Defenders of the Common Core standards insist that they are “standards” and that they do not influence or control either curriculum or pedagogy. Teachers. Are free, they say, to use their own methods of instruction.
As this article in the Washington Post shows, Common Core math dictates how teachers teach. The story is about the resistance of parents to the methodology, but there is no question that there is a specific pedagogy that must be learned and taught.
Even this story repeats the claim that “states and school districts decide how to teach to the standards and what materials to use.” But the story itself demonstrates that the “standards” dictate HOW to teach, and every publisher must align their materials with the CCSS standards.
Diane Ravitch's blog 
I am forced to teach common core math. Teachers are told how and what to teach. There are Math Practices we have to follow the dictate how to teach the material. Also, if we are caught teaching any skills, we get “the talking to.”
What? The math practices are pretty vague. Things like “Make sense of problems and persevere in solving them.” How does that tell you how to teach? Do you not want students to make sense of the problems you are doing? I am a math teacher too. The common core is far from perfect but it is still just a list of topics to teach each year.
Your example is a general Practice Standard.
Here is a grade 3 standard that dictates how to teach area:
“Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.”
Hmm. “Dictates how to teach area”? Really? Let’s give the entire context and judge:
“Geometric measurement: understand concepts of area and relate
area to multiplication and to addition.
5. Recognize area as an attribute of plane figures and understand
concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to
have “one square unit” of area, and can be used to measure area
b. A plane figure which can be covered without gaps or overlaps by
n unit squares is said to have an area of n square units.
6. Measure areas by counting unit squares (square cm, square m, square
in, square ft, and improvised units).
7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by
tiling it, and show that the area is the same as would be found by
multiplying the side lengths. [this is the one you decided to quote out of context]
b. Multiply side lengths to find area of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle
with whole-number side lengths a and b + c is the sum of
a × b and a × c. Use area models to represent the distributive
property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by
decomposing them into non-overlapping rectangles and adding
the areas of the non-overlapping parts, applying this technique to
solve real world problems.”
======================
Now, NYT, in the context of the full standard here, is that dictating how to teach area? I don’t think so. The issue is a bit deeper, isn’t it: the relationships among area, mutiplication, and addition. Undermine your claim too much to look at it in context?
Or maybe you don’t think there’s a relationship amongst those concepts? So you should be free NOT to help students make that connection? How would you teach finding the area of a rectangle with whole-number side lengths (or is that so dictatorial that you wouldn’t teach that at all?) Note, by the way, that the standard says what CHILDREN are expected to be able to do, not what the teacher is to do. Or doesn’t that occur to you? It’s not dictating teaching at all. That’s why it’s a CONTENT standard, not a PRACTICE standard.
Of course, my going to this length to show your dishonesty or confusion will be now claimed as my unbridled support for the Common Core. It’s not. It’s an attempt at honesty. You really should try it. I want to win the war for excellent mathematics education in our public schools. I want to stop the high-stakes testing machine. Lying or misrepresenting what’s actually in CCSS-M is NOT the way to do that. Stakeholders aren’t morons and they can read. The document is freely available online. Don’t be as bad as the people you say you want to defeat. It demeans the effort and makes you look like some sort of desperate ideologue rather than a rational educator.
I’ll make a small wager based on 30 or so years in math education: “caught teaching skills” to you means “teaching the single standard algorithm for doing an arithmetic calculation.” And left to your own devices, you’d do little else, if anything at all. I could be wrong, and if I am, my apologies in advance. But I’ve seen that for a long time wherever any sort of progressive principles of mathematics education are asked for, long before there was a Common Core. Old School teachers are always old school given any opportunity to be so. They know nothing else and don’t WANT to know anything else. Thinking is hard work, after all, and why learn anything new when you can mail your career in for 30 years and retire? Not you? Well, again, I apologize. But not to those who truly are like that. And it’s not something I’ve invented. Hell, I could have been that way if my own experiences as a student hadn’t shown me why that’s a bad idea.
I had to go to a staff development on Common Core math last year and how we had all learned math wrong, complete with smug grins from the Curriculum Coach when we didn’t work a problem backwards with little boxes and “counting on” from the little boxes of ten.
Lining up numbers and regrouping for subtraction is no longer acceptable.
My cousin pulled his child out of public school over this very thing.
I fear teachers’ embrace of Common Core is going to further discredit us in the public’s eyes. When a parent hears a Marshall Tuck ad bashing teachers, these wretched Common Core math assignments will spring to mind and confirm Tuck’s assertions. It will seem like one more piece of evidence that we don’t know what we’re doing and that radical disruption is called for.
Teachers’ unquestioning collaboration with Common Core (and most other trends) dismays me. Perhaps the CC math is the right way to go; the problem is that NO ONE KNOWS. It’s shameful that teachers go along with an unpiloted, untested, unproven curriculum. Where are our professional standards?
A LOT of teachers have NOT embraced the core. It’s not our fault that we are forced to do these things, and I wish that our spokespeople–Randi and Lily–would actually tell the public that instead of doting on the core. In my state, we cannot speak against the core on threat of our licenses, but apparently teachers who love and worship the core can speak out, since they are on the news all the time, praising the core to high heaven.
Standard 4.NBT.B.4 says:
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
So I don’t know why your curriculum coach is so smug or why you say regrouping is no longer taught. The standard (AKA old way) is specifically mentioned.
Uh, oh: that’s too factual for the emotionally-driven folks who want their intense feelings to obviate any need for facts.
Just after graduating from high school my middle son made, I think, the correct observation that if we are not willing to teach math that parents can’t do we can’t teach math at all because virtually all parents did not learn mathematics when they were is school.
TE: your son is one smart cookie! Kudos to him for that astute observation.
Your son has definitely mastered hyperbole.
“Virtually ALL parents did not learn math when they were in school.”
That is an utterly fantastic claim. A nation filled with innumerate parents. Seriously? All the parents who are math teachers, scientists, engineers, technicians, economists, bankers, and more? And Mr. Math himself agrees with this insulting remark. Sounds like MPG could use a math refresher himself.
A. Nonymous,
I don’t think he meant innumerate, just that they don’t know mathematics. Most have been taught to follow an algorithm and believe that mathematics is just a set of algorithms. That is why parents object to mathematics classes that deviate from the algorithms they have been taught.
You might want to read the famous essay A Mathematician’s Lament by Paul Lockhart. After getting his Ph.D. in mathematics at Columbia and teaching at several universities (Brown and UC Santa Cruz), Dr. Lockhart left post secondary education to teach all grade levels of math at St. Ann’s School in Brooklyn, NY.
Here is a link: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
That essay by Paul Lockhart is excellent!
“By concentrating on *what*, and leaving out *why*, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is *the art of explanation*. If you deny students the opportunity to engage in this activity—to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of *mathematics* in our mathematics classes.”
[I’ve added asterisks to indicate where the author italicized.]
The distinction, A. Coward, is between “school math” and mathematics. Some parents learn some degree of the former. Almost none learn about the latter. There’s a universe of difference. And so parents who try to judge what’s supposed to be taught by those charged with ANY approach to mathematics that varies from the narrow school math experiences most parents had are likely to mock it. That mockery MIGHT be a result of deep knowledge of real mathematics, but mostly it isn’t. The kid gets it. You don’t. Sorry that puts your nose out of joint and leads to your trying (pitifully) to insult me while hiding behind a pseudonym. I suppose you could read Paul Lockhart, but if your mind is welded shut, it won’t do you any good.
Don’t worry A. N. – some people just can’t see the forest through the trees. And some can’t see reality through their ivory tower colored glasses.
NY Teacher,
Paul Lockhart teaches at an expensive private K-12 School in Brooklyn New York, not at a post secondary institution. It is likely to be the case that he is not qualified to teach in New York public schools, however.
“Lining up numbers and regrouping for subtraction is no longer acceptable.”
