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.
Related: What makes a good Common Core math question?
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.
Related: Are math specialists the answer to teaching better math?
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?’”
Related: What happens when a robotics class starts the year with no robots?
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.”
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Common Core advocates are probably brilliant mathematicians but they’re lousy educators. Let the teachers teach.
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!
And here my friends is what is wrong with education in this country. Doesn’t matter if it’s common core “experts”, grade level “expert” coaches or anyone else. Instead of showing students new ways to think and solve problems, we are going to dumb down the teaching just so these kids can do well on ONE test at the end of the year.
We no longer care about them being able to have skills to take with them as they grow up, as long as them have the skills to pass that one test at the end of the year so we can then compare our education system with other countries. Not for nothing, but our education system was just find 20-30+ years ago when students were held accountable and held back if they failed. When students were shown mnemonic devices to solve problems. We still graduated students who went on to do great things in this country (and no not EVERYONE is college material, that’s the greatest lie ever told to kids).
Notice how all of these people saying these things are “researchers”, I wonder how many of them are 20+ year professionals in the classroom or if they are just data monkeys looking at a spreadsheet all day. And there my friends is the biggest problem with education. No student accountability, parents let off the hook for not caring, “experts” who are anything but trying to change curriculum and then when their ideas fail for a multitude of reason throw it back on the teachers for not being some Orwellian robot and doing things exactly as they wish.
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.
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.
Common Core “experts” obviously don’t work with children. They happen to be hedge fund managers and politicians. Leave our kids alone!
I think Common Core has gone overboard. It is absolutely ridiculous the way the math is done now. My fourth grader is becoming extremely frustrated and this is just not right. Math was hard enough when I went to school way back when. Now, the math is so convoluted with all these “unnecessary” steps that my son is getting sick over it. His anxiety level during last year’s state exam was unbelievable. I honestly don’t see the point of stressing our kids to the point where they are turned off to the subject when there is an easier way!
MATH is all about the right answer.. WITH ENOUGH CONVOLUTED LOGIC YOU CAN JUSTIFY ANYTHING
According to common core
Let a=b.
so Then
a^2=ab
giving
a^2+ a^2= a^2 + ab
which means that
2a^2= a^2 +ab
which means that
2a^2 – 2ab = a^2 +ab – 2ab
And that
2a^2 – 2ab = a&+^2 – ab
which can be writen as
2(a^2- ab)= 1( a^2 -ab)
canceling out the (a^2 – ab) would allow 2 =1
COMMON CORE SAYS THIS IS CORRECT! BECAUSE YOU CAN SUPPORT IT LOGICALLY!
ALL THE STEPS OF LOGIC ARE RIGHT BUT WITHOUT KNOWING AND APPLYING THE BASIC RULE OF NOT DIVIDING BY ZERO YOU WILL GET THE WRONG FLIPPING ANSWER EVERY GOD DAMN TIME!
MATH IS ALL ABOUT HARD ANSWERS WITHOUT THE RIGHT ANSWER YOUR LOGIC DOESN’T MEAN SQUAT!
You are worrying about grade level appropriate… So you want to hold back the smart kids to Try to elevate the idiots.
ALL IN THE NAME OF PROGRESS AND FAIRNESS.
There isn’t a deep understanding to the order of operations. It is pure convention. We could use polish notation or reverse polish notation or any other notation but we use PEMDAS and you just need to memorize the rules and apply them – deep understanding is impossible. The curriculum specialist who want reasoning better be good enough with the mathematics to know what should have deep understanding and which are just conventions. If this is an example the author made up, fine. If you were told this by a specialist, that is a complete and utter failure.
I get that kids need to know how to come up with an answer but the common core is ridiculous. I’m sorry but I don’t want my kids to have to take 10 minutes to solve an addition problem that takes 2 seconds in your head. I can’t express enough how much I hate this system!
Why wouldn’t you cross out zeroes? You are applying the multiplication property of equality. It also gets to understanding the entire decimal system we use with Arabic numbers. You better know -why- you can cross out zeroes but reducing fractions is a big idea in mathematics. The decimal system is a bid idea in mathematics. Properties of equality are bid ideas in mathematics.
In the “real” world, outside of the classroom, simplicity, quickness, and efficiency is valued.
Complexity, slowness, and inefficiency is looked down upon and can even get you fired in some jobs.
Shortcuts should be taught and mnemonic devices learned because when it comes down to it, GETTING THE RIGHT ANSWER IS THE MOST IMPORTANT THING. It does not matter how something is done, as long as it is done correctly and in most cases, as soon as possible.
When I go to a mechanic, I don’t care HOW he fixes the problem. Just fix it and fix it quickly.
It should be the same with a math question. Just get the right answer, and don’t take 18 steps to do it when it can be done in 5.
