Manhattan District 2 Math Forum

Remarks by Elizabeth Carson submitted to
The Community School Board Two
March 28, 2000


As you are aware, the Parents' Council has arranged for the April meeting of the Council to serve as a district wide forum on math education. The decision to devote energy and meeting time to this particular aspect of our children's education was inspired by a general consensus that there were a considerable number of parents who wanted more information about the math programs, who had an interest in engaging to a greater degree in their children's math education and/or who had questions, concerns or conflicts with aspects of the programs which they wished addressed more fully.

Christine Larson and I were appointed co-chairs of a planning committee, we offered a standing invitation to all Parents' Council members, as well as other interested parents to participate in the planning and in the event.

Lucy West, director of Mathematics was initially contacted and confirmed her interest in participating and specifically in her desire to share the District's perspective on the math initiative, ie the broad goals, an overview of the K-12 curricula and other aspects of District 2 math education. The PS/IS 89 auditorium was reserved for the evening of April17.

It was emphasized to Lucy that parents recognized that there are, across the District, parents who are to varying degrees and with respect to a variety of components, quite satisfied with the math education their children are receiving and have received in District 2 schools. Reasons for satisfaction include support of the progressive model and the inherent goals and standards set by the National Council of Teachers of Mathematics (NCTM) in our elementary curriculum,TERC (Technical Education Research Center) and our middle school curriculum, CMP (Connected Mathematics Project); seasoned, professional instructional delivery; and most importantly, clear evidence of student engagement and achievement.

It was relayed to Lucy that there are also parents throughout the district who are and have been questioning the standards and goals as well as the delivery of primarily the TERC mathematics curriculum; parents who are dissatisfied with their children's level of engagement and achievement. Parents have repeatedly voiced concern with a lack of clarity in the curricula and the lack of textbooks, who have asked questions about what skills their children are to have mastered year to year, in some instances expressed concern with a lack of ongoing assessment of skills. Parents have shared frustration with the perception of being given mixed messages from teachers and math staff developers regarding drill, practice, supplementation and/or tutoring. Parents have to a lesser degree noted similar question and concerns about CMP, and our high school math curriculum, Mathematics Modeling Our World (MMOW), now in the first year of implementation.

Its worth noting that at the elementary level, students have had a wide range of experience with TERC. No two parent stories of their child's math experience are alike. This is so, partly because their children are in different grades of the curricula and of varying abilities. However, experience and perspective also vary because students have participated within the district and through the grades in a variety of combinations of traditional and reform math education.

Experience is further splayed due to differences in instructional delivery from school to school and grade to grade; ostensibly due in part to the staggered implementation of the new programs and gradation in staff development over the past four or more years.

There appears to be to some degree for some number of parents, a conflict between what they wish and expect for their children in a mathematics education and what is given most emphasis in our math programs.

This has led parents, with the means to do so, to supplement and in some cases supplant the math education their children are receiving. Parents have bought workbooks; engaged private or institutional tutoring, including that provided by Kumon and the Huntington Learning Center; and in some cases are literally providing a completely different curriculum at home, using the Saxon series or Singapore's elementary school math books.

We invited Lucy to consider how she might incorporate into her presentation a deeper response and considered discussion of some of the critical perspectives parents continued to have, questions and issues they've repeatedly raised already at the school level. Issues that are, as we'd come to realize, reflected in the conflicting professional viewpoints held regarding our District's curricula and the NCTM standards they are aligned with. We relayed that there was an interest in the math night including address of the fundamental issues in the ongoing national debate between K-12 mathematics educators and members of the mathematics and scientific communities over what, and how to teach, mathematics in this country.

We agreed our goal for the night was to provide opportunity for a balanced debate, where parents were educated about more than one side; an opportunity for open minded and informed dialogue. We agreed our goal was to help establish a well informed parent population, who can speak from fact and who are then prepared to effectively work together with school staff and the district office toward providing the best possible mathematics education for their children.

We agreed we would work to create an evening which would best serve the aforementioned goals, and one where particular attention was paid to maintaining a healthy respect for the variety of perspectives and experiences of the District 2 community.

