By Bas Braams
To:
Ms. Eva Moskowitz and the NYC Council Committee on Education
Council Speaker Gifford Miller
Copy:
Mayor Michael Bloomberg
Schools Chancellor Joel Klein
Dear Ms. Moskowitz, Committee Members, and Mr. Miller:
This email is intended as written testimony in connection with the education committee meeting on mathematics education, today, Wednesday November 5, 2003. I speak from my background as a research associate professor in the department of mathematics, Courant Institute, NYU, and as a steering committee member of New York City HOLD and co-editor of their Web site, http://www.nychold.com/ , from which background I have paid close attention to K-12 mathematics education in New York City and elsewhere. Please note that I recently left NYU and now have a visiting faculty position at Emory University, Atlanta, GA.
My testimony will address these issues.
1. The mandated K-5 mathematics curriculum, Everyday Mathematics.
2. The Children First process.
3. The role of the Council education committee.
This testimony will be brief and will rely heavily on previous contributions, referenced here, which may all be found on the NYC HOLD Web site.
1. The mandated K-5 mathematics curriculum, Everyday Mathematics.
I have written about Everyday Mathematics in an Op-Ed in the New York Sun on February 6, 2003, "Chancellor Klein's Math Problems" [1.0], and in two somewhat more analytical Web contributions: "The Many Ways of Arithmetic in Everyday Mathematics" [1.1] and "Spiraling Through UCSMP Everyday Mathematics" [1.2]; I also co-edit the New York City HOLD page of reviews of Everyday Mathematics [1.3]. Here I will only provide an introduction to those more detailed commentaries. My direct interest has been in the materials for grades 3-5.
The first impression of Everyday Mathematics is by no means all negative. If one takes a student workbook (student journal) and opens it at random then one is likely to find a collection of problems that look reasonable and appropriate for the grade level. This was my impression, anyway, and this impression is not quickly changed if one just flips through the workbooks.
When one starts to read through the workbook pages sequentially, from a random starting point, then things begin to look different. At first it looks as if the workbook does jump around a lot over different topics. At second look, it really jumps around like anything. I found myself wondering how students are meant to focus on whatever they are learning at the time. It turns out that what we observe here is a design aspect of Everyday Mathematics that the authors call "rapid spiraling"; it is deliberate and the motivation is explained in the teacher guides and in articles by the program authors:
"If we can, as a matter of principle and practice, avoid anxiety about children 'getting' something the first time around, then children will be more relaxed and pick up part or all of what they need. They may not initially remember it, but with appropriate reminders, they will very likely recall, recognize, and get a better grip on the skill or concept when it comes around again in a new format or application - as it will!" (quoted in [1.2]).
My Web article "Spiraling Through UCSMP Everyday Mathematics" [1.2], based on the student journals and the teacher manuals, illustrates this rapid spiraling via the example of the fourth grade treatment of multiplication and division. It is in the main a descriptive article, and I only conclude with an observation that the philosophy of the EM authors is for me entirely unconvincing, leaving it to the reader to make his or her own assessment with the aid of my description. For the present purposes I'll say, however, that this rapid spiraling treatment of multiplication and division is just plain crazy, and it is not to be imagined that students will learn the procedures in this fashion.
My criticism of the rapid spiraling nature of Everyday Mathematics echoes what can be read in other reviews, including the Mathematically Correct reviews of 2nd and 5th grade Everyday Mathematics [1.4], [1.5], Matthew Clavel's article in City Journal, "How Not to Teach Math" [1.6], and many other commentaries cited on the NYC HOLD reviews page [1.3].
My other focussed critique of Everyday Mathematics is the emphasis on multiple algorithms of arithmetic and student discovery. The student reference text describes four methods for addition, five for subtraction, four for multiplication, and two for division; and in each case the most efficient traditional algorithm is not or only very poorly taught (it is taught in what I call an early learner's variant for addition, and not at all for subtraction, multiplication, and division). I describe the algorithms in my Web contribution [1.1] and emphasized the point in my New York Sun Op-Ed [1.0].
My conclusion based on careful review of Everyday Mathematics for grades 3-5 and other reviews for earlier grades is that the Chancellor has mandated a bad program. The program requires massive supplementation from the start in order to avoid complete failure. Indeed, the Chancellor has selected with Everyday Mathematics also a supplementary program, Math Steps, but this just highlights the absurdity of the original choice.
There are fine textbooks available, but Everyday Mathematics is not among them. I doubt that a single curriculum should have been mandated across all schools, and would have been more sympathetic to a policy that relies on clear grade by grade standards from which is derived a limited choice of supported textbooks. In that case, the textbooks that were selected in California based on their very clear mathematics standards would be the first to consider. I remark that Everyday Mathematics was twice rejected in the California textbook adoption process.