When I was a physics major in college, the math taught to me in school growing up served me just fine. Common core seems to teach about ideas behind math rather than correct results.
To quote the great doctor Ray Stantz “You don’t know what it’s like out there! I’ve *worked* in the private sector. They expect *results*. “
Well 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.
I am sorry but some of the stuff they are teaching with that curriculum is crazy.
I saw one of the subtraction problems and it was ludicrous on how they are teaching it. I would NEVER allow my child to do subtraction that way. I am glad my child is in China learning Math (math in China is much stronger than it is in America, I wonder why??). If we were in America, they would be homeschooled before I subjected them to that.
I have taught math in High School and University for over 16 years.
common core is a bs way of getting some people rich to come out with nes book. All BS
I bet Albert Einstein would not condone common core math.
Go back to the multiplication tables. Who the heck came up with this junk?
My child is in 2nd grade, between the see/say reading and the obtuse “math” techniques I am fighting the school over this almost daily. They are sympathetic. My family has numerous advanced degrees in or related to, mathematics. My comment is …you cannot build a house without a frame, where is the framework upon which you build elementary education “understanding”? There is no structure to start with. These kids are not being taught the basics. They can’t see the forest (big picture) without understanding the trees.
I was a supporter of common core until I saw first hand how it has become a mess for the teachers and students alike. My 12yo is bogged down by this system. She had a math problem the other day that had nothing to do with math but with science. In science she had to write a paper that related the structure of a cell with a trip to a fair and had to make it a story. What BS!! Can’t we just teach our kids concretely like we have for ages and relate what they learn to real life?! Stop this maddening BS which is only causing more stress on kids and teachers.
You know the reason the “shortcuts” where introduced was because kids where having a difficult time understanding how to solve a problem. So teachers, mathmaticians, and heck the average joe actually working out in real life came up with these “math hacks” to make it easier to do and understand. It is more important in my job to have the right answer as quickly as possible than it is to know the process behind getting the right answer. In that case let’s get rid of all short cuts… no more I before E except after C and words that sound like a as in neighbor, and less toss out Every Good Boy Deserves Fudge in band class. And all the fun ways to remember the elements and order of the planets… Infact, lets make learning as boring, drawn out and difficult so our kids really hate it. Then the drop out rate will really raise . The average person in average job just needs to know how to obtain the correct answer. I say this cause I having two children with Dyslexia and one being autistic with language delays I have had to come up with a lot of off the wall tricks for my kids to learn how to read and write. I guess I could have not given them any tricks and forced them to learn it the “proper” way and have two illiterate children.
Linda Gojak and Phil Daro are mathematical idiots and should not be representing common core methodologies. Nearly all math problems can be solved in several ways. The ‘butterfly method’ simply produces a common denominator in the two fractions, and is a completely valid way to add or subtract fractions. Crossing off zeroes is also perfectly good, and is a ‘trick’ that scientists and engineers use every day. I actually support common core in its effort to get students to understand the math. Now if we could just find common core representatives that know anything at all about math, something good could come of common core.
As a high school math teacher, I agree with some of ideas in the article. For example, PEMDAS, while helpful is sometimes misleading and not applied correctly. I am not a big fan of FOIL either. It’s just the distribution property.
Other things in the article are a stretch for me. Crossing out the zeros when dividing isn’t a shortcut. It’s the result of dividing the top and bottom numbers by 10. Nothing wrong with that. I think the “experts” need to examine when it is necessary and helpful to understand the underlying reasons for certain operations and when it just bogs down the math and makes it too complicated.
Another Liberal created “dumbing up America” with their so called new math. Common Core math along with other Common Core studies has been around for decades. It has been proven that it doesn’t work. Kids, parents and teachers get frustrated with it. Children’s minds are still developing at the age when this is introduced to them. In some schools as young as kindergarten. Children can barely think for themselves, how do you expect them to develop critical thinking skills when their minds are not developed to accept logical thinking not alone critical thinking. I recently took a college course as part of my degree on Critical Thinking. It made about as much sense as sticking your finger in a live outlet. The government along with Bill and Melinda Gates are pushing for this, only because Gates gives political contributions. Gates is the only person who developed the software to support this style of learning and pushed it onto classrooms across America several years ago. He stands to make millions off of this. He doesn’t care about educational standards. He only cares about putting more money in his pockets. Like he needs it. Go back to the old standards of A,B,Cs and 1, 2 3s. Teach the basics first and foremost. Kids understand basics and are not frustrated with it. Why keep trying to fix what is not broken. There are more important educational studies that need fixed and math is not one of them. We have too many adminstrators and not enough teachers. Why should adminstrators who have never even taught school running our states education programs when they don’t get it!!!!
