James Milgram is a professor emeritus of mathematics at
Stanford University. He served on the validation committee for the
Common Core mathematics. He did not agree to approve the standards.
He sent me the following letter. He has spoken out against the
standards in various states. See here
and here.
Dear Diane, In your own writings you mention that the biggest issue with Core Standards is the lack of evidence. This is largely true. But at least in math there is significant international evidence that major parts of the standards will not work. For example, the only area we could find that has had success with CCSS-M's method of treating geometry is in Flemish Belgium. But it was tried on a national scale in Russia a number of years back, and was rapidly dropped. Likewise, the extremely limited high school level content is so weak that Jason Zimba, one of the three main writers described it as follows: First, he defined "college readiness" by stating: "We have agreement to the extent that it's a fuzzy definition, that the minimally college-ready student is a student who passed Algebra II." Perhaps this explains why the only math at the high school level, aside from a snippet on trigonometry, is material from Algebra I, Algebra II, and Geometry. Moreover, the Algebra II component does not describe a complete course. Zimba's definition is taken verbatim from his March 23, 2010 testimony before the MA State Board of Elementary and Secondary Education. Later, in the question period, Sandy Stotsky asked for some clarification. The following is a verbatim transcript: Zimba stated "In my original remarks, I didn't make that point strongly enough or signal the agreement that we have on this - the definition of college readiness. I think it's a fair critique that it's a minimal definition of college readiness." Stotsky asked "For some colleges?" and Zimba responded by stating: "Well, for the colleges most kids go to, but not for the colleges most parents aspire to." Stotsky then asked "Not for STEM, not for international competitiveness?" and Zimba responded "Not only not for STEM, it’s also not for selective colleges. For example, for UC Berkeley, whether you are going to be an engineer or not, you'd better have precalculus to get into UC Berkeley." Stotsky then pointed out: "Right, but we have to think of the engineering colleges and the scientific pathway." Zimba added "That's true, I think the third pathway goes a lot towards that. But your issue is broader than that." Stotsky agreed saying "I'm not just thinking about selective colleges. There's a much broader question here," to which Zimba added "That's right. It's both, I think, in the sense of being clear about what this college readiness does and doesn't get you, and that's the big subject." Stotsky then summarized her objections to this minimalist definition by explaining that a set of standards labeled as making students college-ready when the readiness level applies only to a certain type of college and to a low level of mathematical expertise wouldn’t command much international respect in areas like technology, economics, and business. Zimba appeared to agree as he then said "OK. Thank you." So these are the standards that Sybilla Beckmann recently described by stating that "No standards I know of are better than the CCSS-M." Well, if you believe that then perhaps I can interest you in large bridge in NYC. As to the "third pathway" that Zimba mentioned above, it never actually existed. The version of CCSS-M Zimba was talking about was the March 10 public draft. It had placemarkers for the key calculus standards, but aside from those placemarkers, this version contained about the same material -- only in Geometry, Algebra I, Algebra II and a trig snippet -- as appears in the final version. Moreover, the calculus placemarkers and any hint of a third pathway are gone in the final version. It is also worth noting that Clifford Adelman did an analysis of the odds of completing a college degree based on the highest level math course completed in high school. The odds for Geometry were 16.7%, for Algebra II they were 39.3%, but for Trigonometry they were 60%, 74.6% for Precalculus, and 83.3% for Calculus. So we can estimate that a "minimally college ready student" has a less than 40% chance of completing a college degree. Is this really what the National Governor's Association, the Council of Chief State School Officers, and the Gates and Broad Foundations want for our youth? Yours, Jim Milgram
Diane Ravitch's blog 
Thanks. You are correct. And the Adelman study clearly showed that level of math completed was the strongest indicator of college completion. You need trig for Pre-calc. Minimizing it is a very bad idea.
To me this line of argument just highlights how unwise it is to regard “college and career readiness” as the minimum graduation standard in a single track system and to put too much weight on mandating the absolute minimum standards. By definition the minimum standards should only affect the most marginal students. In high school I barely knew what the minimum requirements were — I was getting ready for college. There was no presumption that just barely graduating meant you were ready to head off and be a successful college student.
Surely you do not think that all students can take pre-calc and calc in high school? If that were a graduation\n requirement many more students would not graduate and the course would get watered down do that many more could pass. Clearly there needs to be differentiation in high school graduation paths. BUT, there also needs to be opportunities for students to change paths.
Excellent points!
The point he is making is that the Common Core Standards are NOT college ready and should not be labeled as such. Parents and students should not be misled that CC will prepare your child for a four year university. Simple honesty could stop this misinformation.
Children differ. The CCSS are a recipe for treating kids as if they were parts to be identically milled, and extraordinarily poorly thought through recipes at that. The “standards” in ELA are particularly ill conceived. But that’s a very long conversation THAT THE COUNTRY NEVER HAD.
cs:
Children differ. The CCSS are blueprints for treating kids as if they were parts to be identically milled, and extraordinarily poorly thought through recipes at that. The “standards” in ELA are particularly ill conceived. But that’s a long, detailed conversation that the country never had.
Clearly, I am rushing. Too many careless errors. My apologies, all.
