James Milgram on the new Core Curriculum standards in math

Just as Sandra Stotsky has criticized the new Core Curriculum standards for English Language Arts in her testimony before the Texas legislature, in his testimony, James Milgram, Professor emeritus at Stanford and a member of the Common Core Validation committee, points out their  flaws in math:

I would like to testify in support of the bill Rep. Huberty filed, HB 2923, to prevent the so called Core Standards, and the related curricula and tests from being adopted in Texas.

My Qualifications. I was one of the national reviewers of both the first and second drafts of the new TX math standards. I was also one of the 25 members of the CCSSO/NGA Validation Committee, and the only content expert in mathematics.

The Validation Committee oversaw the development of the new National Core Standards, and as a result, I had considerable influence on the mathematics standards in the document. However, as is often the case, there was input from many other sources – including State Departments of Education – that had to be incorporated into the standards.

A number of these sources were mainly focused on things like making the standards as non-challenging as possible. Others were focused on making sure their favorite topics were present, and handled in the way they liked.

As a result, there are a number of extremely serious failings in Core Standards that make it premature for any state with serious hopes for improving the quality of the mathematical education of their children to adopt them. This remains true in spite of the fact that more than 35 states have already adopted them.

For example, by the end of fifth grade the material being covered in arithmetic and algebra in Core Standards is more than a year behind the early grade expectations in most high achieving countries. By the end of seventh grade Core Standards are roughly two years behind.

  • Typically, in those countries, much of the material in Algebra I and the first semester of Geometry is covered in grades 6, 7, or 8, and by the end of ninth grade, students will have finished all of our Algebra I, almost all of our Algebra II content, and our Geometry expectations, including proofs, all at a more sophisticated level than we expect.
  • Consequently, in many of the high achieving countries, students are either expected to complete a standard Calculus course, or are required to finish such a course to graduate from High School (and over 90% of the populations typically are high school graduates).

Besides the issue mentioned above, Core Standards in Mathematics have very low expectations. When we compare the expectations in Core Standards with international expectations at the high school level we find, besides the slow pacing, that Core Standards only cover Algebra I, much but not all of the expected contents of Geometry, and about half of the expectations in Algebra II. Also, there is no discussion at all of topics more advanced than these.

Problems with the actual mathematics in Core Math Standards As a result of all the political pressure to make Core Standards acceptable to the special interest groups involved, there are a number of extremely problematic mathematical decisions that were made in writing them. Chief among them are:

1. The Core Mathematics Standards are written to reflect very low expectations. More exactly, the explicitly stated objective is to prepare students not to have to take remedial mathematics courses at a typical community college. They do not even cover all the topics that are required for admission to any of the state universities around the country, except possibly those in Arizona, since the minimal expectations at these schools are three years of mathematics including at least two years of algebra and one of geometry.

  • Currently, about 40% of entering college freshmen have to take remedial mathematics.
  • For such students there is less than a 2% chance they will ever successfully take a college calculus course.
  • Calculus is required to major in essentially all of the most critical areas: engineering, economics, medicine, computer science, the sciences, to name just a few.

2. An extremely unusual approach to geometry from grade 7 on, focusing on rigid transformations.  It was argued by members of the writing committee that this approach is rigorous (true), and is, in fact, the most complete and accurate development of the foundations of geometry that is possible at the high school level (also probably true).  But

  • it focuses on sophisticated structures teachers have not studied or even seen before.
  • As a result, maybe one in several hundred teachers will be capable of teaching the new material as intended.
  • However, there is an easier thing that teachers can do – focus on student play with rigid transformations, and the typical curriculum that results would be a very superficial discussion of geometry, and one where there are no proofs at all.

Realistically, the most likely outcome of the Core Mathematics geometry standards is the complete suppression of the key topics in Euclidean geometry including proofs and deductive reasoning.

The new Texas Mathematics Standards

As I am sure you are aware, Texas has spent the past year constructing new draft mathematics standards, and I was one of the national reviewers of both the first and second drafts. The original draft did a better job of pacing than Core Standards, being about one year ahead of them by the end of eighth grade, so not nearly as far behind international expectations. Additionally, they contained a reasonable set of standards for a pre-calculus course, and overall a much more reasonable set of high school standards.

There were a large number of problems as well – normal for a first draft. However, the second draft had fixed almost all of these issues, and the majority of my comments on the second draft were to suggest fixes for imprecise language and some clarifications of what the differences are between the previous approaches to the lower grade material in this country and the approaches in the high achieving countries.

It is also worth noting that the new Texas lower grade standards are closer to international approaches to the subject than those of any other state.

I think it is safe to say that the new Texas Math Standards that are finally approved by the Texas Board of Education will be among the best, if not the best, in the country. (I cannot say this with complete certainty until I have seen the final draft. But since I am, again, one of the national reviewers, this should be very soon.)

So it seems to me that you have a clear choice between

  • Core Standards – in large measure a political document that, in spite of a number of real strengths, is written at a very low level and does not adequately reflect our current understanding of why the math programs in the high achieving countries give dramatically better results;
  • The new Texas Standards that show every indication of being among the best, if not the best, state standards in the country. They are written to prepare student to both enter the workforce after graduation, and to take calculus in college if not earlier. They also reflect very well, the approaches to mathematics education that underlie the results in the high achieving countries.

