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The Common Core wasn’t necessarily supposed to change how math is taught, but in many schools that’s exactly what’s happening.

Many – some might argue most – American math teachers once followed a simple format: Explain a formula to the class, show an example on the board, then let students practice on worksheets.

Now, many of those same teachers are attempting to lead seminar-style discussions on the division of fractions or the Pythagorean theorem. They’re assigning longer-term projects in which students discover and experiment with math concepts, instead of training students in tricks like the “butterfly method” for adding and subtracting fractions.

Related: Common Core math experts say teachers need to stop using shortcuts and math ‘tricks’

Teachers are trying out these new methods even though Common Core – guidelines, which have been adopted by over 40 states, for what students should know in math and English by the end of each school year – don’t speak directly to how math should be taught.

“The Common Core is silent about how to teach,” said Phil Daro, one of the lead writers of the math standards. “When we wrote the standards we were prohibited from addressing how to teach, that’s not what standards are supposed to do.”

Student work in the hallway of Eastside Elementary shows the “partial product” method of solving a multiplication problem, one of many methods students have learned with Common Core. Many teachers say the new standards go deeper than the old standards and should not be dropped. (Photo: Jackie Mader)

But there’s a debate about whether the new content requirements alone are enough to improve students’ understanding of math. Many in the world of math contend changing how teachers organize their lessons and lead their classrooms is essential to making a difference.

Steve Leinwand, principal researcher at the American Institutes for Research’s Education Program, argues that the failings of the old format for teaching math has led countless Americans to the conclusion that learning math isn’t something they can do.

“We don’t have an achievement gap in this country,” said Leinwand. “We have an instructional gap.”

Like many Common Core supporters, Leinwand says the “I, we, you” model – where first teachers go through a problem for the class, then have the class work together on similar problems and finally have students work independently on problems – has dominated American math education for far too long.

“I, we, you sometimes makes sense,” said Leinwand. “But sometimes teachers need to turn it on its head with some version of you, we, I. That requires students to struggle, explore, share, justify, compare and debrief.”

Some experts question whether it’s smart or even necessary for teachers to overhaul both the content and their pedagogy at the same time, though.

Related: Will weak teacher training ruin the Common Core?

“The problem was with what we were teaching, not how we were teaching,” said Daro at a conference of the Association of Mathematics Teachers of New Jersey. “Countries have varying levels of teacher quality but are still high performing.”

Daro thinks that the Common Core addresses the main problem of the math classes of yore – that curricula went a mile wide and an inch deep – asking teachers to cover so many topics that none were given appropriate attention.

“In higher ed, we were asking why were these students taking AP Calculus, when they needed to spend much more time on algebra,” said Daro.

And indeed, many states and districts – and teachers — are struggling with juggling the huge project of overhauling both their curricula and their teaching simultaneously.

“Are math standards going to help?” asked David Wees, a former New York City public school teacher and a formative assessment specialist for New Visions for Public Schools, a non-profit that advises 75 New York City public schools. “Yes, but there are the standards as written, there are the standards as practiced by teachers and there are the standards as students will receive them.”

He says districts shouldn’t expect for every teacher to master the new curricula and new teaching methods at the same time. Instead, he says districts should work on the changes more gradually.

“Professional development sessions, where you go over things with teachers very briefly, aren’t enough. They need to see it more than once,” added Wees. “ There aren’t very many model teachers in this country and they tend to be concentrated in only some schools. We need to create more model classrooms, instead of trying to fix the teaching of 3 million, we should be trying to fix the teaching of 1,000 good teachers so that their classrooms can be resources that other teachers visit.”

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Emmanuel Felton is a former staff writer. Prior to joining The Hechinger Report, he covered education, juvenile justice and child services for the New York World. He received a bachelor’s degree from...

