Dear frustrated parents of Common Core math students,
Think back to your math education, did you learn the steps required to add numbers? To subtract numbers? Did you learn another set of steps for how to add and subtract fractions? How about a procedure for how to add and subtract negative numbers? Were each one of those procedures different and specific to the "type" of number you were adding or subtracting? What about as you got older? More procedures? Were you successful? If so, you likely had a great capacity for memorization. The ability to memorize multiple steps and multiple procedures and know when to apply each of those procedures. What happened when you forgot just one step? The procedure failed to produce the correct answer. Were you ever frustrated because you couldn't figure out why it didn't work? No? How about your classmates? Any of them ever confused? Don't know? Try this, survey one hundred adults. Ask them, were you good at math in school? Did you love math? Did it make sense? I guarantee the majority will have a negative response. Our generation is full of math haters. Think about it, you would never hear someone say, I'm just not a literacy person, reading was always hard for me. On the contrary, I'm just not a math person, it never made sense... that's common place, socially acceptable. I was never taught to make sense of numbers, I was taught one way to solve every problem, every problem had ONE way, memorize these steps and you will be able to solve this problem. Sorry if you can't remember the steps. This is how we do it. I was robbed. I was not taught to persevere and try to make sense of the problem... who cares what it means, here's how you do it, just do this.
Hold on, why am I crossing out this number and changing that one?
Because you don't have enough to take away. Just do it!
But wait, I have 453 and I'm just trying to take away 17 I think there is more than enough to take away.
No you can't take 7 away from 3... Just cross out the 5. Just do it!
But wouldn't 3 take away 7 be negative...
NO! You can't take a bigger number from a smaller number, sit down, JUST DO IT MY WAY!
Hold on, why do I have to have common denominators?
Because you can't add apples and oranges! Just do it!
But... but... If I add 2 apples to 3 oranges I get 5 fruit...
Stop being sarcastic! Sit down, find common denominators... JUST DO IT!
I was wondering... why do I have to flip the fraction upside down if I'm dividing?
It's not your place to reason why, just invert and multiply! JUST DO IT!
Don't get me wrong, like some of you, I had a high capacity for memorization. I just did it, I memorized and memorized and very rarely made mistakes. I graduated in the top 3% of my almost 400 member class and I went on to high levels of math in college and was quite successful. Now, I'm a math specialist. It's what I do. I have spent four years studying and researching math instructional methodologies. Nothing but math every day for 4 years. Do you know what I've discovered? I didn't have any conceptual understanding of math. That made me angry. I have learned more about numbers and how they work in the last four years than I learned in my 19 years in public and post-secondary education. I have also learned how to help young students make sense of numbers, using their own innate understandings, their own built in mathematical ability. I have learned how to start with what they know, and what they understand and refine that into efficient strategies. In addition, I have also learned that it takes time. I must first allow them to be creative with numbers before I push my own ideas of how they "must" solve a problem. If I have patience and let them make sense of it, they will adopt the most efficient method, and they will become successful in math, not only knowing how to do it the way we learned it, but why that way works and when it's the best strategy.
The "new" methods you're seeing are not being taught. They are methods that students naturally invent. Just the way that mathematicians invented them before our formal mathematics system existed. Believe it or not, simplicity and efficiency are at the forefront of our classroom discussions EVERY day. We are guiding students through their own sense making methods not only to understand numbers and operations but to find the most efficient methods for each problem.
I understand your frustration. I was frustrated at first too. Remember, this is not the way I learned it either. Please be patient. Please reach out to your school's math leaders to help you understand. Please don't rob your child of the opportunity to make sense of math. We are trying to develop math lovers, problem solvers, and creative thinkers. How can that be wrong?
Sincerely,
Lover of math and children
Thank you for taking the time to explain some of the thinking BEHIND Common Core. Most importantly, thank you for not making it a political issue, but instead, keeping the focus on the benefits brought to the students and our future.
ReplyDeletePeople make it political because it IS political. I want my kids to learn as much as any other, in fact, I care about other kids as well. However, having those who produce standardized testing for money concoct this educational reform plan is, in fact, political. I have every right to fight it as well. Even if the standards were the greatest, age appropriate (which, critical thinking tells me they are not because a large portion of them fly in the face of cognitive developmental teachings that HAVE NOT been refuted)- they way they were brought about is still not ethical and has nothing to do with education. What it does have to do with is money. What I can't figure out is why teachers, those who should be teaching people to think, believe the information they are given, provided by the state and federal government paid for by lobbyist and special interest groups. Further, my kids have brought home this crap and it is, in fact, crap. Kids before age 12, largely, not all, do not think abstractly. To force them to do such is to force them to failure, end of discussion. Science, research proves that. Teachers, politicians and large corporations do not get to re-write science, sorry. It's a no go.
DeleteFurther, education shouldn't be political, it shouldn't be driven by money but it is. It is currently and getting federal support and huge corporation funding will only make it worse for teachers. That is a tragedy. Ask yourself this, if a teacher does disagree with CCSS, how are they treated? Can they speak their mind freely without recourse? Can teachers speak their minds freely now? No. They can't. They haven't been able to in years. That is a big issue no one wants to address but it should be addressed.
Delete^^ Nutter,
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DeleteJeremiah, well spoken. My daughter is also suffering through this crap math and I am working hard to get it out of my state.
DeleteI agree with everything the author said, but the problem is there isn't time for patience. State standards are all tied to standardized tests. This means a child has to understand concepts based on a time table. If we want children to develop true understanding, we need to give them time, especially without fear of retention.
DeleteThere is hope! My kid struggled with math... until it clicked. It was all at once, and she knew it. And I swear, she reasons on her own now. She's patient. She's highly motivated. She loves school, and she feels empowered.
DeleteKids think abstractly! They think SO abstractly. You just have to be an abstract thinker yourself and nurture that tendency in your kids. And when they realize that innately, they can do this - it's beautiful to see!
I, too, am dealing with this stuff at my grandsons' school as I help them with homework the 2 days I have them per week. Our problem was long division. One kept coming up with the wrong answer until I showed him the way we learned it-bring down the #'s and put an "x" under the ones you've used already and keep your numbers lined up. Bingo! Correct answers every time! And Jenna, math is not abstract in elementary school it is EXACT, memorize your tables and learn to do the computations the correct way and PRACTICE. My youngest (30 year-old) had this fuzzy math foisted upon him in Middle School and it messed him up badly-so this is nothing new. My other 3 were A students in both math and science so they missed this "grand educational experiment" and went on to university with chemistry, computer science, and education majors.
DeleteBTW, My daughter decided to home school and her kids are WAY ahead of schedule (she is under testing requirements with the state and therefore accountable for those of you who hate homeschoolers)
DeleteAhhh the usual....don't understand that its the curriculum not the core standards that are troubling teachers, districts and the like (unfortunately it seems that schools and districts don't know how to re-train teachers nor do they feel the need to actually review materials perhaps?) Depending on which state you live in determines who you need to complain to (the district or the state agency)...but if you actually read the core- you will see there is not a determined methods of teaching suggested nor is there a curriculum suggested. Its always those who don't understand that complain about the CCSS. I also find it laughable that there is belief that standardized tests drove the core....hilarious. I, along with thousands of teachers across the country, reviewed several drafts of the core in 2009-2010. I don't recall anyone getting paid to do this nor being associated with an assessment company. READ about the process and then take on the curriculum and the process of testing...but finding fault the the actual standards is so shortsighted. I guess you also feel this is associated with a federal mandate...hahaha. So sad.
DeleteJeremiah, do you have kids? If so, clearly you've never been around while he/she plays games and makes up stories. Kids are NATURAL abstract thinkers! They create, imagine, and reason in ways we as adults do NOT understand. Science, research, shows this to be true. Kids learn language better at younger ages. Kids are more accepting of new and unusual ideas at a younger age. It's when they get older that they struggle to let go of the "WAYS" they've been taught since they were younger. I teach 9th grade math. I run into the resistance all the time of "we learned it THIS way in math last year, why do I need to know WHY?" And I kindly explain that they'll need to know the why behind things their entire lives. But the more I read these articles and see the terrible responses from parents that DON'T know the why behind it, it just makes me sad. I see where the kids get it from. It's too bad that society, parents, etc are OK with kids just skating by with the basics, and barely skating by at that... It's time for change. We teachers see that. Are we nervous about it? You bet! That's MY JOB on the line if I can't change my students' way of thinking and encourage them to work harder at it. Their success, or lack thereof, reflects on ME. I've seen the tests. It's gonna be a long, hard road. But I'm confident the kids can handle it. You should be too. Put more faith in your kiddo(s) to think and reason. They can do it.
DeleteCommon Core is a joke. If kids knew the simple basics of Math they would be fine. I challenge anyone to go to any type of store and ask a young adult or teenager to make simple change for a dollar and they are totally lost!!! They do not have a clue and have to have a Cash Register or calculator do it for them do it for them. Inexcusable!!!!
DeleteSo what you saying is we can treat every child at the same level of understanding?? Bologna. This is yet another politician who thought they had a great idea, soldfolks on it because noone understood what the impact would be. It sounded good in theory - learn more than one way to solve 2+2. Who cares.... 2+2 = 4 no matter how you do it. We wonder why we are so far behind from other countries. We are getting paralyzed by trying to do everything 5 different ways vs just getting things don3
DeleteNever underestimate the power of conspiracy theorists to reject a rational explanation by an informed individual when the explanation conflicts with their sincerely-held beliefs, no matter how misguided.
DeleteJeremiah, I am assuming then that if you have children they have no imagination or ability to engage in pretend because it is all abstract thinking.
DeleteUmmm... teachers put this together not paid test makers. It isn't so different from the standards that my state already had. It just made it a little less specific so the teachers can tailor the instruction to individual students. We want to create a generation of thinkers!
DeleteThe more traditional way of solving math problems - the one where there's a prescribed procedure for every situation, where you cross out numbers and flip fractions upside-down, etc. - relies much more heavily on abstract thinking than the kind of math this article argues for. The "common core" method depends on kids reasoning with real-world situations, playing with numbers in tangible ways through pictures and objects, and coming up with their own methods for solving the problem. The methods they come up with may involve abstracting real stuff into numbers, because that's what math is, but it's far more developmentally appropriate than just giving them the abstractions first and making them use them.
DeleteJeremiah you make a lot of broad statements without supporting them. It doesn't sound like you have had hundreds of hours of training in teaching and so I see that your statements come from an ignorant point of point. Please take time to read the standards and respond using concrete or abstract examples. For instance 2.OA.3 is a standard that I don't support because.... Or 2.RL doesn't make sense because.... I look forward to having a conversation about specifics rather than broad statements.
Delete10th grader still failing math.....as much as I want it to be true, its beginning to become a bit hard to believe after the 2nd grade teacher that threw out the multiplication tables said "He will get it, it will click at some point and VIOLA! Sunshine and rainbows".....math is still a dark cloud and the only light is graduation.
DeleteBiblegal, I totally agree with your statement. We had to memorize and memorize and repeat and repeat our times tables, etc., and we were also told the reason we had to take from the column on the left and give it to the column on the right for subtraction. I can figure many everyday problems out in my head, and I don't need a cash register to show me how much change to give back to a customer. How many of today's young workers can say that? They don't teach the basics in school, and do not get our children (or grandchildren, in my case) ready for the real working environment. How are they going to be able to efficiently perform an everyday job if they have to figure out 200 steps to do it first?
Delete"Kids before age 12, largely, not all, do not think abstractly. To force them to do such is to force them to failure, end of discussion. Science, research proves that."
DeleteCan you cite your sources on this point? My experience with children would lead me to guess that they think abstractly *more* naturally than adults do. I'd like to give your argument fair consideration, but you're claiming the existence of evidence without showing it exists.
If a student needs to use the common core method then let them use it. However, most kids do just fine with the quick simple methods. Why do we need to make math more complicated for those kids that don't need an alternative?
DeleteWhen we were taught something new in math I remember the teacher writing a problem on the board and then explaining it step by step. It made sense, but every so often you had the one kid in the class who just didn't get it, so the teacher would have to draw it out or show more work to get the concept across. Meanwhile the other 25 students would be bored out of their minds and resenting the one kid holding up the class. The extra work the teacher would show is what I see when I look at the common core methods. It appears we are treating all kids like the slow kid in class.
Great Job, Leandra....Very well said!
ReplyDeleteWonderful job of explaining why many of our generation hate math. If our parents understood just that part of your commentary we would be worlds ahead.
ReplyDeleteThank you.
DeleteI never ONCE had a teacher say "just do it". Not once. And if any teacher said that to any of my kids, they never would have had the opportunity to say it again. Can you spell S-T-R-A-W-M-A-N? When I "took away" I totally understood why I was doing it. My children learned the same as me; some are better than math than others, but they all can figure a tip and aren't paralyzed without a calculator. How long before anyone figures out if this "new math" is better? Or worse? Count me as unimpressed, by both common core and your argument.
DeleteI also never had a teacher say "just do it". But I do see that other countries that adopted this "new math" back in the 60s and 70s did fine with it, and their kids do better than America's. America did its usual half-hearted job with new math and failed. With this "too hard" attitude around, and this ability of Americans to fool ourselves by thinking of three or four examples that supposedly prove the case while ignoring the millions of examples showing the opposite, it looks like America has already failed again.
DeleteMy kids aren't in school yet but as a former teacher, turned stay-at-home-mom it'll be coming soon enough. Thanks for explaining this to me now so I won't be so frustrated later.
ReplyDeleteCommon Core does NOT allow a student to work out a problem in the way that makes most sense to him. It forces a child to work it out the way the teacher wants so the student can pass a test. CC is trying to teach math on a 4 year spiral scale. While that will work for most other subjects the only way to learn math is to memorize the algorithm's.
ReplyDeleteI'm sorry you've had an experience that caused you to feel that way. It may be due to the learning curve of the teachers trying to implement the standards. I assure you that the educators in our state are being trained that student thinking matters most. If you read the actual standards (www.corestandards.org) you will see that they do not dictate any one strategy but instead encourage multiple strategies.