Please, Joanna: find me a single sentence anywhere in the CCSS-Math that supports that idea. You can’t. It’s not COMMON CORE MATH that is the issue. It’s idiocy coming from a number of sources, including but not limited to publishers, limited professional development (expensive to get the degree that’s really needed), recalcitrant teachers who’ve always as a species of teacher resisted any idea that might make them leave their comfort zone or make them have to think about math from more than the one way they barely grasped themselves as students; really stupid administrators of various sorts (whom we’ve long had among us and who never help matters much if at all); political pressure coming down from the top both within and outside of the school system – some from politicians, some from business interests, some from “pundits,” and all driven by high stakes tests; and last but not least, our continued cluelessness about what might be a hell of a lot better than what we’ve been doing, at heart, for the last 150 years or so, TO our children in public schools, including but not limited to most of the “good” ones.
And if your district can afford to send people around to check on you to see if you’re sneaking in standard math algorithms, you’re in a place vastly more affluent than the districts with which I’ve worked in SE Michigan the last dozen years or so. Most haven’t got the money to fill supervisory positions like that. Principals can’t be in more than one classroom at a time, last I checked, and that goes for APs as well. So who is breathing down your neck so frequently that you have ZERO opportunity to sneak in those standard algorithms? Seriously.
I would LOVE to have someone try to tell me that I can’t teach mathematics in a way that connects each thing I teach to other things I’ve taught and plan to teach in mathematics. When I finished frying his/her skull with pure contempt, there’d be nothing left to report me. And if I were fired for teaching principled mathematics, I’d live with it. It wouldn’t be the first time I stood on principle and wouldn’t be the last. But then, I’m one of those people who can’t live with himself if I have to teach baloney and call it mathematics.
But I don’t think it’s quite that simple in a lot of cases. I don’t yet believe (and find myself believing less and less every day) that things are quite as they’re being painted. There’s too much that is familiar from the ’90s and ’00s in these litanies from teachers and parents about how evil everyone else is and how they try to teach “common sense” mathematics and are stopped from doing so.
Aside from wondering how ANYONE could stop a parent from telling his/her child, “This is baloney” (even if in fact it is NOT baloney), as has gone on for decades regarding ANY variation on standard K-5 algorithmic approaches to math, what I found in classrooms over the last couple of decades was a lot of teachers asked to teach from progressive books who kept them on the shelves EXCEPT if they knew that someone was coming to observe them teach. And teachers who taught with the “hated” books, but undermined the lessons explicitly with what they said to kids (e.g., well, now, THIS is the way I do multiplication and probably how mommy and daddy do it when presenting the standard algorithm, and with various facial and verbal cues while teaching, say, lattice multiplication that it’s stupid, invalid, tiresome, useless. I am not making that up. Maybe that’s not every teacher. In fact, I know it isn’t, because I also worked in classrooms with teachers who got it and could make connections among algortithms (or were happy to learn from me how to do that). But loads of the others. Some perhaps unconsciously putting their entire bodies, not just their thumbs, on the scales against the new.
And that may just be why some pro-Common Core folks (people I know personally who are good, smart people who fought the Math Wars in the ’90s and ’00s against fierce resistance) are glad to have some federal weight to throw around against those who would prefer not to teach anything but “back to basics” math. I warn them against so doing, I argue that it can’t work if those teachers who fight against innovation aren’t helped to see things from a broader perspective, and that coming down on people like gang-busters may in the end be worse than not trying to change their practices at all. But I’m not quite convinced that it’s really like that in a lot of places, by which I mean really knowledgeable progressive math people crushing traditionalists. I think it’s scared people who don’t get it trying to get other scared people who don’t get it to do what everyone THINKS is necessary to keep his/her job. And of course that helps no one, least of all kids, and teaches no one any math at all.
Interesting article. Especially this part: “‘The kids who come to us are a clean slate,’ said Jennifer Patanella, an instructional coach with the Rochester public schools…”
I am curious where Ms. Patanella is finding these “clean slate” children. My experience subbing in all grades of Common Core classrooms is one of kids being rushed to learn brand new strategies and brand new ways of conceptualizing the knowledge they already have (and of ELD kiddos being stumped by vocabulary, in the more and more lengthy word problems that are being added, so they can’t find answers even when they have mastered the strategies), and of all this happening so fast that I have literally seen kids stumped by a Common Core “review” problem that they had supposedly been “taught” how to do, telling them to ask their teacher for an explanation (because I couldn’t make heads or tails of it), then going back a week later to watch them all get just as stumped by the exact same question on a test that counted toward their grade. These aren’t clean slate-kids, these are kids who have to unlearn the old ways they were taught to do things just as much as Mom and Dad do, only their future in school depends on their doing it in an impossibly short amount of time.
Thanks for that view from the ground. “Clean slate” sounded like nonsense to me, too.
“The kids who come to us are a clean slate,” said Jennifer Patanella, an instructional coach with the Rochester public schools. “It’s the adults who have to be retrained.”
That sounds great, “it’s the parents, not the KIDS”, very ed-reformy, adults vs children, but is it true?
Are older kids a “clean slate” in Common Core math? How could they be? Hopefully a 4th, 5th, 6th, 7th grader was doing math in some fashion prior to Common Core. If this is a different approach it’s different for them, too and they’re not at all “clean slate”.
If you just happen to be starting school when the Common Core arrives in your school I guess you’re a “clean slate” but I wouldn’t think that’s true of the vast majority of children who will RIGHT NOW have to deal with it and be tested on it.
I hope there’s some recognition of that reality among Common Core promoters. This cheerleading makes me nervous, because I think we’re headed into alternate reality land again. Can we agree that the Common Core math might ALSO be difficult for children who were taught different methods in younger grades?
Not a slate, a better analogy is an Etch-a-scetch. The Reformers want to just turn statistical knobs hoping a pretty picture emerges. Then, in a few years, the Reformers will blame everyone else, throw a tantrum, shake up their play toy and start over.
*sketch
Maybe it’s me. but there’s always this assumption of bad faith, this assumption of laziness and and slackers in how this is presented.
This is from the US Department of Ed, today:
“Low-income students are more likely to drop out of high school. We’re working to make sure ALL students succeed”
Everyone else only wants certain students to succeed? I don’t believe that. Do they?
Great point, Chiara. The main plank in reformers’ account of the achievement gap is teacher moral and intellectual weakness.
I will always side with teachers above admin and state regulations…I am a teacher and I believe in teachers. I needed to start this comment with that…because I have to disagree with you.
Common Core Standards and implementation here in California is much different than in NYS/NYC. I am originally from NYC and was trained as a teacher at Queens College and earned a Masters Degree. My wife was a member of the NYC Teaching Fellows and earned a Masters Degree from Pace University in Mathematics Education. We both now teach in San Diego County school districts…she teaches Mathematics and is a Math Coach as well as Head of her HS Math Department. We have both been going to Common Core PD and training for years now and my wife has been hired by her district to create their own curriculum. Thats just some background.
I know for a fact (my mother is a NYC teacher) that the trainings and expectations for teachers in NYC and here is Cali is VERY different. CCSS Math here is Cali is a set of STANDARDS. It has an overarching set of 8 Practices that guide the students interaction with the standards and the goal is to have students THINK and REASON on their own to come up with solutions to problems. The teacher’s job is different now…instead of delivering content and skills they formalize and guide the students work and ideas. Guiding them towards concepts and strategies that students MAY use to solve problems…not telling them new strategies that are different than the “old way.”
I have seen my mothers training from NYC and heard her issues with the DOE and NYSED. I agree. EngageNY is a HORRIBLE curriculum for CCSS because it dictates what the students have to know and does not give the teacher the autonomy to decide what the students need.
Some resources (search for names) that really show what CCSS is like in Cali are:
Andrew Stadel
Dan Meyer
Dr. Jo Boaler
Fawn Ngyuen
Robert Kaplinsky
THERE ARE A TON MORE
Thanks for this, Sam. CA is the case study in how to do the new standards right and is an important counterweight to the failed NYS implementation that has become the main source of the anti-standards anecdotes.
