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.”
If you want to really teach math, you have to teach it a the base level. If you want to teach something like multiplication, then simply making a student memorize the multiplication table simply won’t cut it. If you tell someone that multiplication is just addition to a higher level, followed by teaching the “algorithm” of multiplication, the child would be able to go to the next level of math.
3 * 2 = 6
or
a = some number
n= some number
therefore a * n = a1 + a2 + …. + an
or 3(1) + 3(2) = 6
I think we need to consider that the move to Common Core could be as much motivated by the need to find a way to ensure in-person school teaching continues to add unique and irreplaceable value to student education, as it is simply about making a shift in education philosophy. I want to believe that making kids answer the question “why?” on every single topic from the beginning of their math education, even if not always practical, will eventually make them stronger critical thinkers in the end. My more cynical side can’t help but notice though, that the shift to Common Core does have the effect of strengthening future job security for math teachers as they face increasing competition from non-traditional education providers, such as cyber schools and other virtual learning sources.
Someone’s making quite a bit of money from Common Core. Parents don’t like it, teachers don’t like it, but someone’s going to the bank. What about urban students who are already struggling? The USA is not competing with other countries, we are competing with ourselves and it’s not working. Read, “The Philosophy of Dot”, a book that puts world competition in perspective.
My 10th grader is taking Calculus this year & was raised with amazing math reasoning & number sense & some math tricks. Please don’t throw the baby out with the bath water. No teacher teaches only tricks. We teach everything the proper way first & use that logic to explain why the trick works in the first place. Why are we giving people one more reason to hate math, teachers, and public education? Math teachers love math & will do everything humanly possible to try to get their students to see the beauty & fun in math.
First off…let’s be honest. These are not JUST standards. Each math standard comes with a set of examples of how to teach them, and those examples lay out quite clearly what methods to use to teach the topic. If they are in the standards they WILL be on the test, the two are inseparable. The only reason NCTM supported the CCSSmath is because they do push for conceptual understanding instead of leaving it up to teachers to teach however they want (for most that means the way they grew up with, through memorized facts and algorithms).
The US has never been #1 in math, always middle of the pack. The PISA reslts are terribly skewed and practically useful for any kind of comparisons. Countries like China and Korea do not even test all their students and then do not report all the scores of those they do test. Places like Shanghai, which is a city-state, again, does not educate everyone, does not test everyone, does not report the scores of everyone. The US educates EVERYONE, the US tests EVERYONE and the US reports EVERYONE’S scores. HUGE difference. Then when we look at their top scores and our top scores, US students who attend school with less than 10% poverty would score #1 in the world! Students who attend schools with less than 25% poverty would score #3 in the world! In the US education, the problem is POVERTY, and nobody wants to take that on. We spend all this money creating new standards and tests and choice schools and none of it is doing anything to address the real problem. If the level of poverty in the US wasn’t so closely linked to how students score on these tests (both international and local…SAT, too) then we could discuss other things. We learn as much from a students zipcode as we do from all these tests.
I believe that students should be able to explain their mathematical thinking. If students are showing their work and can show two or three different ways to come up with a solution then they are learning several strategies they can apply to any math. In this way students can find what strategy works well for them. It isn’t about who can find the answer the fastest it’s about learning and explaining math.
I believe that students should be able to explain their mathematical thinking. If students are showing their work and can show two or three different ways to come up with a solution then they are learning several strategies they can apply to any math. In this way students can find what strategy works well for them and apply it to math. It isn’t about who can find the answer the fastest it’s about learning and discussing different strategies in math. I find that students have found many creative ways to come up with strategies and some of these are the “old” tricks. Kids are creative and curious lets give them a chance to use their thinking and teach us.
Of course, Daro will defend CCSS; he is one of the three authors of them and the money they received (which was more than plenty) needs to be justified in some ways. It is true that CCSS have increased the emphasis on students’ ability to explain and understand what they are doing in math. This is good. However, in CCSS they go into details to describe for each elementary concept/procedure how it needs to be presented, how it needs to be sequenced, explained, what kind of examples can support it, etc. It would have been fine if the unwarranted advice they provide was good. In the majority of cases it is not. The thing with crossing off zeros when dividing, for example, it is really fine. There is no harm in it. The principle on which this is based (which is much more general than this) needs to be explained and understood. After that it MUST be taught to apply this principle automatically. This is called fluency! It is the same as when a baby learns how to walk. Initially someone has to hold it, and teach slowly to first put the left foot forward, bend a bit on that side and then put forward the other foot and so on. However, it is stupid to still continue do the same with a normal 4-year old. Walking for that kid is mastered and it is at the level of “fluency.” The same occurs with knowledge. After you learn it slowly, understand it, practice it, then you apply it on the fly. And that’s mastery of that knowledge. I have seen some videos of Linda Gojak and I have a really good idea of who she is and how she thinks. Unfortunately, the ignorants of Linda Gojak’s type are omnipresent in math education. She is not alone. Funny enough these ignorants are often chosen to lead math education institutions. That’s just sad!
