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James Milgram’s dishonest critique of the Common Core math standards

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Most critiques of the Common Core don’t hold up to scrutiny. Dr. James Milgram’s critiques never do.  His criticism of the math standards is the basis for most of the rest of the math criticism you hear, but is fundamentally dishonest.

Milgram uses a willful misreading of the Common Core standards to say that California’s pre-Common Core standards for kindergarten math were better.  He claims that, in the Common Core standards, numbers are “nothing more than oral and reading vocabulary,” while the California standards pushed deep into the meaning of numbers.  Actually, the two standards are very similar – both good at guiding teachers to engender a deep sense of the real meaning of numbers – but the Common Core standards are an important advance, as this great article describes.

And, since the California standards were actually so similar to the Common Core standards, Milgram manages to undercut claims that the Common Core math standards are not “developmentally appropriate” for kindergarteners  – a claim definitively put to rest by New Hampshire kindergarten teachers here.

The details

Common Core opponents frequently refer to James Milgram’s critique of the math standards to support their assertion that the standards are not rigorous enough – don’t prepare students for algebra in the 8th grade, etc. – even while complaining that the kindergarten math standards are too hard, “developmentally inappropriate.”

But the closer you look, the more confused this critique seems to be.  Jamie Gass of the Pioneer Institute referred me to this paper by Milgram and Sandra Stotsky as the foundation for this kind of critique.  Milgram, presumably, did the math sections and Stotsky the English sections.  But there are several problems with the math critique here.

First, Milgram seems to have started with the desired conclusion – “The Common Core is all wrong” – and worked backwards to create the evidence.  On page 4, he says,

California’s standards first focus on numbers as objects with special properties—they can be compared, they have magnitude, and they can be also be added and subtracted. But in Common Core’s standards, numbers are nothing more than oral and reading vocabulary in kindergarten.

Then, in the worst form of scholarship, he quotes selectively from the Common Core standards to make his point.  He says, correctly, that the first three Common Core standards are:

1. Count to 100 by ones and by tens.

2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Then, as you can see in the paper, he cites the California standards.  But, actually, the Common Core standards go on to say this:

4. Understand the relationship between numbers and quantities; connect counting to cardinality.

5. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.
7. Compare two numbers between 1 and 10 presented as written numerals.

So, actually, the Common Core standards call for almost precisely the same approach to teaching numbers in kindergarten as California did in its widely respected standards.  Here is a comparison of the early grade math standards that is much more balanced and useful than Dr. Milgram’s.

This example illustrates the fundamental dishonesty of Milgram’s approach to critiquing the Common Core.  It gives advocates like the Pioneer Institute something to say when they travel the country railing against federalism, but it doesn’t stand up to scrutiny.

Beyond that, however, Milgram unwittingly undercuts the charge Common Core opponents make the that standards are not “developmentally appropriate.”  The only real difference between the California kindergarten math standards -widely regarded as “appropriate” and wise – and the Common Core is that the California standards had the kids counting to 30 (as New Hampshire and other states did) and now the goal is for students to count to 100, a goal that New Hampshire kindergarten teachers are finding entirely achievable.


  1. Jack Blodgett says:

    A friend of mine who launched one of the nation’s first, statewide specialty schools in math and science once told me a story about a teacher who walked into his classroom one day with all the principles and strategies of the latest standards for teaching mathematics well in hand. Of course this was back in the days when the National Council of Teachers of Mathematics was busy setting the stage for the development of math standards in the many states that the pro-CCSS Fordham Institute has recently graded as equal or superior to the CCSS. As the teacher proceeded with his lesson, he became increasingly annoyed by a student who was dead asleep, sprawled out with his head down on his desk in the very front row of the classroom. Finally, the teacher could stand it no more and admonished the student for not even giving his innovative teaching half a chance to get him engaged in learning math in a deeper and more relevant way. Startled, the student looked up at the teacher, politely waited for the teacher to finish scolding him, and said: “Well, go ahead and teach then – – – it don’t bother me none.”

    My friend was trying to tell me that it’s not about the quality of a spanking new standards document, or even about the skill of a conscientious teacher in translating words into exemplary pedagogy. Well…I wondered at the time…what IS it about then? If any readers of this blog have discovered an answer to that question for themselves, I think we’d love to hear those stories over and above inquiries into how some new Common Core angels can now dance on the head of a pin.

    • Bill Duncan says:

      It’s about good teaching, Jack, as the Sanborn teachers demonstrate. Standards are necessary, but not sufficient. We should not be wasting our time on this standards debate.

      You need to go out and help change the debate.

      • Jack Blodgett says:

        If it’s all about good teaching, then you shouldn’t glorify the CCSS in your posts. Milgram’s preferred standards could allow for just as much “good teaching,” so why not focus on the teaching regardless of the standards. That’s how you change the debate. Your debate has gone on long before your relatively recent interest in public education.

        • Bill Duncan says:

          I don’t get what you mean by “glorify.” You do realize we’re in a debate about rolling back CCSS, right? It’s not a matter of sticking Milgram’s preferred standards in the schools that like them. I think you may underestimate the disaster for kids if American education were immobilized over this CCSS debate with states half in and half out. The debate needs to be put to bed and dishonest participants like Milgram need to be called out for it.

