Taken very literally, not all students are created equal—especially in their math learning skills, say Texas A&M University researchers who have found that not fully understanding the “equal sign” in a math problem could be a key to why U.S. students underperform their peers from other countries in math.
“About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students,” note Robert M. Capraro and Mary Capraro of the Department of Teaching, Learning, and Culture at Texas A&M.
[…]
“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. […] One cause of the problem might be the textbooks, the research shows.
The Texas A&M researchers examined textbooks in China and the United States and found “Chinese textbooks provided the best examples for students and that even the best U.S. textbooks, those sponsored by the National Science Foundation, were lacking relational examples about the equal sign.”
American edumacation = FAIL.
Easy to understand why the “not-equal” sign is not understood in schools. That is because the ed-ucrats want everyone to be equal.
And there is another side of the story. They might not understand math symbols, but no other country can hold a candle to our kids’ in-depth knowledge of American Idol.
From the article: ““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.””
It is stupid math notation, not a misunderstanding of the equal sign. If they just wrote the problem as:
For the equation 4 + 3 + 2 = x + 2, find x, then it would be immediately solvable. I never heard of using ( ) to represent a variable. I have often seen x or y or any Roman letter to represent a variable. Like I said, “stupid notation.” Students are most likely confused by this notation rather than being confused by the actual math.
Good article. The ‘=’ sign is indeed a very fundamental element in teaching that does get glossed over.
The libs have pushed their equality meme from the schools to the workplace.
EEOC states that honest workers = convicts.
Employers can’t refuse to hire convicts. The EEOC has declared war on all discrimination in hiring — even reasonable choices by employers.
http://eeoc.gov/laws/practices/inquiries_arrest_conviction.cfm
RPN anyone?
#3, so you are saying that American students are just too dumb to figure out what is essentially a “fill in the blank” without it being explicitly presented to them as a single variable equation?
Well this is what happens when instead of using schools to actually teach kids, we use them to feed the massive bureaucracy, and to keep the members of that bureaucracy employed even if they are not doing the job.
To this day I still do not understand why democrats are so against school voucher systems. I know many do not like the religious aspect and I can appreciate that, even if I do not agree with it. The solution always seemed rather simple to me. Just make it so vouchers cannot be used at religious schools, in the short term that would save so many children from a mediocre education. If parents want to send their kids to religious schools then they can pay for it.
Are the politicians so scared of the teachers union that they are willing to sacrifice entire generations, just to keep a political group happy?
Exactly when did Texas decide *it* could criticize textbooks??
Last semester, I had quite a few Chinese students in my college classes, and we had an interesting discussion about the perception that Asians are better at math. Evidently they learn elementary math using an abacus. One young lady told me that, though she doesn’t like or enjoy math, she is always able to do well because she learned to visualize relationships. I’m sure the use of various senses – sight, touch – adds to the learning experience.
Isn’t use of the “=” against state law in Texas?
#7 Sea Lawyer said, “#3, so you are saying that American students are just too dumb to figure out what is essentially a “fill in the blank” without it being explicitly presented to them as a single variable equation?”
Who uses a set of parenthesis as a blank? It is poor math notation to do so.
High school math text books that have the answers in the back, are full of mistakes. Not only that, but teachers refer to those answers as fact, and I’ve seen correct answers of the brightest students marked wrong because the teacher trusted the text book, whereas the student didn’t…. a travesty all around.
Practical example here… My nephews grew up in American public education schools (one is still in high school). Problem I see is how are they were thought Math’ in general. Actual Math’ is a “forbidden subject” to teach. Impetus is on giving kids problems and letting them figure it out on their own, rewarding both correct and incorrect attempts. I call this practice “non-teaching” but people in power in modern education love it.
I usually compare it with example of giving kids examples of problem like “there is a flag on that mountain – how should you get it?” but never ever letting them walk out to something. This will develop great imagination (appropriate for Arts) but given real problem of flag on the mountain, these kids simply will lack muscles and stamina, never mind real world experience of climbing to actually get it. Though they’ll be great in imagining and drawing their potential attempt.
So, it is not textbooks but very concepts of how to teach children Math’. It can’t be fun. At least not all of it. There must be drilling part there with mundane repetition of similar problems with practical instruction how to solve them. That way “Math’ muscles” in their brains can be developed and signs like = ingrained in their heads by the second grade.