Those “tricks” are only ONE part of an overall philosophy. A test/assessment not only evaluates a skill, but also a student’s efficiency in completing an assignment. Common Core experts would have the world believe that understanding the methodology trumps everything. Understanding that 2 plus 3 is 5 should not take the inordinate amount of time these so-called experts want. Try explaining to a student that they understood really well the concepts of the problems they did finish, but they earned an F because they did not finish the assessment thanks to overly-complicated, time-consuming methods. This too shall pass, but the damage inflicted upon students will be significant.
Common Core Math…Just a way to make money. You r a poor excuse for a human.
i guess in physics you should do away with formulas and have the kids newly derive them for each problem. what’s wrong with teaching the “why” but then allowing the practical solving of problems. otherwise we will have a generation that hates math.
Mnemonics for order of operations are fine since we have defined them (not derived them) – in a different algebra, there could easily be a different oder of operations, (or maybe the commutative property would not hold). Something cute to remember the greater than symbol is fine. There is no way to calculate the meaning of >. There is no a priori way to know the difference between > and <. So, where you can't think it through, use a mnemonic or cute game.
On the other hand, teaching cross multiplication is just silly. Why not show that multiplying both sides of an equation by the same thing keeps both sides equal and that anything divided by itself is one
a/b = c/d
multiply both sides by the product of the denominators bd
abd/b = cbd/b
ad(b/b) = cb(d/d)
ad = cd
This way there is no hocus pocus and two key math concepts are reinforced.
Responding to “JOECROUSE, NOVEMBER 7, 2014, AT 8:40 AM”
I am not quite sure if this fallacy is specific to Common Core. The mis-step in Joecrouse example is in the last step, “canceling out the (a^2 – ab) would allow 2 =1”. The problem statement began with the hypothesis “Let a=b” so that means the quantity (a^2-ab) is zero. You cannot cancel out a zero quantity; it’s like saying 234*0 = 546*0, cancel out 0 and you have 234=546. These are math tricks we all used to try out when we were kids. What’s this got to do with Common Core?
RK
I don’t understand you people. Have you seen how many of our high school student absolutely despise math and can’t pass a basic algebra class? Why is that so many students cringe at the site of a simple algebraic equation if our “previous standards” worked so well?
It might come as a shock to you, but we weren’t taught math in school. We were taught mindless memorization and regurgitation to “get the right answer”. Math is not linear “follow these rules and you’ll get the right answer”. Math is ambiguous. There are an infinite way to solve an algebra equation if you have a deep understanding of the mechanics of algebraic operations. The new standards set by common core are creating logical thinkers, and problem solvers, not mindless robots programmed to use bullshit “math hacks” and memorization techniques to get the right answer without any idea as to why that is the correct answer.
Fighting common core is like saying “I’m okay with my child being mediocre and being able to just get the right answer”.
The stubbornness of parents who are probably pretty poor at math themselves and resistant to change are holding back a possible new prosperity in mathematics in our country. Quit being selfish and stubborn and let your children prosper in a subject that the majority of our country is completely terrible at.
There is simply no cause for alarm!
Why does it have to be one way? What a pitiful way to think. There is no one best way, and anyone who thinks otherwise is a fool. Common Core will go the way of every other authoritarian way to teach that America has come up with. It is a commercial venture to steal part of the education industry. This isn’t about education, it is about commerce.
After 30 years teaching kids up to 11, I soon learned that the best way to teach anything is the way that child understands it. All these schemes that try to say there is one way only and are exclusive of other ways just encourage children and teachers, but mostly teachers, to be lazy and just plough the furrow onward – regardless of the result.
Almost all the ‘new’ schemes, and I’ve experienced quite a few, have been around for ever and are in the battery of tools any good teacher uses – when the time is right.
Yes. Children should where possible learn the underlying concept, but if they find that difficult and are at risk of being left behind the others, then any helpful ‘trick’ is worthwhile.