Tell the NASA scientists that shifting away from right math answers is a good idea!! We might as well just hand over all the technical jobs to other countries at this point because our kids won’t be able to do them.
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.
So another words as long as they put some sort of answer do it well be right, Steve Leinward must be a moron or some thing in math you must always get the answer right or what ever you are working on the answer well be wrong. just think if you are building something and you calculation is off by lets say one point that well throw every thing else off.
Mean while in the real world, Chinese, Indian, Korean, and virtually every other foreign competitor are using shortcuts, getting the answer they need and then getting on with their projects.
I’m so upset with common core. My son can’t even do simple math calculations. Instead he is forced to learn Algebra at age 6. I can’t even understand what they are doing with the boxes, circles, 10’s and such. This next generation of kids won’t have parents help, leading to mistrust of parents with school work. We learned to figure out simple problems in a very short time. Same problem takes several minutes and confuses the kids, and parents. I’m in search of an old style math book to teach my son the right way to do math so he can succeed in life.
COMMON CORE is just crazy. I say if it’s not broke then why fix it? Why add twenty more steps to something so simple. Instead of getting the answer and moving on kids are forced to explain, explain, explain. Life as a child is complicated enough without adding the pressure as Common Core does. It has made my 8 yr old son go from loving math to dreading it. He isn’t excited any more he is aggravated and tortured by common core. I hate to see it because Math was his favorite subject.
4000 divided by 100
So, we shouldn’t use the cross-off-zeros method?
If we had a problem like 40000000000000 divided by 10000000, wouldn’t the cross-off-zeros method be the best method? Of course it would. These academia nuts don’t know that in business, time is money. I need employees to know EFFICIENCY. I can’t have them sitting there contemplating which methods to use to come up with a solution. I don’t need to show them that they can come up with the solution in four different ways!
I agree that the “tricks” need to go, because it creates kids who have no number sense. They do need to UNDERSTAND the math behind the problem, but they do not need to make it overly complicated, as Common Core often does. I am a high school math teacher and I am constantly working to “undo” the damage that elementary teachers do with their “tricks.” Many elementary teacher do not understand much math themselves, yet they are charged with teaching the young children – hence the “tricks.” I have said over and over that numbers do not “cancel” (they add to zero or they divide to 1) and there is no such thing as cross multiplication.
Math needs to be taught at all levels by people who truly understand math. Elementary schools have reading specialists…why can’t they also have math specialists?
4000 divided by 800…certainly students can cross off the zeros as long as they know they are dividing by ten to the power of the number of zeros they have crossed off.
And I agree that kids do not need to know four different ways to solve the same problem…they need to know and understand ONE WAY!!
Common Core Standards were written by individuals who consider that education is a business. True, students have to know the basics, but the CCS confuses the child as well as the parent. The majority of the educators that I know dislike the time that is wasted on the CCS. Let the educators do their job without constant changes by people who have not set foot in a classroom for many years. Politicians should not tell educators how to do their job, because educators do not tell politicians how to do theirs. The CCS are just rules that were set up by people that do not know anything about teaching.
Why does Capitol Hill decide what’s best for our kids and our schools? This should be left up to the individual states. These “experts” making all these decisions have never been in a classroom, so what make them an authority on how kids learn best. I have been a public school teacher for 36 years and I don’t like the direction education is going. Federal mandates are not what is best for our schools. As Thomas Jefferson said, “the government that governs least governs best”.
Common Core math is simply BS! My son teaches his son math the way he learned it in school. Therefore, my grandson, is very good at math. And he helps the teacher teach the other children in his class. And right, he is smart anyway, but he understands the math because he was taught the logical way, which is the old way. And that is why he understands it! As I said, Common Core math is BS!
The problem isn’t Common Core (although it isn’t very effective). The ones of you complaining about not being able to help your child are the very reason Common Core was created. You learned the tricks and shortcuts, but never learned the reason why they worked. That ‘why” is the most important part, as it will become more and more valuable as you get into higher levels of math. The ability to see how the numbers interact will make HS and College level math much much easier.
Yes, in the “real” world, the way they are teaching young kids to do math is not the way you would actually do it, you would use the shortcut. However, if the child is taught the basics correctly and well, they should be able to come up with most of those short cuts on their own. A.F spoke of their child crying about the question “3,6,9, what is the 12th number in this squence”. Why? That is how I taught my kids to do multiplication when they were first learning it, while we were also working on the rote memorization of the facts. I watch my 4th grader now, count on his fingers with some multiplication problems. He needs to stop that, but it is the same thing. As opposed to just memorizing 12*3, they are teaching the children it is a sequence, a pattern. Learn to recognize that pattern, and things start falling into place.
I am not saying Common Core is good, but it is an interesting approach for teaching math to students who don’t recognize the patterns and interactions intrinsically.