Perhaps if the teachers didn’t come from the bottom quarter of college students, things could improve.
#8, if you take out the religious schools, private schools become more expensive than public schools.
Americans = < smart. But they do believe in slogans!
Drill baby drill.
All taxes are bad.
Hasn’t John Dvorak assured us that it is more important for kids to learn to use calculators and computers to solve there problems for us?
I’m sure the kids in America are quite good at going to Wolfram Alpha to have their problems solved. Admittedly, it got stumped also by 4 + 3+2 = ( ) + 2
#3, the reason that they wrote it as empty parentheses (more likely it was an empty rectangle on the actual question and the parentheses are just due to the limitations of ASCII) is because if they had written it as ‘x’ and asked them to solve for x, they would have been testing the student’s understanding of basic algebra in addition to testing their understanding of the equals sign, which would have confused the results.
Yes, it is fundamentally a question of algebra, and representing the missing quantity as an ‘x’ or a blank square doesn’t change the answer at all, but comprehending the idea of a letter holding a numeric value is non-trivial for people who have not already learned algebra. People who misunderstand the equals sign are likely not very comfortable with algebra either. It’s more focused test on the meaning of the equals sign if they avoid introducing the idea of variables and rely on the simpler idea of “something is missing here, what should it be?” even if the notation isn’t strictly in line with conventional math notation.
And that’s not even considering the issue of people who have been introduced to algebra but don’t wholly understand it, and when confronted with a problem that has an ‘x’ in it will panic and over complicate the solution.
By the way, the empty-box notation is not without precedent. These sorts of problems when presented to pre-algebra students in late elementary school are often written with that notation (they certainly were when I was a sixth grader!)
I often find it amusing when I have to explain to people why the equals sign is at the beginning in Excel functions.
ie. = SUM(A1:A10)
If we assume the students can’t exceed our expectations, then we’ll teach them not to exceed our expectations.
It’s the blind leading the blind, like Mr. Finnley used to say.
All victims of an inferior public education system whose main purpose is to protect union workers (aka teachers).
When all the text books are picked by the idiots in Texas, I guess you get what you pay for.
WTF…
Someone in Texas needs to die!
#3 – Benjamin,
I agree that this is bad notation. However, find x may be no better for Americuns. You’d likely get an answer like this from a significant number of students.
#9 – Miss peach,
Exactly when did Texas decide *it* could criticize textbooks??
Somewhere around the same time that it decided it could determine the textbook content for 47 of the 50 states.
http://tinyurl.com/32y2dvk
@jbenson2 said, on August 16th, 2010 at 5:45 am
“Easy to understand why the “not-equal” sign is not understood in schools. That is because the ed-ucrats want everyone to be equal.”
I think you’re one of the kids we’re talking about. You got the entire thing backwards and didn’t understand the point. FUNNY!
It’s the EQUALS they’re not understanding. If it’s our evil ‘ed-ucrats’ having the nerve to teach that blacks, gays and Jews are all humans and equal to god fearing whites, if that’s the problem you see, then all the “equality” teaching should mean they DO understand equals (and therefore not equals). But this study is saying they DON’T get that one thing is equal to another.
We should just let Texas keep creating the text books, it’s working SO well. Forget science and rational thought, lets just replace it all by magic, superstition and fear of “them” (whoever they are this week). (sigh)
Actually, I would expect Texas to like the equal sign. Put a few together and it looks just like the barrels of a double barrel shotgun.
>===t====
See?
And no matter how you want to present the question, only people who don’t understand the concept of equality would return 4+3+2=(9)+2=11 as the answer. 4+3+2 is not equal to 11.
dusanmal is on the right track. Math instruction in the US was destroyed a while back when some morons at the National Council for Teachers of Mathematics decided that the methods used for a century were no longer any good. Further, they got the new approach embedded without any empirical studies or unbiased research. My son had a helluva time in college where they still teach math…new remedial courses exist for the poor victims of this nonsense.
Books? “there’s an app for that!”
actually there are a bunch of apps for that!
I watched my 2yr old grandkid match objects on ‘his’ iPhone, and he clearly understood = and …
So, I think ‘books’ are ‘obsolete’ now…