Letters to the Editor

40 Letters

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  1. The Common Core was NEVER designed to tell teacher HOW to teach. It was designed to guide teachers on WHAT to teach. It is a clear, well-thought out roadmap for your child’s education. The goals are doable and logical. They are sequential. There is NOTHING in the core about methodology. Good teachers have been teaching these goals for decades. ALL the countries that are ahead of us academically (too many to name here) have something like the Common Core – standards that are nationwide. If teachers were to accomplish all these goals each year then children would pass from grade to grade with all the foundation that they need to succeed. Quit blaming the Core. Instead – place the blame on politicians who abused and misused the Core for their own purposes – and blame poor administrators who couldn’t teach a monkey how to peel a banana. And get rid of teachers who are not able to accomplish these clear goals. The Common Core was the last chance for our country to get the educational system right in this decade. Now the baby and the bath water are being tossed out into the street. PARENTS – educate yourselves on what the Common Core is — those worksheets your child is bringing home and that are driving you crazy is NOT the Common Core. It is someone’s misguided interpretation of it. Common Core is the only thing that can save this country from educational ruin. And while we are at it we should take a good look at what the “No Child Left Behind” act REALLY is. It is NOT an excuse to pass kids from grade to grade – that is the stupidest interpretation we could possibly take. It means we are obliged to teach these academic and social goals to ALL CHILDREN – regardless of their ability. We teach then to the best of THEIR ability. We don’t water everything down so the high flyers are bored and the slow achievers are still drowning. Other countries are able to rally and join together and fight common causes. Our educational system is a common cause. But because one state can’t agree with another (whatever happened to the philosophy of “UNITED” States …???) we are basically doomed. I am 53 years old and this country has gone to hell in a handbasket.

  2. Strategy and curriculum are intimately connected. You cannot make extreme changes to curriculum and then be shocked that the methodology also changes.

    This is yet another example of “unintended consequences” … politicians strive for simple, one-sized-fits-all answers to complex problems (and sometimes problems that never even existed) that then start to cause even bigger problems.

    In some parts of the country, we have improved education while worsening it in others. Now we have a whole generation of kids who despise learning and hate education. We have not only driven teachers away from the profession, but have assured that students don’t enter the profession at all. Tennessee and Connecticut are already starting to change course … I hope other states take their lead.

  3. Teachers are projecting what they want to do onto Common Core… not that what they want to do, versus what they should do, works.

  4. In many schools the teachers weren’t teaching methods at all. They were just handed out Calculators and even when they did teach a method it was little better than a Calculator. I went back to college a few years ago and sat in a Chemistry class with a whole lot of students who were completely mystified when I solved a problem by solving for X. The really scary thing is that the professor didn’t understand how I solved the problem either. She made me learn a “box method” AKA “plug and chug” which is basically the same thing except that when you solve for X you understand why you are doing the math and when you use the “box method” you are just doing what you are told with no real understanding.

  5. As a current math teacher working with common core, the difficult part is trying to have students learn the material with new methods, and skip ahead when many of them never learned the basics to begin with. Another difficult piece in teaching the common core material is that there are no books published that show how or what methods should be used in the classroom. There are also no questions so far…published that show what type of questions the students are going to be asked with the common core standards. So I have no textbook to guide me, and I have no examples of questions to give to my students…but I must teach common core.

  6. Working from the highly questionable assumption that the CommonCore has a solid pedagogical foundation, the standards are just words on pieces of paper.

    It should be up to teachers to figure out how best to make sure the standards are reached, but in many places around the country, teachers are told exactly what, how and when to teach because their superintendent or curriculum coordinator or some other administrator has either determined unilaterally what the CommonCore means or has bought a system from some purveyor (Pearson-related, no doubt) in order to prepare for the annual assessments.

    The CommonCore is not about learning. It’s about control.

  7. “Sentence first…verdict afterwards”. -The Queen (Alice in Wonderland)

    The need to ask if the math standards “are going to help” is outrageous. This question should have been answered by educational researh long before the standards were imposted on millions of students. I agree with David Wees, who suggests that the math standards should not be implemented all at once. But they should have also been carefully tested, so see if they help or hurt understanding of math, both in the short and long term.

