It's not really easy to find, but I think if they had this in more children's math classes it would make a huge difference in ability. I've always felt kids don't understand equations.
Posted on 08/10/2010 10:13:25 AM PDT by decimon
COLLEGE STATION, Aug. 10, 2010 — 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.
They have been trying to evaluate the success of math education through students’ interpretation of the equal sign. They have published several articles on this topic, with the most recent one published in the February 2010 issue of the journal Psychological Reports.
Students who exhibit the correct understanding of the equal sign show the greatest achievement in mathematics and persist in fields that require mathematics proficiency like engineering, according to their research.
“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.
“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.”
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.”
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.”
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About research at Texas A&M University: As one of the world’s leading research institutions, Texas A&M is in the vanguard in making significant contributions to the storehouse of knowledge, including that of science and technology. Research conducted at Texas A&M represents an annual investment of more than $582 million, which ranks third nationally for universities without a medical school, and underwrites approximately 3,500 sponsored projects. That research creates new knowledge that provides basic, fundamental and applied contributions resulting in many cases in economic benefits to the state, nation and world.
Contact: Keith Randall, News & Information Services, at (979) 845-4644; or Robert M. Capraro, Department of Teaching, Learning, and Culture, at (979) 845-8007; or Miao Jingang, News & Information Services.
Gosh, ya think? The textbooks and other aspect of math instruction. "Equals" is not a difficult concept unless it is systematically obfuscated.
I believe this.
When I was about four as a child I had a toy that consisted of a scale with numbers you hung on either side. When the numbers were equal the scale balanced.
It’s such a simple concept but strangely, I see students don’t think that way. I understood algebra immediately because of that toy.
I’m thinking that in this country where “equal” opportunity means affirmative action quotas, “equal” access means half the parking spaces in front of every store is handicapped only and “equal” rights means only one side can throw a race card, then it’s no wonder our kids are confused as to what “equal” means.
I suspect the problem is something to do with “minds full of mush”, taught by “minds full of mush”. What possible difference could textbooks make to people that never learn to read?
probably because the US text books are full of crap about Susies two mommies and other PC crap and hardly anything about math.
Understanding the equal sign is absolutely necessary not only for Math but for basic programing also. It also goes into other sciences like physics and anything where algebra is necessary. Sad day when people don’t understand that.
It's not really easy to find, but I think if they had this in more children's math classes it would make a huge difference in ability. I've always felt kids don't understand equations.
Math books are a joke. They are full of cutesy color (expensive) photographs and politicially correct biographies to stimulate multiculturalism and seemngly to downplay the dead white male European idea of one correct answer in mathematics.
Besides, we can’t have a mathematically-literate populace because they could never buy Nancy Pelosi’s argument that taking money from one sector of the population to give it to another sector creates jobs. Ignorance is bliss, don’cha know?
What will they come up with next for EXCUSES in shoddy TEACHING and shoddy MATH BOOKS?
“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.”
Restated:
4+3+2 = (7)+ 2
9=9
What’s the big deal? Am I missing something?
People are NOT calculators.
I believe they are purposely CONFUSING students so they don’t KNOW anything. This will make parents MORE dependent on them and they’ll get MORE money.
This may be the crux of the problem. Students today rely on the calculator and have far less ability to "think" through arithmetical calculations than those of us who are older. We learned before calculators. Today, it's reach for a calculator first.
Place a formula such as 4+3+2=( )+2 before today's student, and I'd bet money more would reach for their calculator than would figure it out mentally.
“One cause of the problem might be the textbooks, the research shows. “
Yes, it is the **itty textbooks and **itty teachers that are literally dumbing down kids.
Memorizing what an “=” sign means and how it is APPLIED in Math is not rocket science.
Exactly.
this is stupid! why would a student assume the equal sign to be a running equal sign in this problem? there is only one equal sign in the problem... it’s obvious that the solution is to make both sides of the equal sign, um... equal! we homeschool... my oldest son as been doing math all my himself (with tools we provide him) for the last 2-3 years... he gets it...
This would explain why Obama and Pelosi believe government spending creates jobs. They still don’t understand that every dollar flowing through the Treasury is a dollar that otherwise would have flowed through the private sector. Unless the government is more efficient than the private sector at creating jobs, $1 billion in government spending can’t/won’t create any more jobs than the equivalent amount in the private sector.
Of course, if the government really were more efficient, communism would have worked like a charm.
Likewise, if the First Couple really understood the concept of “equal” they wouldn’t keep acting as if they are more equal than everyone else.
Oh right lets blame those nasty textbooks that wrote themselves. None of the untouchable bimbos in the ivory towers should be held accountable. In fact there was no math problem (ie education problem) until ‘those who are smarter than the rest of us’ took control of education and the sciences. Consider that recent past generations sent men to the moon, created modern computers etc. Many of today’s ‘graduates’ can hardly read or do simple maths. Right, its the text books alright.... :/
Please Excuse My Dear Aunt Sally
she forgot what the “equal” sign means!
My boss had a 4th grade daughter come home with a math worksheet that had several problems marked wrong. One was 9 x 9 = __
She had entered “81” and it was marked wrong. When my boss called the teacher to ask why, he was stunned when the teacher explained that they were learning to estimate and the since 9 was close to 10, the correct answer was “100”.
I think the problem isn’t that students don’t know what the equal sign means, but rather the teachers don’t.
The only thing about the Equal sign that today's students need to know is which one is preferred by their customers as they wait on them in their minimum wage jobs.
-PJ
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