noted, ?, circles, etc.

IQ tests often use "something is missing, please complete", problems. Cognitive theory has it that the brain does not process information straight forward, it takes pieces of what it sees and reconstructs it. That's why we can understand misspelled words, geometric shapes with broken lines, and why visual tricks work on our brain. Understand broken English sentences.

The problem is students are growing up lacking in critical thinking skills. When left with a blank or a void, their minds fail to fill it in properly.

We're heading into a generation that can't understand things unless it's spelled out for them and that is a shame. And if you really have a BS in CS and genuinely could not understand the problem listed above, rather than stubbornly proving a point, then that is very sad indeed.

Re:I guess I'm stupid, too.

[ihatejobs]

Public schooled kids are typically behind home schooled kids because instead of a 1 to 1 ratio, its a 1 to 30-40 ratio. News at 11.

Re:I guess I'm stupid, too.

[arekusu_ou]

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:I guess I'm stupid, too.

[biryokumaru]

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.

Re:I guess I'm stupid, too.

[MerlinTheWizard]

Am I the only one who absolutely DID NOT understand your answer? How do you go from: 4+3+2 = 9 to: ( ) + 2 = 2 ? It makes no sense.

Re:I guess I'm stupid, too.

[INT_QRK]

The important question is how should one feel about 9 = 2 in a more inclusive socioeconomic context? Who are you to judge with your elitist western notions of objective reality? In some cultural contexts 9 = 2 may be a legitimate expression of rejecting repressive colonial monoculturalism. Insensitive clods!

Re:I guess I'm stupid, too.

[gilleain]

___, this is very ____ to do.

I can find at least two solutions :

• "However, this is very easy to do"
• "Unfortunately, this is very hard to do"

:)

This is GREAT NEWS

[lxs]

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

4+3+2=( )+2

[batquux]

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

Don't know what () means

[Neil Watson]

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

[Stormin]

That's because the US educational system is so bad at explaining variables.

I struggled with Math for the entire time I was in the educational system. At the end of each struggle, when the light bulb went on, I almost always thought 'This is so incredibly simple, why didn't they just explain it this way?" I've never seen a math textbook from another country as the article compares to, but I can certainly state that I think the ones written in the US are about at the level of a man page - if you already know the content and just want a quick refresher on some infrequently used bit - they're fine. If you're trying to learn something new for the first time - forget about it!

Re:Don't know what () means

[Neil Watson]

Ah. So () is a helmet. Kids wear helmets for everything these days.

Re:How bad is it?

[Haedrian]

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.

RTFA, it's not that usage which he's objecting to

[Sockatume]

"'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:This is obviously liberals' fault

[bsDaemon]

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

Re:How bad is it?

[Sockatume]

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

[VisiX]

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.

It should be: 4+3+2=x+2 (Solve for x)

[Knertified]

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.

Re:It should be: 4+3+2=x+2 (Solve for x)

[operagost]

It looks like someone's invented new new new math. *sigh* The real problem is that every generation, a new crop of GENIUSES thinks they have a better idea for teaching mathematics.

Re:It should be: 4+3+2=x+2 (Solve for x)

[indeterminator]

My thoughts exactly.

For me, 4 + 3 + 2 = ( ) + 2
=> 4 + 3 + 2 = (empty value) + 2
=> 4 + 3 + 2 = 0 + 2
=> 9 = 2
=> wtf?

Re:It should be: 4+3+2=x+2 (Solve for x)

[SpeZek]

Is it really that confusing? The problem is the lack of logic and understanding of equality. It shouldn't matter what the equation looks like, if one side equals the other, one side equals the other.

Re:It should be: 4+3+2=x+2 (Solve for x)

[Senior Frac]

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:It should be: 4+3+2=x+2 (Solve for x)

[drgruney]

They problem isn't that people didn't know what ( ) means, it's that they can't infer it. Abstract thought is no longer taught very well.