If Ca. is teaching CC to both teachers and students correctly, meaning with benefit in learning math, then it is another kudo to be offered to Tom Torlakson and his leadership as State Supt. of Public Instruction.
I have no problem teaching the “why” behind math. But not all students are able to understand, say, rigid motion as a basis for congruence. Or why dividing by zero is undefined or the square root of a square is plus or minus. Common Core intrusively specifies how a teacher must teach to all students. To some, the angle side theorems might be the best approach rather than just failing the student on the PARCC tests and firing the teacher based on VAM. Not all students are above average nor will we achieve 100% profiency for 100% of students. Teachers must be allowed to succeed with students, not set up to fail.
An approach to division by zero that makes sense might be:
If 3 X 2 = 6, we know that 6 divided by 2 must equal 3.
Further, 0 X 2 = 0, and thus, 0 divided by 2 must also equal 0.
Now, based on how you used inverse operations for the first two problems, try doing 2 X 0 = 0. Would you be able to do 0 divided by 0 and get the 2? No? It appears that division by 0 fails to yield the correct answer based on how we defined division in the first two problems. Division by zero must therefore be undefined.
“. . . rigid motion as a basis for congruence. . . ”
I didn’t realize that they are teaching sex ed in math now!
Don’t know about you, Duane, but for some reason the word “congruence” was the more salient one for me in the sentence. You may have gotten your sex ed at Viagra Public Schools.
No, not at VPS but at Catholic schools were according to the celibate nuns the ideal time to have intercourse was two weeks after the girls period.
I don’t know where to start in trying to counter the claims being made here, both by Diane and by most commenters. So I’ll just jump in here, MathVale: nothing personal.
Tell me: when do we try to get children to understand why dividing by zero is undefined in any of the number sets they learn in school (in other words, if they’re up to learning the rational numbers, how do we make clear that there cannot be an integer b such that a/0 = b where a is, for clarity, non-zero?
Well, we COULD (for kids with sufficient mathematical maturity) try the algebraic approach. Cross-multiply and obtain a = 0*b. Now we have a, which was by assumption non-zero, equal to 0*b, which by the zero property of multiplication must be zero. That’s a contradiction, so no such number b can exist. Division by 0 must be undefined.
But here’s an approach that I’ve used with elementary school children and older, all the way to adults who were math-phobic, with great success:
If we accept for the moment that multiplication can be thought of (in one way) as repeated addition, and if multiplication and division are inverse operations, it makes sense by analogy to suggest that division can be thought of as repeated subtraction (there are limits, of course, to such analogies, and I don’t particularly like the idea of defining multiplication as being EQUAL to repeated addition, as there are important ways in which it is something quite different from addition).
In particular, we can define a/b for integers a & b with b non-zero to mean “How many (complete) times can I subtract b from a until I either reach 0 or have less than b remaining?
Take the case of a = 6. If b = 6, then the quotient is 1, meaning that I can take 6 one time from 6 until reaching 0.
Next, let b = 3. Then the quotient is 2, as I can subtract 3 twice from 6 before reaching 0.
For b = 2, the quotient is 3.
For b = 1, the quotient is 6.
Now, we need to think a bit. What about letting b = 1/2? Well, there are two halves in every 1 whole. So we can take away 1/2 twelve times from 6 before reaching 0.
What about b = 1/4? Right. 24 time.
b = 1/10? 60 times
b = 1/100? 600 times.
Now let your imagination run wild: b = 1/1,000,000 = 6 million
As b gets smaller and smaller, the quotient gets bigger and bigger.
Let b grow smaller without bound but never reaching 0. What happens to the quotient? It grows larger without bound, approaching but never reaching infinity. Infinity is not a real number. It’s a limit larger than all real numbers. So there is no real number that could be the quotient of a real number and 0. Specifically, 6/0 must be undefined.
Or, ask yourself this: how many times can I subtract 0 from 6 until I have 0 left? An unlimited number of times. Infinity. Which isn’t a real number.
I’ve done this in 6th grade classrooms where the teacher believed that 6/0 was 0. Or 6. Or. . .???? She really wasn’t sure and finally asked me. The students seemed pretty pleased with this approach and I didn’t do the other, more formal explanation.
Tell me that children who have some reasonable grasp of the four basic arithmetic operations, even if they don’t have all their facts memorized, and at least a moderate familiarity with fractions (again, even if they haven’t mastered them) couldn’t grapple with varying degrees of success with EITHER of these approaches. Sure, a few in any group couldn’t. But that has NOTHING, ABSOLUTELY NOTHING WHATSOEVER to do with Common Core. I challenge anyone here to prove that the contrary is the case. Because the situation with that sixth grade teacher and her curious students happened in 1993 in Willow Run, Michigan. And one of my closest friends from school, a math phobic who scored in the low 400s on the SAT math in 1967, said after I used that second approach to explaining why division by 0 must be undefined that he got it for the first time in his life. That was in the 1980s.
I will get into Diane’s inaccurate claims about the teaching of mathematics in a separate comment. Let’s keep this comment focused on the one issue of division by 0. I look forward to being refuted. I want to know why the above would be beyond the grasp of upper elementary school children, even those not all that “mathy,” to use a word I don’t care for but which seems to communicate to a lot of people.
“I look forward to being refuted. I want to know why the above would be beyond the grasp of upper elementary school children, even those not all that “mathy,” to use a word I don’t care for but which seems to communicate to a lot of people.”
Kim has one large bag containing 250, multi-colored beads. She wants to separate them equally into ZERO separate bags. How many beads will Kim place into zero bags?
Why would you want to? Case closed!
You closed what case, exactly? And how?
Any number you choose will be wrong, you realize, as no real number times zero gives 250. So you either proved my case (thanks) or failed to make a meaningful point. I am not sure what you intended to do, but your example will cause problems for most adults, let alone children, because it is linguistically but not mathematically sound. Most will say zero, I suspect, which is not correct.
The case that abstract, theoretical math has little place in the world of young, concrete thinkers. The case that much of the early CC math instruction is developmentally inappropriate. The case that lessons like the one you have outlined undermine any attempt to make math more interesting and practical. The case that kids will continue to hate math so long it is taught as and end instead of a means.
That is nice rhetoric, but I missed a single fact about what I wrote, particularly about division by zero. You have something less grossly general about kids and arithmetic? I taught that second approach to 6th graders in a very poor school district. With a chance to have actually prepared the lesson, I would have made it quite concrete. And I disagree strongly with the notion that all K5, let alone K12 math has to be applied math. Kids come to school loving a lot of abstract ideas, like what is the biggest number? I have never met a child who didn’t want to know or argue about that. Math is more than engineering or physics or economics. Much more. And we sell generations of children out because too many grade school teachers are deeply math phobic and math ignorant. How many millions more must we do that to before amateur hour is over in this country?
Would love to read your word problem that would help me understand. Obviously your lesson was not helpful. This further illustrates my point.
I just read your word problem and showed you why it
Your word problem. One with beads.
NY Teacher (got a name you’re not ashamed to put out here? I get so tired of being bashed by anonymous people who hide behind pseudonyms and screen names): I don’t recall promising a word problem, so why are you complaining about mine? You gave one and I showed the reason it refutes/proves NOTHING.