Lots of these schemes initially seem successful but when you get past the ‘evangelist’ stage they sink back to being as good/bad as the others.
The only thing these schemes are good for is reminding good teachers of the methods that CAN work alongside all the others.
The Common Core standards are learning objectives, and it’s up to schools to come up with the pedagogical methods, curricula, and assessments to ensure they’re achieved. The difference is that, in conflict with the “git ‘er done” mentality that values the expediency of getting an answer regardless of method, Common Core’s goal is to achieve real understanding of the underlying principles.
Commentators like Yeldog, professed to be an experienced teacher who feels “the best way to teach anything is the way that child understands it,” are thus challenged to up their game. Using tricks on tests so a child is not “left behind the others” in getting enough right answers for promotion, regardless of lack of understanding of underlying concepts, simply admits that the child has ALREADY BEEN left behind.
Common Core’s math standards lend themselves to particularly bad interpretations that require alternatives to the standard algorithm before that algorithm is taught. For example, the standard algorithm for multi-digit addition and subtraction appears in the CC math standard for 4th grade. Earlier grades call for place value strategies. While nothing in CC standards prohibits the teaching of the standard algorithm earlier than 4th grade, it is not obvious that this is so (by virtue of it appearing in the 4th grade standard and the lack of any publicity by implementing authorities that it can be taught earlier, and by the official CC “Progressions Document” that doesn’t mention this either.)
The point of offering a single standard way of doing grade school arithmetic is that students will develop fluency and automaticity with them, so they will not get in the way of learning higher math. The push for teaching multiple strategies for arithmetic (prior to teaching the standard algorithm) emanates from the belief that, somehow, by teaching multiple ways children will acquire some “deeper understanding” of arithmetic (whatever THAT may be). Wrong. What students acquire by being taught multiple and non-standard ways is confusion. What they don’t acquire is automaticity or fluency.
Teaching the standard algorithms later rather than earlier is similar to teaching students to “read for understanding” by insisting that students continue to decompose words, syllables, and letters into their sounds long after they mastered decoding, phonics and reading. The purpose of learning to read is to allow students to use reading to learn other things; endless demand that they “demonstrate” they know the sound of “th,” or to repeatedly “explain” what’s the purpose of a period, are not conducive to development of fluent reading beyond the beginning stages. Yet with respect to the standard algorithms in math, Common Core’s math standards lend themselves to an interpretation that effectively insists on doing this for years on end.
The understanding that comes from such efforts is at best “rote understanding” .
Ther are so many more useful ways to compute than the standard algorithm. The reason so many adults get upset is because they only learned one way, but their number sense was stunted because of it.
Algebra becomes much easier if kids learn more than one way to add or multiply. Parents need to be aware of their own negative feelings towards math, stop believing that they are the only experts in math and try understanding that there is a bigger purpose to exposing kids to more than one way to add.
Have any of you actually tried to teach subtraction of three or four digit numbers where multiple borrowing occurs? There are much easier methods, but adults are so resistant because their way of borrowing ‘always works.’ So what, my way can be faster and more efficient and it doesn’t include borrowing, sometimes from multiple zeros.
As an algebra teacher the one skill I need kids to have so I can take them anywhere mathematically is Number Sense. Plain and simple Number Sense and it starts with exposing multiple styles and methods. How else do I explain to a student the order of operations is not always the order.
I have a dream, that people will stop saying that there is “one way” to do things. It is intellectually lazy and inaccurate. It is people who say “my way is the best” that do not understand education, and do not understand the wide variety of kids in the world. There is no single answer, or single best way. People like Linda Gojak are the problem, not the solution because they limit the options people have to help kids be successful. To me, successful kids, without lowering the standards, is the goal, not jumping through the “correct” process based hoops.
I teach math with all the shortcuts, because that is how I was taught. I was also required to learn all my math facts by third grade, something that is not done any longer as relying on calculators has become the norm. The way I was taught math worked very well. Some may call it “Drill and Kill”, but in the real world, when one’s boss is waiting for results, the boss is not remotely interested in HOW you got the answer, but that you got the answer. As long as you can do the math, being able to explain HOW you did it, is less important (unless you’re taking a test to show how well your teacher has taught you)than actually doing it. And by the way, this system of Common Core, will drive more teachers OUT of the profession, than into it. I’m retiring after this year, after teaching Math MY way, because of all the BS that has invaded education, just so testing and text book companies, (oh, and Bill Gates) can get richer. It’s not teaching anymore. It’s all about the testing. Kids aren’t students anymore. They are DATA!