Re:It should be: 4+3+2=x+2 (Solve for x)

[Grizzley9]

1. Let a and b be equal non-zero quantities
a = b
2. Multiply through by a
a^2 = ab
3. Subtract b^2
a^2 - b^2 = ab - b^2
4. Factor both sides
(a - b)(a + b) = b(a - b)
5. Remove canceling values (a - b)
a + b = b
6. Observing that a = b
b + b = b
7. Combine like terms on the left
2b = b
8. Divide by the non-zero b
2 = 1

???

Re:It should be: 4+3+2=x+2 (Solve for x)

[NNKK]

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.

Re:It should be: 4+3+2=x+2 (Solve for x)

[DriedClexler]

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)

[he-sk]

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)

[SpeZek]

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)

[JayJay.br]

oh! Whoosh for me then!

(heads on to Wikipedia)

Re:It should be: 4+3+2=x+2 (Solve for x)

[Qzukk]

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)

[SpeZek]

Weird, because I did spend the last 13 years learning math. I'm only on my second year of university (and hell, I haven't taken any college-level math beyond my AP exam in highschool). An equals sign means something is equal to something else. This is so basic it's almost embarrassing to be arguing about it, which is the point of TFA. Maybe the students didn't understand that ( ) was an unassigned value because they hadn't seen it before, but, why didn't they understand what = meant? That's the problem.

Re:It should be: 4+3+2=x+2 (Solve for x)

[maxwell demon]

It is "fill in the blank" - but filling the blank with 9 doesn't make it a correct equation. Filling it with 7 does.

Re:It should be: 4+3+2=x+2 (Solve for x)

[AGMW]

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). 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:It should be: 4+3+2=x+2 (Solve for x)

[aaarrrgggh]

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:It should be: 4+3+2=x+2 (Solve for x)

[SpeZek]

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:It should be: 4+3+2=x+2 (Solve for x)

[canajin56]

I saw that in textbooks right on the cusp of learning algebra, to ease you into it. Only, it's not really "( )", it's, well...Slashdot doesn't support unicode so I can't show you...but, it's supposed to be a circle. TFA didn't use one either. IDK if it's because they're not using the same textbooks I've seen, or just because they don't know how to type unicode, either. At any rate, students would, from their earliest years, be used to seeing "2 + 2 = ( )" or "2 + 2 = [ ]" where those are supposed to be circles or boxes for them to put the number in. Or, perhaps "2 + 2 = ___" a blank line for them to put the answer in. The point was that, with no explanation of the equal sign, they come to the wrong conclusion about that circle. They see "4 + 3 + 2 = circle + 2" and they do what they've always done, by rote, and put 9 into the circle, then proceed on to the next little bit, which is +2, there, 9 + 2 is 11, they wonder why there isn't another circle, and make one.

At any rate, your solution of "just use algebra" is absurd, they haven't learned it yet. Algebra is what they're trying to teach them with this. And the point is, it doesn't matter. If they show them "x = 2 + 2, so x is 4", they just might get it. But, if they see "4 + 3 + 2 = x + 2" they would do the same as before "x is 9, so x + 2 is 11". They're just assigning too low a priority to equality in the order of operations, really...and also thinking in C I suppose, where (x = 9) + 2 does equal 11 ;)

Re:It should be: 4+3+2=x+2 (Solve for x)

[canajin56]

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)

[Pennidren]

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)

[orient]

Mathematics is an exact science. It is supposed to be very formal and have a rigorous syntax. I was amazed that otherwise bright north-american university students (majoring in computerscience and math) were unable to create a simple (half a page) calculus demonstration without using WORDS. They came from highschool with no knowledge of basic mathematical symbols like "exists", "whatever", "it results that", "non". Greek alphabet was, well, greek for them - they were assigning random names to greek letters (omicron was epsilon, epsilon was tau etc).

Re:It should be: 4+3+2=x+2 (Solve for x)

[severoon]

The difference between "unassigned value" and 0 is pretty inconsequential for most people in most real-world situations...

