Just keep making excuses for aggie math students.
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.
Like, maybe, it's because the teachers are as dumb as dirt and are overpaid undereducated drones of the NEA welfare state.
Just keep making excuses for aggie math students.
“’Equals’ is not a difficult concept unless it is systematically obfuscated.”
Those who can, do.
Those who can’t, teach.
Those who can’t teach, teach teachers.
It seems to me that the problem isn't that they don't understand the concept of the '=' sign, but with the problem itself. When I saw this equation, my first thought was, "WTF?" The parenthesis needed to be replaced by a variable, and instructions given, "solve for the variable."
Mark
I still havent memorized the > and the < , good thing I can use my grammer to explain.
I think you're on to something. In the US, students learn that the meaning of equal outside of math is different than it is inside of math. Making one thing equal to another, versus something actually BEING equal to something else on it's own.
I think if students were introduced to the concept of assignment, like in programming, it would clarify things.
= means that the value of one thing matches the value of another.
:= means to MAKE the value of one thing match the value of another (think outcome based education for instance) /sarc
3rd grade cheat on the < or > problem.
< looks like an “L” which stands for “less than”. Still use it after 30 years. :)
There are not many jobs for the below average students so what's the point in keeping them in school any longer, taking teacher time away from the good students? No amount of taxpayer funded public school will bring their employment worth up to the minimum wage. Their jobs are gone and are not coming back.
This is how some voters think that Obama’s got a special stack of money that isn’t taxpayer money to run our government on.
It took 22 posts to get to the Aggie bashing. Disappointing. ;-)
Wow. I took 4 years of math in high school and another 4 in college. Guess the textbooks were too simple as there was never any confusion about what an equal sign meant.
>>Exactly.
Deliberate corruption
3rd grade cheat on the < or > problem.
< looks like an “L” which stands for “less than”. Still use it after 30 years. :)
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I have always had success with ‘It points at the smaller value.’
I used the “alligator mouth” system until I got to stuff like:
SUM >= 4
At that point I had to revert to the < looks like “L” cheat.
I agree the question is poorly expressed. Parentheses already have a role in math notation, after all, in clarifying order of operations. They shouldn’t be used to stand for ‘unknown’ when an X or a blank would serve better.
A living, breathing equals sign.
Calculators have no place in a math class. This is the fundamental problem. I took 33 quarter hours of serious science and engineering major calculus and differential equations, and never needed a calculator (and yes, they were widely available, this wasn’t the slide-rule era). You simply don’t need a calculator to learn serious math. Calculators belong in classes with labs, like Chemistry and Physics, but not in a pure math class.
It’s likely the reason Singapore Math is so popular with homeschoolers. Singapore has one of, if not the best, student performance in the understanding of mathematics. There are still lots of nice illustrations and interesting stuff for kids, but The Content isn’t sacrificed.
Thirty years ago, a friend wrote an Algebra text. The biggest concern of his publisher was that he didn’t use multicultural names in the examples & story problems.
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