Testimony of Elizabeth Carson
NYC Parent
Co-Founder, NYC HOLD
Honest, Open, Logical Debate on Mathematics Education Reform
Before the New York City Council Standing Committee on Education
Eva S Moskowitz, Chairperson
School Mathematics Education Hearing
City Council Chambers
City Hall
November 5, 2003
Honorable Chairperson Eva Moskowitz and Members of the Committee:
My name is Elizabeth Carson. I am a District 2/ Region 9 parent and co-founder of the citywide organization, NYC HOLD Honest Open Logical Debate on Mathematics Education Reform, an education advocacy coalition of parents, educators, mathematicians and scientists and concerned citizens.
I am encouraged by this first and seminal hearing that you've convened today on mathematics education, the first since the Mayor assumed responsibility for the NYC public schools and the first since the launch of the instructional reforms under the Chancellor's Children First initiative. With a new education governance structure, where school boards are in limbo and a Panel for Educational Policy, merely advisory, it is absolutely essential that your committee fulfill the functions of serving to provide public ongoing oversight and accountability throughout these monumental, sweeping education reforms affecting most NYC public schools.
And for these reasons, I am extremely disappointed with the limitations of this hearing to provide you with what I know to be critically important expertise, experiences and perspectives, which you will require to make informed decisions on how best to provide oversight and accountability in the area of school mathematics instruction.
The scheduling of this hearing, the agenda, the exclusive representation you've invited to testify and serve on a panel discussion, and the nature of prior notice - or more accurately, lack of prior notice, in total will leave you with next to no chance of hearing the expert analysis and recommendations of subject area experts: mathematicians and seasoned classroom mathematics teachers; or the experiences, values and standards of parents. You are missing so much of the picture without hearing substantive testimony from these three constituencies.
Indeed it is the absence of the proper integration of the expertise of these three constituencies that has led us to the current content deficient and pedagogically flawed mathematics education reforms, known by the generic terms, 'reform math' or 'constructivist math,' adopted in regions across the country, and over the past several years in some NYC districts, among them Manhattan District 2, and this year in most NYC schools under Children First. [1]
Mathematics instructional reform in NYC and across the nation is, and has been for many years, critically needed. US mathematics education must be drastically improved. We have serious but highly possible work to do in order to get it right. International comparisons, most notably the TIMMS studies, show the US performing about average in 4th grade and progressively worse in the later grades, as measured in international rankings at 8th and 12th grades. [2]
It is unacceptable that the richest country in the world can not provide the quality of mathematics instruction that so many other countries, many far less privileged, are able to provide their children. The Paris based Organization for Economic Cooperation and Development (OECD) found, out of 28 member nations that took part in their study, only Italy, Greece, Portugal, Luxembourg and Mexico did worse than the United States in math. [3]
Unfortunately mathematics education reform efforts locally and nationally over at least the past 15 years, have led to imbalanced, ideologically driven mathematics programs and teaching practices that have not substantively raised student achievement, nor closed the achievement gap, but have effectively diminished the content taught in school mathematics education to an all-time low.