DeleteLeandra, I appreciate your respectful response, but your explanation does not make sense. I do not have much experience with Common Core, but from what I have seen with this issue in the news is that it is teaching children ineffective ways to do math that will not help them in the future. With your examples of memorization, these are not problems whatsoever if the teacher is even remotely knowledgeable in teaching. For example, with subtracting 17 from 453, you are not just memorizing to cross out the five as you have stated; you are taking ten from the 5 (because the 5 is 50) and giving it to the three, so it has 13. Now, 13 is big enough to take away 7. Is that really too hard to explain or understand? Is it not easier than the 10 step process of easy subtraction that was shown in the example of the frustrated parent? And with common denominators, if I have 1/2 of a pizza and I add 1/5 of a pizza, I do not get 3/7 of a pizza; that is less that 1/2. So, we see that we cannot simply just "add up the fruit", as you protested in your example. I need to put them in common terms so that I am adding the same thing. Is that really too hard to understand? Because mathematics is a logical science and every method of “memorization” has reasoning behind it, we can teach that reasoning easily to students in whatever example you present. Leandra, if you had teachers that were that inconsiderate while explaining things to you, I am sorry. But, their inconsideration does not change that fact that you can indeed explain these concepts understandably to a child, that "memorization" is not the issue, and that they are far more effective than Common Core's standards. Hence, we see that there is clearly no logical defense for Common Core’s inefficient procedures to explainable problems.
DeleteI still do not understand why you are trying to defend a system that is less effective and that complicates teaching. This is why indeed it is a political issue, because the government is imposing inefficient standards on our children and is not preparing them for the really world. Do you really think that someone will be hired for a job if they need to use a 10 step process for a simple mathematics problem? The government should stop trying to be a part of everybody’s life in every way and let the market produce the most efficient outcome as it almost always does, something that the government never does.
And with the children creating the teaching procedures: since when were children experts in mathematics? Shouldn't people with years of study, who should be able to explain the examples above as I did, make the procedures of teaching mathematics? Are we to the point that university education is so bad that children can teach better that university graduates?
So, no matter how what the so-called evidence, there is truly no logical explanation to complicate simple mathematics problems, except to put the government into even more spheres that are not delegated to its responsibility, which is also not logical.
It's all still memorization. Now, it's just a whole lot more to memorize to come to the same conclusion for what 2+2 equals.
DeleteBen, I in turn thank you for your respectful response. I do so enjoy positive communication over hateful comments.
DeleteIn response to your question, "Do you really think that someone will be hired for a job if they need to use a 10 step process for a simple mathematics problem?"
No, I don't think that person would be very successful. If that was the only strategy they had past say, first or second grade, then I would think them to be behind. And certainly, if they graduated high school using that method for a simple math problem, then they would not be considered a proficient math student or college ready. I'm not saying that these are the strategies we leave them with. I'm saying these are the strategies we allow them to start with because that is what they come up with on their own when they are present a problem at a young age. We then take them from there... and refine their own sense making strategies into much more efficient (simple) strategies. Helping them to see the short cuts in math after they've spent a considerable amount of time playing with the numbers and conceptualizing how they work.
The common core standards say students should be fluent with the standard algorithm for addition and subtraction by the end of the fourth grade. That means that by the time they move on from 5th grade, they should have a firm understanding of the way we did it. Then in fifth grade they become fluent with the traditional method for multiplying large numbers, and in the sixth grade they leave proficient with long division. We will not pass them on through to high school even without making sure they know and understand the short cuts. The "simple" methods are in many cases more efficient... but sometimes it's more efficient to look at a number and think... oh, that's just 25 away. Take for instance 100 - 75. The standard algorithm would ask that a student stack those two numbers, cross out the 1, change the 0 to a ten, then cross out the ten, and change then next zero to a ten. Then subtract 5 from 10 and 7 from 9. I want a student to look at that problem and say, "75 is just 25 away from 100, so the answer is 25" without having to use the steps in the standard algorithm. But in turn, when they encounter 12,453 - 8,562... the standard algorithm would be an appropriate strategy and much simpler than adding up.
I really just want students to think about the numbers before they assume there is only one way to solve it. I don't understand what's wrong with that.
But it is not memorization. It is in actuality the knowledge that numbers equate to items. By understanding that numbers equate to items or part of items it is fairly easy to understand and work it out. Also, when you use negative numbers adding two negative numbers if you basically take the two numbers and forget the negative for a moment you gain the knowledge then put in a negative. This is more in critical thinking then common core actually does! The example of 100-75 gives to many different ways. Take 100 counters in groups of 10 (again very simple as it is grouped) and understand that you are taking away 7 whole groups of 10 and half of 1 whole group or 5 counters.
DeleteI was very good at math as a child, and when I talked with my friends in high school, I found that my relationship to numbers was utterly different from theirs. I taught myself (or pushed my mother to teach me) at a rate my teachers found distressing (as I was generally asking questions a year or two ahead of the course material). I think mathematics is a beautiful language, one with perfect rules of grammar, and an inherent poetic potency. The equals sign for me was always a promise that something could be expressed exactly. Negative numbers were no more confusing than positive numbers, because the scale of values radiates out from 0, and all numbers are in relation to each other. Numbers are nouns, operations are verbs, equations are sentences, functions are semantic structures. I was always upset at the method of teaching "groups of counters" and "slices of pizza", because though it may be a good entry point, it is to me a very limited way of looking at the concept of division.
DeleteWhen we got to geometry, which I had not studied before taking it as a class, it made such fundamental sense to me that I read half the book in an evening. Symmetry, similarity, the relationship between length, area and volume, and the vague hints of abstraction bordering upon faith (pi) made sense not because there were rules I could follow to get the right answer, but because I could look at the room, the window, through the window to the quad, and see that geometry was the language we use to explain how we created the world we live in. Algebra is the crossword of mathematics. Trigonometry explained how the world moves around us. Calculus explained how the world moves through us.
Mathematics is not just questions and answers, and I have always, from the time I was five years old and asked "what about numbers less than zero", to the time in high school I lost my love of mathematics, due to being forced to memorize and "show work", and said "I am not interested in 'finding the right answer'", thought that the way math is taught in schools is bloodless and stale. Mathematics is applied philosophy, and if somebody had told me that while I was still interested, my life might have turned out very differently.
Do not believe everything your read in the news. Common Core is not a federal government initiative. It is a state initiative that began with a few states getting the experts in math and literacy together to write the standards. Since then, the federal government is pushing more states to adopt these, but it is not and was not started by the federal government. I work at a school that is 93% poverty and we teach Common Core standards. I would put our students up against anyone learning the traditional math algorithms any day of the week. They can explain their thinking, reason abstractly, and critique the flawed reasoning of others. It is impressive to watch kindergarten students who know very little English take on a problem like this: Mrs. Moore had 36 cupcakes. She wants to put 6 cupcakes in each box. How many boxes will she need? In the past, these types of problems were reserved for third grade and higher because, first comes addition, then subtraction, then multiplication, then division. Right? Wrong. The research shows that children think very differently about math than we do as adults. By allowing students to make sense of these problems, they do develop incredible ways of solving problems. I am happy that my daughter will be staring kindergarten this fall at my school and she will be prepared to think inside and outside the box, solve problems, and find solutions that make sense. After all, isn't this what all employers want?
DeleteYes! We have NO idea how jobs of tomorrow will look! 25 years ago we couldn't imagine some of the jobs college grads are getting today. We need to teach them to THINK-so they can become what they need to be tomorrow.
DeleteThe problem is, students are being forced to learn how to solve one problem in a PARTICULAR way which may not be the most efficient way or the way that the individual students understands best. My son understands the traditional way to solve 453-17. However, this is not acceptable in his classroom any longer. He MUST be able to solve it some other much more convoluted method to get to the same answer. I don't know if the "standards" dictate this, or if it is an implementation problem in our school system, but it is not helping him develop a love of learning. He used to love math. Now, it aggravates and frustrates him because he just wants to solve problems efficiently. He is being forced to set aside what he already knows, and use inferior methods to solve a simple problem. I just don't see how this is helping students, but I see how it is helping plenty of corporations.
DeleteTHERE IS NO SUGGESTED METHOD OF WORKING PROBLEMS OUT IN THE CORE!
DeleteSeriously people...its the curriculum that your school district has chosen to use. READ THE CORE. It is only a set of standards (skills listed that students should have at the end of each grade). How it is taught and assessed is up to the states and school districts. Sounds like you have a district issue with training teachers to me. So scary how lazy people are...love to talk but clearly haven't had time to read the core. http://www.corestandards.org/
"I do not have much experience with Common Core" ... but I'm going to develop a lengthy opinion about it anyhow and dismiss the experiences and comments of folks who actually work in the teaching field. [rolling eyes]
DeleteAlso, I'm glad that the last poster (March 27 at 7:12 PM) made the very relevant point that the STANDARDS developed by the states that are called "Common Core" are distinguishable from the curriculum that the individual states and individual school districts may use to ensure that kids are achieving those basic standards. Much of the overwrought criticism either comes from parents not understand the curriculum that's being taught, or, as Leandra says, issues in implementing the curriculum due, perhaps, to learning curves of teachers themselves who are coming to grips with the new curriculum.
I'm one of the adults whose math literacy is woefully lacking. This:
Delete"I really just want students to think about the numbers before they assume there is only one way to solve it. I don't understand what's wrong with that."
100, 1000, 100,000 times, this. I've spent a lifetime, so far, feeling like I'd never ever make sense of math because the "old" way that got drilled into everybody's heads didn't get drilled into mine. I don't have an opinion about Common Core (my mum - a teacher with decades of experience) thinks it's causing more problems than it solves, and she's my immediate go-to with real-world experience, so my instinct is to trust her judgement.
But *if this is how Common Core is meant to work*, I can't find fault with that. (I accept that it may well not be taught this way in practice, in some-to-many cases).
In response to 100 - 75: "I want a student to look at that problem and say, '75 is just 25 away from 100, so the answer is 25' without having to use the steps in the standard algorithm". I appreciate the logic of this thought, but unfortunately it is my believe Common Core does not encourage this level of understanding. In such a situation, I foresee a teacher encouraging a solution using the 'number line' method based on the concept of abstract solutions. The number line approach (start with 100, remove 10, remove 10, remove one, ...) encourages groupings, but fails in providing insight or understanding into logical groupings. Example: 10000 - 750. Using the number line approach leaves tremendous gaps in efficient execution (ie, what is the best number grouping to extract?). Some will start with 10000, and remove 10, 10, 10, 10, 10.... instead of say 1000, 100, etc. Because of this a Common Core teacher now must attempt to explain a logic behind number groupings, relate that back to the already abstract number line, and then hope there is inference to the common understanding that the answer is "9250" without much thought. In this example the best intention of using a common core abstract approach has a high probability to cause additional confusion and understanding. Whereas the standard algorithm, once explained can be used effectively (in my opinion) across all problem sets.
DeleteOverall I do appreciate the intent to teach critical thinking to solve problems, which is a necessary pre-requisite to advance both academically and in society, I believe the Common Core approach has a long way to go.
For my first year exposed to common core, I'm blown away. Helping second graders through a boost program has educated me on CCSS. Some of the approaches to solving math are difficult. This should not be used to pass or fail a student. It should be used to assess a students needs only based on my experience. I have read the literature on paperback regarding CCSS. Its very time consuming. Is this helpful with test taking and accomplishing the goals needed to be learned at the second grade level??
DeleteI read an article in Teaching Children Mathematics once about a young student who had not yet encountered multiplication. His teacher posed him a question, just to see what he would come up with. "There is a man holding three branches. On each branch are three cages. In each cage are three birds. How many birds are there all together?" While I, personally, could just say "three cubed is 27," or "three times three times three is 27," the student--who only had addition and subtraction to work with--came up with an answer on his own. If you add three plus three plus three, that's nine birds per branch, then nine plus nine plus nine gives twenty-seven birds total. The student even spent some time counting on his fingers to solve the problem. While this is obviously inefficient, the student used what tools he already had to solve the problem--and he used them correctly, showing that he understood what was happening even if he didn't have multiplication or exponents in his repertoire yet.
DeleteIf, however, I were to frame that strategy as something a teacher has taught students to do, and ask in conceited-parent-voice "Why didn't they just tell my son to use the multiplication algorithm I learned when I was little," or "Common Core is so dumb, why do they have to do it this long, convoluted way?" I could get so many people up in arms about it...
I think the problem here is that we are stating that it is a method ¨that kids come to naturally on their own¨. Well, apply that to any other subject and we have failed our children. If you let children figure out their own way to spell words and forgo the tedious memorization of phonics you will have left them crippled for future linguistics. Sure, maybe by 4th grade you are going to introduce the ¨old¨ way of reading, but by then you have created patterns that are very difficult to change. As a personal example, I was home-schooled. My mom was great at most subjects but math was not her forte. Therefore it was probably 5th or 6th grade before she realized that I had a completely different way of thinking about math. Sure, I did the problems, and even came up with the right answers, but my method was very different from what the workbook required. What was the result of this, me finding my own way and even coming up with the right answers using MY OWN method?? By the time I got to algebra and pre trig and pre calculus, where for most adults even the concepts get lost in memorized formulas, I was completely lost and inadequately prepared to complete the required assignments, because I had not learned the basics in a simple, systematic, yes, memorized way.
DeleteMy child is almost finished 7th grade and still has no clue when it comes to long division....just sayin
DeleteWe are sacrificing math fluency for complexity. In reading, we use the analogy of a person riding a bike. If you ride too slow, you don't have enough momentum to keep the bike rolling, so you fall over. If you are reading and you have to stop to sound out every word, you lose comprehension. Fluency in reading is essential to comprehension because what we read needs to sound as much as possible like speech. In math, if children don't know their multiplication tables and it takes them 20 minutes to balance an algebraic equation because they have to figure out what 4X6 is, they lose a lot of their ability to understand the equation. It's like a medical student taking human physiology before taking anatomy. Yes, they might make it through the class, but memorizing the parts of the body and their basic functions prior to learning the chemical makeup and inter-relationships of those parts makes it much easier!