For me, at least, this would not be a difficult choice. So for these many reasons I strongly support HR 2923, and hope the distinguished members of this committee will support it as well.

Respectfully, R. James Milgram

Posted on by leoniehaimson Posted in Uncategorized

37 Responses to James Milgram on the new Core Curriculum standards in math

  1. PatriotTeacher

    I say TX should “stick to their guns” and not adopt the Common Core standards. I teach in a state which could certainly rival TX’s standards. Our assessment system is the envy of the nation, in fact. What in the world was my Governor thinking when he & our Democratic legislature said “yes” to Common Core? Wonder if it had anything to do with the monetary carrots Obama was waving at us. My prediction is this whole thing will be a disaster. Thanks for the post.

  2. Bob

    Hey PatriotTeacher, is that you Wilfried?

  3. Dave

    Hey James, great article, and thanks for letting us in on an insider track to a comparison of TX and National Core Standards.

    I am an Algebra teacher from El Paso. I have worked in TX only 2 years now, but my previous state was Indiana (big move!).

    I am very critical of our TX standards. Probably more critical of the states willingness to move to math requirements that don’t come with clear examples and resources or rubrics. And I am wondering what your thoughts were on the TEKS prior to this year’s revisions?

    I would argue that if you thought that they were “among the best, if not the best” in the country before, then wouldn’t we at least rank in the top half of the country, or in the top 25 states for math performance? The following article shows that we are 38th in math SAT scores nationally; a far cry from “the best!”

    And if we have “perhaps the best” standards and the result is not high national rankings, then what is your assessment of the relationship between “good standards” and “results?” If we cannot correlate these two, then our radar is WAY OFF.

    I argue that if your results are poor, then your plan was poor.

    I am desperately looking for some common sense in the TX math standards, and to adopt something that has proven results. Let’s look at the highest ranking states and go to their plan as a start.

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  8. Katie

    Very interesting look at the two sets of standards documents. Perhaps some clarification could be made for my sake though as I’m probably just not understanding the language here, but in the first several paragraphs your argument is that the CCMS were made to be as “non-challenging as possible”. Then you say that you don’t like the geometry because it is so rigorous that there will only be a couple hundred teachers actually able to teach it. Is it just the geometry portion that is too rigorous and the rest are too easy? Or is it just the pacing that is non-challenging?

    • Tom T.

      Katie, the problem with these geometry standards is that it sets everyone up for failure. The problem James sees is with the standards is, to teach rigid transformations, teachers will ultimately have students play with cut-outs of triangles and rectangles because they are not going to know what else to do with them. This will not involve any of the things (proofs and reasoning) that should go into a geometry class.

      Let me give you an analogy. I teach mathematics to undergraduates at a very good liberal arts college. I could have the very high expectations that I take my first semester Calculus students and teach them graduate-level functional analysis. These would be extremely high standards which would lead to incredibly low standards. They would learn nothing because they are not ready for the material. My area is not analysis, so I would not be the best person to teach such a class.

      Standards need to be high, but attainable. Teachers need to be trained in the material sufficiently. Otherwise, nothing is gained from the endeavor leading to no real standards.

      However,
      there is an easier thing that teachers can do – focus on student
      play with rigid transformations, and the typical curriculum that
      results would be a very superficial discussion of geometry, and one
      where there are no proofs at all. – See more at:
      http://parentsacrossamerica.org/james-milgram-on-the-new-core-curriculum-standards-in-math/#sthash.9dKWvB17.dpuf

      However,
      there is an easier thing that teachers can do – focus on student
      play with rigid transformations, and the typical curriculum that
      results would be a very superficial discussion of geometry, and one
      where there are no proofs at all. – See more at:
      http://parentsacrossamerica.org/james-milgram-on-the-new-core-curriculum-standards-in-math/#sthash.9dKWvB17.dpuf

      However,
      there is an easier thing that teachers can do – focus on student
      play with rigid transformations, and the typical curriculum that
      results would be a very superficial discussion of geometry, and one
      where there are no proofs at all. – See more at:
      http://parentsacrossamerica.org/james-milgram-on-the-new-core-curriculum-standards-in-math/#sthash.9dKWvB17.dpuf

      • Katie

        I completely agree that standards need to be high but attainable otherwise there is no point in having them. I guess what I’m not understanding though is he specifically states that the CCMS were made to be as non-challenging as possible, and you are saying that they are unattainable. I’ve never heard of standards being as non-challenging as possible and then at the same time unattainable.
        I can also understand if just the geometry portion of the CCMS were written in a way that makes them so hard they are unnattainable because even our teachers don’t have the training in those standards. That’s what I’m trying to clarify.

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  29. davidshockey

    It’s hard to compare the two sets of standards based on this article. Milgram makes a list of criticisms of Common Core standards but doesn’t show how the Texas standards avoid those same deficiencies. He just likes them better.

    He does say that the Texas standards include pre-calculus standards. Is he saying that all students should take pre-calculus? Just the students going to college? Just the students going to college for STEM degrees? Many schools have an option for students who want to prepare better for college: advanced placement classes. These will continue to be offered no matter what set of standards are in use. Milgram’s primary criticism, that the standards are not rigorous enough, completely ignores the fact that STEM students have access to AP classes or dual enrollment classes. The students that are in these classes are already highly motivated and it is doubtful that a set of standards for this relatively small number of students would be useful.

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