          • Tyler Haslam says:

            Exactly. The debate is doing more harm than good regardless of which way it falls. For example, Oklahoma passed a bill that their new core cannot have any overlap with CCSM ( So what, now you aren’t going to teach any of those things like “count to 100”

      • ajbruno14 says:

        I find the supporters of Common Core prefer to be on the “defensive” when people like Milgram criticize a standard. He was not alone in refusing to sign off as member of Validation Committee. So was Dr. Stotsky, prof. of English Literature. Both of them and three others who refused to sign off had the concerns scrubbed.

        Here in NC when I questioned Common Core, I was told criticisms were ‘myths’ and I should believe propaganda, a familiar response when “snake oil” cannot be sold to an educated public.

        It is a shame that govt. had to use the coercive tactic of withholding Fed fund from cash strapped states to get most to adopt Common Core, a clear violation of the US DOEs own mission statement.

        Thankfully, we are doing something to ensure our children learn rather then be “educated” with an untested standard developed elsewhere.

        NC has decided to replace the CC standard with our own, and uncouple from tentacles of the CCSSO which claims copyright ownership of education.

        NC is joining a growing number of states to see CC for what it is, and more importantly what it is not.

        • Bill Duncan says:

          Interestingly, this is a political response to my critique of Milgram, but no one has taken on the substance, which is that Milgram makes a fundamental and what looks like a willful errors in his analysis. Either he doesn’t understand the standards or he’s opposing them for personal or political reasons. Either way, we should not pay attention.

          North Carolina is systematically dismantling its wonderful system of public education. If the current debate does result in abandoning CCSS, that will be just a detail in a much large tragedy.

          • Roni says:

            The bigger picture is about what kindergarteners should be learning and how it should be achieved. They are concrete learners. They learn from play and hands on activities. From a speech development perspective, quantitative concepts needed for math are later developing concepts. At age 5 or 6 there is a vast range of maturity. Even a 6 month difference between students can be huge. They are developing the motor skills for writing as well as early reading skills. To be asked to justify answers in writing is absurd.

          • Bill Duncan says:

            I agree with a lot of what you say here, Roni, but I don’t think it ultimately conflicts with getting introduced to math concepts as a young child. Which standard are you talking about that requires kindergarteners to justify their answers in writing.

      • Tyler Haslam says:

        Couldn’t agree more. Lets focus our energy on something more impactful.

    • Of course, “your friend” (or you) was adopting a vastly older story that in fact applied more aptly to more typical and traditional classroom teaching of many subjects and which cuts far deeper than NCTM or Common Core, as an honest critic would admit up front. James Milgram is a very knowledgeable mathematician. What he knows about the core issues for teaching K-12 (or more importantly, K-5) mathematics is highly debatable and in practice approaches zero, other than the fact that I’m sure he knows about the natural, whole, integer, and rational numbers and their operations, though not likely how to explain to or lead any kids to understand them, particularly not without already being at or near the level of advanced calculus and/or abstract algebra. Not my go-to guy on real problems of teaching mathematics to children. Not close. Nor are any of his Mathematically Correct and NYC-HOLD compatriots.

      Far better would be to read and heed the work of people like the oft-maligned (by the above two groups) Constance Kamii, a student of Jean Piaget. And dozens and dozens of mathematics education researchers who have taught elementary school in recent memory, actually work with real children and their real teachers, and are familiar with the main body of research literature in the field.

      Our MC/HOLD buddies disdain such people and their work, UNLESS their conclusions happen to dovetail with anti-progressive biases. Otherwise, Milgram would sooner listen to Sandra Stotsky, who has no background whatsoever in mathematics or mathematics education, is a paid stooge of the Walton Family in her position at U of Arkansas, and gets to serve on these national math panels because. . . ? ? ? Politics and money, period. Yet our James thinks she hung the moon. Deborah Ball, a former elementary mathematics teacher, doctorate in mathematics education, dean of the University of Michigan School of Education? Not so much. If you don’t think that’s odd and unprofessional and highly political, then perhaps you need to think more than you do about what’s going on.

      I say everything above as an OPPONENT of CCSS-I, but not of particular ideas within them that make sense and have since they first appeared anywhere between 25 and hundreds of years ago. But the Math Wars types like Milgram are never going to bother to read the history of mathematics or care about it if they did. They’ve not had a new idea about math teaching since they left grammar school and never will. They’re fighting to preserve the principles and practices of 19th century Prussian military training in the mistaken belief that these are all-American in every way. But of course, they’re quite other than that, anti-democratic, anti-freedom, and most of all, anti-child.

      If the kid in the made-up anecdote wants to sleep, that’s his call, but why he wants to may be in some part on the teacher, the school, the curriculum, the insipid assumptions of American schooling (as opposed to educating) that don’t reach a vast number of kids, including the ones who seem to be thriving in it, but instead are just playing the game of studenting, not learning).