Now, if you could get off your political horse for a second, and your personal antipathy for me (because you very incorrectly see me as pro-Common Core, regardless of countless posts I make against it) and speak to the question: why is division by zero undefined in the real numbers, rational numbers, etc. and how can we make that a sensible point to kids, not just a meaningless rule to be memorized? then either refute my claim (which you can’t, though you seem eager to refute a bunch of things I’ve not said, EVER, which seems to be a very common problem with certain people with whom I try to discuss things about math education: I imagine it’s far easier to refute straw people than it is to do so with those who rely on factual, sensible, logical, mathematically-sound and historically true arguments), or accept that I’ve made a perfectly decent explanation that upper elementary students who’ve learned to some reasonable degree the four basic operations of arithmetic, how they are connected to each other, and a little bit about rational numbers and their operations, or at least who haven’t been utterly ruined by mathematically-ignorant people at home or in school or on the street – maybe their friends don’t know that 6 6 in Monopoly has another meaning besides just that you can move 12 spaces or how to split a candy bar in half, but I kinda doubt it – can grasp as to the problem with division by zero.
Now, frankly, none of this has squadootch to do with the Common Core and you know that perfectly well. As should Diane. And her readers. And when the smoke clears, I strongly suspect that a lot of the people weighing in here so vehemently against the things being taught in school the last couple of years in math classrooms will still be railing against anything that doesn’t fit their own usually very limited grasp of school mathematics (let alone higher mathematics). It really isn’t all about computation – or at least it need not be – and frankly it is unbelievably racist and classist to insist that little kids are too stupid to learn some important and deep but accessible – if presented reasonably to them – mathematical ideas that connect with much of their ordinary experience. And particularly tragic to insist upon this because their poorly-educated (in mathematics, at least) parents, relatives, peers, or, yes, teachers are terrified about having to stray an angstrom out of their personal experiences and comfort zones.
The more you whine, NYT, the more I see you as another sad case of a teacher who tells me at PD that “my kids can’t learn that” when what they are really saying is, “I can’t learn that.” The kids can. And do. When they are given a chance. I would prefer not to make this about you or me, but you leave me little choice other than to just ignore you. So if you can’t speak to the mathematics, I’ll have to do the latter. Arguing with your fear and loathing of math and your belief that anyone who doesn’t scream bloody murder about EVERYTHING to do with Common Core must be a stooge of the Gates Foundation or Arne Duncan or whomever, or doesn’t really oppose CCSSI or any of the other bilge you’ve said and written about me here is a waste of time and only gets away from the things I am interested in. Like seeing that the kids in this country can escape the ignorance of all the past generations when it comes to math.
Your smugness is astounding, Michael. A lot of us cannot put our names in here because of very legitimate fears of retribution. In my state, we have been threatened with our licenses.
I have no problem with various approaches teaching division by zero. Infinity is a concept, not a number, but it takes abstraction and physical development to understand. Not all 6th graders have that level of cognitive ability, nor should we expect them to. I do not want a faceless econometrician telling my students they are failures because they cannot conform to a narrow definition of learning. That is cruel.
Over the summer my soon to be 6th grader decided she wanted to start a club at school. She was trying to figure how many representatives she needed from each grade level. Instead of good old fashion division she drew boxes and used tally marks to get the answer. I was floored . She is an honors math student and fluently knows her multiplication and division facts. CC math is ruining our children. Last week we started our percent unit in 6th grade math . After a weeks worth of lessons the unit only shows how to find percent of a number using tape diagrams. Its truely sad to think of how our children will need to draw pictures and diagrams when they are adults.
You seriously believe: 1) that kids won’t learn numerical/symbolic approaches under Common Core math: check the actual standards, check the textbooks, then state that again with a straight face; 2) that your honors math student isn’t capable of doing this problem any other way and never will be? If so, don’t save money for sending her to college. But you know full-well that either the term “honors math student” is not appropriate for your daughter, or she just hasn’t decided to do the problem any other way yet. A couple of weeks is hardly worth worrying about, Tricia, believe me. If you want her to have a mechanical ability to crunch numbers but be unlikely to understand all that much of what she’s doing or why, pull her out of school, get Saxon Math, and have her grind away. I’m sure she’ll get it and you can rest at night and stop feeling sad about the future.
By the way, drawing pictures and diagrams has always been one very effective part of solving problems. I’ve taught mathematics for 30 years and I still like a good picture or diagram when dealing with a problem I haven’t already mastered. But then, if I’ve mastered something, it’s not a problem – it’s an exercise. That’s a world of difference. And perhaps your daughter hasn’t transitioned to the point where percentage problems are exercises. But I bet that when she does, she’ll be vastly better at them the most people from my generation who were taught in the “back to basics” way with memorized procedures that confused them and which they had trouble keeping straight. Just a very strong intiution of mine based on a very long career.
One problem with CC math is that the teaching of a deep understanding of ratios and percents ends at an age (11 -12 yrs) when most students are not yet capable. After 7th grade, these two critical mathematical concepts all but disappear from the curriculum and will never be seen on the tests. Big mistake. And no way to correct it.
And doing away with CCSS math will remedy that how, even if that is true? These issues predate CCSS-M and will long outlive them as long as people can’t or won’t separate the issues. And doing so is not an acceptance of the testing or the books or the politics. It’s a necessity if you want to avoid a return to the Dark Ages of the back to basics movement c. 1970.
In a perfect world, math standards would be open-sourced, and voluntary. Wouldn’t it be a good thing if you could lend your expertise in such a way. Doing away with CC math does not demand we return to “Dark Age” math instruction. The simple fact that experts in your field cannot agree is telling.
“The fact that experts in your field cannot agree is very telling.”
Mostly that’s baloney. Most mathematics EDUCATORS have agreed for decades on the things that informed the Common Core Standards for Mathematical PRACTICE (that’s why they are so similar to the NCTM Process Standards). The arguments are mostly between mathematicians who are educationally and usually politically conservative (e.g., the Wayne Bishops and R. James Milgrams of this world, who despise anything that isn’t the sparest, most abstract approach to math imaginable, but want poor and minority kids to get a nonstop diet of repetitive computation, since all they’ll ever need to do is make change at McDonalds or WalMart), and those of us who are politically progressive, anti-corporate, and deeply engaged in ensuring that everyone has a chance to learn more mathematics and more varieties of what it means to know and do mathematics. We want kids to escape the endless, Dickensian world of math as nothing but number crunching. And for our trouble, we’re called “math-hating fuzzies who want to avoid, water down, dumb-down, ad nauseam, “real” math. As if. On which I call BS.
I must point out, finally, that your sentence quoted above sounds very familiar. It’s precisely the argument anti-evolutionists use to “prove” that “evolution is only a theory. Nice one. You should really be proud to be in that wonderful company.
I’m going to stick an oar in here as a former special ed teacher who for some reason ended up teaching remedial math in middle school. Many of my students had gotten lost years before because they were not able to move beyond rote memorization. None of them had a handle on simple arithmetic operations, and their calculation errors left them mystified by each new operation. Somehow the curriculum I was handed expected mastery of content well beyond what they had internalized. They were so used to failure that they just wanted me to tell them how to do it. They hadn’t understood what was going on in the past and didn’t figure that was going to change. With the advent of the calculator, too many teachers had handed them calculators and had them punch in formulas when they lagged too far behind. We went back to a very simple level of understanding. Does your answer make sense or is it at least in the ball park? I became a fierce advocate of students understanding what they were doing, so they didn’t have to rely on “tricks.” If they understand the math, they are not going to forget it. I have to say I learned more about teaching math through figuring out how to help them than I did in school where I had fallen captive to the mantra that girls just don’t do math. I will never be a mathematician, but I actually learned to thoroughly enjoy picking apart concepts, so I could help students to understand as well. (I rather liked your explanation of the division by zero as undefined, Michael.) Whether the concepts and methods being used are developmentally appropriate is still an issue especially at the youngest ages. What and how concepts are taught is equally important for children who are struggling for whatever reason. One size fits all is never appropriate. How anyone could expect a good reception of such a massive, rushed rethinking and implementation of instruction largely without teacher input is beyond me.
And once again we have Michael Paul Goldenberg whose personal beliefs about math instruction supersede EVERYONE ELSE’S lived experiences of how CCSS math is being taught, mistaught, mis-applied, abused, etc. but it doesn’t matter to him because he believes in the standards and therefore anything anyone else has to say is irrelevant and immaterial.