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:It should be: 4+3+2=x+2 (Solve for x)

[Anonymous Coward]

1 + 1 does not always equal exactly 2.

Yes; yes it does.

1 + 1 always equals 2. You aren't adding 1 + 1 when you're adding .5 and .5, you're adding .5 and .5. There's a 50% difference; your answer will reflect this difference.

To use a first grade example, if I have one apple and put it in a bag with someone else's apple, that other person's bag now has two apples. Now, if I have taken a bite out of my apple, the other person has one bite less than two apples - which, as any person might be able to see, is absolutely less than two apples. Relatively speaking, however ("depending on your point of view") the person with the bag "has two apples".

This might also be called rounding, which, while not incorrect, is not true equation; it's an approximation. This does not change the absolute nature of 1 + 1 = 2.

Re:It should be: 4+3+2=x+2 (Solve for x)

[japhmi]

So, it's a textbook problem in your opinion. I think that you're right (and that kids shouldn't be using calculators for quite a while into math).

My daughter's math textbook is more old-fashioned, and it has find the missing addend type questions starting in 2nd grade IIRC. They use the notation of an empty box for the child to fill in.

Re:It should be: 4+3+2=x+2 (Solve for x)

[Senior Frac]

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)

[Actually, I do RTFA]

In English - four plus three plus two equals something plus two.

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".

Why are people throwing out the rules when they come upon an unknown?

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.

If they understood clearly, concretely, what "equals" meant, there wouldn't be the sort of confusion that's been going on

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?

I think another poster had a good theory, that nowadays "=" is seen as "solve it" due to its use on calculators.

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)

[sarkeizen]

I'm not sure if the brackets were literal or just a typographical convention. However historically it wasn't uncommon to see boxes instead of variables at the younger grades - they may still do today. Also without the paper it's difficult to say if this is the only kind of test they put to students. I think your argument is kind of bogus though - You could just as easily level the same criticism at word problems...or perhaps you believe that word problem need a highly rigorous and pre-defined format. Math, as I see it anyway isn't just taught so that you can manipulate symbols deterministically. To me a good test of *knowing* math is to be able to recognize and solve mathematical problems without needing it to be spoon fed to you. Otherwise...what's the point? Machines already outstrip our ability to compute - why outside of extremely simple addition and subtraction would you bother ever learning a lot of math EXCEPT to use it so that you can recognize solve problems that are not handed to you in exam question format.

Re:It should be: 4+3+2=x+2 (Solve for x)

[mmaniaci]

Bump for great justice. I had no idea what the equation was trying to ask until I read all the posts that explained () is notation for a variable.

Re:It should be: 4+3+2=x+2 (Solve for x)

[honkycat]

I presumed it to be the text equivalent of an empty box on a printed worksheet. In my hazy memory, a blank like that was the standard way of writing algebraic questions like this in elementary school. It requires less abstraction than the 'x' option, since you don't have to get into the business of "assigning" a value to x and that whole business. You just visually complete the box (or empty line) or whatever so that there's a true statement on the page.

If you had seen this on a sheet of paper, I think it'd be more obvious.

Re:It should be: 4+3+2=x+2 (Solve for x)

[Dread_ed]

A circle? Oh thats soooo easy! You just fill it in using a #2 pencil.

Re:It should be: 4+3+2=x+2 (Solve for x)

[petershank]

Yes, my 3rd grader is given that kind of problem, but with a longish underscore instead of the parentheses. Sometimes it's a box, but the underscore is better, because it's a familiar holdover from learning to read, where a drawing of a feline is accompanied by "__at" and they're told to fill in the blank. I agree that using parentheses would be as poor a choice as "()at" when you want them to produce the three letter synonym for feline.

