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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.'"
So I'm not being a curmudgeonly old jackass when I think this generation is stupid.
This is a sig. It is like every other sig in the world, except that it is mine, and it is different.
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.
I blame it on calculators where the evaluate button has "=" on it.
It means that even after China abolishes it's sweatshops there will still be a source of cheap unskilled labor in the world.
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.
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"'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.
No kidding!!! What do you say at this point?
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.
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
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.
"Work is the curse of the drinking classes." -Oscar Wilde
So that explains the MS Office Ribbon?
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
"Researchers at Texas A&M struggle with Meaning of Parenthesis."
I am very small, utmostly microscopic.
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.
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.
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.
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.
___, this is very ____ to do.
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.
Where are you from, so that I can make up a ridiculous name for your nationality?
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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.
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.
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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?
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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.
Do not look at laser with remaining good eye.
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.
which is totally what she said
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.
Alexander Peter Kristopeit bought his basement from his mommy for one dollar.
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".
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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.
"Work is the curse of the drinking classes." -Oscar Wilde
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.
"I disapprove of what you say, but I will defend to the death your right to say it." - historian Evelyn Beatrice Hall
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.
If I have been able to see further than others, it is because I bought a pair of binoculars.
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.
Alexander Peter Kristopeit bought his basement from his mommy for one dollar.
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.
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.
___, this is very ____ to do.
I can find at least two solutions :
You're a good dad.