  8. This week we are preparing for Fall Finals at the High School Level As instructors of mathematics the core curriculum drives what we are teaching. What we as a group found that the traditional tasks are now taught as a lower level, but unfortunately not all the students are entering High School with those skills. The example is that what was taught prior to core curriculum in 9th Grade Algebra is know taught in 7th or 8th Grade Algebra. As high school teachers we have also preparing our students to go beyond the traditional multi-choice standardized tests to the Reasoning, Modeling, and Application thinking by students type of standardized test. So our mind-set is to avoid the “dumbing down” and go to the “brightening up” I personally anticipate that this proding students to the next higher level is going to be an on-going challenge and not for the weak (socially, emotionally, or physically)

  9. This is the new baby! In a few years it will be something else. Test scores cannot be the single factor we use to determine how good teachers are doing. Society itself is failing and how can we expect teachers to work miracles when students have no accountability for improving their learning? In my state students finish standardized tests in 10 minutes with no consequences. How can you judge a teachers performance when some students simply don’t care? Until we get the communities as a whole to buy into education and get involved with the schools, nothing will change! Please stop spending millions of dollars on technology because that isn’t fixing the problem either. Hardwork and more hardwork is the answer! Not shortcuts or dollars.

  10. Highly questionable? Not about learning? Please see this study of the CCSSM by the American Educational Research Association. The authors describe the relationship between the standards and student achievement.

    http://tiny.cc/r6nrqx

  11. I agree with Nancy. The additional problem is the publishers of material are still breaking up the standards into little chunks resulting in the same type of teaching that was done with the old standards since teachers are required to use the materials their district purchase. The “I do, we do, you do” method is also still pushed by the district.

  12. Mathematics has not been mathematics for along time it has been arithmetic you know the stuff you put in a calculator. Mathematics is just like reading. A reader is someone who can decode and comprehend. Mathematics has not had the comprehend part only the skill part. Ask some why you count decimal places when multiplying decimals or ask somebody why you change the sign and flip. See this is what we grew up doing and to undo it will take time but we will create a large group of mathematically proficient students if we do not we will only grow big calculators than can talk and drink beer.
    The last thing it is is control it for many will be freedom from poor teaching and no learning.

  13. If you change the learning expectations for students, it makes perfect sense when the instructional practices change as a result. Traditional teaching practices were used because they supported the rote expectations we had for the low level of understanding that we wanted students to have. Now we want student understanding of mathematical processes to be deeper, so it make sense that traditional instructional practices will not be sufficient to bring kids to that level.

  14. This article purports “”The Common Core is silent about how to teach,” said Phil Daro”… but in NY State, teachers were handed a SCRIPT in Sept 2013 showing what examples to do, what to actually say before/after the examples, etc. It was incredibly insulting. I completely agree with the idea of discovery learning and mixing it up between I, we, you and you, we, I. Concept learning beats rote learning any day in my book. However, the CC curriculum is even MORE mile wide and inch deep than the previous curriculum which leaves even less room for exploration, discussion, all the things they seem to want. I would’ve been an easy person to win over in the common core movement, but they’ve definitely lost me.

  15. Common core is a set of standards. Most textbooks are not written with common core as a basis. The publishers “find” relationships to the standards from existing texts. There are still major curriculum failures. This is on the school boards or superintendents or whoever determines what curriculum to use and how to instruct. If common core is taught with meaningful deep understanding of topics, then it should be immensely better than our recent shallow teaching. I tutored a 6th grade student a few days ago who was trying to remember when to “flip” the inequality sign. I showed her how to solve the problem without flipping the sign and she immediately understood how to get the answer without the trick and it only took two more short steps to find the solution. More importantly, she was confident that her answer was correct.

  16. The Common Core standards of promoting creative thought and math understanding are admirable and long overdue. Common Core has started to shift the focus of math education away from simply “doing the math”, toward understanding and using it.

    But what many people don’t seem to understand is that this is a complete paradigm shift that goes much deeper than changing a few math teaching strategies in class.

    “Learning” simple facts and skills, ie “doing the math”, is well-suited to memorization, testing, and traditional homework. Learning to think and reason creatively is a different type of learning, and requires a very different type of learning environment.

    To think and to be creative, children have to be willing to risk being wrong and making mistakes. In a context of grades and testing, that is just not going to happen. Kids’ only concern is–and must be–getting the right answer and doing it the right way for the test.

    The only way to really free kids up to think and reason, in the way Common Core is trying to achieve, is to create a safe space of exploration and playful math learning, where kids are free to think without fear of mistakes.