To him.
His world consists of him, people who agree with him, and the losers who haven’t achieved knowledge of him.
We hates him, to quote Gollum.
Its easy for him as a “math coach” working in a state that hasn’t been slapped upside the head by CC testing. He truly is a legend in his own mind. Too bad that some of his reasonable points are obscured by his obnoxious, arrogant, and insulting style.
You hates him because he’s using logic and reason you can’t refute and doesn’t toe anybody’s party line.
And if you think MPG is totally on board with common core, you know as little about him as you apparently do about math education.
Thanks, Dave Eckstrom. I do wonder on occasion here how folks like NYT manage to get it so consistently wrong about my views, but as one of my favorite enemies says, “religion is like that.”
I am not on board with CCSSI and never have been. But they use some excellent ideas about math teaching because some of the actual authors of the math standards have been on board with those ideas for over twenty five years. The deep evil of this new war is that we have idiot Tea Party people attacking everything in CCSS now because Bengazi and Fast and Furious didn’t get Obama impeached, so now it’s Common Core that is part of the Communist Muslim plot to destroy America, and people like NYT on the other side agreeing with idiots because the enemy of his enemies Re his friends. Or so he thinks. But they aren’t. Not by a very long shot. So anyone who asks for the slightest nuance is a corporate shill, in that analysis. Which makes me the poorest, least paid shill in history. Sucks to be me: I can’t get even 30 pieces of copper, let alone silver, for my betrayals. Unless, of course, maybe I have some vague clue as to how this battle fits into the larger war, and my long association with progressive education and politics dating back to the mid-60s is not a sham. But that’s impossible: like Obama’s birth certificate, I am part of a very long conspiracy, my own sleeper cell in the big plot.
Sheesh, I wish I could get paid to write fantasies about my own evil doing, at least.
And to those who call me smug: I don’t hide and my honesty has cost me jobs now and again. I have a family to feed, a son to try to send to college, and lots more that playing ball with the system would have taken care of. But I sleep at night because when I fight, it is in my own name. Smug? Too bloody bad.
Prissy, you are so off the mark to say that I believe in the standards that pointing you to my body of work opposing the very idea of national standards would be a waste of time. I was fighting high stakes tests when you were trying to learn how to spell “Gollum.” Or how to write a coherent attack on someone that actually is on point.
I can’t think of a more fitting example of why so few people here agree with or support MPG.
He explains that everyone here is wrong about him and his views. See, it’s their fault, not his inability to explain himself clearly or his huge ego and rude delivery, LOL.
A legend in his own mind? Agreed. Also a big enemy of good math instruction due to his obnoxious attitude and personality too, unfortunately.
If only we would all sit back and let him be in charge . . . . he will gladly tell us all what to think, do, and say, right MPG?
From the article:
“Almost every parent comes in and says, ‘This is not how I learned math,’ ” said Melissa Palermo, an energetic fourth-grade teacher who coaches other teachers in math at the Nathaniel Hawthorne school here [in Rochester, NY].
Palermo is a believer in the Common Core, a wholesale and controversial change in American public education, because she says her students are reaping the benefits of the new standards. They are showing a more sophisticated understanding of math and are able to perform operations they otherwise wouldn’t have learned until they were older, she said.”
“Reaping the benefits of the new standards”
An interesting way to define educational “benefits” – having 95% of your cities students labeled failures – for two years in a row.
Yeah, there’s a REAL benefit in Utah, where up to 70% of students failed the new Common Core SAGE tests this past spring. The numbers are now coming out, and now officials are scrambling to justify them, but when even the ultra-privatizing news organization Deseret News begins to question what is happening, you know it’s trouble. I really hope the outcry kills the standards in the state:http://www.deseretnews.com/article/865614569/What-Ogden-reveals-about-the-SAGE-test-teaching-and-how-students-learn.html
This may be petty, but one of the big turn-offs for me about the Common Core promoters is how they seem so eager to “rip off the band-aid”
We’re talking about tens of millions of public school children taking tests they will fail. There’s something repulsive about a bunch of adults who never had to deal with this when they were in public school eagerly anticipating that as “truth telling” .
It’s really easy to say someone else needs “more rigor” in their life.
Not one of the adults pushing these tests took anything like a Common Core test when they were third graders. I know I didn’t. This sort of breezy “oh, the KIDS will be FINE” attitude they project is very off-putting to me. I never took a 9 hour test in 3rd grade. I don’t know what that’s like, and either do any of them. There’s this sort of “get tough on the kids coming up” attitude that just bugs the hell out of me coming from adults who never had any of these measures applied to them when THEY were in public schools.
Classic top-down, command-and control speak. All their talk of accountability rings hollow when they have none.
My friend who teaches special education is now being told that her students should get all “1s” (the equivalent of a D in elementary schools) because her students aren’t “meeting the standards.” How can we do that to little children who already have extra challenges.
‘This may be petty, but one of the big turn-offs for me about the Common Core promoters is how they seem so eager to “rip off the band-aid” ‘
Totally agree.
Not that I expect people to care much, but number line skip counting and area model multiplication, the two explicit examples set forth in the article, are both well established models far older than the CCSS. And the Practice Standards are clear expectations of what mathematically proficient students should be able to do- things like explain their reasoning and critique their reasoning of others. They are not strictures for how to teach your class, unless “teach kids so they can do these things” is too much guidance. And if it is, I am intrigued as to which of the Practice Standards you consider too onerous. No one ever gets into that bit.
As for how your admin treats staff who revert to old curriculum in place of district-approved curriculum, that is a local issue, and not a new one. Districts have always frowned on those who refused to follow the adopted curriculum, though districts do vary on how much tolerance they have for adaptation and supplementation.
Basically, I find the article off-putting in tis ignorance of current classroom techniques and would be surprised it was promoted here if I didn’t already know that there would be loads of teachers here pushing the same context-free myths in the comment section.
But it’s confusing and sounds contradictory to people outside education because they’re promoting this as a huge change on the one hand and then insisting that it won’t be any problem for kids on the other.
To an adult that sounds like a contradiction. If it’s this huge change then wouldn’t some concern about how children handle it be justified? Downside risk? Unanticipated consequences?
To me, they can’t have it both ways. It can’t be sold as huge and revolutionary but also risk-free. Big change involves big risk. Either it isn’t that big a change or they’re downplaying and dismissing the risk.
Once they start saying something is a “gamechanger” they can’t come back and then say it’s really no big deal and kids will easily adjust. It’s this dual message that I think is confounding parents. It corrodes credibility.
The COmmon Core math standards and the way teachers are “encouraged” to teach add up to a ” de facto” curriculum. I seriously think it is a push to divorce parents from the ability to direct their children’s schooling and enforce a “way of thinking” on the “blank slates” …..scary, indeed.
Also, the amount of time devoted to pretty simple concepts/ units amounts to beating a dead horse. If you understand multiplication and can demonstate that you get it, then you should be able to move on!!! Why should you have to explain partial products, the lattice method, blah blah blah when all you really need to be able to do is multiply and divide. So much time is wasted reteaching simple concepts twenty different ways. Kids that understand it never get to move on, and are penalized for taking the more efficient route to problem solving!
“Tabula Rasa”
Tabula rasa for the math
Of Common Core, uncommon path.
Blankest slate to write upon
Testing on defenseless pawn
CC Practice Standards in Math:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
On face value, none of these practice standards are “too onerous”
They become onerous when they are implemented in ways and at grade levels that defy all we know about brain development, cognitive learning theory, and the effects of stress on brain physiology. They are onerous when thay are used to construct designed to produce an artificially high failure rate. They become onerous when we use them to label 70% of out third through eighth graders as failures in math, year after year. They become onerous when they are misused as a Trojan Horse for the corporate take-over of the public schools. They are onerous when they are indirectly used to intimidate and threaten the careers and livelihoods of math teachers. They are onerous when they are seen seen as one of the two, “be-all and end-alls” of the public school experience. They are onerous when the pressure to measure many of these unmeasurable (an mostly unteachable) skills limits the potential of 50 million children by expanding the null curriculum and robbing students of more important experiences, They are onerous in how and why they are being used – as just one of the main weapons of the test-and-punish federal regime.