The mathematical pedagogy is fine; they're trying to develop numeracy (numeric literacy) by instilling the idea that there's more than one way to "express" 7, but they don't (yet) want to muddy the waters more by mixing letters and numbers and using phrases like "solve for"

Re:It should be: 4+3+2=x+2 (Solve for x)

[Shin-LaC]

All these people complaining about the notation need to switch on their brains. Obviously, the parentheses (which were probably a circle or oval field on paper, anyway) are not the problem. How do I know that? It's simple: the students filled them in! They understood perfectly that the blank space was supposed to be filled in with a number.

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:It should be: 4+3+2=x+2 (Solve for x)

[jc42]

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. ;-)

Petkovsek, Wilf, Zeilberger A=B

[bo-eric]

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

Re:How bad is it?

[Buggz]

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.

Is it really plural, though?

[Millennium]

Do your Barbie dolls say "Maths are hard"?

Re:Is it really plural, though?

[The Grassy Knoll]

No, we say "Maths IS hard", as in "Mathematics is hard" Not that it matters, I just thought I'd point it out. .

Re:Is it really plural, though?

[dyingtolive]

They do in the south.

Re:Is it really plural, though?

[nospam007]

Sice everybody seems to be too lazy to check, here's an excerpt from Wikipedia.

Etymology

The word "mathematics" comes from the Greek (máthma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study", even in Classical times.[9] Its adjective is (mathmatikós), related to learning, or studious, which likewise further came to mean mathematical. In particular, (mathmatik tékhn), Latin: ars mathematica, meant the mathematical art.

The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural (ta mathmatiká), used by Aristotle, and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek.[10] In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.

It would help if they finished quoting

[MikeRT]

“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.”

It's not the calculators... it's the students and teachers. You cannot blame a machine for students either failing to understand or just never grasping that going from "4+3+2=( )+2" to "4+3+2=( )+2=11" is nonsensical. Don't make excuses for them. I say this as someone who barely got through math classes (and being 27, I'm in the same generation as most of these kids), and even I looked at their thought process and muttered "W... T.... F....?"

Re:Pictures

[TaoPhoenix]

So that explains the MS Office Ribbon?

Headline should read...

[gatkinso]

"Researchers at Texas A&M struggle with Meaning of Parenthesis."

Re:Headline should read...

[swillden]

Except they didn't use parentheses. Apparently it's just the submitter who doesn't understand the meaning of parentheses.

Re:All part of their plan.

[Anonymous Coward]

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.

The problem

[AhabTheArab]

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:The problem

[AhabTheArab]

I wasn't going to come out and say it, but yes, females tend to be more guilty than males at that. That's all it's good for though - getting through school. They memorize the facts or procedures for the topic they're currently learning about in a class, but once the class moves on, they forget just about everything. It's fine if all you care about is a good GPA, not so good if you care about learning.

What?

[Overzeetop]

Since when is a set of parentheses a proper substitution for a variable? Seriously, part of the problem is that the standards for writing and evaluating mathematics in (especially) earlier grades is subject to what' I'll call "local interpretation".

As the father of a rising third grader, and a professional engineer with masters degree that included more math than I care to admit, I've puzzled over the way problems are written. At least one in ten homework assignments require that I look at the answer sheet to determine what the question is actually asking. Some of the answers appear to be wrong, except when interpreted in a very specific way which is counter to standard practice. Others are simply misleading.

Re:RTFA, it's not that usage which he's objecting

[Monkeedude1212]

I also wonder how these kids cope when a second variable is introduced.

Re:Calculators in school

[biryokumaru]

My electrical engineering professors seemed to be of the opinion that we were allowed to use a computer when we knew how to design it from scratch.