    This would be a complete paradigm shift for schools, and it would mean changing not just teaching techniques, but the entire culture of school and classroom.

    Obviously, this would require a much more intensive and strategic approach to teacher training than the occasional in-service day.

    I think the author’s suggestion of focusing on model classrooms and working out from there is an intriguing one.

    Play, innovative thought, and creativity are tightly connected. Many top organizations like Google are aware of this, and incorporate time for passion and creativity into their workplaces.

    There are many initiatives around student-centered learning, projects, and innovation, but there is also tremendous resistance to changing the traditional school model of testing and homework.

    If we truly want our kids to become thinkers instead of simply rememberers of information, then we must re-work the structure of schools to match our changing goals.

  17. first, how many teachers have the opportunity to visit a model classroom in another school, and a long distance away for many rural area teachers? the answer: very few.
    second, a visit does not lead to excellent practice or even an attempt to make changes. It is no better and likely worse than a 1-day PD if the PD is in-depth with hands-on practice.
    to be effective, the 1000 teachers need to be in schools where they can continually coach. This has been said many times for years. So what is needed are expert coaches locally available to model, observe, support, give constructive feedback and guide teachers one step at a time.

  18. Common Core has more to do with control and profit rather than any kind of new “magic.” Someone has invented a new wheel and everyone is supposed to buy into it no questions asked. Those that would argue that teachers have the flexibility of teaching in a way that is best for their children are simply not telling the truth because many districts have scripted exactly what teachers are to say in lessons of science, math, and reading. Sorry. That is not education. That is indoctrination!

  19. Most of the best teachers are screened out by the process.

    Real STEM teachers are often kept out of the classroom because they refuse to put the emphasis on pedagogy, state values or district priorities.

    The very best teachers are often unemployed and usually found in places like McDonald’s sipping coffee and griping about how poorly the system works.

  20. Teaching from a constructivist viewpoint is nothing new, and was being implemented in certain places before common core. Since the writers of common core claim it isn’t supposed to inform instruction, and since the ultimate goal is to have students pass tests, for every teacher who adopts a new approach to teaching, there will be at least one, or possibly more, who will double down on test prep teaching.

  21. Permit a few basic questions:

    1. Is there research to support the notion that having uniform standards in a nation as geographically and socially diverse as ours is beneficial?
    2. Is there research to support the apparent belief that standards have a positive impact on learning outcomes? (Dr. Duke Pesta – University of Wisconsin/Oshkosh – notes that since the beginning of the standards era there have been over fifty research projects attempting to measure the relationship between standards and student learning. To date, it appears standards, whether good one or bad, have virtually no impact on student learning. If Pesta’s assessment is correct, why have we turned American education on its head in order to implement national standards?
    3. Supporters deny that Common Core has become a federal initiative, but hundreds of millions of federal dollars suggests otherwise. Does the Constitution and/or federal law permit such federal involvement in our schools?

    Too much of the Common Core debate centers on peripheral piffle.
    Let’s get to the core of the issue!

  22. The Common Cure, or whatever the hell it is supposed to do, as with everything else educrats have devised in decades of the past, and all the hand-wringing about reasoning, computation, or classroom techniques does one thing for certain: It shows kids that their success is a function of what the school does, not what they themselves do. Therefore, these creepy and anesthetizing school administrator and education reformer types, who seem fresh out of a disturbing Aldous Huxley novel, are doing nothing more than encouraging kids to withdraw their efforts out of ALL learning situations. So now, kids do not see themselves as part of their own success. Thank you, all you sterile school designers out there making our jobs much more difficult and meaningless! Thanks also for driving great talent away from our profession. #numbschools

  23. Stephen Krashen above it exactly right: The standards were never tried or tested by ed researchers to even SEE if they were any kind of improvement! The standards are really a small group of people’s theoretical idea of what they THINK might work. No one knows. There were no trial runs done. The testing of the standards themselves should have been done long before states were basically forced to sign onto them! It’s all a grand experiment so far. This, NOW, IS the trial run. Even Bill Gates who largely funded the entire CCSS experiment says we won’t know the results of it for 10 years!