I’ll just put this out for the usual screaming counter-attacks: if you confuse the textbook(s) your school is using (or in the case of NY and Louisiana, the online modules) for math with what’s actually in the Common Core Standards for Math – Content OR Practice, you’re making an enormous mistake. I have opposed, repeatedly, the Common Core Initiative and continue to do so. But the majority of what people are yelling about when it comes to math the last couple of years and what’s actually in the standards are light years apart. If only people could separate their specific objections (some of which are reasonable, some of which are not) to a given textbook series from what’s SPECIFICALLY required by the Common Core (which frankly isn’t all that much, in the sense that there is lots of wiggle room there for any district/school/teacher with the willingness to take advantage of it), from POLITICAL objections to Common Core, be those from the progressive or the reactionary end of the spectrum, then it would be CONCEIVABLE that we could have meaningful and productive conversations about math education.
Sadly, that’s rarely the case. So we get a lot of screaming and very little light is shed on anything about math education.
Yes, parents are mostly clueless. And were in the ’90s when NCTM Standards math was showing up in schools. And in the ’60s when various flavors of “the” New Math showed up, mostly in the form of SMSG materials, unfortunately – lots of much better things were produced in the late ’50s through early ’70s that were part of New Math, but few made it into many classrooms because of marketing/publishing issues. Robert B. Davis’s Madison Project up in Syracuse and later in suburban St. Louis produced fabulous materials that could be used today but were left to wither on the vine for the most part (though you can download some of them free if you just Google). Other materials were also good. But of course, they would have made too many parents have to actually think about math the way that mathematically knowledgeable people think about it, and that was just too much for most Americans, including my dad, who studied engineering in the ’40s before becoming an accountant. He COULD have learned the stuff my brothers were expected to learn, but he became a bit freaked out by not knowing how to do “elementary” mathematics all of a sudden. Bad roll out in the ’60s, bad roll out in the ’90s, and, unsurprisingly, bad roll out now. Someone could use a knowledgeable mathematics educator or two who also understands public relations, but unfortunately, neither NCTM and its affiliates nor the Common Core producers seem to know any, and the publishers have taken over, along with the test-makers and the Wall Street types and politicians, and the result is, unsurprisingly, that once again we’re in the midst of a Math War that you will (almost) NEVER get a straight article about from the mainstream media (mostly owned by those with vested interests in publishing, by the way: WaPo is now a wholly-owned subsidiary of Amazon.com and educational conservative idjit Jeff Bezos).
Well, by all means, don’t listen to anyone who actually has a solid historical perspective on what’s going on. Just react emotionally, don’t bother to sort through what’s valuable from what’s part of the politics of corporate educational agendas, and continue to convince yet another generation of kids that the “right” way to do math means to not think.
Unbelievably sad. And there are so many smart people who should know better but can’t let themselves see past the politics or the hysteria.
Arguments for what’s good about CC math standards are irrelevant until they are de-coupled from the current test-and-punish federal regime. Period. Your perspective from UM probably makes this fact hard to appreciate or even fully undertsand.
I am not at UM, I oppose the high stakes tests and have done so for fifty+ years. Take your blinders off, if you dare.
At times you seem to contradict this stance with apparent support of CC math standards. If you oppose high-stakes, test-and-punish reform, you cannot support the CC standards. they are Siamese twins, joined at the wallet.
You have a problem, NYT, not I. You can’t accept that the ideas that are in these standards were there before the standards existed, and that some of us are defending the ideas because they are sound. And will do so when the Common Core is gone. What bothers me is: 1) all the people who hate the ideas and did 25 years ago and will 25 years from now, the Common Core notwithstanding, and 2) people like you who seem to be so narrow-minded that you can’t conceive of anyone discussing mathematical ideas in a positive light if those ideas showed up (rather unsurprisingly) in a set of standards you despise for (mostly) political reasons. But the ideas and the politics are only connected INSIDE the abstraction of something that didn’t exist even 10 years ago and won’t likely exist 10 years hence. I won’t be bullied into selling out those ideas for five seconds to please people like you. You’re too rigid and dogmatic for me to consider any sort of potential ally when the CCSSI is done and we need knowledgeable people to fight for these principles and ideas nonetheless.
If that doesn’t make sense to you, I’m sorry. But I don’t think “sense” is what you’re interested in. You need BADLY to understand me as either an enemy or a 100% ally. I’m neither. And can’t be. Not for you. Sorry. Make me into your enemy then, because every time your respond to what I write, you make me wish you weren’t such a donkey about math teaching and learning. And someone like that is always going to find someone like me a very big problem.
“they are Siamese twins, joined at the wallet”
That’s the truth.
Supporting what you view as salvageable CC math standards now is counterproductive. You give people who are ignorant of the politics the false notion that the standards are independent of the tests and the evaluations and the data harvesting. You are like every other ill informed educator who says “I like the standards, its just the testing I am opposed to.”
I think you put your finger on it Michael when you talked about repeated bad roll out of elementary mathematics apart from any objections to CCSS. Mathematicians really have to ask themselves what they need to do to advance mathematical practice i.e. how to teach it. I suffered through an abrupt switch to new math when I moved. After a year of confusion and disorientation, I took a placement test for high school that place me in advanced level algebra class. I recognized a lot of the material from my old school. Unfortunately, any confidence I had had in my ability and any enjoyment I had in math was gone.
Do you ever wonder, as I often do, how with all the reform/deform initiatives in math, science, and literacy dating back for more than a century in the US, and all the money spent on them, they always screw up the roll out? Are they that stupid, or do they just fail to learn at all from history? Or remain utterly ignorant of it?
It boggles the mind.
“Common Core Math”
“Facts, formulas, shortcuts and tricks”
Who needs those when you have sticks
Boxes, dots and number lines
To calculate your late book fines?
Every set of standards implicates curriculum and teaching methods. The writers and the defenders of the CCSS insist on misrepresenting the standards as “neutral and non-prescriptive” in relation to curriculum and instruction for many reasons
First, the specter of having a national curriculum with prescribed teaching methods would be too hard to sell. Just deny that the CCSS have any implications for curriculum and how to teach. Lies aren’t noticed.
Second, USDE needed protection from charges that it was funding a prescribed approach to curriculum and specific teaching methods because that is unlawful. Never mind the law. USDE paid for curricula to make the PARCC and the SBCA tests possible. Illegal. No inspectors general are investigating.
Third, the CCSS must to be used verbatim. They are not a pick and choose menu. You can add 15% more standards (in ELA and math respectively) but these add-ons have to be segregated from the CCSS so they do not “contaminate” the tests that are in the works and designed to produce scores that can be made comparable. The UDSE funded tests are to be “comparable” even to the point of cut scores. That is illegal.
Fourth, the writers of the CCSS set up publishing criteria for curriculum and instructional materials shortly after the launch of the CCSS and have been tweaking them. These have morphed into a rating system for judging materials (2014) put out by Student Achievement Partners (SFP) with the NGA, Achieve and CCSSO—a ready-to-use 392-page document filled with iron-first rules and rating criteria.
Any claim that the CCSS are disconnected from how to teach and what teach is down the tubes.
This new rating system for CCSS-compliant materials begins with two “non-negotiables”
“Non-Negotiable 1. Freedom from Obstacles to Focus. Materials must reflect the content architecture of the Standards by not assessing the topics named before the grade level where they first appear in the Standards.”
Scoring is “Meets or Does Not Meet/Insufficient Evidence.” (No review of content from prior grades).