The content-lite direction in mathematics education began around 1985 and continues to the present. Mathematics instructional reforms have been guided primarily by the National Council of Teachers of Mathematics "vision statement" outlined in a 1989 document, subsequently revised in 2000. [4]
The NCTM vision denigrates the discipline of mathematics by advocating personal solutions in the formative years, over and often to the exclusion of mastery of the basic skills and procedures, fundamental to the discipline. The vision reviles explicit instruction, memorization and practice. [5] [6] This vision works in tandem with a philosophy of teaching and learning, that has become dominant in our schools of education. The philosophy dismisses the classical construct of teacher as learned authority responsible for endowing children with knowledge, and instead promotes guided discovery with the teacher a mere facilitator and with an instructional relativistic stance, rooted in a fundamental questioning of the existence of any objective reality. The teaching philosophy denies a priori the very integrity of knowledge in mathematics. Translated into classroom practice, one can well imagine a classroom where there is no right answer, for whose concept of right is more right - we cannot ever know for certain; and so students can not be asked to trust the authority of others, to trust the truths of others, by committing to mastery the principles of mathematics developed over hundreds of years, traditionally present in foundation mathematics courses. Whatever method a student discovers, for example, to divide quantities, such as pictures, repeated subtraction or some form of reasoning is equally valid and useful to the elegant and efficient long division algorithm. [7]
Constance Kamii, whose writings have often been distributed to District 2 parents to explain the philosophy behind the 'reform math' states: "When the teacher decrees that an answer is correct, all thinking and initiative stops." "Teaching algorithms force children to give up their own thinking." "Refrain from teaching conventional algorithms and instead, encourage children to invent their own procedures for solving problems." [8]
The now infamous US Department of Education's expert panel's controversial endorsement of 10 "exemplary and promising " 'reform math' programs, several years ago, included the Chancellor's elementary program, Everyday Math, and other programs still used in "wavered" schools in NYC. The US Department of Education has since renounced the panel recommendations; the list is no longer presented on the Web site. The ideological views of one of the leading members of that expert panel, Steven Leinwand, a state education official in Connecticut, bear a striking resemblance to Kamii's: "Its time to recognize that for many students, real mathematical power on the one hand and facility with multi-digit pencil and paper computational algorithms on the other, are mutually exclusive. In fact its time to acknowledge that continuing to teach these skills to our students is not only not necessary but counterproductive and downright dangerous." [9]
One mathematician committee, in a report to the NCTM regarding the algorithms of arithmetic wrote: "We would like to emphasize that the standard algorithms of arithmetic are more than just ways to get the right answer, that is they have theoretical as well as practical significance ".. "For one thing, all the algorithms are preparatory for algebra since there are (again, not by accident but by virtue of the construction of the decimal system) strong analogies between arithmetic of ordinary numbers and arithmetic of polynomials." [10]
Mathematicians were and are appalled with the extremes in the constructivist philosophy and the resultant programs which bowdlerize important areas of arithmetic and algebra.
This strikes at the heart of the conflict in views on school mathematics between constructivist mathematics educators and mathematics experts.
The common debate framed in press reviews, as concepts (only advocated by math reformers') vs. basic skills (only advocated by critics of reform math) is misleading and false. Critical mathematicians who object to 'reform math,' insist on mathematical content but also hold equal regard for conceptual development and problem solving; viewing the three as inseparable [11]
Together the NCTM vision and popular education school 'constructivist' ideology has led to adoption of content deficient programs, doctrinaire imposition of process over content teaching methodologies, and the development of local and state standards that lack coherence, grade specific content standards and the rigor necessary for the vast majority of today's students. NYC and NYS seriously suffer from all of these maladies. [12] [13]
I can not begin, in this context, to provide you with a proper presentation of local evidence of program imbalance, content deficiencies, inefficient and ineffective teaching approaches, wasteful pedagogically heavy professional development and poor outcomes among some subpopulations of students, all associated with "reform math" program adoptions in local school districts, among them Districts 1, 2, 3, 10 and 15. Similar evidence exists in regions across the country where the Chancellor's choice of universal math programs and teaching approaches have been tried and failed.
I would be happy to participate in such a presentation at another time. You may wish in the interim to visit the NYC HOLD Web site to study the vast array of references we've gathered for the NYC community.