    The new math standards, in particular, are quite different from former standards; teachers MUST teach to the standards since their job performance is now tied to student test scores on the CCSS-associated tests that go WITH the standards; so teaching must change. Very little has been done to inform teachers what that new teaching should look like. Teachers are having to experiment. Either that or use pre-packaged modules like EngageNY.

    It will take years for teachers to find their way into the BEST ways to teach to these new standards. They’ve been given precious little support, few resources, and next to no time to figure out how to accomplish this huge change in their instruction. Several weeks of dedicated work time, planning together in teams, would be appropriate—several weeks a year for a few years. Not happening. Yet in many states the new testing will still happen very soon, too soon. More students will fail, and teachers will lose their jobs because of the unbelievably poor pre-planning and implementation of the CCSS.

  24. Common Core is a top down, corporate developed, mishmash of elitist standards developed to further denigrate our best teachers and public schools. Yes, NCLB on steroids. If you read all of the comments above, they tell a story. The story is that everyone thinks they know better than another, and that each individual needs to tell the next how certain they are that they have the answer to what’s so wrong with our public schools. I mean, give me a break. Add it all up, it amounts to nonsense and chaos. To “save” our public schools (which are truly not nearly as bad as the hyperventilating president, congress, and fat cat billionaire CEO’s want us to believe), we need to get off the backs of our teachers and return full ownership of all public schools to them. Decades of parent surveys at the grassroots local level consistently show great satisfaction with the job each school does for their child/children. But somehow, so-called experts, think-tank organizations, business leaders, politicians -everyone but teachers and parents- wrap themselves in the common core flag and wave it around like it really is the holy grail for having perfect public schools and shiny happy students. Get a grip folks if it’s not too late. The common core is doomed. Sorry if I’ve ruined your day.

  25. This is in response to Maureen! Maureen, you need to watch REAL
    Educator and researcher/Assessment expert, Dr. Christopher Tienken on YouTube (Dr. Christopher Tienken Don’t drink the Common Core Kool Aid). You will find REAL Research Statistics about how the United States Compares to other Countries in the world that disputes everything you are saying about the NOT True statements that the U.S. is behind other countries. You are spreading the exact fears that these money grubbing education initiative pushers are using to justify an unproven, not benchmarked education initiative that was pushed through in an unethical and underhanded manner. If you actually take the time to listen to Dr. Tienken, you will understand why this is a fear tactic being used, without evidence to show that apples to apples comparisons exist. Also see (Dr. Tienken The Assessment Landscape and The Current School Reform Landscape). I’m not just making a statement to disagree with you, I’m citing the evidence (LOL, since we only care about Evidence in text and not about reader opinion, since Common Core has been implemented), so there you go!

  26. The whole discussion on “Common Core” or any other academic standard is irrelevant. Because the whole concept of institutional learning is so far from the proper path of bringing up a child. Public schools have particularly failed in every way for over a century. Because they don’t teach the things that are truly important. Preserving the childhood innocence, building humility, spiritual insight, and ultimately becoming a selfless individual.

    Instead. Schools promote the opposite or “N/A”. Institutional learning is a conspiracy against the family unit. To bring up those who are selfish, love money and materialism, and work to support politics and corporations. That sums it all up. And in my mind that makes public schools highly irrelevant and unfit to keep my children. We are talking 40 hours a week for our kids to absorb unnecessary and harmful information. Toss in bullying as a bonus.

    There is a long standing tradition in schools to extract the innocence from a child and convert them to whatever Uncle Sam wants them to be. Well let me tell you. When we gave birth to our children, we volunteered to be parents. Not some of the time. But all of the time. Those precious 40+ hours a week are included. They stay at home where they belong. It is very difficult for children to go through life without learning what they need to know. The academics they need are very little. And they sure as Hell don’t need to know the names of US Presidents. The past is the past. It died. Leave it buried.

    We get so many remarks from family and friends on the behavior and knowledge of our children. Because they are unlike those in public schools. And when they ask me how we do it, I always tell them it all revolves around spiritual guidance. We choose to follow the moral principles that were demonstrated and recorded by Jesus Christ. And we don’t need to go to church to do that. We don’t brand ourselves as Christians either. The responsibility to raise our children right is universal and works for all people if they care enough to try.