“Non-Negotiable 2. Focus and Coherence. To rate Non-Negotiable 2, (do this) first rate metrics 2A–2H each of these eight metrics must be rated as “Meets” in order for Non-Negotiable 2 to be rated as “Meets” …. “
Materials must “be clearly aimed at helping students meet the Standards as written rather than effectively rewriting the progressions in the Standards.” (p.127). (A restatement of the verbatim rule).
These and all of the other rating criteria for instructional materials— comprehensive textbook or textbook series; lessons, units and modules; grade or course-level tests; and individual test passages, items and tasks—are as hard-nosed as the voices of the authors of the CCSS. Tasks and items–that is specific.
This 397-page rating kit is available at http://achievethecore.org/page/285/materials-alignment-toolkit).
Although many teachers are already working on the CCSS, there is a challenger to this 397-page rating system. A press release (Politico, Aug, 19, 2014) announced the creation of a ‘CONSUMER REPORTS’ FOR THE COMMON CORE, a nonprofit outfit with start-up funding of $3 million from the Gates Foundation and the Helmsley Charitable Trust.
The launch is being managed by the PR firm, Education First, founded by a person who worked as a marketing expert for the Gates Foundation in promoting the CCSS. The website for the ratings, EdReports.org is under construction. Additional start-up funding comes from the William and Flora Hewlett Foundation.
These ratings will put publishers on the defensive (much like the Gates-funded ratings of teacher education). Ratings will be online and invite responses from the publishers. The initial ratings are for widely used K-8 math curricula, including Pearson’s enVision Math, McGraw-Hill’s Everyday Math, Houghton Mifflin’s Go Math.
These Gates-Helmsley-Hewlett ratings are intended to reduce the options available. So far, there is no evidence that this “user friendly” rating scheme will be coordinated with the hard-nosed 397-page criteria from the primary authors of the CCSS.
Bottom line, the writers of the CCSS want to micromanaging content and instruction…even if the standards left a bit of wiggle room.
I was talking to a Russian emigre last night. In fourth grade there kids were doing algebra. When she arrived in the US in fifth grade, the teacher was explaining greater than and lesser than signs. She thought to herself, “What have these kids been doing all these years? We learned this in kindergarten.” She remarked that schools in the USSR seemed to contradict PIaget’s claims about stages of development. I said Piaget’s words are treated as Gospel by many teachers here, but he’s just a theorist like Freud; he’s not supported by hard science.
Why don’t we try Russian math?
Be careful with Russians about math. They act like everyone over there is doing calculus in Kindergarten. They’re not. We hear the same nonsense about China and other Asian countries. Read Diane’s excellent review yesterday of Yong Zhao’s new book.
That said, they are right to doubt Piaget (or at least the Piaget CULT. He wasn’t dogmatic, but loads of folks have learned how to use him to justify nearly any position, usually by taking the “stage theoretical” aspects of his work as some sort of Law of Nature, which is far from what it was). I like his work, and recommend when it comes to primary grade math that people try reading the research of his former student, Constance Kamii, who is still working at one of the U of Alabama campuses last I checked.
But there were some fabulous researchers in math education in the old Soviet Union, the best of whom, for my money, was V. V. Davydov. He approached K-3 mathematics from the perspective of measurement rather than counting, developed a marvelous curriculum for early elementary students (versions of which are still used in Russia, etc.) and worked with others to do a lot of things that mostly were and are ignored here. However, a few American mathematicians and math educators know his work. Susan Addington, a mathematician at UC-San Bernardino, has a curriculum for elementary math teachers grounded in Davydov’s ideas. A former math teacher in Maine, Peter Moxhay, also developed materials for K-5? based on Davydov. So has mathematics education professor, Barbara J. Dougherty.
Also worth looking at, from a different tack: Alexander Zvonkin’s book, Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers, which might suggest to people like NY Teacher that the world is bigger and has more things in it than dreamt of in his philosophy. I worked a bit with Zvonkin on trying to get that book translated from Russian and published here, but failed. I’m so glad he kept at it and finally found someone good to do it. Great book full of amazing material worth thinking about before shutting one’s mind to what young kids are capable of AND eager to do in math given the right set of circumstances. Starting with teachers who don’t fear and loathe mathematics.
While I do agree that the CCSS most definitely dictate how students should learn math (more conceptual understanding, less reliance on memorized algorithms – although not a complete abandoning of them) these “practices” come from years of research by the NCTM, preCC. If we want to discuss the misplacement of some of the topics, the fact that the CCSS are not the promised “fewer, deeper”, the scripted curriculum often chosen by districts due to the rush job of the CCSS implementation, the high stakes testing, the corporate involvement and any other of the myriad of things wrong with the CCSS…that is one thing. If the “old way” was so good, we would not have adults (parents and teachers included) who were taught preCC so happily admit they were never good at math, that they chose their college majors and careers based on the amount of math required (or not required). Many adults have these feelings, but then are unwilling to have their children exposed to a more complete understanding of mathematics. If one wants to see this supposed “new math” in action and successfully implemented, one only needs to go to a Montessori classroom where they have been using this kind of learning for close to a hundred years. And Montessori started her curriculum in the slums of Italy. So many, many reasons to HATE the CCSS, the math practices are not one.
Neither of my sons have a “deeper understanding” of math in the now three years’ worth of instruction with Common Core. They are just lost. And I hear that from a lot of students every day.. They are left to try to figure out the math on their own, and many cannot. These are junior high and high school students.
This will be the legacy of CC math. Thank you TOW.
NY Teacher,
It seems to me that students have been lost and confused about mathematics long before the CCSS.
If the powers that be really wanted all children to understand and be proficient at CC Math, why didn’t they phase it in slowly one year at at time? Why is a NY fifth grader expected to do new CC math as if she or he had spent the last four years learning in this new way? Why not start with basic concepts in prek and kindergarten and build on prior knowledge? What was the rush? Why won’t they slow down the implementation even after 70% of NY children are labeled failures? I sure hope it doesn’t have anything to do with Gov. Cuomo’s promise to “push new teacher evaluations” which, as we know, are tied to student test scores. Sorry if that sounds political.
I don’t think comparing Russian math to ours is all that helpful, without a lot of context. How long ago did she emigrate? What SES level did she come from? How many Russian students go on to engineering and math careers? How does tracking work in her Russia? What if a student was poor at math as a kid, were they written out of a whole area of career choices from a young age? Is the Russian schooling system really the one we want to emulate? Or Korea? Or China? Would you want your kids going to anything resembling those school systems?
There is a significant irony in the way that Common Core was developed, given that it is supposed to teach students how to solve problems.
As anyone knows anything about problem solving appreciates, the very first (and most important) step in solving a problem is understanding and defining the problem one is trying to solve.
From what numerous early childhood experts have said about the inappropriateness of Common Core for early childhood learners it appears that those who developed Common Core failed their own effort at problem-solving at that very first step.
In fact, given that there were no K-3 classroom teachers or early childhood experts on any of the panels that wrote and reviewed Common Core, it’s clear that they didn’t even make an effort to understand early childhood learners.
If one does not properly understand and define the problem (which in this case might be described as ” develop -age-appropriate standards for early childhood learners”), any solution one comes up with is of dubious value.
I don’t know who says that CCSSM does “not influence or control either curriculum or pedagogy.” What would be the point of standards that did not influence curriculum or pedagogy?
If the complaint is, as the WP article describes, that the standards require understanding instead of rote use of algorithms, yes, the standards are guilty.
CC standards don’t just influence curriculum and pedagogy – they dictate with scripted lessons (read test prep in disguise). Its bad enough that the over emphasis on MATH and ELA has expanded the null curriculum but CC standards are also narrowing math and ELA as well.
Scripted lessons are supported by exactly what part of the actual standards fir math, Content or Practice? Cite anything to back your claim. From those very public documents. You can’t, can you?