A sampling of what you will find on our site: District 2 math performance of poor black and Hispanic schools; District 2 parent survey responses, letters and testimony; District 2 teacher interviews; District 10 School Board resolution calling for a halt to replication of District 2 math reforms, and the development of a coherent grade specific framework to guide adoption of new content rich and rigorous math programs; the text of 2001 NYU Math Forum talks given by a distinguished panel of mathematicians and scientists from NYU, CUNY, Manhattan College, University of Rochester, Harvard, and Lehigh University; over 80 news, television and radio reports about local parent dissatisfaction and the concerns of the mathematics community about 'reform math;' mathematician's analysis of local 'reform' programs and the NYC and NYS mathematics standards; reports on the paucity of valid and reliable mathematics education research; sources of funding for 'reform math;' articles on the undue federal influence via NSF EHR grants for reform math;' open letters to Chancellor Klein from concerned parents asking him not to adopt 'reform math' programs; mathematicians' letter to Chancellor Klein warning of the grave content deficiencies in the 'reform' programs, among the authors, Charles Newman, the Director of the Courant Institute of Mathematical Sciences at NYU, and Robert Feinerman, Chair of the Mathematics Department at Lehman College and Chair of the CUNY Mathematics Department Chairs; and the NYC HOLD Children First survey responses which provide an impressive array of responses by knowledgeable parents, K-12 teachers, math tutors, and mathematicians, that in total give a wealth of expert analysis and recommendations with which to inform a proper direction for NYC to take in mathematics education reform. [14]
We are presently very, very far from a proper direction. About the new universal mathematics program, Everyday Math, Emory research physicist Bas Braams (formerly at NYU) stated, "Everyday Mathematics requires massive fixes at the most basic level. The program does not teach the standard procedures at all for subtraction and division, and offers a hopelessly confusing potpourri of methods for all the four elementary operations." [15]
Stanford Mathematics professor James Milgram, in a panel discussion on math education hosted by the NYU Steinhardt School of Education last year, when asked what he projected for NYC student math achievement as a result of the Children First reforms, he replied: "..the situation will be a disaster." [16]
NYC, right now, is well positioned to make the necessary sharp turn in mathematics education reform to correct the substandard math achievement in NYC and by example, for the US. To do so will take at the start, the commitment on the part of the NYC educational community and the political will on the part of elected education policy makers to honestly, openly and logically rethink the Children First initiative; and to then establish a system for design and expedition of educational reform that embraces and fully utilizes the diverse and rich expertise and views of NYC education stakeholders.
The New York City Council Education Committee could lead the way in support of the needed redirection in instruction in order to provide all NYC students with a sound basic and quality mathematics education, the foundation students require, in order to have open to them the greatest number of educational options at the high school level, and subsequent college math based coursework and careers.
Here are my recommendations on how to start:
I Convene several additional City Council Education Committee hearings and/or town hall meetings, the latter in the evening, and ideally held in several boroughs. This will insure the Committee is more fully apprised of the overall current state of mathematics education. Invite involved local mathematicians to give testimony or presentations. Encourage parent participation in town hall meetings, use various means of parent communications: PA, SLT, Presidents Council, CPAC and UPA to give notice, well in advance, to parents. In addition to hearing from individual parents, solicit expertise in invited testimony from school SLT's to learn the views and recommendations of teams who have looked deeply at mathematics education in their schools. Arrange for the opportunity to hear the uncensored views of K-12 experienced classroom teachers. Be aware that many teachers do not feel free to relay their real views and opinions for fear of administrative retribution or future disadvantage in professional opportunities and advancement. Solicit analysis and recommendations from local school boards.
II Education Committee ongoing oversight of Children First instructional reforms
A The Education Committee should orchestrate a means for ongoing public engagement in issues and aspects of school mathematics education.
B The Education Committee could operate as a whole or might form a subcommittee that could provide oversight and support for the expedition of the recommendations that follow.
It is possible that some of the recommendations might be assumed by the Chancellor's Math Advisory Panel, headed by Uri Treisman; but I would advise Council oversight in any such instance. And more generally, I advise Committee oversight of all assignments and subsequent work of the Chancellor's Math Advisory Panel.
1. Advocate for balanced representation on the Advisory Panel and any other committees convened to develop or provide oversight of any component of NYC mathematics education, ie program adoptions, program implementation, teacher certification, professional development, standards, and assessments. (further defined in advisories below) The balance should ensure the greatest potential for full and meaningful participation of mathematics experts and seasoned classroom teachers at elementary, middle and high school levels.