    Sending kids to public school is a cop out. Parents make many different excuses as to why they don’t take them out and raise them at home. But there are millions of homeschoolers today that prove that one parent can stay at home. Stop living in big homes. Stop buying fancy cars. Stop shopping all of the time. Put your focus on living up to the responsibility GOD gave you when He sent you a child. There are no excuses for anyone. If you don’t know how to teach a child then ask for help. Don’t cop out. There are still millions of people who shouldn’t be raising kids. Because they throw their kids in government daycares 5 days a week. Institutionalized children today are very self centered and materialistic. They are allowed to go online and act like fools on webcams and look at porn. And if they don’t do those things, the kids at schools are telling them about it. Shame on all of you for sending your kids to the wolves.

  27. The concept of common standards throughout the country is a wonderful idea– especially in our society of mobile families, moving from state to state. Concept based teaching is not new, it is just new to many teachers of math. There was a survey of hundreds of math teachers done a few years ago that indicated as many as 70% of elementary teachers were not comfortable teaching math. If that is so, how can we expect those same important educators to teach concept-based mathematics? Of course the Common Core is changing methodology! Of course parents are frustrated! When parents and teachers do not have a conceptual understanding of math themselves (only formulaic plug and chug methods), how can they teach or help their students? Adopting standards and tests without preparing the professionals who provide the instruction is the bigger problem. If students arrive to middle and high school without the requisite basic mathematical knowledge, they will not suddenly get it. What happened to remediation and reinforcement after school, in summer school or in tutoring sessions? Oh yes, budget cuts ( to staff and transportation). The biggest issue with Common Core is the sales job. We cannot expect students to know more or know “deeper” without having teachers that do also.

  28. Standards are what to teach not how to teach. I went to college to learn that. If the publishers and the test promoters would leave us alone we could teach the standards using different methods according to the way children learn

  29. I am wondering if others who are using a pacing guide and a sprial curriculum are overcoming these challenges, and if so, how?

  30. The role played by developers of crappy curriculum that is “aligned to the Common Core” should not be discounted….. Teachers are often required to teach using poorly written materials instead of working together to create what’s best for kids. Mr. Wees’s comments are offensive to me as a teacher and curriculum developer. There’s already a process in place to identify “model teachers,” and if Mr .Wees is unaware of that work, he has no business advising educators.

  31. Amen. Expert coaches are a must. This is a whole new ball game. It is outrageous to consider asking teachers to dramatically change the way they have been teaching without the support of an effective, highly-trained coach.

  32. Those of you who are using CC as your political platform, take a few minutes or have your advisers, (because we know you don’t read any of the research or you would sound more informed) EDUCATIONAL EQUITY! It’s kind of a big deal. Then take the time look at a piece of research titled The Proficiency Illusion. Once you have digested that, move out of your upper class neighborhood, unenroll your honor students in their private school and send them to one “those” schools, and tell me the education system in the US doesn’t NEED the Common Core.
    All students should be entitled to same learning expectations regardless of geography.

  33. I can not support any education reform that did not request the input of the majority of America’s K-12 teachers. The writers of the Common Core consisted of very few actual K-12 educators. This was a major mistake in implementing what could of been meaningful reform. For this reason it is destined to fail. A new plan will be drawn up which will involve more teacher and parent input. The financial backers and intellectuals behind the Core seem to have forgotten that we are a passionate democracy.

  34. The Common Core does imply how math should be taught via the Standards of Mathematical Practices. These habits of mind, developed along a continuum K-12 can only be developed by shifting instructional delivery from “I, we, you.”
    Regarding the perceived “lack of input from teachers,” this is a myth. The CCSS is consistent with the NCTM’s reform initiatives that began over 20 years ago. While all K-12 math teachers are not members of NCTM, it is open to all and is clearly the organization that best represents the advancement of professional practices to advance the teaching and learning of mathematics.

  35. Can someone tell me how having 5th grade students work ONLY on fractions and decimals for four months straight is a wise educational move?

  36. I rarely see any mention of the Common Core Mathematical Practice standards although I did find it in one of the responses to this article. These are the most important standards relating to better instruction, in my opinion. The content of the standards hasn’t changed although the timing has.

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