DeleteBut doesn't that slow them down? When I was a kid my math timeline was like this:
Delete1st - Addition
2nd-Subtraction
3rd- Multiplication
4th- Division
5th- Fractions
6th- Integers
7th - Pre-algebra
So in that sense its slowing these kids down, because by the time they are becoming "proficient in addition and subtraction" a kid in the 90's was already proficient in 4 different processes rather then just 2. Plus, I remember doing long division in elementary school, probably the same year they taught division! Math is ultimately a language. Do you want your kids taking 4 years to learn how to say Hello and Good bye? its stupid. Granted, as an adult you truly only need to be proficient in Pre-Algebra. Frankly I think if more schools focused creating more well rounded, intelligent students by reinstating art and music classes instead of complicating basic processes that are only such a small part in the intelligence of children.
BTW - I am also a parent with 3 kids AND I went to public school.
Actually, you will find a lot of similarity with the common core standards to the list that you posted. The focus of K-2 is arithmetic but rather than separating addition and subtraction fluency with a small set of addition and subtraction facts is developed in K (within 5), 1 (within 10), and 2 (within 20 memorized, within 100 pencil paper). That's what they need to do fluently but they work on building an understanding of a wider set of problems than what they will be fluent with in a given school year. 3rd graders need to be able to fluently multiply and divide within 100 and add/subtract within 1,000. In grade 4 students need to add and subtract within 1,000,000. 4th grade is the beginning work of multi digit multiplication and single digit division. Those are challenging skills. Students have until 5th grade to demonstrate fluency in multi-digit multiplication using the standard algorithm. 5th graders do still learn about fraction operations in 5th grade. In sixth grade students learn about integers, but they have to demonstrate fluency with the multi-digit division and multi-digit decimal operations using the standard algorithms. In 7th grade students need to be able to fluently solve problems in the form of px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
DeleteI agree with you. There is urgency for students to develop competency with these skills. I remember when I did a field experience in a third grade classroom in 1998. I asked the teacher when the students needed to master their multiplication facts and she said they didn't really need to master them until 6th grade. YIKES!!! The timeline for fluency within the common core standards make much more sense. But also note that the scope of what I shared are the standards that specifically say "fluently." These are the essential fluencies that we need to help support all students in the learning of them because without these fluencies the students will be at a disadvantage as new concepts are taught. But as a more general concept, fluency should always follow instruction. Once a concept is developed, we need to help the students become more fluent with it so they can benefit from the automaticity fluency provides.
Simple math should remain simple. The biggest issue with common core is not making kids think. It's FORCING kids to (hopefully) critically think through problems when they really don't want to. Here's what is happening; They are being taught how to think through the problems, and are giving answers just to make it through the year, without actually gaining new knowledge. The issue remains the same with high school students... "What do I have to do to pass?". Not one student has said to me (as a math teacher) this is great. I like this better. Most hate it.
ReplyDeleteMy wife, who teaches elementary, has said that Common Core in Kindergarten is requiring students to be able to write in complete sentences. Kindergarten!!! Some come into school without knowing what letters are, and rather than blame the parents for not nurturing their children from Birth to 4 years old, the blame is put on the teachers, that "you didn't teach them enough"
Common Core is just the latest fad that WILL NOT LAST!!
It's not that kids don't want to, it's that they can't! Their minds are still growing, still forming. While some students can think critically at a young age, not all of them can. CCSS directly ignores this line of science and says otherwise. No educators wrote it, just people who stand to make a profit.
DeleteNot sure how to respond to this one. I don't have an argument for why teaching kids to think critically is a bad thing.
DeleteI do agree that a huge part of the struggle is taking kids who are in high school... who have been told exactly what to do for year's and trying to make them think for themselves. They don't have the foundation needed to be problem solvers. That makes me sad. What happens when they go out into the world and the problems they encounter aren't the same ones we taught them how to solve?
The implementation could have been much smoother, a lot of our older students are caught in the middle.
I have met 2 of the 3 men who wrote the Common Core Math standards. They are Math Ed professionals and practitioners. They were commissioned by the National Governors Association, not an assessment firm. I'm sorry you have been misinformed. I work with students day in and day out, helping them find a way to use some of the math I try to teach them. Holding a degree in math education, I understand that in higher education they will need to be capable of more than choosing the right answer out of 4 possibilities. I also know that in the work world there are no problems worth solving that come with an equation and exactly the information you need to plug in. I apologize if you student is uncomfortable explaining their reasoning and engaging in a little meta cognition at the end of their career in public education, but I would rather they struggle now than fail in college or life because they are ill equip to reason through problems and recognize when math could be helpful in finding the most efficient solution. Our school system was not designed to produce the workforce we need now and will need in the future. It is designed to produce the 15% management and 85% unskilled labor that we needed when it was designed in the 19th century. Our schools need to change and the Common Core is the best start I have seen in my years in education. I truly hope it helps to bring about some of the changes that our society needs.
DeleteIt sounds like a lot of you are underestimating the abilities that children have. They can do AMAZING things if you allow them to think for themselves and struggle through something with the support of their teacher or parent. I also believe that kids pick up on your negative attitude toward the new ideas. When their own teacher or parent is constantly pointing out that the math homework needing to be completed is "crap" why is it a surprise when they also have that attitude and in turn become more frustrated with their work. Give them some credit. They can do hard things!
DeleteI disagree that people cannot become problems solvers without this common core curriculum. I am 50 yrs old and do fine with my math skills. In jr high I took geometry, Algebra, then in HS, Calculus, but didn't want to continue w/ Calculus 2. Math isn't my thing, but I use it constantly, daily. Leandra, you have been very kind in your responses, but I think you are making all of us who came before the Common Core out to be idiots- or at least that is what this last statement said to me when you said:
Delete"I do agree that a huge part of the struggle is taking kids who are in high school... who have been told exactly what to do for year's and trying to make them think for themselves. They don't have the foundation needed to be problem solvers. That makes me sad. What happens when they go out into the world and the problems they encounter aren't the same ones we taught them how to solve?
So what about all of us who were never taught the Common Core? I saw a CC example and it took me a few minutes, but I figured it out. I still don't believe in the "Common Core." I see no use, no sense and critical thinkers will continue to be critical thinkers and problem solvers with or without the CC. America is not ready for this, and the people will revolt on this CC debate, I am afraid. America is already in a big mess, this just adds to it. But this is only my opinion- an old school critical thinking, problem solving, wave making, glass ceiling breaking woman. (GDavis)
Amen, GDavis. Apparently, all the successful people in the world before Common Core are just posing as successful people. How in the world have we managed to even feed ourselves? This is all so ridiculous. I'm afraid you have fallen victim to a snake-oil salesman, Leandra. I expect you will suffer much embarrassment in the future from posting so much support for the latest failing fad in education. Maybe it will comfort you that you will have plenty of company as you aren't the only one who has bought this bill of goods.
Delete@GDavis: "Leandra, you have been very kind in your responses, but I think you are making all of us who came before the Common Core out to be idiots"
DeleteWell, if you read her initial post, she actually includes herself in the group of folks who "came before Common Core" when she's explaining why an approach that actively fosters a better conceptual understanding of math is preferable. I don't get the impression that she considers herself, or any of us, to be idiots; she's simply making a case, as a math teaching professional, that maybe, just maybe, we can improve on how it was when we learned things.
I, too, am a Math instructor and was very successful in school and afterwards so you might say that memorization and low level math instruction was successful. I didn't discover how woeful my math knowledge was until I attempted to develop understanding with my students. Why? is a question we don't often ask in math class but it is necessary! Of course some students fight it because it's easier if they are just given a problem or formula to solve in a certain way, usually the one that I just taught them. Thinking involves much more effort and some don't like it. I agree that the older they are, the harder it is to implement. As their teacher, it's not my job to make them happy or comfortable. It's my job to make them think, explore, question. I've taught this way for the last 10 years (and most of my students DO love it) so I don't see this as a CC topic. It's just good math instruction. To me, CC is the way that we make sure all our students are taught at the same high level. Good article. People, open your minds and want more for your kids than you had.
DeleteI can't comprehend why every parent against Common Core lauds keeping low standards for kids. Learning is difficult at any age and level. It's ok for kids to struggle a bit. It's ok to not get it right away. Resilience/ grit is one of the best indicators for success later in life.
DeleteMy kids go to a private school and have been learning math this way from day 1. Now in 4th and 6th grades they pick up new concepts and more and more difficult math problems easily because they understand how math works. They are even able to adapt the traditional algorithms we learned as kids easily because they have such a strong understanding of math concepts.
I'm sure as a teacher it is hard to switch gears - teaching one way for so long and then having to learn something new. But why expect so little from kids when they're actually capable of so much?
I do agree that Standardized Testing should be eliminated. Or at the very least, only given 3-4 times throughout a child's educational career.
Leandra and Jacob- As a math teacher AND parent who likes Common Core and agrees with EVERYTHING you both said, THANK YOU! I get tired of trying to explain to others that traditional math is not "simple" for everyone and how and why it is failing students and that telling is not teaching and that Common Core is not just about doing something different, but about learning when sttategies are most appropriate and so on and so on. It is so nice to see others, who, might I add have more experience and research- based knowledge with math education than the critics above, who recognize the need for change.
DeleteWhy would I make a child take the long way around to get to the bottom number. Sorry 5 + 5 = 10 no matter how hard you make me work to get to it. Most children learned very early that they have 5 fingers on each hand and they can count them to get there if need be. Children have been doing the common core practice and just never had to write it out and sorry people I do not understand what was ever wrong doing it that way. Get rid of the extra work to get to the answer let it be like it always has been, use your fingers or tick marks what ever but why should you have to show how you got there as long as the answer is right. Why do we need this and yet never bother to teach common sense, which is what the work force needs. They do not need people that are book smart but can not think for their self. I really hate having an employee look at me when I ask a simple question that should be answered with a simple sentence. Really teach them what they need not what they already figured out in kindergarten. Why are we letting them use calculators rather than their minds also. Have never understood how I can go into a store and buy something for $1.50 and I gave the person behind the counter $2 and the computer is down and they can not figure out they owe me $.50 really what have we done to the younger generation.
DeleteIf you can't memorize why 2+2=4, then you're really not cut out for math. And I know that a lot of people want to do well n school without any effort or memorization and have As given to them merely for having a pulse, but doing well in school require memorizing procedures, just like in History, Geography, Spanish, English, or any other subject. So, if you're so opposed to memorization, clearly school isn't for you either.
ReplyDeleteBen,
DeleteThat's a straw man argument. No one's opposed to memorization. Rather, the poster is simply making the rather noncontroversial argument that memorization alone doesn't necessarily foster a strong conceptual understanding of a topic.
Just curious Ben, in your current job do they value your ability to memorize facts without actually applying them to anything, or do they value your critical reasoning skills?
DeleteBen, consider some study on how people (children in particular) learn. While there are bit of facts we do "memorize," and appropriately so, most mathematical learning is not this sort of "social knowledge," rather a logico-mathimatical knowledge that is necessarily generated by the learner as they organize experiences. When viewing mathematics as only things to be memorized, it is sensible to make your critiques. But math educators recognize that people learn math by doing math, not having it told to them. This fact is well-known, owned, and accepted by mathematicians (see Arnold Ross https://twitter.com/blaw0013/status/449674141847654400) and math educators (see: all) alike. A first read on how we learn math might be Constance Kamii's "Young Children Reinvent Arithmetic." http://www.amazon.com/Young-Children-Reinvent-Arithmetic-Implications/dp/0807739049
DeleteBen, I don't know where you seem to be getting stuck, but if you can't see past rote memorization to critical thinking skills, you needed CCSS when you were in school. What I haven't seen here in this thread is the CCSS component of social emotional learning and college to career readiness. We're taking kids to think and process beyond, not instead of "2+2=4". I hear the most negativity from those who so clearly don't understand it. Learn the facts.
Delete"I do not have much experience with Common Core, but from what I have seen with this issue in the news is that it is teaching children ineffective ways to do math that will not help them in the future." I suggest you research Common Core and not just buy into the political interpretation you hear on the news. Believing everything you hear on the news without researching the facts is kind of like being taught that 2 + 2=4 without ever being taught WHY 2+2=4. I teach my students to be critical thinkers who are not satisfied until they understand why they got the correct answer. The previous math standards being taught in most states gave students a very shallow introduction to many math concepts without allowing time to provide them with a deeper understanding. We introduced division and then had to move on to the next concept before most students mastered division. This results in the majority of students having a "swiss cheese" education that is full of holes of missing information. This missing information is supposed to build the foundation for the harder concepts learned in high school math classes. Common Core requires deeper understanding of fewer concepts at a time so that students have the foundation they have to be successful later in school and their career. If they gain this understanding in the beginning, they will understand why they are doing the standard algorithms they learn later that our generation learned first...but they will having a deep understanding of why those algorithms work and what to do if they miss a step and get the wrong answer.
ReplyDeleteSaying "If you can't memorize why 2+2=4, then you're really not cut out for math" does not solve any problems. Everyone needs to know math, and it is our job as educators to see that every student that leaves our classroom understands math, whether they are "really not cut out for math" or not.
Well said Erin. Thank you for your insightful explanation.
DeleteThis comment has been removed by the author.
DeleteI completely disagree that that was well said or insightful. First, the fact that you attacked someone for not being completely involved in Common Core is ridiculous. Do you really need to be a teacher or have a student in Common Core in order to form an educated opinion? Stop attacking people just because they aren't teachers and for critically thinking about issues when they are presented to them.
DeleteNext, what you have stated is false about "swiss cheese" education. As seen in the comments below and with personal experience, most schools before Common Core did not give this type of education. Further, this is exactly the type of education that Common Core gives. Just because your school did not teach well does not justify us changing the whole system into a guaranteed failed system of teaching. Clearly, the solution would be to fix your school, not make hundreds if not thousands of other schools teach ineffective and confusing methods.
And, Erin, some people are not cut out for math. We can want to not offend people all we want, but it's the truth. The fact that everybody needs to learn math does not change that reality. I don't want people pursuing math if they can't memorize why 2+2=4 . Maybe that's a Common Core standard, but logically it doesn't make sense.
So, you can defend it all you want, but anyone who values intelligibility, effectiveness, and is sick of trying to baby our kids from hard work and make everything easy for them, will be opposed to Common Core, if they're directly involved with it or not.
" Do you really need to be a teacher or have a student in Common Core in order to form an educated opinion?"
