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Think back to your elementary school math classes. Were you told to think of a greater-than sign as Pac-Man or to cross-multiply when dividing fractions? You weren’t alone. Tricks to help kids get the right answers to difficult problems have long been a staple of American math education.
But if Common Core supporters have their way, shortcuts like these will soon disappear from the nation’s classrooms.
In the age of Common Core, getting the right answer to a math problem is only step one. The Common Core math standards, which are in place in more than 40 states, say that it is just as important for students to understand the mathematical principles at work in a problem.
This emphasis on principles poses a problem for popular techniques like Please Excuse My Dear Aunt Sally, a mnemonic device for remembering the order of operations that teachers complain is imprecise, and the butterfly method for adding and subtracting fractions. If correctly applied, the tricks always result in the correct answer, but math experts say they allow students to skip the sort of conceptual thinking the standards are trying to encourage in students.
Linda Gojak, president of the National Council of Teachers of Mathematics, is waging a war against the old advice that students should cross off zeros when dividing, for example. Using this technique students can quickly solve a problem like 4000 divided by 100 by eliminating two zeroes from each number and simplifying the problem to 40 divided by 1.
“I get teachers that get mad when I tell them they should stop,” said Gojak. “But I envision students dragging in a big bag of tricks into standardized tests and not really thinking about the questions.”
“It is your justification that makes your answer right or wrong,” Gojak added.
Critics, including parents who remember the way they learned math in school, worry the standards are throwing out proven computational techniques in favor of overly complex methods. They say new, convoluted approaches are turning kids off of math.
But Phil Daro, one of the lead writers of Common Core math, says math tricks have already tarnished the math brand for countless students.
“Take the butterfly method. It doesn’t articulate any mathematics,” said Daro at a conference of the Association of Mathematics Teachers of New Jersey last month. “Nothing in school is perceived to be useful by the kids, but in math they are going farther and saying, ‘why are we even doing this?’”
Steve Leinwand, principal researcher at the American Institutes for Research’s education program, also argues that America’s math teachers should embrace the shift away from right answers.
“Common Core has the audacity to use the word understand 218 times,” said Leinwand.
Daro does see some limited room for shortcuts in math.
“Now students have to arrive at a grade level way of thinking about the problem,” said Daro. “You can spend the first two-thirds of a lesson letting kids use the varied ways of thinking but for the last one-third we need to get them to the standards’ way of thinking.”
As for the tricks, Daro says, “I’d only settle for something like [the butterfly method], some days for some kids.”