The Common Core “experts” have not spent enough time in a classroom of 25+ students to truly understand how children learn. They are the theorists and we are the practitioners.
We basically have to teach a concept a day to our students when other countries don’t. If I had the time to “explore” mathematical concepts rather than teach to the test then I would fully embrace Common Core.
The instructors for the US team that entered the World Math Olympiad constantly tell their team “Use logic!”, or “Think it out!”, or “Use your brain!”,,,etc. And yet the only perfect scores came from an anonymous Chinese kid that when asked why he did so well said “I use my heart.” Clearly the US program has a long way to go.
So I guess it is better to make a student take 15 minutes to solve a problem that would normally take less than two because why?
What they need to do is throw the common core in the trash. period!
Dear Coder, Pardon my french but bullcrap. How many of these kids are going to be mathmeticians???????????????????????? There is no need for these concepts in schools/ Teach them to the math majors in college duh!
Common Core is nothing but a headache and is causing our children more stress than is necessary. Who care how you come up with the right answer–I had to point this out to an 8th Grade math teacher six years ago. There is more than one way to solve a problem. She was adamant that the students solve the problem her way and only her way or they got it wrong. I explained that a GOOD Math teacher should be able to explain how to solve the problem in several ways because NOT ALL YOUTH LEARN IN THE SAME WAY! I later learned that she has actually made some of her students cry in her classroom because she talks down to them and basically calls students stupid. This is what Common Core is doing.
Some of the best discoveries comes from “thinking outside the box”. This can be applied to science and math just as well as it can in management. If the Education system wants to bring LOGIC back to the way we develop our thinking processes–start teaching LATIN and bring back the Greek Philosophers–Plato, Cicero and the like. We are dumbing down our education. Let them cancel the zeros–
Yikes. The number of comments that say the right answer is the only important thing, doesn’t matter how you get it, is disturbing…the point is, it’s NOT only about getting the right answer. The problem solving and critical thinking process is extremely important in developing good thinking skills. I would much rather have a student with a wrong answer, but is demonstrating his thought process and where he got stuck so that we can work on it that a kid who puts down the right answer, but isn’t able to say why. I support common core. Learning the “why” behind these concepts will only help these kids in the long run.
“Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.” –George Orwell (Nineteen Eighty-Four). “It is your justification that makes your answer right or wrong” turns Math into some politically-correct “narrative” that can be manipulated to eliminate freedom.
“It is your justification that makes your answer right or wrong,” Gojak added.”
I couldn’t read anymore after reading this. 2+2=4…there is no justification that can make that wrong. 2+2=5…there is no justification that can make that right.
It’s not too hard to search the common core standards for yourself and find out what they say. I’d suggest to anyone reading the comments here that they verify what commenters are saying, rather than taking everything being stated here as true. Most of the anti-common core statements I’ve read CANNOT be supported by evidence.
My kid goes to 5th grade here is the way the teacher taught 2 digit multiplication.
20
x 34
———-
4*0
4*20
30*0
30*20
——–
Add above all you get multiplication result with no explanation on how he arrived to this answer.
The teachers are so poor they are building kids to never learn logical thinking.
One teacher in 4th grade says we have calculators why we need to learn multiplication on face so what motivates them to teach or what motivates kids to learn.
Not all teachers are like this but 50% of them are damage kids brains.
@joecrouse
You may have fooled the gullible into buying your pseudo-math argument, but not those of us who understand mathematics even a little.
Very clearly 2(a^2- ab)= 1( a^2 -ab) does NOT mean that 2 =1, if a = b, as you have stated. Instead it means that 2*0 = 1*0, which, of course, common core and anyone else would say is true.
You have inadvertently made an excellent case FOR the Common Core. Those who blindly follow the algorithms they have learned in traditional algebra instruction could easily come to the conclusion that 2 = 1, based on your “logic”. After all, none of the algorithm steps are done wrong.
It is the fundamental misunderstanding of what it means for “a” to be equal to “b” that would cause someone to conclude that 2 = 1, based on this reasoning. This is exactly the kind of operation without understanding that the CC is trying to move our children beyond.
Regardless of the failure of your example, your overall point is that the Common Core accepts incorrect answers as correct, as long as they can be supported by faulty logic. This is patently false and cannot be supported by any reference to anything in the CCSS documentation.
Please politicians stay out of education, that is way out of your realm of expertise. The common core is going to cause more problems than it solves. The arguments over the family time over homework will accomplish frustrated parents and children. The common core is just complicating math. Families don’t have hours to spend helping their children out with homework. By the time dinner is done you are looking at 6 or 7 in some cases depending on work schedules. That doesn’t count the revolving door for those who participate in after school activities. The common core is garbage. I refuse to lose family time and relaxation time with my family in order to give myself a headache over trying to figure out the common core method. I got enough on my plate already.