Tilting at windmills is romantic, but a waste of time and energy. Your lack of confidence in everyone but you to see political nuance is one of your central difficulties. If the entire nation is that stupid, we are doomed anyway.
You still don’t get it, do you?
MPG, this has nothing to do with citing documents. This has to do with what is actually happening, in real schools, right now, as a result of this political initiative. Are those two different things? Based on what you’ve been saying, and comparing it with what teachers and students are experiencing, it sounds as though they don’t even have a passing resemblance.
The more I read about this, the more I think the “standards” are designed to weed out the majority of students, so that corporations like Microsoft don’t need to test them, or bother with their resumes. Of course, they will also have less to do to train those who do run the gauntlet. All of that work — the weeding and the training — will have been done for them. This is the source of their sudden interest in education.
I think it’s admirable that you want to teach real mathematics. I believe it changes how a person thinks, and that it has a hugely positive influence on their mind. It sounds to me like the CC program, as it is being implemented, will make sure that most kids won’t know real mathematics. This will make it easier to sell them various “investment products,” and to indebt them with exotic mortgages and so forth.
Mathematics education during the Sputnik era was not half bad. Mathematics education was gutted during Reagan. I don’t think it’s an accident. The parents of today’s primary school students are mostly products of the Reagan era schools. Figures.
There was a traditional way of looking at how different people grasp mathematics. It’s a bit archaic, but it’s not pointless to consider it. Some were said to have an “algebraic spirit,” and others, a “geometrical spirit.” Simplistic, yes, but the point is valid. Trying to teach mathematics the same way to everyone is a very bad idea. We know it won’t work. We KNOW. Furthermore, the idea that practicing with algorithms will never lead to higher understanding is false as well. Practice with the right sorts of materials, with problems arranged in the right order, does lead to discovery of larger patterns.
The materials that have been foisted on teachers with CC disadvantage those who are bilingual. Some of those kids used to be the best math students. Math was the highlight of their day. Now that’s gone, too.
BTW, I’ve shown students of all ages why dividing by zero is undefined, and I thought your explanation was rather confusing. But that’s just it — suddenly, mathematics is “discursive.” Well, for some, it’s “intuitive.” For some, it is not verbal at all. And their reasoning is faster than my explaining. They just “see it.”
The fact that I don’t particularly like how you explained the impossibility of division by zero is meaningless; if a student wrote what you wrote, they would deserve full credit.
Finally, there is not one elite private school that has adopted this program. If it’s all that great, why not? Why do they avoid it like poison?
Sonja, you call the standards a “political initiative” and then proceed to discuss them in political terms (as a benefit to Microsoft…math gutted by Regan…etc.). Teachers in the classrooms I see treat the standards as an educational tool rather than a political tool and when they do, they find big success.
Bad materials can be “foisted on teachers” no matter what standards are used and that’s certainly happening. But the real lesson here is that teachers need to do what good teachers have always done and develop their own lesson plans. There are no good commercial “programs.”
There seems to be no way so far to stop states like NY from putting out scripted programs but that’s not a Common Core issue.
Sonja,
I think you would likely find mathematics instruction at St. Ann’s school in Brooklyn, where Lochhart teaches, is likely to look take an approach to mathmatics that is much closer to that in the CCSS than traditional math instruction. I hope that mathematics instruction at Bard College at Simon’s Rock also teaches actual mathematics.
Excuse me, Bill Duncan, but if this is a political initiative, why should it not be discussed in political terms — at least insofar as it is political?
Your logic escapes me, I must say.
We are still talking about two things — what the documents that embody the standards say should happen, and what is actually happening under this initiative.
Now, if CC is so great, I ask again, why are the best private schools teaching “something like” what CC does (or does not) suggest, or mandate, or support, or whatever word you like, but they are NOT adopting CC?
I think the answer may be in the part of my comment you didn’t address: Mathematics is not something that can be taught to everyone in the very same way. Interesting, because in the end, when we begin with the same assumptions and the same questions, we all do get the same result. Yet the process by which we become able to do math will be unique to each person.
Educational theory had recently caught up with the best research on the neurological bases of acquiring expertise, and wouldn’t you know it, but in a time of austerity, this knowledge just happens to get chucked for a one-size-fits-all curriculum.
In a time of austerity, people with serious money can get very far with their agenda, whether that agenda is good for the students or not. That is not their concern in any case. They have other goals in mind. People need to recognize that basic fact, the way they used to. You don’t expect a corporation to have your best interests at heart. That is not its job. The corporation is not your Mom. They have something to contribute to the conversation, but nothing to dictate, to any of us.
It seems to me that you are trying to suggest that all those opposed to CC Mathematics are opposed for illegitimate reasons, perhaps for one of the worst reasons of all — because they don’t understand it themselves. Sorry, but that story will not wash.
You cannot divorce standards from curriculum.
I’m not sure who commented that the rollout of CC was similar to the premature rollout of new computer operating systems that we’ve seen so many times, but I think they got it exactly right.
Except that these aren’t computers, these are kids we are experimenting with. This is much more serious than blooper software, which eventually gets fixed. If these kids lose a year of mathematics, there is a risk that many of them will never recoup. This will force down wages even further, and put people at the lifelong mercy of creditors. Not to mention the unquantifiable loss of the opportunity to learn and enjoy one of the coolest things in the world — mathematics.
Oh, and speaking of money — yesterday I looked up the total tuition for one of the most prestigious private K through 12 schools in New York City. Over $550,000 for those thirteen years. Remarkable, isn’t it? Their website talks about educating the whole person. There is no trace of CC rhetoric or mentality to be discerned. Well I wonder why.
Sonja,
How many student’s interest in mathmatics are destroyed by the traditional teaching of mathmatics? In my little local district it is essential that strong math students are moved out of k-12 math education as quickly as possible.
Is whataboutery fair play?
(Sorry for being flippant, but I fail to see why one bad program should be followed by another.)
Sonja,
What does fair play have to do with the discussion here. Could you elaborate on this point?
It was a pun. You know, “is turnabout fair play?”
I substituted “whataboutery.”
Okay. I’ll refrain from that in the future. I guess I read too much British press.
Yes, I do wonder whether “fair play” has much to do with public education in America. That isn’t intended to be funny. It is a very good question, regardless of your position on Common Core.
MPG
You are every CC reform advocate’s pet dream. Intelligent, experienced, superb command of your subject, very well read, and accomplished in your field. And you advertise for them for free. Somehow still ignorant of the fact that you can’t have it both ways. You cannot be for the standards and against the high-stakes testing. Yet out of the other side of your mouth you will, after your endless diatribes, say that you’re also against national standards. The corporate take over of public education and the founders of CC math don’t give a whit about better math education. Refusing to attack the weakest link in the chain tells me all I need to know. And so I bow to your superior intellect, your rock solid logic and unbeatable arguments. yet I pity the blinders that you have on. Blinders that hinder the chances for real, meaningful math reform in this country as they are simply enabling the test-and-and punish regime to maintain its stranglehold on the children and teachers of America.
NYT, why the psychoanalysis instead of just responding to MPG on the substance?
A lot of the examples that I see in the anti-common core math posts seems to come from the TERC Investigations curriculum that has been around for years and was what was in fashion when my daughter was in elementary school. What I noticed while she was going through K-5 is that the thing that makes the difference is how these things are covered. Some teachers taught TERC algorithmically where they made the kids memorize steps for breaking apart numbers to add or using an area model to multiply or memorize the steps to using the number line method without really explaining it. A lot of these methods rely on fluency with other skills and how the instructor delivers the content and like anything it worked with some students and not others and many of the non-standard algorithms break down with decimals or some types of numbers. I don’t believe there was ever a time where math was intended to be taught only as rote memorization of algorithms and with each new iteration of teaching arithmetic that’s the claim. (https://investigations.terc.edu/)
Thanks for this perspective, Sarah.
Reblogged this on 21st Century Theater.
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