Take out common core and just say – with my math masters and a teacher 20+ years… YES TAKE THAT JUNK out.. tricks become baggage by the time HS folds around and YES KIDS FALTER… the data (how many math-science degrees do we do a year in colleges by US educated students??? it is LOW)…. the data suggests that we stop this… the teachers who do it are just trying to fit in answers and get it done – they are just passing the buc to the next level and beyond..
I believe strongly that is is very important for us to guide students to learn mathematics meaningfully rather than literally forcing them to learn short-cuts to arrive at answers because the latter will not do them any good. In seeking to encourage teachers to teach conceptually, and also, for students to see the rationale why they need to learn conceptually and present logical reasoning for arriving at a solution to a mathematics task, it is imperative that we have a serious look about they way we assess. How do we assess? Do we portray to students that there is the need for them to learn to justify their answers? These are some questions we need to consider during assessment if and only if we really want students to learn conceptually and avoid using short-cuts and tricks.
I read James’s comment about the Common Core’s flaws with interest. He claims that the American education system before the Common Core achieved great results. Every sentence in his comment except one contains at least one grammatical or spelling error. I am forced to wonder about the quality of his mathematical reasoning as well. I agree that the implementation of the Common Core has plenty of problems, but so many of its critics oppose it without actually studying and understanding it. That undermines the validity of their opinions and does no one any good.
Can you guys do an article on how middle school math classes should be longer? I believe that teachers spend too much time rieviewing the homework from the night before and not enough time on the homework that will be assigned to them that night. If you could just consider the following.
The most salient point made in this article appears to have been an unintentional one: “Were you told to think of a greater-than sign as Pac-Man or to cross-multiply when dividing fractions?” Cross-multiplying is typically used for comparing fractions, not dividing them (that’s where the old “Ours is not to reason why, just invert and multiply.” chestnut comes in to play). I can’t think of a better way to illustrate the inherent problems of memorizing without meaning than for the author of the article to misremember one of the so-called “rules” of elementary mathematics. CCSM is long overdue.
I teach my school kids the tricks I learned. Once their brains catch up, they’ll be able to understnad the mechanics, and the theory. I teach the way I learned, not some new method that some professionals who have never taught in a classroom say so. I’m retiring after twenty-five years, because I’m tired of those who think they know, but don’t teach, try to tell thiose of us who DO teach, HOW to teach. Data is more important than learning. It should be about students-not numbers!
Actually other countries allow their students to learn tricks because they know that their students have a strong mathematical understanding in place. Tricks are NEVER taught first in China or other high performing countries because they are shortcuts and like all shortcuts they work sometimes and do nothing for building a foundation for strong mathematical understanding. If all our students know are tricks and shortcuts then we have failed as educators, and we perpetuate the chronic problem in this country of the acceptable attitude that it is ok to not be good at math. No one would say it is ok for an educator to not be good at reading. Many poorly trained educators are fighting common core because they are weak in math, which is NEVER the case for math teachers in counties that are outperforming us. We must understand and accept that our students are in the middle of a technology revolution that like the Industrial Revolution will change their lives in profound ways. If we cling to the tricks and shortcuts then we guarantee that our students will be nothing more then China’s workforce!
I’m a student,who makes all A’s, and my math teacher uses these TRICKS
and guess what it HELPS me UNDERSTAND MATH and I’ve awnsered questions TO JUSTIFY MY AWNSER and the STATE has said that I got it RIGHT. So take that and also you probably don’t know how a 5th graders mind works.
As a biomedical engineer with a PhD who is currently teaching at a math teach center part-time (temporarily), I think the main reason that people are opposed to Common Core math standards is that they themselves… are bad at math. This includes most teachers, and their parents.
Common Core is about ‘numerical fluency.’ It is absolutely essential that students have excellent numerical fluency, because otherwise they just memorize algorithms and apply them blindly without understanding what they’re doing — and the result is they very often do the problems incorrectly (because they’re GUESSING). If you have good numerical fluency you can do relatively complicated problems *in your head*, and in fact you’ll get the *correct* answer much faster than the traditional way because you can quickly and logically find the steps needed to get to the answer.
The only reason your kids are having trouble in school with Common Core is that most teachers don’t have numerical fluency themselves, so they aren’t equipped to teach it. Having worked with many children, I assure you that this is absolutely the best way to teach math, and kids can absolutely learn it with this method. The best part is that once they do learn it, future math becomes easier, and they’ll be better thinkers overall.