YES, YES, YES and YES!
James Milgram is a math traditionalist who hates basically anything that prioritizes student understanding rather than drill and kill and monkey math. He opposes the standards largely on those grounds. Similarly, CCSS-M have suggested standards for study beyond Alg2. They are threaded throughout the HS standards document and aren’t hard to find. So his complaint that they don’t exist is a complaint that they aren’t mandated, which is actually the opposite of your usual complaint. In general he hates the standards because he wants learning to be less creative, more didactic, and overall less supportive of student understanding, which again would seem to be the opposite of your complaint. Perhaps featuring his complaints should be reconsidered in that light.
Don’t know much about Milgram, but I would be surprised if he truly were “less supportive of student understanding”. However, I do agree that his complaints are unusual ones; not sure how an argument that the CCSS-M standards AREN’T rigorous/deep enough (which is how I read his complaints) plays into the larger debate about the standards themselves.
He certainly wouldn’t put it that way. He just states that the only way to true mathematical proficiency is hyper-traditional drill and kill. He has major issues with the NCTM standards and NSF math programs and has been at the forefront of a back-to-basics approach in math for decades. His problem with Singapore math, for example, is that it isn’t enough like the Russian program from the 50s that it was adapted from.
Here is what Milgram says about Singapore Math:
http://mathexperts-qa.blogspot.com/2011/04/math-experts-q-with-jim-milgram.html
2. Do you prefer Singapore Math over Everyday Math (EM)?
There is a pretty good program hidden inside EM. But no more than 1 in 500 teachers are capable of locating and delivering it. However, that one teacher would almost certainly be able to do better on her own.
Singapore math, on the other hand, is very solid mathematically and in terms of the problems students are given. But there are some limitations. It isn’t quite as effective for ALL students as the pure Russian program. Also, there are many elementary school teachers who don’t know enough mathematics to deliver the Singapore program effectively, and need extensive professional development. (Singapore adopted the Chinese curriculum in 1984, but this was the program the Chinese adopted from Russia in 1955. However, the Russian program requires teachers who are even more mathematically knowledgeable than does Singapore.)
3. If you had to pinpoint two/three main deficiencies in EM and Singapore, what would they be?
There are no major deficiencies in the Singapore program, just a few points where it could be better than it is. On the other hand, the recommended lessons in EM are mostly useless.
4. Does it make sense to try to merge the two programs?
Not from my perspective.
5. Do you think using EM is actually doing a disservice to our young generation and impairing our future economic competitiveness?
In general, yes.
Are the Trig and Calculus standards actually “threaded” through the Alg I, Geom, and Alg 2 standards? That’s what I understand you to be saying. Am I correct?
The HS standards aren’t broken down by course. They are separated into content areas (like Functions; Geometry; Statistics; etc). Then there are recommendations for which standards within the categories are for each course, including some which are recommended for “further courses”. This is to accommodate traditional and integrated frameworks, as well as to allow flexibility in delivery while still giving a framework for what college prep looks like. So, for instance, vectors and matrices have been beefed up a bit, but are suggested to be moved out of Algebra 2 and into further courses. The idea is to get the depth of a thorough treatment instead of the generally cursory treatment we give in A2.
There are no calc standards included as calculus is not generally considered college prep, but rather 1st year college. If students hit it in HS, that is great, but you can still go on to a successful college career, even in a tech field, taking Calc 1 in college. Some colleges prefer or demand that you retake THEIR calc course anyway.
If you get twenty math guys to validate college readyness standards, of course they would split hairs over trig or pre-calc content, which I suppose is valid for the upper half of students. That’s college ready.
But what about the lower half of the high school population? Probaly need to get twenty teachers who teach community college remedial math to set these standards. Know your times tables, be able to manipulate fractions and percentages, know how loans work. That’s life ready.
In Massachusetts, concerned parents were told by officials, including the governor, that the new
Common Core standards were at least – if not more – rigorous than the former standards!
The idea of everyone attending college is absurd. A four year college education probably requires an IQ of approximately 110 and thus is suitable for only about 25% of the US student population at most. Of course whether one needs Algebra II for college at all depends on the particular student’s educational and career plans. For many careers it is unnecessary. Incidentally the college degree attainment rate of 83% for people completing a high school calculus course simply means that such individuals have a relatively high average IQ not that the completion of such a course makes them any smarter.
To socratic_me – James Milgram is a very distinguished mathematician who has made important contributions to mathematics. That fact doesn’t mean that his views on mathematical education are necessarily correct but I think the tone of your remarks is not appropriate given his stature as a creative mathematician. I think it’s pretty silly of you to say that he does not want students to understand mathematics.
I am glad that he is a distinguished mathematician. He has proven himself an utter ass as regards pedagogy (and how he deals with others who disagree with him on pedagogy). I don’t think the former can be used to paper over the latter. And as I said above, I know HE wouldn’t put it that way. He would just insist that valuing understanding gets away from driving procedural understanding via drill-and-kill. He isn’t shy about that point and makes it early and often.
