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.”




  1. Benjamin says:

    #28 Well, give me one or two solved examples and I could figure out the notation (or any math problem.)

    In any case, nowhere is an unknown variable represented as a pair of parenthesis. Of course the answer is 7, but I would rather they used variables or at least blanks. It was confusingly laid out.

    Obviously where it was taught, the teacher didn’t use solved examples, so the students had no way to figure out what to do. THe teacher needs to teach whatever notation is necessary for the students to understand how to solve the problems.

  2. Sea Lawyer says:

    #31, you keep apologizing for the students’ inability to infer the meaning of the notion because you don’t agree with the notion. The whole point is that there is an equal sign with something on each side. What makes the left side equal to the right side? A student who understands that to be the meaning should not answer back some 4+3+2=(9)+2=11 nonsense. And that is the whole point of the study.

  3. sargasso_c says:

    I blame the electronic calculator. The “=” sign is a logical expression, not an “execute” key for a compiled computational routine.

  4. Sea Lawyer says:

    #33, that’s an interesting point.

  5. The Monster's Lawyer says:

    I blame Dog. That and I’m a little sledyxic.

  6. #35 – Monster’s Lawyer,

    Slebus Oy!

    #33 – Sargasso,

    You probably nailed it … unfortunately. However, we must actually be able to do some basic math in our heads … I think. Or, perhaps we should just give up and let these guys win.

    http://tinyurl.com/ye9h2vd

  7. bobbo, we think with words says:

    I like the study that shows x% of students think Alaska is an island because in so many maps it appears in a circle next to Hawaii in the middle of the ocean.

    Context Rules when the subject is symbolic. Still, I have to go with Benji at #31. I can easily see confusion THE VERY FIRST TIME our kiddies are presented the = problem. But after a solution or two, the ambiguities are resolved.

    So, “something” is not being fairly presented unless you think news report = the truth.

  8. Benjamin says:

    #18 Tyler McHenr said, “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”

    That actually makes sense. Still should we be hiding the fact that kids are learning algebra so they don’t get too intimidated to do the problem?

    #24 Misanthropic Scott said, “You’d likely get an answer like this from a significant number of students. http://tinyurl.com/cbup9n

    That is funny.

    #32 Sea Lawyer said, “you keep apologizing for the students’ inability to infer the meaning of the notion because you don’t agree with the notion.”

    Yes I hate the notation. However, #18 had the most probable explanation.

    #37 bobbo said, “I like the study that shows x% of students think Alaska is an island because in so many maps it appears in a circle next to Hawaii in the middle of the ocean.”

    Of course I had parents who showed me a larger map when had that same fallacy when I was 6. Also Hawaii isn’t in a square ocean within the borders of Mexico.

    “Context Rules when the subject is symbolic. Still, I have to go with Benji at #31. I can easily see confusion THE VERY FIRST TIME our kiddies are presented the = problem. But after a solution or two, the ambiguities are resolved.”

    Hopefully any sane teacher will teach the notation as they teach the subject.

  9. Al_Gebraic says:

    What’s so hard to understand? Equal….this amount is the same as that amount. I don’t get the problem here.

  10. Angel H. Wong says:

    This is the reason why Texan kids are stupid

    http://glbtq.com/images/entries/slideshows/symbols_hrc_equality.gif

  11. Guyver says:

    An attempt to reach out to children who are victims of a government-run education system: http://tinyurl.com/2c6pyxc

  12. BigBoyBC says:

    So it’s the textbook’s, not the Teacher’s fault…

    Maybe we should start hiring better textbooks and discontinue using out-of-date teachers…

  13. yankinwaoz says:

    I went to high school in the US and outside of the US. I think the problem is the way we teach math in the US.

    In the US, each year or semester you focus 100% of one aspect of math. For example, 1 year of algebra. One semester of trig. 1 semester of stats, 1 semester of calculus, etc.

    Overseas, they teach all of the math disciplines together.

    Here is why it is better. When you learn them all at the same time, you learn how they relate, and how you can use different methods to solve problems. You can solve a problem using trig, algebra, or basic calculus.

    Also, another problem in the US, you forget what you learned. I can’t remember my trig because I spent a year working on stats.

    By teaching them together, you get the benefits of cross reinforced math skills, making you much much stonger.

  14. Angel H. Wong says:

    I thought the reason for American kids to suck at math was that the general idea of a male kid getting good math grades rather than good Football scores meant that he’s queer.


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