Common core is a set of standards, not a method of learning. The objectives are reasonable goals, although sometimes expressed in fancy mathematical or educational terminology which is not easy for the average person to understand.
When my daughter was in 4th grade, our school district dropped the advanced math curriculum due to budget cuts, so I volunteered in her classroom to help provide some math enrichment. The standard math textbook for her age was filled with silly stories and games, made-up “real world” applications, and confusing algorithms, but short on substance. One day I was working with students on multiplying 3-4 digit numbers by 2 or 3 digit numbers…two students each got identical wrong answers but insisted they knew how to do the work. We sat down together and I watched as they showed me how they arrived at the answer…turns out that they moved the 10s place over, as shown in the textbook, but then put the 100s place directly beneath the 10s place instead of moving it as well. The book didn’t explain why the second line moved over and it showed only one example of a multiplication problem involving two digits and no example of anything higher. The students were just supposed to pick up on the concept of place value by osmosis! Come on…look back at history…there were entire civilizations that didn’t understand place value…do you really expect 4th graders to catch on without explanation?
I agree with other comments that elementary teachers often are language oriented and don’t have a good numerical understanding. How can someone teach a subject that they don’t truly understand, upside down, forwards, backwards and inside out?
If we wish our students to understand math, we adults have to make a concerted effort to demonstrate the importance of learning math. Adults who dismiss their own lack of knowledge with comments about how they found it too difficult to learn make it too easy for children to give up.
My problem with Common Core math is at the high school level. In North Carolina, the state implemented Common Core at the high school level by creating integrated math I, II, and III. These courses mix algebra, geometry, and even some trig together each year. This means switching from one new topic to another in every other day. It is insane. Only kids who are really, really good at math will master this curriculum. (And don’t say that that the standards aren’t a curriculum. They are a master plan for a curriculum.)
Here is one example. My 9th grader spent one day trying to learn rational equations in Math II. One day!? That’s insane. It took me 4 hours just to teach him how to get the common denominator for the different parts in the rational equation. Rational equations are difficult and should be studied for a few weeks before there is an exam.
He had one day of instruction, and I had to supplement with hours and hours of extra instruction at home. If the students can only pass the course before their parents happen to know a lot of math and can teach them at home, then the curriculum is not working at the schools.
This has been the most frustrating and anger-inducing curriculum that I have ever encountered. At this point, I just want to go back to Algebra I, Geometry, and Algebra II. Common Core sucks.
Wah! That’s all I here. Guess what parents, eventually your child is going to have a teacher that is harder than most. Stop crying and DEAL with it. These concepts are TOOLS for thinking rather than cheat-like short cuts. You parents remind me of the incredibly prevalent tendency among kids to brag that they “beat” a video game really fast. Sure ya did kid, by playing on easy and skipping ALL of the fun side quests, turning an epic into a short story. They miss the entire point of playing: to have fun! And the point of education is to gain tools to help you eventually teach yourself as an adult. Shortcuts are novelties that are crutches to true knowledge. So, yeah, all I hear is, “Wah!!! I’m lazy brained and how dare you make me study and think!”. Stop whining.
Oh my goodness, people! So much in this string makes me sad, shocked, even embarrassed! Math education is not a liberal or conservative political talking point to be bantered about with sarcasm and ignorance! It is mathematics… which should be taught with deep understanding, particularly in elementary and middle school, so that a strong foundation is built for future, more advanced math. (if the math behind the “trick” is taught and understood, then it is no longer a “trick” but instead a short-cut that can and should be used!) A couple of years ago I heard something that really resonated with me. We are at a point in America, with our math and science education, that is teetering on a national security issue because we can’t graduate enough math/science majors to keep us competitive with the rest of the world. We have a responsibility to future generations and to keeping this country great.
One of the recurring themes in this string that makes me sad and even angry is that not everyone is cut out to do mathematics. When people, including parents, tell me (I am an elementary math specialist) that they are not good at math, I tell them they were just never taught properly. Come on, people (particularly you parents!) want more for your children than just an A on their report card! When parents would argue that their child should have a higher grade, I would ask them what grade they wanted their child to have and I would “give” it to them. It wouldn’t mean anything because their child hadn’t earned it and most parents would see my point. Champion math learning and our children’s understanding of what they are doing, not just mindless, rote nonsense!
The Common Core leaders are not brilliant at all. They are just trying to make themselves feel important and needed by introducing this unnecessary and complicated Math.