  2. Scott Marion says:

    This is a good discussion. I agree with Bill about the importance of being honest about the standards and I think it is very important for US education for the standards to be well implemented. I also agree with Jack that standards alone won’t solve the problem (but I don’t think that Bill is arguing that). I’ve found Dick Elmore’s “instructional core” to be a useful framework for thinking about the complexity and simplicity of this work. I paste below a portion of something I’ve written, pulling heavily from Elmore and colleagues:

    One of the key design principles in our work has been the “Instructional Core: The systems must strengthen and support the relationship among the students, teachers, and meaningful content (and skills).” Before discussing capacity building, it might help to provide a bit more background on the instructional core , a set of principles articulated by Richard Elmore and his colleagues. To quote from City, et al (2003):

    “There are only three ways to improve student learning at scale:
    You can raise the level of the content that students are taught. You can increase the skill and knowledge that teachers bring to the teaching of that content. And you can increase the level of students’ active learning of the content. That’s it. Everything else is instrumental. That is, everything that’s not in the instructional core can only affect student learning and performance by, in some way, influencing what goes on inside the core. Schools don’t improve through political and managerial incantation; they improve through the complex and demanding work of teaching and learning (p. 24). ”

    Elmore and colleagues further elaborated this notion, but defining seven principles of school improvement.
    “Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement.
    Principle #2 :If you change any single element of the instructional core, you have to change the other two.
    Principle #3: If you can’t see it in the core, it’s not there.
    Principle #4: Task predicts performance.
    Principle #5: The real accountability system is in the tasks that students are asked to do.
    Principle #6: We learn to do the work by doing the work. Not by telling other people to do the work, not by having done the work at some time in the past, and not by hiring.
    Principle #7: Description before analysis, analysis before prediction, prediction before evaluation (p. 23).”

  3. James Milgram is a Stanford professor, a mathematician, and a standards expert who has helped a number of states craft excellent math standards. What exactly are your qualifications Mr. Duncan? Apparently none.
    As I see it, in the world of mathematics education, you would be referred to as……”Bill who?”

  4. A Teacher says:

    Having read the California Standards and the CCSS, I agree with Dr. Milgram. Two dimensional vs. three dimensional doesn’t seem necessary for kindergarten kids, now does it?

    • Bill Duncan says:

      What do you think about his misrepresentation of what the standards actually say?

      • Roni says:

        I don’t find you offering anything of substance to prove Dr. Milgram has been deceptive.

      • Flash toso says:

        From kinder garden math standards
        Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
        Analyze, compare, create, and compose shapes.
        Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length).

        California standards from
        California Common Core State Standards for Mathematics, Adopted August 2010 and Modified January 2013 (DOC; 6MB) (April 2014 Version)

        (2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.

  5. There’s the other end of the K-12 spectrum about which Milgram also lies like a rug. He repeatedly gripes about the lack of calculus standards as part of his complaint about CCSS-Math. But it’s patently obvious that there are no calculus standards stipulated because we already have national standards for calculus: they’re the AP curricula and exams.

    Furthermore, it’s pretty obvious that one reason there has been a “push-down” of some topics in the primary grades is because of Milgram’s ceaseless litany of nonsense about international competitiveness. If you’re supposed to be getting “every child” in the US calculus ready by 12th grade, then there’s less time to ensure that most kids actually have a solid foundation in the mathematics they’re likely to need and use for their entire lives, even if they don’t become professional mathematicians, physicists, engineers, or other high-end math users. The fundamental elitism that Milgram and his allies in anti-progressive groups like Mathematically Correct and NYC-HOLD exhibit repeatedly is obvious to anyone who isn’t snowed by their bluster.

    I wonder if you’ve read a somewhat obscure interview with Milgram that I blogged about a while back here: from which I think it is evident that the professor has stripped a few of his gears.

    By the way, I should make clear (and you can see evidence of this elsewhere in my blog and in my contributions to the @the Chalk Face blog that I’m not a huge fan of the Common Core Initiative. However, I’d like to think that my critique is better founded than Milgram’s who, as you correctly point out, is utterly full of it when it comes to this (and many related) issue(s) in mathematics education.

    • Bill Duncan says:


      No, I hadn’t seen that 2006 Milgram interview.

      “The people holding the power in the education community today hold the belief that the major function of the public schools is to keep children out of the workforce….They also believe that kids should have a good time in school because implicit in their belief is the conviction that kids will not have a good time as adults.”

      It shows both that he’s off the rails and that he has been for a long time.

      I look forward to connecting…

    • Roni says:

      As a parent of a 9th grader, our district tried to scramble to do 8th grade math and algebra at the same time to play catch-up so students could take finish through to calculus in high school. It didn’t work. The amount of pressure coupled with procedural changes made this unsuccessful for many. It was stressful- self abuse- kids shutting down. Way to go- all of you who think common core is so wonderful-I guess you don’t have kids.

      • Bill Duncan says:

        I guess I don’t get how you link the Common Core to the troubles your school has had. Algebra has long been taught in the 8th grade and, under the Common Core, still is. And it’s also true that too many students – students who are not really ready – probably take it. All of that has nothing to do with the new standards.

  6. sammy says:

    As a parent I am concerned with “dumbing down” of math standards. My district will no longer be offering advanced math to middle school students now that they have adopted common core. Yes, our HS has AP courses, but if students cannot take Algebra until 9th, they will not be able to take Calc in HS. For some kids this is fine, but kids who can handle the advanced curriculum (and plan on a STEM degree) will not have the option…

    I’d be interested in thoughts on this article in which Milgram addresses problems with math standards AFTER Kindergarten (comments about the author being “off the rails” aren’t really helpful, but specific comments on his claims would be!):

    • The level of algebra your school offers to 8th graders is entirely up to your school and is not based in the Common Core. As you will see from p. 80 of the appendix, the standards provide very carefully for offering that advanced pathway. And you can find elsewhere on this site a useful discussion of the pros and cons of Algebra in the 8th grade.