DeleteYes, if you're going to oppose something, you should have some kind of vested interest - or at least some knowledge - in what you're opposing.
Matt I disagree. I think as a parent it's important to be educated about the core, I think if you don't read the actual standards and understand the reasoning behind the learning goals it's very ignorant to form a judgement.
DeleteI think many parents were unaware before all of this that there even were standards every year that teachers followed. Teachers have always had standards, and found their own way to implement them and tailor them to the needs of their students, and good teachers have found ways to make it fun, creative, and hands on.
Many people do say they don't like math, and I believe for many of them it was they way it was taught, (or ultimately the quality of their teachers, but that is a whole other rant.) :-)
I did math as I was told in high school, even through calculus, but I never had a teacher explain WHY until I was in college. It was like a light bulb turned on, and then I was able to explain things to my daughter in 5th grade that was struggling in math (yes, before common core there were students and parents who scratched their heads at math assignments) Now she's in the 8th grade, doing well in math, and feeling proud to go into honors math for 9th grade.
I believe other parents are stressing out because it is different than how they were taught, and many schools have done a poor job of explaining what they're trying to do. The point of these standards was to look at what skills students need by the time they reach college and work backwards from there. To me that makes sense. Rote memorization doesn't necessarily lead to quality of math abilities, or instruction. If you look at the National Council of Math teachers, people who research the best ways to teach math, they want increased focus on reasoning skills. Don't we want students who can reason and do problem solving as opposed to robots who know how to regurgitate the correct answer?
Did you need to be a German citizen to be concerned about the Holocaust? Or be a Jew? Did we need to know a Haitian to be concerned about the earthquake a couple years ago? Did people need to be African American to be concerned about the civil rights movement? Or the slave trade a century earlier?
DeleteClearly, my argument wasn't that we can be uninformed. But Erin's comment bashing the earlier guy who was saying that he doesn't know everything about Common Core is ridiculous. The mere fact that it is our country and education system allows and requires people who aren't teachers of parents to need to be concerned about the issue. So, if you really think that you need to be a teacher or a parent to form an opinion, you're excluding many people who are interested and concerned about the quality of education and therefore, to a large extent, the quality of our future work force.
Clearly, you can have a "vested interest" in the subject matter without being a parent or a teacher. Excluding all others who educate themselves concerning it and consequently have an opinion is unfair, haughty, and bigoted.
She was taking issue with the fact that, rather than bother to actually educate himself on it, he was opining based on misconceptions he had gleaned from the news.
DeleteOf course you don't have to be a teacher or a parent to give a hoot about education in our country -- but, just as with any other issue, folks need to do their actual homework before popping off half-cocked.
I am currently teaching common core math to second graders. You should know that addition fact fluency, which is timed, is required in common core. Subtraction fact memorization is also taught, but not timed. The biggest struggle I see with common core is that while some students are standing up in the front of the room sharing their newly discovered methods of solving a problem, other students are getting very confused. We are expected to let students explore on their own, then force them to use the strategies they will have to use on the test. For example, go ahead and solve 23 + 64 by breaking apart numbers, or drawing a picture, because that's what makes the best sense to you. But on the test you better know how to draw a base ten model or solve it on an open number line or you'll get points off. They are learning so many different ways to solve a problem, for the intent to help them understand how numbers work, that they are getting really frustrated. In the meantime, their parents are teaching them the algorithms at home before they have a concrete understanding of what they are doing and why. Bottom line, common core was rolled out before it was field tested, before teachers were given training, before curriculum and assesments were completely written, and before resources were made available.
DeleteIt would be nice to hear an argument against the Common Core that is, for once, actually against the Common Core instead of some made-up imaginary opponent pulled from fantasy and thin air.
DeleteI won't get into common core - I will let my highly educated teacher husband fight that front. What I take issue with is you saying that no one would ever say "reading just wasn't for me". UM - YES - I hear that ALL the time from people my age. They got through at the bare minimum because THEY HATED reading. And now, as long as they can read enough to pass the test, they graduate. They still hate to read. I have been asked if I legitimately have read all the books on my shelf and if I did it because someone told me "I had to.". It happens all the time. We have to find a way to nurture a love of learning in the classroom, rather than make it a "know this for the test!!", "do all the steps!!", "just get through it" mindset.
ReplyDeleteYou are absolutely right. I apologize for the way I phrased that. What I was trying to get across was that it's not as socially acceptable to say, "I never learned to read, I wasn't good at it" but it is acceptable to say, "I'm just not a math person, it never made sense to me." Slightly different in that, one has to do with an ability to read vs a like for reading. Like you said, I know many people who don't like to read, but they can read. On the other hand, I know many people who don't like math and often times, they can't do much of it beyond the basics because it never made sense to them.
DeleteI also agree that we have to get away from the "know this for the test" mindset. Standardized assessments have caused a teach to the test mentality. It makes me sad.
I should say "most can read"... and if they can't they often hide it.
DeleteForcing students to take more steps to solve an equation does nothing to "nurture a love of learning". I posit that it does more to nurture a contempt of learning. We all had story problems, as part of our learning, as children. No need to turn everything into a story problem.
DeleteAgain I agree. Problem solving through story problems is definitely a big part of what's happening, and I'm not a proponent for "forcing" kiddos to take more steps. Just want them to make sense of what they're doing and sometimes that means starting with more steps. In the end though, they will certainly understand the meaning of the shortcut methods we learned.
DeleteMental math strategies, estimation, and just number sense in general are also a big piece of the puzzle. It's not all about story problems. Student thinking matters most. That's what I believe.
I've heard college math professors say they get students in beginning algebra classes that still freak out when they give them story problems. They are more comfortable with cut & dry 2+2=4 problems. Being able to use logic and reasoning to solve problems is crucial! If a student can't understand that having 2 apples and getting 2 more is the same thing as 2+2, then they don't really understand the problem. Look at most math books, usually there's been only 2-4 story problems at the end of a lesson, how well has that been working?
DeleteI have a third grader being taught using common core. He has a lot of homework using story problems. He doesn't love them, but the story problems are what save them from being asked to think strictly abstractly.
Delete"It's not all about story problems." So true. But it's not all about what "methods" or "strategies" are taught either. As youngsters, kids learn and develop so much by PLAY. That's a kid's true job: to play. And when they play more as little ones, they're better equipped for thinking and problem solving and learning when they're older. But let's step back a little bit and visit this whole 'learning' business... If student thinking is what matters most, then what sense does it make to spoon feed them strategies on which they will be tested across-the-board? It seems to me Common Core is a bit myopic; it's meaning well, but failing to see the impracticalities of a real classroom (with almost thirty kids, five of whom have IEP meetings (three of those have different 504 accomodations), required lunch duty/bus duty/whatever, projects to grade, lessons to plan, documentations to record, parents to call, discipline problems to solve (without any real authority, btw) - oh, and teaching too. Common Core is a standards-based-system trying to act and look like the holistic, oftentimes child-led education one might encounter in a prestigious private school or a homeschool setting; but as a matter of course and reality, neither of those settings is reasonably-compared to a public school setting. ...It's requiring pigs to make sense of how to put on lipstick their own way -- and then proclaiming: "It only looks bad when the wrong colors are implemented. As well, when it comes to beauty, it's what's on the inside that counts." ?
DeleteLeandra and Erin, I too was one of those kids who had trouble getting math from as far back as I can remember, and I think the common core approach would have made it a lot easier for me. I have always used unconventional ways to get my answers and I wish someone would have guided me using more of a big picture approach where connections between the abstract and what it represented were made. Your example of an alternative way of calculating 100 - 25 is exactly the kind of thing I do. I am looking forward to Common Core not just in regard to math, but in other disciplines as well. It's long overdue.
DeleteWhat's wrong with not being a math person...or reading person. That doesn't make you less valuable as a person.
DeleteLet me tell you... my 7.5 year old LOVES math. He does it in his head, he does it all day... he calculates how much time it will take to get somewhere at a given MPH and whether we have enough gas etc. He LOVES Khan Academy. What does he hate? He hates the ridiculous common core math sheets they force him to do. How many times I have stared at the same paper, with as much contempt or more, saying "I don't get it, either" or "just draw the things out they want you to draw out" (because he's being forced to draw out 100 items and "regroup" them so the teacher can know he understands regrouping... I mean, they only spend 2-3 WEEKS on regrouping, OMG! No wonder he hates math in school. And if you think that my story is unique, it's not... I know of another boy two grades ahead of my son who also has come to hate (school) math, THANKS to Common Core. I am sure these two little boys are not alone. The idea that showing all the reasons we can regroup is not going to make a whole lot of people great at math, or love math. Instead we'll have someone who becomes a mathematician who can look back and smile that they always knew why they could regroup? Huh? Is the Common Core math we are teaching based on what other countries with excelling math students are teaching their kids? Not a rhetorical question, really, because I honestly don't know. But if it isn't, it makes me wonder why we think this is going to improve our kids' math abilities?
DeleteThanks Anon at 8:31. My thinking exactly. My daughter had to read To Kill a Mockingbird in 8th grade. I know for a fact she's the only kid who finished it, and the teacher was furious because she finished it in a couple of days. She didn't go through all HIS ridiculous steps on his time frame; instead she just read a book and loved it. To this day she carries a copy in her purse.
DeleteTo Anon with the 7.5 year old... It makes me sad to hear stories like yours about the misguided implementation of the Common Core. Having met the lead author of the math standards, and having worked with a large group of teachers and math leaders to develop training on the CCSS under his guidance, I do not believe that it was ever their intent to force children to draw pictures such that you are describing. As a matter of fact the following is a kindergarten standard:
DeleteCCSS.MATH.CONTENT.K.OA.A.1
Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
You can see that it expects students to represent addition in subtraction with a variety of options listed... equations being one of them. The research I've read (Teaching Children Mathematics - Levi et al. and Teaching Developmentally - Van De Walle) indicates that when students are posed a problem that they don't know how to solve, they will naturally draw pictures. This can be backed up by my own experiences. We then build from their understanding to develop the more formal mathematics that they are making sense of with pictures.
To answer your question, "Is the Common Core math we are teaching based on what other countries with excelling math students are teaching their kids?"
Yes, the authors spent much time researching and visiting other high performing countries in an effort to develop the standards after what they saw happening in those countries. Here is a video of Phil Daro, one of the authors, speaking about some of the changes they saw were necessary based on what they saw in other countries: https://vimeo.com/79916037
Well I am 50 yrs old, I hated Math then and I hate it even more now :( I hate reading ( even though I can read and majored in English!) I am a Visual person. I am attending school now and they are teaching CC and I still can't get an answer I understand as to "WHY" it's done that way and "HOW' did you come up with that? I can see where you get the answer correctly but most explanations is "this is this so that is that. HUH??? I still do not get where you came up with the answer except you "memorized" something or you just Get it! I believe it still depends on each person. I see it with my kids ( 5th grade & 9th grade ADD/ADHD kids) the 5th grader who has some Resource classes is doing far better because he gets the "extra help" and he loves doing the math and getting it correct. He explained to me how to do Order of Operations where as my 9th grade daughter was a total mess in explaining and is failing :/ She too will not read ( she can, she just hates all those words running together! How boring, No pictures, no visuals!!) CCS may be a good concept but FORCING it on every student, the ones who have trouble with the Simple is wrong! I do not want MORE steps to get my answer I want to know why, how and just see every problem and know exactly why and how! I can understand the procedure but then you mix the numbers up and oh well, I cannot use the procedures you just showed me to work it out :/ My dad was/ is an Engineer and Yes, I hate math!
DeleteI was one of those kids who "didn't get math". I still hate it - other than counting money, figuring tips and weights and measure I don't use it on a daily basis. I would have loved to know "why" and had some other methods to come to a correct answer. The memorization method did not work for me at all.
ReplyDeleteI was taught math over thirty years ago. I always had a certain contempt for memorizing things. That really hurt me in anatomy class. I also taught math from 80-82. The idea of teaching why is nothing new. I find the requirement to teach things a specific way burdensome. I also don't like the idea of being tested on intermediate steps. I have a problem with needing to communicate in writing how you do math. Math has its own language, numbers. A child who has shown her work has communicated all she needs to to show that she know how to work the problem. A child that loves math but hates to write has now seen his favorite class ruined.
ReplyDeleteMy daughters high school teacher insisted that problems be worked the way she had taught them. I always felt that this was a bit much on the "Memorize an algorithm and know where to use it." side of things. I sometime helped my girls with their homework, helping them think through other ways the problem could be solved. This was generally resisted. I did not think they had a good math teacher. Whatever she did worked. My oldest daughter was not gifted in math but still did quite well. My middle daughter is graduating from college with plans to go into bio-medical research. My youngest plans to major in engineering.
The CC doesn't require that things be taught a specific way. If you have a beef about that, your beef is with your state or your school district, not with the CC.
DeleteAlthough I see the writers point, they assume that we (I'm 40) were taught in the "strike the number out, just do it!" or the "just invert the faction and multiply, just do it!" method. I wasn't. I started AP math in JR high, were I was taught "why" you strike the number out, why you reverse the fraction and multiply, so that made perfect since to me. Math is built on simple core standards (add/subtract), as it gets more complicated, you can break it down into the simple core standards. IE, multiplication is just a repetitive addition. Granted I'm sure there are reason to do core knowledge "new" math, I just see why the old way was scrubbed just because we couldn't teach our kids why we did old math the way we did.
ReplyDeleteI completely agree -- I am 32, and the beginning of this article reads like something my grandparents experienced. I shared it with my father, an engineer, and he could not recognize his own math education in this author's version of events at all. In fact, the way my colleagues teach with the Common Core is remarkably similar to how they've always taught -- good teaching is good teaching, especially when it comes to math. Trying to make a case for "new math" while completely misrepresenting most adults' experiences in learning math makes the author seem out-of-touch and, sadly, distant from current and past classroom practice.
DeleteLeandra,
ReplyDeleteI have to preface this with stating that I don't have much experience with common core. I am an engineer that uses math and science every day to do my job, so math is something very important to me. What I struggle with is that fact that for years we have taught math in a certain way. This way has produced brilliant mathematicians, scientists, engineers, etc.. In recent years we have seen a decline in the ability of students to understand math, as well as all the other fields of education. So what is the source of this problem?
