Math researcher says equal sign misused

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VERNAL — Greg Wheeler talks about math the way a teenage girl talks about Justin Bieber.

The cadence of his speech picks up. He gestures expressively with his hands. His smile grows wider and wider.

"I think the equal sign is really cool," Wheeler said. "I just wish I could get the rest of the world to understand how important it is and quit ignoring it."

On Friday, during the 12th annual Uintah Basin Research Conference, Wheeler presented the results of his study on how well college students understand the equal sign.

That's right, he quizzed more than 600 students in freshman and sophomore level classes at a major university on their use of the equal sign. He found that when students "focus on solving, evaluating or coming up with 'the answer,'" to an equation, "they fail to recognize the contribution of the equal sign or other indications of the equals relation in a given context."

"There are students that actually think, 'I can use this as a 'compute' symbol or I can use this as a 'for same' symbol,'" he said. "In a math situation, when you're using the equal sign, you're dealing with one mathematical entity expressed in two different ways."

I think the equal sign is really cool. just wish I could get the rest of the world to understand how important it is and quit ignoring it.

–- Greg Wheeler, USU

Wheeler, who holds a doctorate in education, began teaching math as an undergraduate in 1995 and is now a senior lecturer in the subject at USU Uintah Basin.

He is not alone in his concerns about what he calls the "abuse" of the equal sign, and the apparent impact it has on U.S. students' ability to comprehend algebra and other complex forms of math.

Recent studies, Wheeler's included, have found that most U.S. students view the equal sign as an indication that they are supposed to compute something the same way their calculator would if they hit the "=" button.

"That's fine for arithmetic," Wheeler said. "But when I'm teaching algebra, we shift the focus from computing things to trying to understand relationships and generalize mathematical principles."

In 2010, the journal Psychological Reports published a study by Texas A&M researchers that found that roughly 70 percent of middle school students in the U.S. had "misconceptions" about the equal sign. Such misconceptions were not exhibited by students in Korea and China, countries that regularly outperform the U.S. in math, the study showed.

"Most of the Asian countries don't use the equal sign at all in arithmetic," Wheeler said. "They have a symbol for 'compute' or 'derive'. Equals has a very special place in mathematics.

"The equals sign really means that you have the same mathematical entity on each side, being expressed in a different way," he added. "It's an indication of a relationship of the same and that's how an equal sign is supposed to be used."

But most students, even in college, aren't getting that.

The equals sign really means that you have the same mathematical entity on each side, being expressed in a different way.

–- Greg Wheeler, USU

In his study, Wheeler presented students with the equation 10+x=10x, asked them which side of the equation held the larger number, and then gave them several possible answers.

"Forty-two percent of the students chose that they are the same," he said. "More than half of the students chose that the right side was bigger because you're multiplying, or you can't tell unless you know what 'x' is.

"They're just totally ignoring the meaning of (the equal sign)," Wheeler said, noting that for some equations as few as 7 percent of the students in the study responded with the correct answer.

The turnout for Wheeler's presentation Friday was modest, but he has plans to present his findings to a far larger audience.

"The next step that I'm actually looking at is going to academia, asking math people their opinions," Wheeler said.

He believes the solution may be to teach students arithmetic using another symbol in place of the equal sign. What that symbol might be though, he doesn't know.

"It could be a great contest," he suggested. "You could get people decide what the new symbol for 'compute' would be."


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