Re: Nonstandard notation

[Sithech]

In the elementary and middle-school texts standard notation is rarely used. I've got a doctorate, but helping my kids through their math often is a real stumper. It is very common to use a box, a blank, or a parenthesis to indicate something that they are to fill in in a "number sentence". The theory seems to be that you don't need to teach about unknowns and variables because that would be confusing. So this notation is somehow intuitively obvious to the least observant. As they may not cognitively be ready for the concept it becomes even more obscure. Have a look at the books sometime - you'll want to scream. I can testify that the methods used up until the mid 1960's were MUCH more effective in creating mathematical literacy. The Stanford Studies Mathematical Group (SMSG) series of math texts was, to my memory, the flying wedge of what was termed then "The New Math". The strategies like 4+3+2=()+2 come from that movement. Truth is, the "New Math" is a dismal failure and resulted in the destruction of the mathematical competency of two generations of American students. Unfortunately the math teachers now all came up through that system and have no idea that there is a better way to teach math.

Re:== vs = ?

[maxwell demon]

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 :)

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:uhhhh?

[maxwell demon]

Hmmm ... I just noted that 6*9 / 6 is, of course, 9. So maybe the true problem is all of them knowing the Hitchhiker's Guide to the Galaxy, and the testers didn't get the joke :-)

Understanding and not memorization is the key

[zero_out]

When I was studying multiplication, I just could not comprehend it. I was getting failing grades constantly, while my classmates were memorizing their multiplication tables and acing exams. I just couldn't understand it. Then, it dawned on me... multiplication wasn't some new mystery math, it was just addition in a new form!

Then I became better at multiplication than all my classmates, and stunned the teachers by how I went from getting 80% of my tests wrong, to getting 100% correct, and faster than my classmates. Unfortunately, it was at the tail end of the unit, so I still got a bad grade on my report card.

The teachers thought I was cheating, too. They had me take tests in front of them, during recess, to prove that I wasn't cheating. They then accused me of being lazy and not paying attention previously. No, I just didn't understand the mystery math they were trying to teach me, because they were expecting me to memorize things, and not actually teaching me to understand it. I don't think they ever accepted that truth.

So it is with addition and =. Children are taught to do this, then that. They are taught process, not meaning. They need to be taught from the bottom up, not from the top down. Teach them that = means equality, not evaluation.

Oh, and use standard notations, not this ( ) garbage that nobody uses.

Re:Texas?

[fishbowl]

The bible comes this close to giving us the square root of 2.

Rev 21:16 -- And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal.

And this close to giving us pi.

2 Chron 4:2 Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.

Oh well.

It's the calculators, you dummies!

[Kaz Kylheku]

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".

Social problem.

[MaWeiTao]

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.

RPN!

[metamatic]

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:RTFA, it's not that usage which he's objecting

[MBCook]

4+3+2 is not equal to 9+2.

That's the problem the students have. My reading has it going like this:

• 4+3+2=()+2
• OK, I'll add those
• 9=()+2
• OK, the answer to the first part was 9, so put that in the blank in part B
• (9)+2
• Now I can get an answer
• 9+2=11
• The answer is 11

They're taking the blank as a "fill in the answer from the previous part", working the equation from left to right, instead of understanding that the right side is related to the left, and not "part B" of the problem.

This makes perfect sense to me. Helping my little sister with her homework just a few years ago, I would manipulate equations (like moving something to the other side or dividing both sides by two) and she would say you couldn't do that, so I'd have to tell her you could and then give examples that show it was correct. Her teacher didn't get the point that the equation is a whole across, she saw it as two separate things with a symbol in between. But she could usually get the right answers by memorizing the 3 or 4 steps for solving that kind of problem the teacher gave her. But if the problem has a trick in it or isn't formatted right... the students don't know what to do and intuit (incorrectly) how they are supposed to do it.

And I have to call BS on the writers of the study.

[macbeth66]

I just asked a ten year old boy, whose mother brought him into the office. His answer, without hesitation was '7'. And this kid is not in any special program or considered a whiz of any kind. He did not even understand the explanation of the wrong answer. 'Huh? That's stupid', was his response. Out of the mouths of babes.

Did the researchers get their subjects from a school for the mentally challenged and not realize it?

   

Re:Who ever came up with this should be fired.