2. Advocate for and support the development of a coherent, grade specific, mathematics curriculum framework. This does not presently exist. NYC relies on the grade banded NYS Standards, the process oriented New Standards Performance Standards for Mathematics, and the Standards Based Scope and Sequence for Learning - of which none are adequate. [17]
A curricular framework should include definition of the skills and knowledge students need each year (pre- K- 5) in order to attain a foundation in elementary arithmetic sufficiently rigorous to provide equal opportunity to advance into high school math and science coursework, and to advance to college math based course and careers This sequence would necessarily have to differentiate at high school ( to accommodate criteria for students who wish to fulfill coursework to prepare for the Regents Math A, a basic Regents diploma, and for the college bound students, coursework to prepare for the Regents Math B. Sequence differentiation may well necessarily occur at the middle school level to accommodate criteria for those students with ambitions to advanced math and science high school coursework and entry into specialized science high schools.
The framework would align with city and state assessments. The framework would reflect the requirements needed of, at minimum, incoming CUNY freshmen as defined by the CUNY mathematics departments.
3. Advocate for and support committee work that includes content analysis of the adopted programs and supplements and of programs used in 'waivered' schools, and alignment to a new framework; a similar analysis should be done before approval of any new adoptions
4. Advocate for and provide oversight in the development of professional development that follows the new framework and program analysis, to insure coherent and comprehensive classroom coverage of math content deemed necessary year by year, grade by grade
5. Advocate for and develop advisories on curricula for the remainder of the high school years, left undefined by New York State (now Regents A is considered a 1 and 1/2 year course, and will soon be reduced to one year course)
6. Advocate for and support NYC participation in imminent state standards revisions and curriculum advisory, and subsequent work to align city curricula
III Advocate for and support enlisting an outside agency to provide independent research and analysis of Children First reforms and their evolution
IV Advocate and support rigor in the mathematics courses required for state certification at all grade levels, K-12
I close with excerpts from two parent letters and one teacher letter sent to me. The first is written by a District 2 parent, and sent to me last year, her child attended what is now a 'waivered' school, exempted from the universal math curricula and so continuing with the math program she wrote about. The second letter is written by a Queens parent last week. The third is authored by a veteran NYC teacher, sent last month.
There are many implications in the three letters for the existence of serious problems in mathematics education in schools using the universal programs, as well as in some of the 'waivered' schools.
I am a physician who was initially mathematics major in college. I just found your Web site today and wish I had known about it 6 years ago when my oldest daughter began kindergarten in District 2. It was not until third grade that I realized just how little math she was learning, and how behind she was in basic skills. According to her teachers, everything was fine, but then no testing or assessment was done, other than the state wide tests - and I recently discovered that our teachers do not even get access to their student's individual results!
Needless to say we've been struggling ever since - we tried Kumon, had a private tutor, and have used the McGraw Hill Math series workbooks as well -. Unfortunately, attempts other than tutoring, such as workbooks don't teach -they just provide for practice of taught skills.
My daughter is a bright child, but math is not "natural" for her. She has never done well "inventing" her own ways to do problems, and I have been stymied as to why the school was not teaching her how to add, subtract, multiply and divide, etc. Once taught, and after sufficient practice, she gets it. I was never asked to invent math - I was taught the ways that math scholars developed over the centuries - why are we asking our children to reinvent the wheel? Our best year of math at PS --- was 5th grade, when all the teachers were new to NYC, all three having come from teaching in the Midwest. Suddenly there were worksheets coming home and quizzes in class, and my daughter had a sense of what she was expected to know, and I did too. All too late as far as I am concerned. Now in sixth grade we are still catching up I have now ordered the Saxon series to aid me in teaching both her and her 2nd grade sister (who unlike her older sister gets math almost intuitively, so it will be much easier going)
At any rate your mission statement summarizes everything I have been saying to friends and other parents at school for the past 4 years. I too, am convinced that our school has for far too long been taking credit for the extra work that the parents are doing in math - this is why our children are doing well, not because of the curriculum!
My wife and I were very happy to receive your e-mail. It is comforting to know that there is a group of people out there that feel as we do about the education of our children. It was only last month that we found out about the new curriculum, Everyday Math, that is being taught in the public schools.
I cannot believe that this curriculum was brought in without the parents even having a chance to voice our opinions. Our daughter --- is a 4th grade student in a gifted program at P.S. --- in District --- (Queens) P.S. --- that was on the exception list as is P.S. --- (also part of the gifted program). However, both principals decided to teach Everyday Math anyway as did many other schools in this District and in District ---.