[1.0] http://www.math.nyu.edu/~braams/links/oped-nysun-0302.html
[1.1] http://www.nychold.com/em-arith.html
[1.2] http://www.nychold.com/em-spiral.html
[1.3] http://www.nychold.com/em.html
[1.4] http://www.nychold.com/em-arith.html
[1.5] http://www.nychold.com/em-spiral.html
[1.6] http://www.city-journal.org/html/eon_3_7_03mc.html
2. The Children First process.
I have commented extensively on the Children First process since well before the first results were released in January, 2003; many of my comments may be found on the Web page "Chancellor Joel Klein's `Children First' New Standard Curriculum for NYC Public Schools" [2.0], which I wrote on behalf of NYC HOLD, and further on my page "Contributions to the Children First Initiative and New Standard Curriculum for NYC Public Schools" [2.1].
Here above I criticized one aspect of the outcome of the process, viz. the Everyday Mathematics mandate for grades K-5. For very convincing detailed criticism of the mandated reading program I point to the letter by leading reading researchers [2.2], and also a contribution by Mary Damer [2.3]. Many more references to reviews of the Children First outcome may be found through [2.0]. Here I want to focus my comments on the Children First process.
Ostensibly Children First involved listening to many stakeholders and making a choice based on careful study. There were ten working groups, including a literacy, a numeracy, and a special populations working group (these three are most relevant for curriculum). The composition of the working groups was kept secret, but this information was extracted by NYC HOLD through a Freedom Of Information Law (FOIL) request [2.4]. A subsequent FOIL request for the Charge to the working groups and for the reports of the Literacy, Numeracy, and Special Populations working groups elicited the information that the Children First working groups operated without written Charge and that at least the three named ones did not produce reports; I am guessing that the other ones - including the very important Leadership and Organization working group - also did not produce reports, since no reference is ever made to any. These FOIL requests and the replies are documented in [2.5].
I was dumbfounded. I had expected the Children First process, under the leadership of Diana Lam of whom I knew a certain reputation, to come up with bad choices in matters of curriculum. Indeed, I documented my hopes and expectations in several email letters to Chancellor Klein [2.6], [2.7]. I had not expected the blatant disregard for process that is expressed in the absence of a Charge and of working group reports.
I cannot imagine a process that involves a careful evaluation of alternatives and that does not result in written reports. In a careful process one has to inventorize alternatives, obtain outside advice and opinions, and look at performance of local schools and try to correlate this with curriculum. One also has to assess evaluations of textbooks and studies of curricula done by others. In a committee of 15 people or so one cannot do this without producing paper. The absence of committee reports is strong evidence that none of these components of a careful study were done. On the NYC HOLD page we write that we find it remarkable that Chancellor Klein would select a uniform mandated curriculum in such a cavalier manner.
I suspect that once the choice was made to have a uniform curriculum, a choice that makes a leader look strong, then it was inconceivable that the mandated curriculum would not be either the one that Ms. Diana Lam mandated in San Antonio or the one that she mandated in Providence, since a third choice would make her look weak and waffling. So instead of the atrocious TERC Investigations curriculum [2.8] in K-5, Ms. Lam's choice in Providence, we now have the bad, but not degenerate, Everyday Mathematics [2.9], which she mandated in San Antonio.
Late in the process a group, mainly mathematicians, of New York City HOLD met with (only) the manager of the numeracy working group, Mr. Evan Rudall. Our talking points for that meeting are on the Web [2.10]. Before the meeting many individuals associated with NYC HOLD had also provided responses to a Children First numeracy group questionnaire, and these responses are on the Web as well [2.11]; collectively they provide very detailed and what should have been very valuable advice to the working group. (However, we have no indication that Mr. Rudall saw it fit to share these responses with the working group.) As a follow-up to the meeting I provided additional advice on curriculum in two emails to Mr. Rudall [2.12].
This entire interaction has contributed to my perception of the Children First process. I was disappointed and consider it against good practice that our group, which included high level NYC mathematicians, was able only to meet with Mr. Rudall alone. We do not know, and I do not believe, that our input was communicated to the working group or used in their deliberations. In further obstruction to a constructive contribution from our side, we were not given any meaningful insight into the thinking of the working group. For example, we were not told which curricula the working group was considering most seriously at that stage. Our input was therefore not as detailed and focussed as it might have been. (We did provide a very detailed critique of the New York City Scope and Sequence for mathematics [2.13], and the contributions [2.10], [2.11], [2.12] do address specific curricula). My assessment is that Mr. Rudall was disingenuous in having that meeting with us; the meeting allows Chancellor Klein and Deputy Chancellor Lam to say that local mathematicians were consulted, but this consultation was not in good faith.