      RE “…two years behind…”: Milgram has repeated that for years but, to my knowledge, has never documented it. That said, I’m sure he must know, as other professional math educators do, that, yes, the U.S. has been so far behind in math education that it would not have been possible to catch up in one step. You must have seen that we already have big debates about whether the math standards are developmentally appropriate in the early grades. Just imagine if we set our standards at the level of Singapore. If we stick with the Common Core standards we will be on the path to catching up, but it will take time and future revisions of the standards.

      He goes on to say vague things about remedial work being necessary in college. True. That’s what the standards are made to help remedy.

      Do you think – or do you read Milgram as saying – that calculus should be part of the standards and, therefore, that all high school students should take calculus (5-15% do now, depending on the school)? Only students planning on certain careers need that. Again, a well established point that Milgram continues to argue. But it is a point made for political purposes. I know of no high school educator who would assert that all students should take calculus.

      If you feel Milgram’s point about an “unusual” approach to geometry is a serious one, better ask NCTM. It’s a little vague and abstract to me.

      If your child has achieved numeracy by the 5th grade, as the standards demand, math at any level will be open to her. That will be a big step forward for many American children.

      • sammy says:

        thanks for your response… I do understand that cc does not dictate when algebra can be taught and that AP Calc. may still be an option at some High Schools. However, the Algebra in 7th grade is absolutely not an option anymore for students at my local middle school BECAUSE of cc: those implementing cc (at least in CA) seem to have a strong belief that Algebra should not be taught to ANY student until 9th grade, so I imagine my district (and many others) are simply going along with this even though they are not technically required to. In fact a State CC rep. that came to speak to parents about the math standards went to great lengths to convince parents that Algebra in 7th grade is a terrible thing for kids…I have a HS student now who took Algebra in 7th and now as a 10th grader is taking Pre Calc(she is 2nd in the class; #1 is another 10th grader), her brother in an 8th grader in Geometry who will follow the same track as he is grandfathered… their brother, who is now is 4th grade, will not be allowed to follow this track no matter how advanced he is in math. So,that means no AP Calc Jr year for sure, and I’m not certain many (any) kids would be able to get to calc by Sr. year. So, I’m left wondering if my HS will even keep offering calc at all and if they do keep it it will certainly be impossible for my youngest to get AP Calc and AP Statistics under his belt before college. So, I’m not saying at all that ALL kids should take Calculus (and AP Stat) in HS, but I tend to think that the option should be there for those who are up to it and plan on a STEM career. Not sure yet if my youngest will be in that category and it’s possible that the slower pace will be better for him, but I’m worried that CC is yet another “one-size-fits-all” approach (at least as implemented in my district…).

        • Sammy, there is ample evidence that as things stand now and have stood for decades, algebra for ALL students in 7th grade is a disastrous goal. The educational conservatives pushed that in California starting in the late ’90s and it failed. They blamed poor teaching. No doubt there is some of that. But the big problem is simply trying to force all kids into a mold that most of them aren’t suited for at that age. Period. Could that change in time? I believe it could. But you don’t fix high school & college math in middle school. You fix it throughout K-12, and also in college in terms of what is taught and how. That is, in theory, what CCSS-M is intended to do. It’s questionable that it can. And that’s a much bigger issue than James Milgram and the “dumbing kids down” crowd are willing or able to cope with.

          But if you have kids that are ready for algebra earlier, by all means exercise your democratic right to: a) put them in a more advanced school – public or private – if you can find one and can get your child into it and, if necessary, pay for it; b) relocate to a more advanced district; c) find a place that does math enrichment either in school or after school; d) find a private after-school program to supplement what your child can get in school; e) point your child to some specific free online resources and make sure s/he has access to them. You might have to do some exploring on your own or with your child.

          That doesn’t exhaust the possibilities. But I can tell you right now that one size has NEVER fit all, and it never will, but other approaches tend to be more costly in various ways and spending big $$ in education on TEACHERS is not in fashion. Computers? Software? Other hi-tech? Sure. So there is a political issue here that is unavoidable. Imagine what it’s like for urban and rural poor kids. Imagine living on an Indian reservation. Common Core isn’t the issue, by and large: it’s vastly bigger than that.

          Again, I don’t think I would wait for schools to be “fixed” or “ruined” by this wave or any wave of ‘deform’ but rather would draw on other resources inside or outside my local schools. Parents who’ve done that over the last century or so generally are much happier. Whether their kids are is another matter.

        • mach says:

          As far as I know, Algebra 1 in 8th grade up to Calc 1 in senior year is pretty standard (Alg1 -> Geometry -> Alg2 -> Trig/Precal -> Calculus), so I’m pretty sure a lot of students would make it? Of course some students are advanced and may do it earlier.

          Your youngest could still take AP Statistics junior year, it doesn’t require precalc or calc by any means (non-calculus based statistics is sort of silly to start with, but it’s worth it for the credit and background heading into college).

          In my situation, I took Algebra 1 in 7th, and then my school didn’t have a class for me for 8th grade (small town, I was the only one doing it), so they let me go to a first period geometry class at the local high school and go to the middle school starting at the next class period (there was about a 30 minute delay in starting times, so it worked), assuming we would find a transportation solution ourselves.

          There’s also the option of forgoing AP Calculus in senior year, going to a local college, and taking Calc 1 in the Fall and Calc 2 in the Spring to get both by graduation.