Abruptly changing the way we teach children math says that there is an issue with a system that has worked for years, which I can't agree with. Children are capable of learning math the way we all did growing up, just as children are capable of learning math the way CC suggests. Most of us are the fruits of that labor. The issue I have is that I don't think CC addresses the real problem, which is why has a system that worked for years stopped working? Until that question is answered, math being taught the "old way" or using CC will not be successful.
As a fellow engineer... math really didn't make sense until a mentor of the slide rule days turned on the light bulb for me some years after uni. The gurus of the early Apollo era were forced to understand math from the get go or they'd be dead in the water... us calculator guys (granted, my era only had 4 bangers) combined with decent memorization skills could fake it for years. It didn't help that not one math teacher could explain why... it was always you just need to know this. The worst part in all of this were the insane attrition rates... 400 in a university class to start, and by the end of the year, 30 would pass. While not all were engineering / science focused, there is no doubt that many potential scientists and engineers washed out because of bad math skills going all the way back to elementary school.
DeleteThe "common core" math is not new. I love that you are defending it. It works. My inner city school district has been using methods like that since 2002, through Everyday Math. I was using alternate methods with my remedial math kids from 1983 to 2000. But Everyday Math taught various ways to solve problems that even I didn't know! It was great. I operated by the premise in the old days, that if the kid doesn't get the regular way by 4th grade, they had to learn a different method. But learning the different methods as you go along is way better. I disagree about having to learn the traditional method by 4th grade, as they really should use the "traditional way" only if it works for them and when they are ready. When they are comfy with math, they'll most likely want to learn the short way (traditional). That happens at different ages at different ages. If you start with manipulatives for first, second, and third grades, moving to pictorial representations in third grade and then to more abstract ways like partial sum, partial product, partial differences, there will be much greater understanding and kids will not be afraid of doing the math. Our scores were way better that they had been when I retired in 2012. My fifth graders were not afraid to tackle problems and they could use whatever worked for them. The 6th grade teachers used to thank me every year when they got my kids.
DeleteI still remember my algebra teacher becoming so frustrated with me because I did the work in the way that made sense to me --- but not to him.
DeleteI am an excellent elementary math teacher, as judged by my test scores, and my students' praise and liking for math. I give credit for my ability in part to MY fifth grade math teacher, back in 1962. He discovered that I had memorized the division algorithm, but did not understand at all, and went looking for new ways to teach. He found the partial products method, advocated by what was then called "New Math", and suddenly, it all made sense. He taught me that math had to make sense, and to work at it until it DID make sense. As a teacher (now an intervention teacher) of math, I have always presented alternate ways of achieving the same end, along with manipulatives and pictures.. Imagine my delight when one of our fifth grade teachers was explaining to me this new method of teaching long division that was part of a common core activity book. It was partial products division! The pendulum swings back. And to address the issue of what happened, why there has been a drop in math ability-- I'd blame it all on NCLB. Pushing standards down on lower grades, requiring fifth graders to understand the surface area of rectangular objects, asking sixth graders to compute the probability of dependent actions. . . Information that for me was high school or college, pushed into 5th grade, and then we wonder why they can't learn it. Really? The legislators need take courses in child development, or better yet, actually listen to real teachers instead of educational publishing companies.
Delete"In recent years we have seen a decline in the ability of students to understand math, as well as all the other fields of education. So what is the source of this problem?"
DeleteI agree with Anon the excellent elementary math teacher on your question of what caused the decline. I believe it has been the implementation of yearly standardized assessments. Several years ago standardized testing was not tied to anything... it was just a way to collect data, but not anything teachers felt pressured to perform to... it has evolved over the years to and "end of course" assessment at every grade level. Teachers wait anxiously to see their scores published every summer and to get a peak at the released items as well. The more they study the released items the better their students perform on the test because they know the problem types that will included... for the last several years much of the staff development offered around math instruction included strategies for answering multiple choice questions, and disaggregating data to determine our weakest area and then rearranging our curriculum so that area could be taught directly before the test. Teachers have felt so much pressure to "cover" everything that teaching has changed from helping students understand why and how things work to just teaching them an "answer-getting" strategy (https://vimeo.com/79916037) to help them get past this problem so they can pass the test. I have put forth a lot of effort in my recent trainings to try to help teachers see that if they will help their students to be critical thinkers with a deep understanding of the concepts at their grade level then it won't matter what types of problems are on the assessment, the assessment will take care of itself. Believe it or not, I get a LOT of push back. The assessment means everything to teachers because the higher ups have made it so. Even if they want to take time to develop understanding... the entire 3rd quarter becomes stop, drop and test prep. Worksheet after worksheet of here's how you solve this type of problem, and here's how you solve this one. When I tell teachers they can spend more time on addition and subtraction and not worry about concepts like probability in elementary school, the response I get is, "Yah, but it's on the test." Sad but true.
This is my problem with the system. My 4th grader is very good at math, she works the problem and gets the answer, and then the teacher tells her she has to do the same problem 4 other ways or she hasn't mastered it. She's not exploring the ways that make sense to her she is memorizing 4 additional algorithms and doesn't understand why. It is terribly frustrating for her and turning her off math altogether. When I try to help her think about the issues in the problems she gets frustrated because I'm not using technique #3 that she has to use on this pass of the problem so I am not helping her. Understanding is not being taught.
DeleteI don't see any value of adding more steps. Memorizing a few tables is a bad thing? I've had to memorize tons of stuff to get through school. I've seen some of the first grade questions from CC and doesn't exactly seem like a critical thinking age.
ReplyDelete100-75 is only 25 away. That was obvious to most everyone back in the day before CC.
By the time my 3rd grader graduates from college, all the jobs that only required an ability to memorize facts or steps will be automated. Good luck finding a job if all you are taught is rote memorization! I love watching her conceptual understanding develop with the new standards. Also, my 5th grader passed all those timed tests with flying colors, yet if you ask him to add and subtract beyond the basic facts, he uses his fingers to count. I only wish he had the same instruction my 3rd grader is now receiving.
DeleteThe standards do ask students to develop fluency and automaticity with basic facts. You'll also see algorithms come into play. The key is that this automaticity grows out of wide experience with place value, the relationships between the operation, and the properties of operations. Check out the standards and you will see support for your points. But let me also say don't dismiss a first grader. I'm constantly impressed with their thinking :-)
DeleteNo one's abolishing memorization. The difference is that CC includes more activities to develop understanding of what they memorized so it can be generalized to problems they haven't seen before. It's great that you're happy doing the same problems you did in third grade, but this isn't a good reason to block the rest of America from catching up with the rest of the developed world, where standards like the CC have been in place for decades.
DeleteAnd 453-17...I wasn't taught to "just do it"
ReplyDeleteAs you say you can't take 7 from three so you add 10 from the previous column, now the 50 is a 40, and you have 13 now. That "why" was very clear to me and everyone in my class. I had excellent math teachers and was never told to "just do it" without an explanation why. CC is just another way to do it. Better for some perhaps.... and worse for others perhaps.... but just another way. We have much more problems in our schools than finding different ways to add
Oh give me a break! We were taught WHY too. We just weren't made to draw thousands of circles and write out every answer as if it were a dissertation for a Phd.... TRY AGAIN.
ReplyDeleteHa ha ha. I couldn't agree more.
DeleteBest comment here.
DeleteWhat difference does your one little case make? Say something that applies to the majority of Americans.
DeleteI've got a daughter in 1st grade and a daughter in 3rd grade. So I have a pretty decent insight into what they've been doing in common core math. I will address only the 3rd grade here because this post would be far too long otherwise. At the start of the third grade my daughter had not even started multiplication. Couldn't multiply 2x2. In the semester before Christmas of this year they had done multiplication including what I would consider some very complicated (for 3rd grade), multi-step, word problems. Then they moved on to division for like a week and a half, then perimeter for a couple of days, then area the next, then fractions for like a week, then they were back to multiplication, dabbled in division again, then some stacking of blocks thing, then graphing and more word problems. Now, I am not a mathematician...but this seems mindbogglingly silly. They are barely given a chance to learn their math facts, much less master them and they've moved on to something else. This week my daughter brought home algebra equations with variables. Sure they were basic, but come on...they're 8 and 9 years old! Should I expect calculus in 6th grade? And I would like to mention something to your point about they are teaching the "understanding" rather than the memorization. They are teaching 20 different ways to solve 9x5=45 instead of just asking kids to memorize the math fact and moving on. They are making basic math much more complicated than it needs to be and by adding so much "fluff" they are forgetting to teach and kids are failing to understand the very basic. If they don't have a solid foundation they will stumble in math for many years to come. This will definitely NOT teach a love of math. More than teaching a deeper understanding it's just leading to a lot of confusion and frustration and my daughter has an A in math AND has known her math facts since about a month after school started! A lot of her friends are really struggling. Many of the problems are followed with the phrase "explain your answer". I don't know about you, but back in my day I HATED having to "explain my answer". One of the problems on my daughters worksheets actually said 5x9=___. The next line was "explain your answer". Seriously? Um, because 5x9 =45? Then there was these blocks in columns and rows. They had to write an equation and somehow the takeaway was the 2x5 does not equal 5x2. Whaaaaattt? I had to email the teacher on that one because evidently I've had that wrong for all these years. Leandra, I would suggest that you consider that you are a math specialist. You love math. Perhaps that is why you seek this deeper understanding. But these are very young kids. In practice this "understanding" is causing alot of confusion. Understanding comes with practice and experience. If kids don't know the basics, they will never grasp the understanding. I was quite content growing up knowing that 9x5=45 because 9+9+9+9+9=45. That's all I needed to know. (continued on another comment...)
ReplyDeleteWhy didn't you explain that 9x5=45 because 9+9+9+9+9=45?? How is that not an acceptable answer? Those blocks in columns and rows were probably an array (a common math word that adults should know) and understanding that 9 rows and 5 columns would make 45 blocks. This will help build not only a foundation of multiplication, but geometry as well.
DeleteIf you don't understand, you should probably go do some research and try to understand.
I'm with Sandra! Help!
DeleteThank you for the word I couldn't place at time of writing. Yes, arrays. I articulated what I was trying to say badly. What I was trying to communicate is that teaching an 8 year old that JUST learned to multiply that 2x5 is not the same as 5x2 is strange. Also, I would like to say that both me and my daughter LOVE her math teacher. She is fabulous. This is not about the teacher. This is about the curriculum.
DeleteIt's interesting that you say that because Common Core is NOT about curriculum, it is about teaching strategies and good teaching. At least that is what every educator I know has been told, including myself.
DeleteSadly one of the problems with implementing Common Core, or any Core, is it's only as good as the quality of teachers teaching them. Some teachers invest the time into learning the new curriculum and how to do it well, some don't, just as some teachers before would take the time to explain why, while others didn't. Some teachers themselves aren't comfortable with math, and if they are anxious about that the student will know.
DeleteI am also with Sandra. All the extra steps and expecting our kids to learn 20 different ways to solve one multiplication problem and then explain how they came up with their answer is mindbogglingly silly. "Helping them to see the short cuts in math after they've spent a considerable amount of time playing with the numbers and conceptualizing how they work." Really? My son didn't get a considerable amount of time to play with numbers but CC has been thrown in causing him to be overwhelmed with all this extra nonsense expected to be done in half the class time they use to have. This is without any doubt been damaging to his grades. His over all GPA when he reaches graduation has already been affected which in turn may have lost him much needed scholarships to be able to attend college.
DeleteIf ever your explanation for a math solution is just, "because it is," then you are a prime example of why kids get lost in math in later years.
DeleteIf ever you think that math just is one way, and dont understand why, then good luck hitting those curveballs in calculus.
And yeah, I hope we do get to teaching calculus by 6th grade. WE'RE BEHIND MOST OF THE DEVELOPED WORLD IN MATH AND SCIENCE LEARNING. If you refuse to wake up to that, get used to reading about US students continuing to lag far behind. Personally, I'd rather not continue to read that. I'd rather see us do something and get back to the front, or as close to it as we can.
Memorizing math without an understanding is DUMB. Why? Because we then ask them to continuously add more levels of complexity until they're done with the math they need for a college degree.
If you don't know the "why" behind math basics, you will really struggle to utilize the tools that are necessary with later math courses. Y'know, those totally unimportant ones like infinite series and integration and imaginary numbers.
Totally, Sandra! EXACTLY!!!
DeleteEven through the answer for 2x5 is the same as 5x2 the problems are not the same. One is 5+5 and the other is 2+2+2+2+2. Stop using the memorized method and look deeper into what the numbers represent. If I said (2x5)+2 or (5x2)+2 the answer would still be the same if you look at the problem with a bigger understanding you will quickly recognize the question is 6x2.
DeleteJust to wrap this up, it seems to me that this new curriculum is moving way too fast and teachers are stuck teaching very advanced and abstract concepts to kids that really are too young to "get it". From my perspective this is the U.S. trying to keep up with other countries because we are "falling behind". I agree with one of the other comments that said math has been taught the same way for ages and educated many brilliant mathematical minds the old fashioned way. If we are falling behind as a country it certainly has nothing to do with the way we teach math. Their are many other factors at work, way too lengthy to get into here. There is absolutely no factual data to confirm that this "new" way of teaching math will be successful. But instead of implementing it in small scale to see if it works, they have gone and implemented it nationwide. They are gambling with an entire generation of children. Goodness, I hope it works. I expect the really bright kids will probably do fine. It's all the others that are in trouble. Pretty soon all the standardized testing will align with the common core so private schools will have to change their curriculum as well. Then there will be no getting away from it. I hope this experiment works.
ReplyDeleteLast year, my third grade son was melting down nearly every day at school and every afternoon at home. I found out later that 100% of the school meltdowns were during math. The teachers were asking me to help him at home with concepts they just didn't have time to cover in class. We are homeschooling now. It has taken me several months to undo the damage this crazy math has caused him. He thought he couldn't do math because he was stupid. In less than a year, he can add and subtract multiple digits, and multiply.