[2.0] http://www.math.nyu.edu/~braams/links/cf-blueprint-03.html
[2.1] http://www.math.nyu.edu/~braams/links/cf-contrib.html
[2.2] http://www.educationnews.org/Letter-from-Reading-Researchers.htm
[2.3] http://www.illinoisloop.org/md_wl_nyc.html
[2.4] http://www.nychold.com/cf-wgmembers.html
[2.5] http://www.math.nyu.edu/~braams/links/foia-02.html
[2.6] http://www.math.nyu.edu/~braams/links/let-021126.html
[2.7] http://www.math.nyu.edu/~braams/links/let-klein-021218.html
[2.8] http://www.nychold.com/terc.html
[2.9] http://www.nychold.com/em.html
[2.10] http://www.nychold.com/cf-num-021211.html
[2.11] http://www.nychold.com/quest-0211.html
[2.12] http://www.math.nyu.edu/~braams/links/let-cf-0212.html
[2.13] http://www.nychold.com/scopeseq-0212.html
3. The role of the Council education committee.
I understand that the committee has an oversight function, and the committee should not and does not think that it is managing the school system. However, in order to carry out its oversight function the committee needs to be informed.
There have been many attempts from New York City HOLD to obtain the interest of Ms. Moskowitz and the education committee in the matter of mathematics curriculum. In connection with Children First, for example, I wrote to Ms. Moskowitz on March 2, March 10, and March 25, 2003, in connection with a hearing of the committee. My emails (except for the short note of March 10) are on the Web [3.0]. The first of the two emails suggested questions to ask of Chancellor Klein, and foremost among my suggested questions was a request for the reports of the working groups and for the considerations that went into the outcome of the process. The March 25 email provided detailed criticism of Everyday Mathematics.
Ms. Moskowitz and the committee can have, of course, different views about mathematics curriculum than I, and they can also make the informed assessment that they will not review the mathematics curriculum choices in detail. I am disturbed, however, by the lack of interest shown by Ms. Moskowitz and the committee in the reports of the Children First working groups, or in the absence of such reports.
As the first phase of Children First was drawing to a close, in December 2002, I knew that, no matter what the outcome, I would want to see the reports - hence the FOIL request [2.5]. When the results of Children First came out and it could be seen that Chancellor Klein had decided to impose a uniform curriculum on a school system the size of that of a small country, as well as perform a massive managerial reorganization, of course the City Council education committee should have been interested to see what considerations went into the choices that were made. As a matter of routine, and without prejudice, Ms. Moskowitz and the committee should have wanted to see the Children First working group reports and understand the background of Chancellor Klein's choices. Such an interest by Ms. Moskowitz and the committee would be only a reflection of their responsibility; it would not indicate criticism or even scepticism over Chancellor Klein's choices, it would only indicate that the committee is aware of its oversight function, recognizes that schools transmit the content of a curriculum, and the choice of mandated textbooks (and even that there be a system-wide mandate) is a matter of importance.
Ms. Moskowitz replied to my email of March 2 [3.0] as follows:
"As I am sure you know, as a member of the legislative branch, I neither select panelists nor administer the Children First initiative. What I have done, however, is review the concrete policy decisions made by Chancellor Klein. I would therefore be interested in any specific criticism you have of Everyday Mathematics or any recommendations you have for how to improve mathematics instruction in our public schools. Please feel free to keep me up to date on your thoughts and concerns."
Of course I obliged with my detailed critique of Everyday Mathematics in the second email under [3.0], but I could not avoid the sense that I had been given some busy-work and there was no sincere interest and no intellectual curiosity on the side of Ms. Moskowitz. Indeed, my detailed critique and all the other contributions of NYC HOLD have been systematically ignored by Ms. Moskowitz and the education committee.
As I said earlier, of course Ms. Moskowitz and the education committee need not share my concerns over Everyday Mathematics. I do believe, however, that Ms. Moskowitz and the education committee have an obligation to ensure that they are informed, as necessary to carry out their oversight function. Ms. Moskowitz and the education committee should have asked for reports of the Children First working groups. When informed that these reports do not exist they should have become extremely upset and used whatever power they have to extract testimony, records, anything to document the reasons for Chancellor Klein's mandates. (In a detail that goes well beyond the level of "we decided that this was best for the children of New York City".) The lack of intellectual curiosity that Ms. Moskowitz and the education committee have exhibited is, I think, contemptible. Ms. Moskowitz and the education committee cannot carry out their oversight responsibility with such disregard for the need to be informed; they cannot even think that they are providing oversight.
[3.0] http://www.math.nyu.edu/~braams/links/let-moskowitz-0303.html
Bas Braams
November 5, 2003
Bastiaan J. Braams
braams@mathcs.emory.edu
Emory University, Atlanta, GA
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