          If not, try to work out something with the school to let your son learn one of the high-school math subjects one summer. He might have to do more independent learning, or you may need to hire a tutor or something. We never had trouble finding a teacher and school that would cooperate and at least to the level of proctoring some exams and letting me skip the class if it went well (although usually they didn’t mind to also field questions from me if I had any). It can be tough to self-teach math from a book without people around who know (or remember) how to do any of it, I think it was a valuable experience.

    • Sammy, I wonder if you looked at the interview Milgram gave that I wrote about in my blog (and provided a link to in a previous comment). If you did, I think you’d grasp why it’s relevant to suggest that not only is Milgram dishonest and highly political in his assertions, but he has shown clear evidence at times in the last decade of being delusional.

      His arguments against the Common Core are intriguing to me in that they are so transparently false that anyone with familiarity with US math curricula at the secondary level can read through them. He claims CCSS-M won’t have kids ready for college math, and yet comparing them with the vast majority of the state standards they replace makes clear that if anything, these standards push many topics DOWN the grade band (which upsets many parents and teachers, but not Milgram for some odd reason), in order to make way for getting “algebra for all” down to the 8th grade level and, conceivably, to 7th grade, a project that Milgram and his Mathematically Correct and HOLD pals in California were able to force down the throats of Californians until things became so ridiculous there that algebra in 7th grade died a well-deserved death. Not that it’s inconceivable that at some point we could teach a lot of kids meaningful algebra in 7th grade, but to do it we’d need to improve the quality of K-6 math TEACHING far beyond what is typical now. And Milgram hasn’t the foggiest idea how to do that. Neither do his friends. So instead, they blame the teachers, unions, and, of course, schools of education, all favorite conservative targets to begin with.

      Given that many of the folks driving Common Core are also enemies of teachers and unions, and would LOVE to see the privatizing of public education, it’s a little difficult to understand why R. Jim isn’t pro-Common Core. Neither are a lot of his educationally-reactionary pals. And yet, once you get past the nit-picking over what’s in the Common Core or what isn’t, a game that only began in earnest on the Right over the past year or so, when all the other issues they tried to destroy Obama with flamed out and suddenly education policy caught their attention, it seems to me that pro-voucher folks who are legion in Mathematically Correct & HOLD should be creaming their jeans over the Duncan/Obama educational agenda.

      Maybe it’s a paleo- vs. neo- conservative thing that I can’t fully sort out from my left-wing perspective (or don’t really care enough about to try). But while I know that most of the folks Milgram is politically allied with hate Obama, there’s a lot of cutting off of noses to spite faces going on with them, it seems to me. Or maybe it’s just that Math Wars ideology for some folks trumps everything else.

      Odd, though, that long-time Mathematically Correct/HOLD allies, UC-Berkeley’s emeritus mathematician H. H. Wu and U of Wisconsin mathematician Dick Askey, both very anti-NCTM going back to the late 1980s and always on the same side as Milgram, Wayne Bishop, and the rest, have come out to varying degrees in favor of the Common Core Math standards, particularly Wu, who has written hyperbolically in support of them multiple times over the last half decade. But then, he was always a mild apostate, having publicly testified less than glowingly about the execrable Saxon Math books, much beloved by the MC/HOLD crowd, at least until they fell in love with SIngapore Math.

      And speaking of the latter, I am finding it truly amazing that angry, anti-Common Core Math parents on Facebook are lumping together ALL the books that have “Common Core-aligned” on them. Since a lot of districts either had already gone to or are now going to Singapore Math for K-5, and since it, too, has the CCSS imprimatur (though I doubt they had to change much to honestly claim to be so aligned), for those folks, SIngapore Math is now a horrible, awful, destructive program (it uses a lot of diagrams, which they hate, but Wayne Bishop and friends long argued that the Singapore bar diagrams were GOOD diagrams, unlike any use of diagrams and other models in, say, Everyday Math or TERC Investigations. Gosh, a person trying to sort this all out could get REALLY confused. Or really amused.

      Getting back to R. Jim, I find his most blatantly disingenuous claims surround the issue of high school calculus. He has complained repeatedly about the fact that what’s in the Common Core leaves US students without any calculus (someone please call a cop! I mean, imagine graduating high school without it! How did we manage to win WWII or the Cold War coming out of an era when algebra was primarily a COLLEGE subject, and when only a tiny percentage of American students took calculus before they entered university, if then? It’s just amazing. Must have been the fact that God was on our side against those nasty Germans and Japanese and Italians. Or something.

      First of all, as I’ve pointed out repeatedly, the US curriculum and materials and assessments for high school calculus have been around for over a half century. They’re called Advanced Placement calculus. And for some lucky kids, there is the IB curriculum, which if anything is more “rigorous” (I despise the abuse of that word in these debates), but more importantly probably requires more thinking and problem solving than most of what American kids have been force-fed in math classes for well over a century. So why does Jim act as if that has all vanished, or that schools are dropping AP calculus, or that suddenly fewer kids will be in a position to take it? My guess is that actually more kids will, but since I don’t find high school calculus all that bloody important, and in fact I wish that instead we taught a course that gave kids a survey of what college math is about: a bit on limits, some discrete math, some number theory, some real linear algebra, some linear programming, a real exposure to solid geometry, maybe some group theory, etc. – not all this stuff, but every senior gets a chance to sample a selection of rotating topics, perhaps – and that is actually implied in the Common Core Standards if you look at one of the suggestions for a 12th year math course besides statistics or more typical precalculus. And again, anyone who finishes high school at the precalculus level will have a legitimate shot at freshman calculus if s/he so desires. And anyone who is motivated to go through the Common Core curriculum faster can get AP calculus if that’s what will make mommy or daddy happy (because any kid who REALLY wants to learn more math can do so more readily today than ever, given all the free university calculus courses from Penn and Ohio State and NYU and Harvard and Stanford that are available online, just for starters. When Richard Feynman wanted to learn calculus in secondary school, he walked to the library, got CALCULUS FOR THE PRACTICAL MAN out, and learned it. Imagine that!