ReplyDeleteI look at these crazy examples popping up in the media and I can clearly see that this "new" math is trying to give kids number sense, but they are going at it backwards. Most kids will not be able to take the abstract problem presented to them and create the concrete example, especially in the two dimensional plane of a piece of paper with written explanations required in the answers. Kids at the elementary age, what we used to call grammar stage, are absorbing information. You want to teach a sense of understanding for 10's, 100's, 1000's, give them tangible items to count; give them games that have them adding and borrowing. Montessori is the absolute best I've seen at this, but even her end goal was for the kids to understand the standard algorithms, which are the most efficient. In her setting, kids were doing these types of math equations, including algebraic equations as early as kindergarten. Now Common Core is saying that kids aren't going to be able to do simple math until 4th grade? That is a huge problem for this parent.
I can tell from your writing that you care deeply about your students and that you have tremendous passion for math and teaching. I'm guessing that many of your students will be just fine, but that will be because of a good teacher, not because the method is a good one.
I feel your pain, my daughter is in 3rd grade this year and having the same issues. (see my comment below) Unfortunately we can't home school because my husband and I both work full time and have to have both of our incomes. We have hired tutors 4 days a week and she has still made 65 or below on every report card, continues to have the meltdowns, and has even changed personality wise. We don't know what to do anymore. I feel that this is really inflicting mental and emotional distress and may have long term consequences on my child.
DeletePersonally I think this is a teacher problem. Some teachers aren't prepared enough with a solid math background and can't teach math. If teachers aren't willing to learn enough, put in the necessary preparations, or if they're nervous about it themselves it's going to have a negative impact on the students. I have heard teachers say that they don't do more hands on math explorations because students make messes, put things in their mouths etc. Well that's a classroom management issue. My daughter was really struggling in 7th grade math last year till they changed what period she had math. In her other class there were 38 students, and the teacher admitted regularly that there was a group of boys that was a behavior problem that she couldn't handle. After my daughter switched classes she went from a D to an A and got the highest end of level score in her class.
DeleteWhat school tells a young child, learning to do math, JUST DO IT? Any teacher that teaches that way should be fired on the spot. Your break down of 453 - 17 is foolish. Teachers are supposed to the the rules behind why you would turn the 5 into a 4 and carry back the 1 that then turns the 3 into 13. You don't hand a kid a bunch of wire and then them to wire a house for electricity. You have to teach them the science behind electricity. How it moves, what wires and switches can handle a given voltage. What happens when wires cross.
ReplyDeleteThe idea that "The "new" methods you're seeing are not being taught. They are methods that students naturally invent." is moronic. Are you trying to make us believe that the students are given a problem in class, they each create a new way to solve said problem, submitting their solution for the the problem to a major printing company, waiting for the copy to arrive at the school and then learning how to do said problem? Yes, I know that question sounds ridiculous and it is complete sarcasm. But it is far more logical than Common Core is invented by kids.
There is a major problem when parents can't figure out 453 - 17 when using common core standards. And ANY TEACHER that supports Common Core is not worth the degree hanging on their wall and will not be teaching my children.
Common Core is not invented by kids. The strategies they use to solve problems are. When posed a problem they don't know how to solve, they will invent a way to solve it, which may not look like the way I would have solved it. It happens every day in classrooms around the world, including the United States. It happened even before the Common Core... there is video and research to prove it. But I'm not really sure why I'm even responding to this comment, as I am not worth the degree hanging on my wall.
DeleteTaught one way to add fractions?
ReplyDeleteNow, children are taught no ways to add fractions.
I bet people hate sport as well. Why are they taught just one way to address the ball in golf?
I'm over 50, but I was taught both memorization of math facts AND the "why" behind it. I was taught that 9 x 5 was really 9+9+9+9+9. But after a while it was easier and faster to memorize 9x5=45 so I could complete the work faster and move on to more complicated problems. I also didn't continue to sound out words that I came across over and over again. I memorized those "facts" too in order to speed up reading. And to keep with the reading analogy, i memorized spelling and definitions before I understood the Latin or Greek roots. My problem with Common Core Math is that our teachers seem to be solving long complex story problems that apply concepts that the students haven't mastered yet. There is no more rote. The PPP (practice, practice, practice) is what trains your brain. Applying the concepts is VERY important but it is being emphasized instead of gaining the foundational skills in our school. Without a solid foundation, the application is not sticking nor understood either.
ReplyDeleteI may not be over 50 (or 40 for that matter), but I couldn't agree more!
DeleteHear hear!!
DeleteRe: "The "new" methods you're seeing are not being taught. They are methods that students naturally invent."
ReplyDeleteThis is a silly statement. These methods *are* being taught. One may be able to make the argument that they appeal to more people, or maybe present the case that they seem more natural to the target audience, but to assert that somehow teachers formally presenting these methods to their students through drills and lessons (and expecting to see evidence that they're being followed) is conceptually different than the *teaching* of *methods* is ridiculous.
This also seems like a confused starting point. If we followed the statement to its logical ends, then I think you would see a whole lot less teacher explanation than what you saw from your own disappointing past experience. Students are just naturally inventing these methods on their own, after all, right?
To "teach" a method, is to say to a student, start with this number and add on this amount, now add on this amount, now add on this amount. Now add up what you added on to find your answer. In the classrooms I work in, these methods are not being taught. They are being fostered. Students are being given the opportunity to experiment with number and sometimes, adding up is a method they invent when solving a problem such as this:
DeleteYou have 4 apples, your mom gives you some more, now you have 20 apples. How many did your mom give you?
Some students may look at this problem and say "20-4 is 16" other may say, if she gave me one I would have 5, five more and I would have 10, ten more and I would have 20. 1 + 5 + 10 = 16. Algorithm invented.
I will not tell a 7 year old, I'm sorry honey, the way you naturally think about solving that problem is incorrect, you must subtract. Likewise I wouldn't tell the student who subtracted they were wrong either. Any teacher who forces one way or the other is misinterpreting the standards.
On the other hand, the student who added up... they have a good understanding of this problem and what it means, but their initial strategy isn't very efficient... or at least it won't be when the numbers get a lot bigger, or farther apart I should say... so I will work with them and share other students strategies, and discuss efficiency, until all my students see and are able to use efficient strategies to solve problems. Any problems, not just the ones on the test. They will be able to think through any problems.
"Hold on, why am I crossing out this number and changing that one?
ReplyDeleteBecause you don't have enough to take away. Just do it! "
That's just lazy teaching. The "old" way of subtraction works on the concept of taking the ones away from the ones, the tens from the tens, and so on. If there aren't enough ones, take ten of them from the tens. The problem isn't the math, the problem comes from the way the educators were educated in college.
I have no issue with common standards, but the method of teaching it is not working for every child. My child has never had an issue with math or any other school subject until this year. The only difference is the curriculum changed to common core. She was coming home and crying while doing homework, she was making bad grades, she constantly complains of stomach aches the pediatrician says are stress related, and she went from loving school to begging us to not make her go. I have seen my carefree, happy daughter turn into a stressed out, depressed, defensive, argumentative child. She is failing math, even though she has a tutor 4 days a week. Because she is failing math, she will probably have to repeat 3rd grade because even though all her other grades are fine you have to pass math to be promoted to the next grade. I had/have absolutely no problem with common standards, what I do have a problem with is a system that leads to unhappy, stressed, unhealthy kids, and keeps children from being able to be successful and progress on their own the way that works best for them. Everyone has a different way they learn best. This way is not working for my child yet they just continue to emphasize it to the point where she has lost all confidence in her ability to even try to do math.
ReplyDeleteI'd just like to note that if you have time to work with your daughter on her struggles, take her to the doctor, and see a tutor four days a week, then you have time to homeschool her. I guarantee life will improve.
DeleteWhat a jerk^^^
DeleteI appreciate what you are trying to do here in explaining this new approach to math. What you explain makes sense, and I understand the good intentions behind it. I am left, however, with two conclusions:
ReplyDelete- The job of explaining this new system should not have been left to random bloggers, no matter how passionate and informed you are. This is our children's education, something we are deeply invested in. Before such radical changes were made, even if the changes were justified, educators at the state and local level should have reached out, offered seminars, youtube videos, etc., explaining the new system. Perhaps some areas did this, but most did not. Instead, the first you hear of it is when your child brings home these worksheets that seem like absolute gibberish. It's not too late to make those connections and explanations, but the fact that it's been left up to people like you to do this just reflects very, very poor planning and a missed opportunity.
- This change in approach sounds great in concept, but I think we're seeing very real implementation problems that should not be just explained away as resistance to change. How well does your average 2nd or 4th grade teacher really 'get' this approach, and how bought in are they? Why isn't there more parental involvement, since parental involvement is a key part of student success, in teaching us how to work with our children using these methods? Open floor-plan schools seemed like a great idea in the early 1960s and 70s, but were a complete, unmitigated disaster because no one really understood how to implement such a radical change. I fear history is repeating itself here.
Again, I appreciate this explanation. It is very helpful. But why did I have to stumble upon it on some friend's facebook page? It should have been front and center all along.
Agreed.
DeleteI think my entire argument with common core is that in an odd sort of way it punishes those students who do understand the why and how of the relationships between numbers. I am all for teaching critical thinking. I am all for teaching more than one way to do something. If students are successful at completing and understanding subtraction, why must they take the extra 100 steps to draw the diagram, etc? In a way common core tells kids that they are not possibly smart enough to understand things without proving it in a method approved by the common core standards. In my time as a teacher I saw so many teaching fads go in and out. I still believe that children and adults for that matter have different learning styles. Cookie cutter does not work in a learning environment. If common core would integrate the (forgive the term) old fashioned way of doing things in with some of the strategies and not penalize them for being efficient, I would be all for it. It sort of reminds me of when the entire concept of invented spelling came out. At some point you have to accept that sometimes there is only one right answer.
ReplyDeleteThat's an instructional concern and not specifically a problem with the standards. When teachers see that a student understands a concept, we need to move kids on to more efficient methods. Search the standards and you will find that they use algorithms to put the capstone ona concept because they have the ability to work in any context. Teachers need to be very careful with number choice at the beginning so that students can see the relationships without making the work too tedious.
DeleteI'd rather a student's teacher teach the subject in whatever way the student learns best. I did just fine with the old style and others don't. One size fits all doesn't feel right to me :-(
ReplyDeleteThese curricular changes always seem to be implemented with the understanding that the curricula are at fault for the decline in education. I believe that it's the implementation that determines the success or failure of a given math program. I teach developmental math at a large university, so pretty much all the students I teach have problems with math. These students have had bad experiences in math classes and they were taught using a wide variety of high school math programs/approaches/curricula. When I first started teaching in developmental math classes it was easy for me to blame these students' high schools, teachers, etc., but after 10 years I started to realize none of those things were really to blame. It was the disconnect between the students, their teachers, and the material being studied. Ultimately for a new curriculum to be successful, the teachers need to be trained in how to use it, shown the reasoning behind it, and given the opportunity to have their issues with it addressed. Often teachers feel that these sorts of "reformed curricula" are forced onto them without their input or consent, and then they are expected to have better results. Teachers who feel respected by their schools will do a far better job with the same curriculum than teachers who feel unappreciated by their schools.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteIt seems that a lot of people are lumping both standards and their implementation under the rubric of "Common Core sucks!" I work in IT and every day I see similar issues: a utility that does something well is used poorly because the people using it don't understand what it was designed to do, so they get the idea that "this tool sucks!"
ReplyDeleteA lot of schools seem to have terrible CC implementations. I would wager that they correlate very well with schools where the administrators and/or staff don't understand or are actively resisting Common Core. It's just like any IT product migration: f there is resistance, the end product will be forced to suck by those doing the resisting.
And no, telling students to take one from the tens column and add ten to the ones column isn't really "telling them why" -- why do you take one and end up with ten? That's a question best answered by concrete manipulation of items -- "here I have a bead. Ten beads is a string. Ten strings is a sheet. Ten sheets is a block", etc. (You find this teaching method employed in Montessori schools, incidentally -- they've been doing it that way for literally decades and by all accounts Montessori kids do fantastically well at math.) Eventually those concrete manipulations lead to manipulating the abstract symbols as units, and then to abstractly manipulating abstractions (algebra, geometry, calculus, etc.)
(I distinctly recall being deeply suspicious of "borrowing" in subtraction. It didn't make sense in my six-year-old brain and none of my teachers at that age knew enough abstract math to explain why it works. It wasn't until years later that I really "got it" when I understood better what "place" actually means in arithmetic.)
I must have been doing Montessori... at a public elementary school. We had those physical representations and that made it easy for me to make the connection.
DeleteThanks Joe. That was a thoughtful and informative response.
DeleteThis comment has been removed by the author.
ReplyDeleteI'm also over 50. I also got sensible explanations for borrowing and common denominators. What has held me back in math that I did not memorize larger number times tables, addition, and subtraction. I have to work things things through that other had students committed to memory. That made me slower at math tests and more prone to errors. Heck, I have to pause to remember which hand is my right hand. Imagine how annoying it is to have to pause and think when someone says, "On your right!" I have excellent reasoning ability, and a pretty good memory, but there is a time when it's easier do rote memorization and that's when you should become facile with math tables (among other things). Rote is boring and tedious – and extremely valuable.
ReplyDelete^ Yeah that
DeleteMemorization is indeed important, which is why Common Core requires it. Some people seem to think that kids can memorization and critical thinking are either/or. They aren't. From the standards:
Delete"By end of Grade 2, know from memory all sums of two one-digit numbers."
"By the end of Grade 3, know from memory all products of two one-digit numbers."
Has been an interesting read -- the first I've seen where someone discusses the pros and seriously attempts to address people's concerns. My mind isn't made up on how I feel about the curriculum, but this is what I know as a teacher of high school Algebra 1 and Geometry ... every term I am more and more flabbergasted at what I consider "simple" (like, say 100-75 or seriously, even 12 x 10 or 8 x -1, forGET fractions or decimals) that my students cannot do without a calculator, though some ARE capable of doing the long-hand for whole numbers. It was challenging to teach when I first began in '97, but the percentage of canNOTs are well overtaking the CANs.
