By Emmanuel Felton
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.
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.
[The American Institutes for Research, it should be noted, makes money in part by creating Common Core tests.]
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.”
Here are a few comments from the original post at The Hechinger Report. What do you think?
November 7, 2014 at 8:13 am
really? Why are we saying we are trying to compete with superior math countries like China when they use mental math and tricks to help kids learn faster. Why are we trying to slow our kids down? Why should everyone be forced to do it one way? Common Core is something both liberals and conservatives are against!
November 7, 2014 at 8:17 am
The problem is that Common Core assumes children under the age of 11 are capable of conceptual thinking when in fact they are concrete thinkers. It’s like expecting a toddler to run a mile. Sounds good in theory but is unachievable.
November 7, 2014 at 8:28 am
Kids live in a technology filled world and have for quite some time. Teachers need to have ways to relate concepts to something the children already know and understand. Lets go back to the greater than less than sign mentioned early in your article. Regardless of which we use the alligator mouth or the Packman game character, it gives them a visualization to relate the concept to thus increasing retention. Now, I challenge you so-called math experts out there to do all of your teaching without relating the subject or topic to something that your students already know, understand, or are familiar with. Go ahead, lets start with something basic and at the kindergarten or first grade level and teach them to the point of mastery the concept of the greater than less than symbols with out relating it to something they already know or are familiar with. After all, you are the experts…right? Please, do let me know the details and results at the end of you study. Please provide the pre and post test data that will help to demonstrate the gains and or proof of their mastery. Oh, one more thing. Good luck…you will need it.
November 7, 2014 at 9:19 amWell my son’s second grade teacher will be retiring next year because she says she doesn’t want to deal with common core since she’s taught regular ways for 35 years. I agree. Common core tries to mesh math with reading comprehension. Try doing multiplication in long drawn out word form like this one: 3, 6, 9 what is the 12th number in this sequence? My son can’t just read that and think the 12th number automatically. He has to write them out. He also cries over this type of math. They don’t have actual math books either to show examples. They have math workbooks. :/ So if I can’t help him figure it out, I end up having to go on the internet to get answers, because even I get confused with what the problem are asking for.