      The bottom line for me remains that Jim Milgram knows absolutely nothing about teaching or learning elementary mathematics and his input on what should or shouldn’t be taught there should be taken with a few tractor-trailer loads of salt. His smug, supercilious attitudes towards mathematics educators and K-12 teachers might be fine if the conversation turns to various topics in abstract algebra and the like, but really are mostly smoke when it comes to what most kids want or need to learn about mathematics in school. When mathematics majors and graduate students are the topic in question, his thoughts take on far more weight. But in the less rarefied air of what goes on in K-12, he’s just an ill-informed elitist who appears delusional about what mathematics educators and other education faculty do, say, or believe. To paraphrase David Mamet, Milgram cracks out of turn when he doesn’t know the shot. That he keeps getting away with it indicates just how easily swayed Americans are when someone with a Ph.D in math or science weighs in to say what they’re already inclined to believe. But Milgram’s not the only mathematician with views on K-12 mathematics. Why don’t those who disagree with him count? Can you say ‘politics’?

      • Whew! Thank you for this, Michael.

        Sammy, as you can see above, Michael is no fan of the Common Core. But he’s intellectually honest and that’s why he doesn’t buy what Milgram is selling. Michael writes from an honest difference of opinion about the right way to teach kids. You see none of that in Milgram.

        To Michael about the privatizers: We agree that many of the same folks behind the Common Core support the privatization of American education. But it’s more complicated than that. CCSS actually comes out of the generation-old standards movement, idealistic educators, not privatizers. And I know you agree that, even considering your critiques, CCSS is an honest step forward.

        Now it’s the supporters of the private market as an alternative to public education who are the core of the opposition on the right to the Common Core. And the strength of that opposition actually does succeed in damaging our educators ability to lead and teach.

        • As you know, Bill, my concerns are much more with the “big picture” of the Common Core Initiative than with the Teabilly ideas that the various standards are about dumbing kids down and the rest of the post-Reagan, Chicken Little nonsense with which folks like Milgram try to frighten little children (and a lot of adults).

          There are specific things in both the literacy and math standards that I disagree with or question. But I don’t see any particular conspiracies behind what emerged from the groups that wrote them (much as I personally find David Coleman to be a jackass who buys into notions of literacy education that as a former doctoral student in literature I find appalling). BIll McCallum and Phil Daro (the latter is under yet another hysterical attack from Mercedes Schneider today ; she is a good policy analyst who gets at a lot of the dirt going on in various states and in DC, but she despises progressive math teaching and simply goes nuts when writing on anything to do with math education. And frustratingly, she will NOT even consider the possibility that she gets ANYTHING wrong on that score. She just clams up and becomes sullen when challenged or even slightly doubted. . . 😦 ) are reputable mathematics educators, as were some others who worked on the math standards in various capacities. I’m not convinced despite circumstantial evidence (there was certainly unreasonable participation in and input from folks with heavy ties to Bill Gates, the ACT, Pearson, and the ETS) to the contrary, that the math standards, at least, represent the work of evildoers. I just don’t like the very idea of national standards in the first place, particularly with the high-stakes testing machine and the financial issues associated with Race to the Top, an idea whose time should NEVER have come, so thoroughly interwoven into the overall initiative.

          And as I’ve said before, there is still too much privatization money backing CCSSI for my liking. But where things have gone screwy for people like Ms. Schneider and many others, some from the left and some (many) from the right, is in vastly overgeneralizing about specific ideas in the standards themselves, particularly in mathematics. Some of that seems to come from ignorance. Some of it can and should be blamed on NCTM, NCSM, and other professional organizations who have failed abjectly to educate the general public and have badly lost the PR battles in the Math Wars to smaller, but much savvier groups of people like Mathematically Correct and HOLD. And of course some of this comes from those latter groups, in which Milgram happens to be deeply involved. Add to that mix the anti-Obama sentiments from the far right, the racism that fuels a significant percentage of that hatred, and you have precisely the insane mess we face now.

          So as well-intended as the authors of the various standards may be, I fear that at least when it comes to math education, they are doing more harm than good. I wish, in fact, that they had NOT included the Standards for Mathematical Practice (which I truly believe are sound, but which I also know are fueling much of what Milgram and his allies are saying), not because those ideas are bad, but because they’re good and I’d like them to avoid being tainted by the stench of Common Core. I wish, too, that we were having a SANE national conversation about math education, but I fear that it is next to impossible to do so. As soon as ANYTHING that doesn’t look like 1950s-style math teaching is on the table, all the usual epithets (‘fuzzy math,’ ‘rain-forest math,’ ad nauseam) are hurled, and all attempts to explain things as obviously important as ESTIMATION are branded as stupid, idiotic, crap. What a country!