ReplyDeleteHaving curriculum dictated by the Federal Government and pushed by big money makes me nautious. But the HUGE need for something to address our growing problem of kids not THINKING about what they are doing and why is why I struggle with just cut-and-dry saying "screw Common Core" ... having worked through the Algebra 1 and Geometry with my students (though our district has given us freedom to address if with our professional objectivity), it is obvious there are currently gaps where it is written toward students who will eventually have had the curriculum for their previous years in school but as of yet have not, so we teachers are currently having to fill those gaps ... but when used with fidelity, I see how the MATH curriculum is meant to create thinkers, problem solvers.
One problem which must be addressed if we are to continue using this curriculum, though, is that there is a WIDE range of abilities for students entering ANY grade, but it is at its widest in high school. Students entering who have NOT mastered the "shortcuts" and who have been unable to begin to "reason through" will get left behind quickly. First term this year, my stronger class caught on well and I believe actually benefited from the way the curriculum helped make them think through, reason through higher-level thinking about real-world scenarios related to the Algebra (leaving Geometry to the side for a minute) -- real-life scenarios has been challenging to many high school Algebra teachers that I have known, especially the higher you go, so I appreciated the breakdown. Anyway, only one student in that class ended up failing, and he was a late-starter to the school. My Algebra 1 class made up of repeaters and weaker math students, though, presented with the same curriculum, struggled to make connections (many because of an inability to do those "short cuts" which should be ensured by high school) and as a result couldn't seem to ever gain traction as a class. There were a handful that rocked it, but right at 60 percent of that class failed the term.
All that said, if this curriculum is kept at the high school level, these types of concerns need to be addressed, possibly by district, as freshman year Algebra is OFTEN where students decide if they will stay in school or drop out ... at least "in our neck of the woods".
Just to get it straight: curriculum is not "dictated by the Federal government." The STANDARDS were developed by a group of states, and the CURRICULUM used to teach students is up to the states and the school districts to develop and implement.
DeleteAre you defending Common Core or are you defending an alternate method of teaching math?
ReplyDeleteYou agree with the new method that Common Core has implemented to teach math to kids. Your brain understands it; you are able to effectively teach it. Can you confidently and truthfully state that ALL students in the country will learn math better using this method? Can you confidently and truthfully state that NO math student taught before this method understands math correctly? Can you confidently and truthfully state that you would stand by the Common Core math standards when they are changed in the future?
The problem with Common Core is not just that it teaches one way to learn math. The problem is not just that a lot of kids are struggling with it. The problem is that it allows for NO freedom of voice or choice in altering the methods to fit the child. The problem is that it may or may not be drastically altered in the near or distance future to something unrecognizable or irrelevant.
If you are going to defend something, defend the kids, defend education, defend learning, defend control at the local and state level, defend educators who WANT to teach each child to the best of their ability! Please don't defend Common Core.
Americans shouldn't be complacent about this because it's "not that bad." No, the math standards may be okay for now. For now. But, there is NO guarantee it will last.
-Trisha
"You agree with the new method that Common Core has implemented to teach math to kids."
DeleteCommon Core does not mandate new methods.
http://huppiemama.com/common-core/
Common Core actually does not require anything method-specific except that students at a certain point be able to do standard-method arithmetic. The curriculum is deliberately separate from the standards and left to each school authority. Many districts, in adopting Common Core, have also adopted the Everyday Math curriculum and that's generating controversy -- but EDM was released in 1998, long before Common Core development began.
As stated above, Common Core is simply a common set of standards developed by a group of states who wanted to ensure that kids in their states were being educated to a level consistent with other states; developing and adopting the CURRICULUM and the implementation of the curriculum is up to the individual states and school districts. Some are obviously doing a better job than others at implementing curriculum, but that's not an issue with the standards.
DeleteThis entire blog post is a letter defending "common core math". Are you disagreeing with my comment or with the basis of this blog post?
DeleteEither way, I still would like to know if the blogger is defending common core or a new approach to teach math.
I was taught essentially this way when I was younger. I am 31 now and generally faster at math than anyone I know. I seldom write anything down and convert the problem at hand to a more manageable problem wherein it is easier to add/subtract quickly in my head. Regardless of the size of the problem I never really seem to have an issue. I learned about common core recently and figured out very quickly that this is how I understand math and why I was so advanced at such a young age. My parents still talk about how I would go to a (candy) store with a couple dollars and spend everything down to the penny with tax included at age 4. Certain methods work for certain people and this method is still used in my head today, 27 years later. Math was my favorite subject growing up and even in later years in Algebra, Calculus etc, my classmates who were "equally" smart in math were not even close to the mental math and seeing conclusions to math without writing everything down or following a process with a TI-83 etc. Granted, most of this later math cannot be solved in your head, all of its parts have basis in what I was taught and I literally felt like everything was manageable and approachable because I had a strong math foundation of things that made sense...
ReplyDeleteAlso, not all common core "problems" you see posted online are the best examples... they like to display the worst possible example of something simple and straight forward on paper and trash common core's approach.
Knowledge is power. The USA as a whole ranks horribly in Math in comparison. A better Math foundation and a new approach CANNOT be worse than what we are dealing with now.
My kids have been in Montessori schools from toddler to Middle school. My 8yr old could do long form division at the start of the year. All three of them could read at college level before what would have been 5th grade.
ReplyDeleteA system already exists for doing what is best for the student and the Core is not it. CC is developed around the PC principle that we have to treat all children equal. I'm sorry but some kids are sharper than others and some just learn differently then others.
It is not too much to ask to have each child learn in their own best manner, It is being proven in Montessori schools around the world. Where class rooms with 25 to 30 children can be "Guided" by one instructor, to learn by what attracts them to the knowledge and then use the child's own interest to develop those areas they seem less proficient in.
As a child I took home a second grade math work book and completed it over the weekend. When I returned to school I wasn't rewarded with the next level book, I was punished for wrecking the semester of instruction the teacher had "lesson planned". And that is what CC will do to an entire generation of kids. 1000's of genius level students will wither from lack of challenge, disheartened by apathy/
Rome burns and we're fanning the flames rather than trying to put them out.
Without standards, lots of kids will end up learning nothing. I went to Montessori schools as a young child myself and think that they are great for younger children, but there's a reason that there are few Montessori schools for middle or high school.
DeleteNothing in Common Core prevents kids from getting ahead. My own daughter will do a math camp this summer and begin Algebra 1 in 7th grade at her school. Kids who exceed standards should indeed be allowed to advance faster, but that has nothing to do with setting a minimum level of achievement.
This is SO sad. The OP talks about "just do it" teaching. That's AWFUL. Nobody should be taught that way.
ReplyDeleteI was taught to LOVE math from an early age. Sure, there were math facts and methods to memorize but we also got to play with enough physical representations so we could "see" the answers. Blocks, arrays, balancing (comparison).
By 4th and 5th grade we were having so much fun we were begging the teacher to show us more involved ideas. I actually learned how to calculate square roots and cube roots... in public elementary school!
The fun continued... calculating batting averages, odds of dice rolling (our class rolled dice literally a million times... and didn't get the expected curve so that caused quite the interesting discussion :) )
From my experience, the key is giving kids tools that are age-appropriate. And unfortunately I'm seeing too many crazy-inappropriate examples in CC. That's horrifying... kids should NEVER be taught to hate a subject.
I'll bet that the parents that are the most vocal against this method are the ones that try to do the work for their child instead of letting them figure it out for themselves. I work in the public and see this kind of coddling and spoiling of children all the time. Back off and let them figure it out for themselves. That is the whole point of this method of teaching. It's a form of guidance that works. If your child simply refuses to try, then congratulations! You have taught your child how to hate out of ignorance and the cycle will continue. Be a real parent and support your educators.
ReplyDelete"I'll bet that the parents that are the most vocal against this method are the ones that try to do the work for their child instead of letting them figure it out for themselves" Wow. What a ridiculous statement. I take it from your quote that you belief that anyone who has an opinion about CC that does not align with yours is not a supporter of educators. That is just a totally lame thing to say. Your comment is full of emotion and zero facts. Try again.
DeleteYou still have a lot more convincing to do. As I read the blog, the second, third, and fourth paragraph seem very misleading. I was not taught "just do it". It was explained why you would do that and it made sense. If the instruction no longer does this, we should address the explanation. The comments that Common Core is not being taught and it is a method students naturally invent also is questionable. If that was the case everyone would be able cover this easily. I read this more as we should not learn from others. We need to reinvent the wheel each time we have a challenge. I am trying to be open, but this seems VERY political and lacking in validity.
ReplyDeleteI appreciate your post Leandra and have been pleasantly surprised by the polite (for the most part) replies. I have a child in 5th grade and a child in 2nd- I think my main complaint is that it is difficult for the children that have been taught the "memorization" method to learning math since kindergarten to now have to change their thinking and to now be forced to show multiple steps to answer a simple question. For example- the question may be 543-123. My son may know the answer is 420 but if he doesn't show all 10 or 15 steps to showing that answer, then he is marked incorrect.
ReplyDeleteI think Common Core may have more supporters if they had implemented CC with the incoming kindergarten classes (and all kindy classes thereafter) and then had it follow them over their school age years, but to force this new way onto children that have been following the traditional ways for years is unfair. It takes times to learn a new way of thinking, but sadly these children do have the luxury of time- they have approx. 180 days to learn everything that they need to know for that grade level and then they move on to the next grade.
Again- I appreciate your original post and your explanation but sadly I do not necessarily agree and just don't know if CC will ultimately help or hurt our children in the end.
Best regards,
Diana
Totally agree! Exactly the problem my child is having. He has been taught "memorization" and has had no problems until now when something totally different and so time consuming has been thrown on him. It isn't fair and he feels like all his efforts for good grades were for nothing because now he is struggling to pass.
DeleteYeah, having it all implemented at once is a challenge, but teachers should be teaching with reasoning in mind and not just memorization. A good teacher should also be differentiating so if a student clearly masters that skill you have a more challenging activity for him/her. But, if your child can't explain why the subtraction works and can only subtract with the algorithm then the teacher has a responsibility to help them understand that concept because subtraction will not always be set up for the algorithm.
DeleteKids are naturally memorizers, and the younger grades are built for that. I think part of the problem is that schools heap kids into big groups, and learning is not really a big group activity. If as a country our scores have been steadily falling compared to the world, why not go back to the one room school house books and strategies that once worked? I have read Jacob's Algebra, a very old school book, and it's definitely not common core.
ReplyDeleteI teach 5th grade Math and am thoroughly enjoying the new curriculum that the county is using. My lessons usually begin with an exploration activity where students usually end up working toward a method, concept, or skill through modeling, problem solving, or conversation. By the time an algorithm or skill is introduced to them they already understand the reasoning behind it and it makes number sense. I have never had so many amazing conversations happen in my room where the students are arguing, elaborating, questioning, and teaching each other. There is significantly more real-world problem solving and more inventive thinking. So, if your argument is that the kids should just memorize the steps and learn the facts, I welcome you to my classroom to spend a few weeks working with them and observing them. I also think it takes a much higher level of thinking to truly understand a concept than to simply memorize some steps that have no meaning to you.
ReplyDeleteYes!! Completely agree.
DeleteI don't understand. There are four operations in basic math. Four processes to know. What are all of these procedures you're memorizing? How about instead of teaching all of these convoluted, outrageously multi-stepped procedures we teach addition, subtraction, multiplication and division? We've got the cart way out in front of the horse once again. Solid foundations = effective education. Third graders don't need to understand math theory, and they don't have the cognitive ability.
ReplyDeleteSincerely,
Former chemistry and math teacher
(Note: former is due to the fact that teachers are no longer allowed to teach in this country. STOP THE INSANITY!)
How would you teach a young student to add fractions with different denominators when they consistently add the denominators because they forget to make common denominators. Sure, you could keep reminding them that they need to find the LCD (unless they get it confused with the GCF, NFL, AT&T, etc) or you could have them spend one day using fraction strips so they come to the conclusion that they need to exchange the fractions for equivalent fractions that have common denominators. From then on they understand that it wouldn't make sense to add thirds and fourths and end up with sevenths. From the perspective of an elementary school teacher, this is an incredible improvement and when we introduce algorithms the steps make sense to the kids and there's a deeper understanding there. We aren't getting rid of the tricks, we are building a solid foundation of conceptual understanding so the tricks make sense.
DeleteI teach 8th grade math, and I am just dumbfounded by the number of students who don't know what 3 x 8 is without trying to count by threes on their fingers and run out of fingers and give up. They can't subtract, they can't divide....when I was a kid, we MEMORIZED our math facts. And it worked. We had flash cards, we played around the world. Repetition worked. These kids aren't going to make it through high school math without knowing these basic math facts. I agree with the person who said young kids have not yet developed the ability to think abstractly. I'm not saying you shouldn't explain the whys or hows of math, but for goodness sake, also teach them HOW TO DO IT! Waiting around for them to figure it out on their own isn't working. Then it's time to move onto the next concept, and they haven't learned how to do the last one. They are SO far behind, they will never catch up now. My 5th grade daughter comes home SO frustrated at these "models" they are FORCING her to use to multiply decimals. I studied it and studied it and couldn't figure out what the heck it was. I finally showed her how the way I learned it, and she got it right away. Frustration gone. But her teacher wouldn't take her correct answers. She got marked wrong because she didn't do it using the models that she didn't even understand.
ReplyDeleteSounds like you're just upset that you couldn't understand 5th grade models for multiplying decimals.
DeleteAre you aware of the 3rd grade CCS math standards?
Delete"By the end of Grade 3, know from memory all products of two one-digit numbers."
http://www.corestandards.org/Math/Content/3/OA/
That's crazy...wow
DeleteI read your blog on how math is currently taught to children. However I don't agree with your assessment about kids creatively coming to discover and love math. Instead I find that my son comes home daily with math homework and he has no idea how to solve the problems or even where to start. So instead my husband spend a couple hours each night actually teaching math to him so he can do his homework. Then, in parent teacher meetings when I complain to the teacher that he isn't learning math in class, she points out that he is one of her best students, so clearly he is learning. Yeah, I think, he is learning from his Dad.
ReplyDeleteWhat you are doing is called "after-schooling". It is the forerunner to homeschooling. When you finally realize that the hour or two spent with your child each day is more effective than all 8 or so spent at school, you'll be pleased to learn how easy, low-stress, effective, and superior a home education can be. Go Dad!