I have to post this here and with any link I offer to this particular entry on Diane’s blog, though of course people are free to believe what they like. It would be nice to do more than just speculate about where Dr. Milgram is coming from regarding mathematics education. While I plan to write a response to his letter, this is something I wrote and posted on my blog in 2010: http://rationalmathed.blogspot.com/2010/03/you-just-cant-make-this-stuff-up-or-can_25.html
If your mind is made up and don’t wish to read anything critical of Jim Milgram, by all means do NOT go to that link.
I found his statements about the purpose of educators was to keep kids out of te workforce as rather bizarre, but I have found with my special ed students over the years that their reliance on calculators to perform simple operations masked a profound lack of understanding of basic mathematical concepts.
New math happened to be my downfall. I moved from a traditional program where I was taking algebra in 8th grade to a mishmash of set theory and base2 that I have never used probably because it destroyed all confidence in myself in mathematics. It wasn’t until I was called upon to teach math to struggling students in middle school that I developed a determination and a fascination with helping them to understand what they were doing and be able to apply it.
That being said, I am obviously in no position to comment on any ongoing disputes in the math community. I just know that my students had maxed out their capacity to memorize incomprehensible (to them) algorithms.
I read the Jo Boaler link. It’s horrifying. Milgrim seems like a real nut-case in so far as education goes.
I was taught by drill and kill with NO attempt at understanding what I was doing in math or why, and although I did well enough on the SAT to get into a top flight college, when I hit Calculus I in Freshman year it turned out that I was completely unprepared to learn it. I call that educational malfeasance.
OF COURSE, it may have been that math at that level was just beyond me. It may be that my “intelligence” was verbal not mathematical. Still I like to think that if my mathematics education all through school had been up to snuff that I would have been ready for Calculus i as a Freshman.
I see no opposition between “understanding” and drill. When I had to memorize the quadratic formula I simply had to write it down enough times so that I had memorized it. It was kind of interesting to see the proof of how we get from a^2 + b^2 = c^2, and someday I’d like to learn to reproduce that proof, but for most of Algebra II or III or wherever I encountered it, it was sufficient to have the formula memorized as ONE of the ways to solve a quadratic equation (factoring, completing the square, are there others?).
I can’t imagine that understanding the math would in any way interfere with one’s ability to DO math. I also suspect that most Elementary and maybe even some Middle School and High School math teachers may not have much deep understanding either. I remember a colleague who was my school’s gatekeeper to Calculus, who taught Algebra III (Pre Calculus), saying “I don’t do Calculus” meaning she didn’t teach it because she didn’t grasp it well enough to teach it. My son had a killer experience in her class.
I’m glad to learn that Milgram’s opposition to the CCSS can be largely discounted whatever other reasons there may be for repudiating them.
By the way, Michael, your photo on your blog is SO sweet faced, I wish you’d replace your angry Donald Duck face with it. Once I have my fall schedule settled, which I don’t yet, I’ll call you to see if you have time to fill me in on the background of the Math Wars. I know the new principal at Burns Park, and if every paying job application I’ve got in falls through, I think I’ll ask him about volunteering to tutor arithmetic. Maybe you will have an idea or two as well.
” I just know that my students had maxed out their capacity to memorize incomprehensible (to them) algorithms.”
James Milgram’s argument in general is that this is a failing in your students, not in the way we teach mathematics. Furthermore, attempting to add meaning to the algorithms is wishy-washy feel goodism. Rote memorization will lead to conceptual understanding at some later date.
Whatever the merits or demerits of Milgram’s views on mathematics education the use of personal vituperation in discussing them may actually weaken the appeal of your arguments.
The last person anybody should be listening to about ANYTHING is James Millgram: he has a long history of impeding educational innovation, and is notorious for the harassment he committed against one of his colleagues at Stanford University, the universally respected and adored educator and “true reformer” Dr. Jo Boaler. For an account of the terror Millgram imposed on Dr. Boaler, please read this statement: http://www.stanford.edu/~joboaler . I beg you, Diane, retract this blog post now!
I read the Boaler post. Absolutely shocking. This Millgram sounds nutty when it comes to teaching children.
There is a free download of my e-book on Amazon for the next 2 days: How To Solve the Beal and Other Mathematical Conjectures
Millgram sounds nutty for questioning Boaler’s research? He just wanted to prove or disprove it, as Boaler’s claims were startling. Instead of sharing research, he had to hunt down the information after Boaler stonewalled him. If doing research and questioning existing findings is nutty, we need more nutty people. By the way, Millgram states that in the long run, the schools that adopted Boaler’s methods had such dismal results that they dropped her program to go back to the traditional methods. Boaler’s research and MOOC are interesting, but there is little to no larger studies supporting her methods, and instead of her countering Millgram, she attacked him to shock people. Personal attacks and ignoring are not refuting.
She also claims to have been bullied when it is obvious from Dr. Bishop’s response that she in fact was the bully. http://math.stanford.edu/~milgram/Jo-Boaler-reveals-attacks-AccusationsResponse-trans.html
How did Boaler handle it when Milgram challenged her research?
She sent the state police to investigate a benign remark about “blowing up education schools;” a remark made by most non-education academicians who function in the real world.
“Nutty,” you say?