          • I obviously don’t agree, Michael, but look forward to discussing it all with you. I can see the common ground – even from here. (And pay no attention to Mercedes Schneider.)

      • sammy says:

        thanks, I will try to wade through all this in the next few days. part of the problem is that this is a debate that has been politicized (on BOTH sides). Makes it hard for parents who just want the best for their kids….

        • Sammy, keep in mind that the resources available free on the Internet now, including books, lectures, videos, etc., as well as a lot of amazing software, so far outstrips what was available when I was a K-12 student (’55-’68), let alone what was available in the 1920s, when Richard Feynman (and my parents) were young that it’s remarkable. And Feynman learned calculus as a young teen by reading a book he got from the library (CALCULUS FOR THE PRACTICAL MAN). There is so much available that if you don’t like what they’re doing in school, you have a host of options to point your child towards, completely free.

          No one knows with certainty what is best for any child, let alone all children. People promote either what they believe in (that is the only thing I WILL speak favorably about) or what they have a vested interest in promoting. My best advice is to be careful whose advice you take: ask what their angle is. The more they appear to be interested primarily in selling something or in pushing math in a way that makes it accessible only to the most gifted students, the less I personally would be inclined to trust their advice.

      • Roni says:

        Why should students have to take AP calculus? What is wrong with regular calculus. The point if a student starts algebra in 9th they do not have the prerequisites by senior year to take AP calculus. Like any other honors course you must be approved for the course- can’t just take it.

        • Oh, please, Roni. Most students don’t take calculus in high school. Most students never take calculus at all. Calculus, despite it’s impressive-sounding name, isn’t all it’s cracked up to be, either in or out of the world of mathematics. Milgram wants to determine K-12 math curricula for EVERYONE based on the narrowest imaginable ideas about what matters and what works. He’s a fine mathematician or was in his day. As an educator, he’s basically clueless. But he’s maneuvered himself into the heart of the national conversation, along with his puppet, Sandy Stotsky, and now he doesn’t know how to keep quiet and listen when given a chance to shoot his mouth off.

          Any high school/district that wants to construct or adopt a NON-AP calculus program is 100% free to do so. I challenge you or anyone else to find evidence to the contrary. I read those standards over and over two years ago when helping a suburban, working-class Michigan district put together its precalculus standards. They already offered AP calculus, but we discussed the possibility of also offering a section of “regular calculus” as you put it (what you mean by that for high school kids is unstated, of course). There was no objection at any level in the district, other than that there was zero demand for it. If there had been, we could have easily constructed and offered such a class. Or other alternatives to AP calculus, some of which are mentioned in the CCSS-M standards. You should read them and not rely on a highly-prejudiced, highly-political fellow like Jim Milgram.

          If someone means that typical high school students should graduate ready to walk into Introduction to Analysis (aka Advanced Calculus or Honors Calculus) at the college level, s/he’s living in a dream world. Only a handful of such students enter college ready for that and that’s not anything new (or problematic). Same is true all over the world. The problem is whether we get students through high school interested enough in mathematics or math-intensive disciplines, with an actual level of mathematical maturity (which, yes, includes actual mathematical knowledge and facility) to move along rather than have 50% of them drop math forever at each year after they are allowed to stop, beginning in high school. We don’t do that, and the problem isn’t what JIm Milgram and his elitist friends claim and never has been.

      • Glenn Hefley says:

        Seems many people are getting this same look about this man. The tirades alone are a bit scary.

        Have you looked into Stotsky? She’s amazingly dishonest and absolutely cracked.

        And Jane Robbins. She’s a good one to look into.

        • Will be interested in what you have to say when you post your link. Yes, been following Stotsky for a long time, strictly someone with the right connections who gets to spout off about math when she doesn’t know what she’s talking about.

          Have never heard of Jane Robbins as far as I know.

        • Bill Duncan says:

          If you search anhpe on Stotsky and Milgram, both, you’ll see quite a bit here. But I don’t think they are that persuasive to regular people. Haven’t heard of Jane Robbins.

          • Glenn Hefley says:

            Jane is a whole different breed. She’s the real thing. I don’t know how much you know about marketing, copy writing, the use of implied fact, injection or molding.. but I knew quite a bit when I started in Aug. I didn’t mean to start, just kind of happened. I noticed a few error filled claims, offered some awareness and reference, and got attacked. The response was so numerous and violent that I had to figure out why. The area was the WJ so it wasn’t like someone’s backyard or a extremist blog I was posting on.

            Tea Party of course. Honestly, again, I really wasn’t into this but the more I looked the deeper I got. What encouraged me the most was the backers weren’t just disagreeing with Common Core, they were making stuff up.. actually making things up about it. Why? Why go so far? Especially on the Internet where it is so convenient to check the facts? Curiosity turned to near alarm when I began looking into the schools. I had this thought one morning, “well, how back could it be if they drop this CCSS?” That afternoon I was committed to stopping … who ever it was .. and keeping CCSS healthy.

            I’ve got a list of the “real” the professional misinformationists. Most of them come from three places The Heartland Institute which is a major and successful propaganda outfit … which they now call “think tanks” .. kind of a code word I guess.

            The American Principles Project is in full active mode.

            Then there is the Thomas B. Fordham Institute — again they have been around the block and are successful in what they do.