I am a graduate of Harvard University. I scored 730 (98th Percentile) on my SAT Math. I scored 710 (98th percentile on my GMAT (standardized test for Business School, which includes math). I usually score in the 130 – 140 range on these online IQ tests, which is described as “borderline genius.” By anyone’s standards, I am highly competent in Math (and also in the sciences where I also excelled in school).
I am telling you that this new Common Core Math is not helpful at all, and it will probably drag millions of American students down, rather than lifting them up. My own son used to love math, and he was good at it. He not only got the right answers, but he understood the concepts, which aren’t all that hard in grade school. You know. Concepts like, if you put three eggs on the table and then add 2 more eggs, you will end up with 5 eggs on the table. Now, he hates math. Common Core has destroyed my son’s enthusiasm for math, and he is a naturally strong Math student, with a strong family history in Math. I hate to think of what it will do for those who aren’t naturally strong in Math.
This is what happens when we give the federal government too much power. They just screw things up. They pitch it as “raising the bar,” but what’s really happened is that the bar is being lowered.
The people who wrote this stuff are self-important bureaucrats who are doing nothing but trying to justify their own jobs by ramming this crap down our throats.
Down with Common Core! Down with Obama!
This is ridiculous. You teach the concept, yes. You ensure that the concept is solid. Then you teach the trick. The point is to get conceptual understanding and then solve problems IN FINITE TIME. I am a statistician, and an applied mathematician. Every time I solve a problem, I look for a trick to make it easier. Tricks are also a way to get kids interested. These common core fanatics seem to think that learning is static, and that it never evolves. If so, people will take FOREVER to solve a simple problem.
Love the emphasis on thinking and many ways to reach an answer.
Wow…”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 incorrect answers are fine if you understand how you got the wrong answer? We put a man on the moon and did other great things with our math back in the day. And when mathematicians from Stanford feel compelled to write a paper on how Common Core isn’t even close to what was proposed originally for math, there is something seriously wrong.
I feel that students’ should be able to explore math and come up with their answers, the way that they choose and be able to explain their way of thinking.
I agree with Patricia. We have different types of learners in each class, so why wouldn’t we have different techniques of teaching certain subjects. While I think that CCSS should be the basis of our lessons, it is not the “BE ALL, END ALL” of teaching. If students are not getting a particular math concept, of course, you teach them another way (ie. the shortcuts/tricks). I’m trying to say that these should be used as a way of supplementing your instruction that has already been put in place. Think about it, if you were at a board meeting, trying to explain a project to someone in so many words, and they didn’t understand, what would you do? Explain it in a different way, right? While students getting to the correct answers is a great accomplishment, they will need to know the “HOW” they got there in the future (ie. when they build on those foundational skills in the following grades). The goal of the “WHY” is to make critical thinkers, that aren’t just after getting an answer to be “DONE” with their work. They are deep thinkers that are engaged in not only the Math problem placed in front of them, but future problems to be solved.
I know that many people are not fans of the Common Core methods, because they feel that we are making things “too difficult” or we are forcing them to do things differently. The US is behind many countries when it comes to our math abilities so just because it is not how we did it before doesn’t necessarily make it the wrong approach. If students can arrive at the answer in multiple ways and understand why there were able to find the right answer then maybe that’s exactly the kind of creative thinking that we want our students to be able to do.
Common core is just to hard for us parents to teach to our students if we don’t even know what to do. Go back to the old way of doing math.
I agree that some math tricks, like the butterfly method, are not useful in the long run because students forget how or when to use them. In addition, when tricks are used as a sequence of steps to follow, the students do not gain an understanding of the concept.
Students don’t learn conceptual thinking when they are taught math tricks. It’s a way to figure out answers without understanding why they work
Tricks only get students to find the right answer. This article stated that getting the right answer is only the first step. It is just as important to understand the mathematical principals at work. That is what the common core focuses on.
Students need to understand why the answer is correct, not just that it is correct. They are focused so much on the tricks, they are not thinking about what the question is asking and using the conceptual thinking that can be used across the board.
I think students should combine tricks and exploring numbers on their own, This is the way that it should be in math. It doesn’t matter what method they use if the result is the same.
Engaging students Knowing the “Why” not the “How” and being authentic is the true way of learning. Their pride of ownership through collaboration with peers creates the discovery for their lesson. This method promotes critical thinking . No tricks for true learning. Math tricks do not promote conceptual learning.
I think it is ok to show students ways to feel comfortable with math before exploring the meat of the meaning. Many times students are intimidated and this may be a way for students to engage without feeling intimidated.