Mathematics and Education

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Comments on Ravitch’s MLA Speech

with 2 comments

The historian Diane Ravitch gave a speech to the Modern Language Association on January 11 about the past, present and future of the Common Core State Standards which was posted on a Washington Post blog. There’s a lot to like about the speech when it comes to rethinking uses of tests and test scores. I’ve been in favor of caution about testing since at least 1999 (see my article here).

However, the speech has some statements that are unclear, appear unaware of research in mathematics education, or seem uninformed. Some concern:

Characteristics of standardized tests.

Field testing standards.

Developmental appropriateness of the CCSS.

Development of the CCSS.

Details are below.

What is a standardized test? Ravitch states: “Standardized tests are normed on a bell curve.” Not necessarily.  Here’s a definition from the Office of Technology Assessment book Testing in American Schools:

Standardized tests are administered and scored under conditions uniform to all students. Although most people associate standardized tests with the multiple-choice format, it is important to emphasize that standardization is a generic concept that can apply to any testing format—from written essays to oral examinations to producing a portfolio. Standardization is needed to make test scores comparable and to assure as much as possible that test takers have equal chances to demonstrate what they know. (p. 5)

Thus, in the OTA definition a test does not require norming to be called a standardized test. Instead, norming may—or may not—occur in the process of interpreting scores. The OTA book notes that there are two basic ways, the first of which often involves a bell curve:

One is to describe a student’s test performance as it compares to that of other students (e.g., he typed better than 90 percent of his classmates). Norm-referenced tests are designed to make this type of comparison. The other method is to describe the skills or performance that the student demonstrates (e.g., he typed 45 words per minute without errors). Criterion-referenced tests are designed to compare a student’s test performance to clearly defined learning tasks or skill levels. (p. 5)

Similar distinctions are made in National Research Council report Early Childhood Assessment: Why, What, and How (see “criterion-referenced assessment” and “norm-referenced test” in its glossary).

What does field testing standards mean? Ravitch states that she urged leaders to field test the CCSS. Despite my interest in and involvement with standards since at least 1999 (when I was an additional writer on NCTM’s Principles and Standards), I had never heard of field testing standards and wasn’t sure what it meant. After some search (including search of her books), I finally found this description from Ravitch on her blog:

I have worked on state standards in various states. When the standards are written, no one knows how they will work until teachers take them and teach them. When you get feedback from teachers, you find out what works and what doesn’t work. You find out that some content or expectations are in the wrong grade level; some are too hard for that grade, and some are too easy. And some stuff just doesn’t work at all, and you take it out.

I suspect that underlying this comment is a fundamental difference in perspective on teaching and learning. Ravitch’s background and training is as a historian of education rather than as an educational researcher. My impression after reading three of her books (from 1995, 2010, and 2013) is that she’s not familiar with subject-specific education research. In particular, she does not appear to be familiar with research in mathematics education and may not even be aware that it exists. Thus, she probably doesn’t see the relevance of work on learning trajectories for early grades and their implications for later grades.

Research on learning trajectories reflects the rather commonsense notion that what you already know affects what you’re prepared to learn. In this view, field testing standards at a given grade (say, grade 5) would require testing them on students who had achieved the proposed standards at grade 4, which would require testing them on students who had achieved them at grade 3, and so on, down to kindergarten.

This would take years. Fortunately, in early grades much research has been done to field test sequences of objectives rather than single objectives. That research is reflected in the references for the CCSS.

Developmental appropriateness. Ravitch writes:

More than 500 early childhood educators signed a joint statement complaining that the standards were developmentally inappropriate for children in the early grades. The standards, they said, emphasize academic skills and leave inadequate time for imaginative play. They also objected to the likelihood that young children would be subjected to standardized testing.

This appears to be a reference to the Joint Statement of Early Childhood Health and Education Professionals on the Common Core Standards Initiative. As its title indicates, the statement is about the initiative, which includes more than the standards and their content. This statement was released on March 2, 2010, three months before the final version of the CCSS was released. As its title does not indicate, not all of its signers had affiliations suggesting expertise in early childhood. For example, one was an assistant professor of civil engineering. (An interesting feature of the version currently posted is that not all of the original signers are listed.)