            Then there is the Billionaire’s think tank ALEC who was involved but apparently as backed off now. They are very expensive, and in Sept they lost nearly 75% of their clients all at the same time.

            Jane plays with all three. Near the end of Oct I had digested enough of the others to undersand what I was playing with. Basically it was heavy handed marketing without any control on details like truth or accountability. Then I hit a page which was part of Janes’ campaign. I swear to you I stopped, opened a beer and saluted her, after I could take my eyes off it. I understood marketing and word play, but I had never seen it weaponized before. I learned more from that page than my entire time in college.It was brilliant.

            From what I can tell, she’s astounding in person, and she’s not bad on video.
            Here’s a good one.

            Now, when you are watching that , She’s going to hit you with things pretty fast and al lof here stuff is “true” but.. not. She’ll talk about data collection. Here is the gov site on that topic To get the full effect, don’t go through the regs until after.

    • Tyler Haslam says:

      Calculus will be available to them through CC just as it was through any previous standards (though possibly not in their Jr. year–which was a rare scenario in old standards anyway). Here it is in the form of “honors” courses in grades 9-11 which cover the necessary prerequisite standards. I think that is how it works everywhere that adopted the Integrated standards (Math I, II, and III) for 9-11 grades. I cannot speak to the traditional Algebra/Geometry sequence of CC. It’s possible that it might be different in your district, but rest assured it is still a possibility to take AP Calc in high school.

      …as a side note, I’ve noticed that my AP Stats students are much better prepared for my course due to CCSM. I can breeze by the whole first half of our textbook in just over a quarter now. We’ve had 100% pass rate since CC!! …knock on wood:)

  7. Bill, given the broad range of my last comment, you can’t be disagreeing with all of it. 🙂

  8. Tim Cocrin says:

    This comment is for people who came here by random googling as I did while investigating Milgram to learn more about the ongoing Common Core math debate, leave. Leave right now. You won’t learn anything useful about either side here, you’ll just read a long series of rhetoric.

    To start, the second sentence of the second paragraph of the Summary section apparently doesn’t post the entire sentence of Milgram that is quoted but instead cuts off the remaining sentence only to then paraphrase what was cut out. This alone wouldn’t be suspicious except that the whole article follows identical or similar argumentative strategies.

    Milgram later gets called out for selectively quoting from the Common Core standards for mathematics and yet it’s never explained why the selection is a poor or biased one. Milgram’s quoted selections (within the paper they’re drawn from) are chosen because Milgram is comparing the Common Core standards for kindergarten mathematics to California’s standards for kindergarten mathematics. The counter argument to this is that Milgram was being biased by citing only three of Common Core’s kindergarten math standards to contrast against four of California math standards, however, this argument cuts both ways given that in lieu of this unfairness the author of this article decides to list four additional Common Core kindergarten math principles but makes no effort to illustrate the unstated California standards (a seemingly important piece of information) before declaring the two sets of standards to be “almost precisely the same” in terms of approach.

    Put simply, if you’re looking for reasons to believe/doubt Milgram you’ll find them here. That said, they’re non-quantifiable reasons that exist mainly to facilitate debate. If you wanted an article discussing Milgram’s qualifications in terms of experience with mathematics, creating educational standards, experience working with children, or the validity of his arguments against Common Core mathematics this article has no information of use to you.

    • Bill Duncan says:

      Tim, Milgram’s resume is, indeed, what he is trading on but that is not the issue. I would urge you to dispute the content of the post rather than the punctuation. If you do, you will be the first.

    • Milgram is an ideologue on math education. He has no background in teaching kids and suggesting otherwise is dishonest. That doesn’t mean he’s not qualified to comment: of course he is. But only to a certain extent. And he consistently steps way beyond the bounds of his expertise. That’s a reflection of his egoism and intellectual dishonesty.

      When Keith Devlin weighed in on an issue of K-12 math teaching a number of years ago, he repeatedly stressed his awareness of his own limitations (despite being a Ph.D in mathematics who also teaches at Stanford). You will never find any such modesty from Prof. Milgram. And that is a key reason why I find him a dicey source of information when it comes to issues outside of abstract mathematics, his actual area of expertise.

      It’s clear, Tim, that you oppose the Common Core. Hence, you feel obligated to disparage any critique of Milgram’s critique. But while I am critical of many aspects of the Common Core and have been before Milgram weighed in on any of what’s specifically in the standards (I oppose the idea of national standards on principle, not just these particular standards because they don’t fit my politics, which is where I believe Milgram is coming from based on years of reading his thinking on math education), I remain highly skeptical of Milgram’s commentary.

      Finally, if Milgram is so right about the Common Core math standards, why does his long-time ally, H. H. Wu of the Cal-Berkeley math department, find so much to praise about them? I believe it is because Wu is not an ideologue. That isn’t to say he’s always right, but his track record suggests that he’s far more honest than most of those who have been affiliated with Mathematically Correct and/or HOLD. Wu will speak his mind even against “holy texts” like Saxon Math, and even in favor of “forbidden” ones like the Common Core math standards.

      • mach says:

        I’m a math PhD, and I’m certainly quite clueless in terms of elementary school math education. This credential and that topic are separated by a huge gulf.

        I could mention what I find the be strong or weak points in the incoming freshmen I teach, probably say a bit about high school math curriculum, and possibly a bit about motivating high school students, but beyond that, I have no credential related to the topic. We shouldn’t expect mathematicians by default to have any expertise here.

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