DeleteNice job, Dad! I agree, for some people, that homeschooling can be a very effective way to educate and invest in your children. If you are spending all that time anyway teaching them, why not make the jump and do all of it?
DeleteTeachers who assign difficult homework to young children will have a special place in hell. There are plenty of studies showing that there is no academic benefit to homework in elementary school, and only a small benefit in middle school. The only real purpose of homework in elementary school is to train kids to do it (for when they need the habit in high school). Homework should be easy for kids in elementary school, and parents should indeed complain when it isn't.
DeleteWell I am going my my own son's opinion of CC. I asked him the other day how math is different this year. He is in 6th grade. He said that he loved common core. It made more sense. It was easier. I asked him to explain further. He said, that before they just give a bunch of instructions and made everyone follow them and do the problems. Now students have to explain things and understand how they work. Once again he said it is so much easier.
ReplyDeleteB. S. The common core way is a waste of time. Who the heck wants to do 20 steps instead of 2 to get the right answer. After 20 steps you usually wind up in the wrong diection and get the answer wrong. And crossing out to borrow is explained, and the reason is simple. Dont even try to sell that the long unnecessary steps of common core make any sense, or try to make it sound more knowledgeable by calling them concepts, I ain't buying it.
ReplyDeleteI am in my late 30s. In my school, we started multiplication the last few weeks of FIRST GRADE. That was the math we did for 2nd grade. of course with subtraction, and addition. ALL YEAR. It stuck. By the end of third grade, we had mastered long division. We knew all of these four (addition, subtraction, multiplication, division) inside & out by the time fractions and decimals were given to us in FOURTH GRADE. To fill the time when we weren't doing math, we wrote everything in cursive. That started 2nd grade, mid year. The point of all of this: We had repetitiveness. It stuck. That prepared us all for the memory of the formulas we were to learn in the future. Did I like math. NO. Did I know it. YES. Time was given to students that may have been slower. It wasn't LEARN IT NOW, WE'RE MOVING ON. For we all learned differently. The time spent on it was early, & it was long. It stuck. Never once did we have to take a number, write it 3 different ways to find out what an estimate was. We rounded it up, or down. DONE. AND, we were learning to write proper letters, & checks in fourth grade & up. Is it to now be assumed children will not need this? Will not need to know how to balance their account? They are to estimate it, as in my childs math? By 5th grade, we had classes on real life, once a week. How the world worked, for it was going to be universal. We would know to subtract money from our bank accounts if we spent. Know what was to happen if we charge too much. Start young, keep it the same, for I am fine flipping & multiplying. It got done, in less than half the time. There are ways to teach our kids to think for themselves, with out trying to break them like wild horses. I see people can agree to disagree.... As far as having our future love math?? They will or they won't. Like our past. There are plenty of math lovers, our wonderful teachers are great examples of that. As long as there is common core, children will go home, upset they don't understand. Parents will rage, google it, rage some more, and show them the easier way they were taught. That in turn will show children to not like it. WAnt it to stick?? Then start classes for parents to relearn it all. That will make everyone happy. NOT.
ReplyDeleteStart young. Their minds are waiting for it. Take lessons from private schools. It works. :-)
I have read all of the comments. I appreciate Leandra's excellent explanations. I also understand the frustrations of those who object to CC. As a retired teacher, I have seen "new" math three times. When the new math becomes the old way, we, as humans, move on and add to our knowledge. CC doesn't take away or refute the old. It adds to even deeper understanding. Parents, I beg of you, please discuss the differences in methods with your child in a calm, rational, "open-minded" way. Kids are incredibly smart. Don't sell them so short. And please do not send them off to school, to work hard, at what you call crap. How dispiriting is that?
ReplyDeleteOur state office of education linked this blog post and I'm glad they did. I think there is a lot of confusion about what the common core is (a set of rigorous educational objectives) and what it isn't (a curriculum program, a set of academic materials, abstract vs. concrete thinking, Federal/UN conspiracy, etc.). While math is really important in our technical society, the ability to think and reason and problem solve is even more crucial. Interestingly, the *process* of solving difficult problems - even if a student doesn't arrive at a single "correct" result - develops the brain far more dramatically and in more important ways than being a whiz at computational procedures. American innovation (we do lead the world there) is all about applying creativity and skill (intelligence) to reduce complexity into simplicity. But there is a *huge* difference between simplicity and simplistic thinking. The elegance of a concise yet powerful equation (for example, one of Maxwell's equations) didn't arise from simplistic approaches. It takes a remarkable amount of unpacking and observation and academic expansiveness - laying the groundwork - before all of that enlightenment can be reduced into its simplest form. This divergent-convergent cycle is a critically important skill in a data-driven world, where creating representational models of a given process (along with the ability to reason on that process) is becoming essential in every discipline. By contrast, developing computational/procedural acumen becomes little more than a fun parlor trick as any application to a larger context fades quickly. Sure, it sounds impressive - like seeing a three-year-old recite all the capitals of the United States - but such tasks don't develop any genuine understanding. Like Leandra says, frustration can be mitigated by stepping back, approaching a problem incrementally, determining what you do and don't know, actively seeking to disprove your own assumptions, and ultimately seeking breakthrough understanding. This process works at all ages and levels of sophistication. If your child gets stuck, get out a notepad, draw a diagram, talk it out, listen to some music, or even have her go outside for a moment to clear her thoughts. The ability to get the mind into a problem-solving state is an important skill in its own right and that definitely looks different from child to child. But the rewards are great. I've watched kids just LIGHT UP when these breakthroughs occur. Such moments are FAR more valuable to their well-being than whizzing through page after page of multiplication tables. Fortunately, these types of expansive experiences are available to a wide range of students. They will be well-served in academics, careers, and in life by practicing these skills early and often. Truth is, common core can be adapted to either lend extra weight to computation or to problem solving. How they are implemented in a state or district can vary greatly. So in a sense, it's kind of a moot point to be disparaging the objectives themselves as they're really quite innocuous on their own. At least there is the assurance that a lot of thought and experience from some incredibly bright and capable people went into drafting the standards. It's going to take a similar effort from local school boards and staffs to reduce the standards to practice in constructive and meaningful ways. That being said, traditional thinking isn't a viable option, not if we want to remain competitive and continue to lead out as the engine of innovation and productivity.
ReplyDeleteThe way math was taught years ago worked and it is not working today. Which leads me to believe we do not need to recreate the wheel.
ReplyDeleteFrom- a very unhappy parent of the incompetent Maryland public school system
Let's state the obvious, right at the Top: This is a blatant Strawman Argument. No elementary teacher ever said what you are claiming they said.
ReplyDeleteSecond, isn't it interesting that you claim this fictional teaching method is the reason that all of our students hate math, yet you are the first counterexample among many ... most math teachers included. If you are looking for a cause-effect relationship, you've disproved it.
This comment has been removed by a blog administrator.
ReplyDeleteI have to respectfully disagree. The new Common Core methods demands a cogency in translating math - one area of thinking - into another unrelated skill. This is not about teaching, its about trying to create a fluency in mathematical pragmatics which is wholly inappropriate for almost all children.
ReplyDeleteMath is its own language. It has it's own rules and its own grammar and should be respected as such. One does not argue the rules of French in French class or demand children write stories about why a noun is feminine or masculine. Its simply an acceptance of the rules. We do not tell children 'do it my way', we show children that mathematics has constants, rules and ways to resolved equations. As they get older, we show them that these equations are translatable into their daily lives.
Schools may be guilty of lacking in practical applications or vocational links of mathematics to life or professions. They may be guilty of not providing more more support to girls in lauding achievements and reducing gender bias in classes. We could certainly have more supports in class for the various types of learning styles. This dumbing down of math, however, is not a good answer. It is an affront to the absolute basics of mathematics and discourages people with natural math aptitudes from pursing math as many have no similar aptitude in composition or verbal skills.
In a practical world, getting math incorrect results in people dying. Perhaps your new math kids can write their eulogies.
At Connemara Maths Academy, where we coined the phrase "fluency in maths", learning through discovery, creativity and technology is the cornerstone of our educational philosophy. We wholeheartedly agree with your letter.
ReplyDeleteI happened to randomly stumble upon this article, but I am very glad I did! I do not know much about the Common Core Math, but I can vouch for how accurate this article is regarding my own experience with math as I reflect back on my education. I was always a "top student" in my math classes, but it was because I could memorize well. I like the structure of how to solve problems and that it required various steps to solve an equation. When I took geometry in high school, I hated it! That is until I realized how to go about solving problems using a sequential pattern. Throughout the years and my undergraduate education, I have taken algebra, multiple calculus courses and a graduate level statistic course. I received high marks in all of these classes... and I didn't hate them. Now, however, I am a medical student and when I attempt to do any sort of math, I find myself struggling. Mental math does not come quite as easily to me, and I feel like it takes a while to "warm my brain up" to remember the steps I need to do to solve a division problem or work with fractions, etc. I found this article very interesting and now attribute my "lost math skills", more to the fact that I probably never really understood math to begin with. It was my ability to memorize that helped me to be successful in classes, and since I have been out of practice solving problems, that information isn't quite as fresh anymore. If this curriculum is focused on helping students truly understand math and help it become more second-nature to kids early on, then I say more power to it! It is frustrating for me to look back on my many years of education and feel like I wasted countless hours memorizing how to do different types math rather than learning to truly understand it.
ReplyDeleteThe problem that is addressed by neither the old standard or the new: the application of math.
ReplyDeleteI am discouraged to see "apples" and "oranges" still being used. What kid cares about apples and oranges? I have 9 & 10 year old boys, and at every chance I use "fun" things to talk about math. i.e. Science.
Math and Science go hand in hand, and need to be taught that way. You want to get a kid excited about math? Talk about sound waves and radio waves, torque and rotation, atoms and electricity, planets and gravity.
Until this is fixed, until math is taught as an actual application to a real problem in real life, there will still be those that hate it, or don't understand it.
I was excited to see a couple of years ago that "x" was being slid into my 2nd graders' addition problems. Why? Because algebra should not be taught separately, and should NOT wait until the 7th grade. Algebra is only another tool in the box. Sadly, I no longer see "x" now at the 4th grade level, and am still angered that fractions continue to be taught without the relationship to factoring, multiplication and division.
The common core doesn't prepare students any more than the old way. I am studying differential equations and linear algebra as part of an engineering degree, because a college professor taught me: to love math, that math can be hard and that's OK, that math is the universal language. It wasn't until college that it was taught correctly with an application at every step. I don't support the common core, and when my kids bring home a question, I show them the standard way to do it, with the application of what it means. And we talk about fun stuff, both of my children are maintaining an interest in math and science and would like to become engineers and scientists.
Make it exciting, not a tedious chore, whether memorizing 2 steps or 108 steps. My son asked me if we could cut a pie into a trillion pieces (thinking as a fraction). We made it fun, we calculated how many years it would take us if we cut one piece every 2 seconds for 16 hours a day. That's a whole lot of multiplication, and some conversion lessons too...and he loved it.
My main problem is that the instructions on the homework, are unhelpful or nonexistant. If i am expected to help my child to learn this method i need to have coherent instructions and/or examples. otherwise i have to resort to "here is how i learned it..." i want to be on the same page as my kids' teachers but i shouldn't have to talk to them once a week just to learn how to help my kid with his homework. Give me the tools to help him succeed. don't just shove a new way of doing things down my throat without explanation, i am capable of reading, put some instructions in there. How much should i have to google to figure out, or email the teacher or call the teacher? seriously, i dont mind them changing things as long as they make it so i can explain it to my kid. My kid came home recently with homework i literally had to study it for 30 minutes to make sense of what they were trying to accomplish. I took calculus in my junior year of highschool, i am not math illiterate by any means, i just want to understand, and my son is 8 and can barely explain the homework to me. and he has been able to multiply and divide since kindergarten.
ReplyDeleteI feel like this is inefficient. I have to take more of his teachers time than i should have to. It would be nice if there was a common core reference site that all i had to do was go to the site and put in the CC reference to the homework he is doing, which would have detailed instructions and examples. can someone make this happen?
I own a math tutoring center, and I have also seen a lot of homework assigned that has almost no instructions on it. I believe a lot of curriculum makers rushed Common Core material onto the market before it was ready.
DeleteThere are curricula that explain what is happening. Parents can demand better.
Hey there Mindful Mathematician check out my blog when you have time. You might also enjoy my house of math...
ReplyDeleteHere's a math problem for you. There's a direct correlation between between "people who are outraged about common core" and "people who are the most ill-informed about common core."
ReplyDeleteOne commenter after another is complaining that Common Core doesn't require children to memorize the multiplication table. That's wrong.
The Common Core standard is that by the end of grade 3, "Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers."
http://www.corestandards.org/Math/Content/3/OA/C/7/
As a middle school math teacher I can say that rote memorization may not be in style but it certainly worked when I was in school. There is no way that the majority of students in my class at junior high would not have even known their multiplication tables, but that is the case with my students year after year. To say that children should think abstractly at such a young age is ludicrous. I also agree that if a teacher is not trying to explain the concepts of things such as subtraction and are simply saying, "Just do it," or, "That is how it is done" should be fired. But because common core is so fast and jumps back and forth so many times students do not have the time needed to master any area of math, much less the more complicated ones. I have very few middle school students who can do long division, and even the ones who can generally mess up the problem if there is a zero in the middle of the problem (this is also true for subtraction). Who would have ever thought zero would be the biggest culprit to children understanding how to do math? I am old enough to remember the song, "Zero, my hero!"
ReplyDeleteI have always been great at Math, even throughout college. This CC stuff is garbage, in *MY* opinion. How does one just scrap everything that's been taught since the beginning of time, and expect everyone to follow suit. As a parent of four, how am I supposed to help my children with some mess that completely unravels everything that earned my As throughout my entire matriculation if I haven't been taught that way? I certainly hope that the government doesn't expect adults to return to colleges and Universities to enroll in classes to learn *new* math. It seems we'd have to in order to effectively help our children with their grade school homework. I live in Texas, so thankfully, we are not dealing with this. The rumors are swirling, though.
ReplyDeleteSo can someone explain how common core solves the problem 100-75?
ReplyDelete