We are going to compile a list of all the schools that are exempt but decided to teach Everyday Math anyway. When we went to speak with our daughter's teacher we found the desks arranged in little groups of four and found that although her teacher is not happy about the curriculum, she has little say in it. We were told by the principal that they would give the children enrichment and extra math but her teacher said that Everyday Math fills the whole time period and they would not have time for any other math.
When we asked her principal why she decided to teach the curriculum when her school is exempted she told us that they are not really exempt. We asked her if there was a letter from the department of education saying they were not exempt and she said there was nothing in writing and she couldn't say anything more about it.
She told us that the citywide math and reading tests would be changed to favor the Everyday Math curriculum and so it which would lower the test scores of the schools opting to teach their students traditional math.
I am a 15 year veteran of the NYC education system. I currently teach ESL at - in Brooklyn. I am appalled, not only as an educator, but as a mother, by the new Everyday Mathematics program that is being forced upon our schools. My daughter is in the first grade at PS --- in Brooklyn. I often have to clarify her mathematics homework and properly re-teach her concepts that she could have readily understood if they had been presented in a structured way. I firmly know from my experience that children do not learn intuitively after being subjected to confusing "lessons" that simply serve to baffle them. The other day, after my daughter told the teacher that she didn't understand a math game, the teacher's response was that she did not have to understand.
This is unacceptable!
Thank you for having such a wonderful informative web site.
[1] The Second Great Math Rebellion, by Tom Loveless, Education Week (1997). http://www.educationweek.org/ew/1997/07love.h17
[2] Trends in International Mathematics and Science Study, NCES http://nces.ed.gov/timss/
[3] U.S. Students Prove Middling on a 32-Nation Test, Diana Jean Schemo, The New York Times ( Dec 5, 2001)
[4] Principles and Standards for School Mathematics, NCTM (2000) http://standards.nctm.org
[5] Standards in School Mathematics, by Ralph Raimi (Letters, AMS Notices, Feb. 2001). http://www.ams.org/notices/200102/commentary.pdf
[6] Good Intentions Are Not Enough, by Richard Askey (1999). http://www.math.wisc.edu/~askey/ask-gian.pdf
[7] Mathematics Education Constructivism in the Classroom, Math Forum, hosted by Drexel University http://mathforum.org/mathed/constructivism.html
[8] 52 X 8: The Importance of Children's Initiative, Constance Kamii, et al, The Constructivist (Fall, 1997)
[9] Math Problems: Why the U.S. Department of Education's recommended math programs don't add up, by David Klein, American School Board Journal (Apr 2000). http://www.mathematicallycorrect.com/usnoadd.htm
[10] Reports of the AMS Association Resource Group, with a short introduction by Roger Howe, Notices of the American Mathematical Society (vol 45, no 2 February 1998) http://www.ams.org/notices/199802/comm-amsarg.pdf
[11] Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education, by H.-H. Wu, America Educator, (Fall 1999).
[12] Serious Defects in Proposed NYS Standards for School Mathematics, a letter from Herbert A. Hauptman (Nobel Laureate, Chemistry) and others to New York State Schools Chancellor Carl T. Hayden (August 21, 1997 http://www.math.nyu.edu/~braams/nychold/let-hauptman-970821.html
[13] Math A Position Paper for NYS Regents, by the Association of Mathematics Teachers of New York State (AMTNYS), October 8, 2003 http://www.amtnys.org/amtnys_math_a_position_paper.pdf
[14] NYC HOLD Honest Open Logical Debate on Mathematics Education Reform http://www.nychold.com/
[15] Chancellor Klein's Math Problem, Bas Braams, NY Sun (Feb 6, 2003) http://www.math.nyu.edu/~braams/links/oped-nysun-0302.html
[16] When Worlds Collide, by Jessica Raimi (May 13, 2003). http://www.math.nyu.edu/~braams/nychold/let-jessraimi-0305.html
[17] analysis of various standards documents, NYC Standards and Assessments, NYC HOLD Web site http://www.math.nyu.edu/~braams/nychold/#nyc-standards
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