Equal 
Not Equal 
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.
I don’t get the difficulty with greater than / less than. Is it so hard to understand that the big side points at the bigger number and the small side points at the smaller number? Seems awfully intuitive to me.
Somehow I doubt whether they ‘belong’ or don’t belong in a math class has much influence in today’s scholastic world. If the kids insist, who are the teachers to interfere...?
I have no problems with calculators in math class once students have demonstrated mastery. Years ago, I took a Calc I class for leisure and a significant part of the class involved the instructor teaching the students how to use their calculator to graph the functions, etc.
Equal
Not Equal
I’d guess many weren’t taught that “cheat” when they were in primary school, because their teachers didn’t really like or understand math themselves. I’m amazed how many things I’ve “discovered” over the years that seemed quite intuitive and would have made learning math concepts much easier if only a teacher had mentioned it.
Our students understand very well what “equality” is. Because they do, they cannot understand what “equals” means.
Doh ! looks like I’ll have to try that method.
Thanks for your input. . .
When kids are taught
homosexuality = heterosexuality
and
my team 4, your team 3 = we all won
no wonder they’re confused.
Perhaps understated is that “=” has multiple meanings.
X=3 can mean either a statement of truth that the value of X is 3, or as an assignment operation causing X to take on the value 3.
As a professor teaching introductory programming, the semantic difference is important.
“Calculators have no place in a math class.”
‘xactly
Gosh, ya think?
Yep. I thought the reason AC (my youngest niece) was having trouble with math was that she was a hands on learner. That was only part of it. The rest was the < censored > text books. I tried to read their text and found they were using high school level vocabulary to explain things to a third grader.
I knew they were messing up reading and writing but I never thought it was possible for them to mess up math.
Just b/c they come exit school functionally illiterate doesn’t mean they didn’t learn anything. The govt is happy to keep them there for the complete indoctrination course. What you have at the end are voting govt dependents. See public education does have a purpose. ;)
Not having to memorize the arithmetic facts is another problem.
Too many textbooks are written by people who don’t understand the subject themselves, and who approach the unknown by trying to talk it to death.
If you understand basic algebra and can follow directions I can teach you object-oriented programming in 20 minutes.
Very nice!
Do they throw in the Scales of Justice as PART of the course too? Or was that not part of the lesson?
No, just my mental image... if you keep the scales balanced as you move terms around, you will get the right answer.
If the teacher was looking for an estimation, then it should have have stated differently.
Yep, 9 x 9 = 81
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