The statement had four main parts which I’ve labeled S1–S4. These are in italics below, followed by comments from me.

  • S1. Such standards will lead to long hours of instruction in literacy and math. The only example given was for ELA rather than mathematics.
  • S2. They will lead to inappropriate standardized testing. Certainly this is a concern for any set of standards. Note however, that the signers were concerned about inappropriate standardized testing, not, as Ravitch wrote, standardized testing. Standardized testing can be done in ways that are appropriate for young children. A non-academic example is the Agpar test for newborn babies, which is a criterion-referenced test. As the National Research Council report Early Childhood Assessment: Why, What, and How states:

Well-planned and effective assessment can inform teaching and program improvement, and contribute to better outcomes for children. This book affirms that assessments can make crucial contributions to the improvement of children’s well-being, but only if they are well designed, implemented effectively, developed in the context of systematic planning, and are interpreted and used appropriately.

  • S3. Didactic instruction and testing will crowd out other important areas of learning. Again, this is a concern for any set of standards. This is one reason why the way in which implementation occurs is so important. Concerns about implementation were raised in 2009 at the Conference Board of the Mathematical Sciences Forum, and reiterated a year later. These are summarized in white papers for the 2009 Forum and 2010 Forum.
  • S4. There is little evidence that such standards for young children lead to later success. Not so. There is for mathematics. (Because I am not familiar with research on literacy, I will not discuss it. However, note Bill Honig’s comments on this subject.) This evidence is given in the references for the CCSS. These include the National Research Council’s Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. For mathematics, the CCSS work and feedback groups included three people who were on the committee that produced the NRC report. See bios of Beckmann, Clements, and Fuson here. Fuson (as well as several others involved in the CCSS development) also served on the committee for the NRC’s Adding It Up: Helping Children Learn Mathematics (also listed in the CCSS references). An overview of research informing the CCSS is given in the draft front matter for the CCSS Progressions which can be downloaded here.

In summary, S4 concerned evidence for the draft CCSS. The other statements offered few specific examples and seemed mainly to concern the effects of any set of standards for young children.

The CCSS development process. Ravitch says that she “objected to the lack of any democratic participation in their development.” I’m not sure what she means by “democratic participation,” but given that she seems to approve of its development, I assume that she thinks the development of National Council of Teachers of Mathematics Principles and Standards for School Mathematics (PSSM) involved “democratic participation.”

As an additional writer for PSSM, an editor for CCSS, and member of mathematical society committees, I’ve seen quite a bit of both development processes. In my opinion, the big difference between CCSS and PSSM was time. The CCSS took about a year and PSSM took three years. However, CCSS came a decade later and had the advantage of building on PSSM, other NCTM reports, and much other work.

The development processes for PSSM and CCSS were similar in that:

Both solicited comments from mathematics societies. NCTM’s involvement in the CCSS development and support of the result is described here. I’ve written about the involvement of the Association for Women in Mathematics in an article posted here. Similarly, as reflected in the Association for Symbolic Logic Association Review Group report here, comments on PSSM drafts were solicited from mathematics societies.

Both solicited comments on draft versions from the general public. This is described for CCSS in a March 2010 Education Week blog post.

Have I misinterpreted something? Comments consistent with the comments policy are welcome.

Update: A reiteration from Ravitch of her views on field-testing and composition of the CCSS writing group (along with a non-response to my mention of this post) is in the comments section here: http://dianeravitch.net/2014/02/25/new-york-time-for-accountability-for-state-board-of-regents/

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Written by CK

February 13, 2014 at 9:09 am

2 Responses

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  1. Reblogged this on MathSugarOff and commented:
    Even if you haven’t followed Diane Ravitch’s evolution as an education analyst, you may have seen evidence of her influence. Here is a careful commentary on Ravitch’s claims about the CCSS.

    Priscilla Bremser

    February 13, 2014 at 10:14 am

  2. […] Kessel does a terrific job of addressing each of the above issues raised, demonstrating that there is research that has been wholly ignored by certain Common Core detractors, and that the lack of nuance with which the issues have been handled is incredibly disappointing. Read the full post here. […]


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