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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.'"
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.
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I blame it on calculators where the evaluate button has "=" on it.
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?
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?
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Let's see here.. I'm going to go with:
4+3+2=(21/3*981727612785316256514034236^0)+2
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."
If libertarians are so opposed to effective government, why don't they all move to Somalia?
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. :-)
It must have been something you assimilated. . . .
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.
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.
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
No, we say "Maths IS hard", as in "Mathematics is hard" Not that it matters, I just thought I'd point it out. .
They will never know the simple pleasure of a monkey knife fight
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.
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.
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.
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?
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.
"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)
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
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.
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.