[Qzukk]

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

[Dynedain]

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.

[clone53421]

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.

Bad research: it is a operator precedence problem

[imnotanumber]

Someone already said: it is a operator precedence problem, not about students' interpretation of the equal sign. Looks like the researchers could not pinpoint where the misunderstanding is.

Math education in America is pathetic

[Ereth]

Math education in America is pathetic. I went through my nephews High School textbook and there wasn't any MATH in it. There were lots of pictures of butterflies and "Why are we learning this?" columns and the whole thing looked like it was designed to be entertaining, rather than educational. The math was an afterthought, with hardly any problems, no explanations of those problems or how to solve them, and no answers. I was stunned, especially when I learned it was written by four math professors.

There is some argument, of course, that this is on purpose, and that we fail our duties to educate our children because an educated populace would be a danger to those in power. I'm not prepared to accept that, but I do think we've completely failed in our duty, and the uneducated masses of today is evidence enough of that.

My father has a saying, "There's no teaching if there's no learning. Until there is learning, you aren't a teacher, you are simply a presenter". I think we have far too many presenters, and not anywhere near enough teachers.

Re:Math education in America is pathetic

[EmagGeek]

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.

What's wrong with Ohioan and Wyomingite?

[Animaether]

What exactly sounds weird about Ohioan and Wyomingite?

More to the point.. why would those sound any 'weirder' than people from TexaS being TexaN or people from Puerto RicO being Puerto RicAn, while people from Massachusetts aren't Massachusettan but Massachusettsan?

Not to mention Connecticuter.. cuter? Surely for pronunciation that should have been Connecticutter?

At least Ohioan makes it more clear it's somebody from Ohio than New Mexican does for somebody from New Mexico.. that should have been New Mexicoan as well.

Then again, I'm from The Netherlands, or Holland if you prefer, but you English-speaking folk insist on calling us Dutch.. so maybe I'm just used to these sorts of shenanigans ;)

Re:What's wrong with Ohioan and Wyomingite?

[Anonymous Coward]

Then again, I'm from The Netherlands, or Holland if you prefer, but you English-speaking folk insist on calling us Dutch

Hang on. The Dutch I know are always bitching about being called 'Holland' because that's just the name of a region in the Netherlands not the whole of it.

You mean to tell me that now, when I've finally got the hand of that, Holland is now fine, but 'Dutch' is wrong? What other word for Dutch is there?

You guys are just making this up as you go along.

Re:Go back and read your basic English book!

[jeremyp]

Nope. That's not what it means at all. The apostrophe (that's its name) is used to denote the possessive e.g. JeremyP's post. It's also used to show that you've missed out some letters, as in "you've" or "it's" or "couldn't". So technically "math's" is correct, but nobody ever writes it like that.

Null Pointer Exception

[medv4380]

So they don't understand NULL. That's acceptable. 70% of people saw the equation had a memory leak and carried data over into the null that just happened to be the last equation they saw. That happens all the time to a computer program that's not properly debugged. I'm more worried about the 30% of people who saw null and created X. Who are they to just randomly initialize variables to catch an exception that they didn't know was going to come there way any time soon.

Re: Nonstandard notation

[oldmac31310]

I agree completely. See my post re Singapore Math. My mathematical abilities are nothing special at all, but the way these books for elementary school are put together is awful. There is a reason for standard notation and syntax and throwing that out to make it easier to understand with no standard way of doing it makes it even more confusing. I expect that my sons will have an even more difficult struggle with mathematics than I had.

Re:All part of their plan.

[tuxgeek]

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.

Re:= for assignment not unique to C-style language

[Steve Max]

Fortran (at least up to Fortran77) uses "=" just for assignment. For comparisons we have to use (x.eq.y). The system works pretty well, and much simpler than C. However, typing .eq., .ne., .gt., .and., etc at every logical group is a royal pain in the ass.

I am not from the US...

[KritonK]

...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!