To guide discussion and planning of the nights' format and focus, a list of parent questions relevant the District's math education, a website resource list and a math education reference list were drafted and distributed at several Parents' Council meetings, to other interested parents and teachers and to Lucy, herself. We invited Lucy to provide comment and analysis if and when possible, about issues raised in the documents relating to our math programs and to advise us of any reference pieces that she deemed most appropriate to provide parents, and of any she thought not appropriate or lacking factual merit. She has provided two pieces for inclusion, which we've added to our reference list, the NTCM s "Frequently Asked Questions" and a paper published in the University of Chicago School Mathematics Project Newsletter, "Educating the Public About School Mathematics."

To broadly engage parents, and to further inform focus and specific questions for a Q and A session, a survey was distributed to all the schools, asking parents to indicate aspects and levels of most interest in our K-12 math programs, and inviting specific questions or comments. The survey in no way was intended to, or should be construed as, a gauge of the relative level of parent support or criticisms of their children's math education.

We relied on the efforts of parents and staff at the school level to copy and distribute the surveys. School participation has been uneven; some, as yet unknown number of PA/PTA leaders have opted not to engage their parent communities. However, significant effort has been made at some schools, perhaps most notably at PS 124, where a Chinese translation was drafted and distributed to the their parent community. Subsequently, we provided the Chinese translation to other schools identified as having a large non-English speaking Chinese parent population. Unfortunately, the resources for a Spanish translation of the survey were not available.

The district office is providing translation services for a flyer announcing the math night, which will be distributed in English, Spanish and Chinese. We will be able to provide limited opportunity for simultaneous translation at the math night. (We have 30 translation headsets, purchased by the Parent New Standards Committee).

Many of the decisions about focus, format and panel representation remain to be made,

In early April, following the survey response deadline, a meeting of organizing parents with Lucy West will meet to finalize plans. Survey responses will be looked at, considered and conclusions drawn about where parent interest predominantly lies.

Preliminary conversations, many via e-mail, established an agreement that a panel discussion would be an effective way to present and also to field questions. Exactly who will serve on the panel has not been agreed upon. Lucy has suggested consideration of District math staff developers, math teachers, and possibly a math educator from NYU, who participated in the development of CMP. A parent, who is a TERC tutor has been given preliminary approval by Lucy. Some parents are advocating for a more balanced panel, and are asking consideration of professionals who can speak to the concerns locally and nationally. Several persons have been suggested, including a District 2 parent, who is a seasoned teacher of mathematics at Stuyvesant, teaching BC Calculus and the Intel research course, and also one of several highly regarded mathematicians from NYU, who are familiar with our curricula, and who can speak to the criticisms and recommendations expressed by mathematicians and scientists regarding our math programs and the NCTM standards.

In an interest to engage the board to the fullest extent possible, Christine Larson and I have prepared notebooks for you, containing hard copies of all of the documents listed in the "Math Education Reference List for Parents."

Not a perfect list, not to be interpreted as a comprehensive reference list, but rather representative of some of the research we and other parents have engaged in and wish to broadly share with other parents and educators.

We hope the list provides a variety of entry points for parents interested in gaining a deeper understanding of

Those reviewing the documents should readily become aware that the math controversy is an extension of the ongoing tug between progressive and traditional education advocates.

The documents include perspectives of the NCTM, the publishers of TERC and CMP, the University of Chicago School Mathematics Project (UCSMP), individual members of the mathematics and scientific communities and collectively, in Dr David Klein's letter to Secretary Riley, and both the Mathematical Association of America (MAA) and the American Mathematical Society (AMS). We've included an article with a commonly held viewpoint on the "pendulum swing" of math reform, authored by Tom Loveless. There are pieces about The Third International Math and Science Study (TIMSS) often alluded to in discussions about math education, the ranking of participating nations, at the fourth, eighth and twelfth grades, the executive summary of the eighth grade "Videotape Classroom Study" and an article about the TIMSS results and implications. Teaching pedagogy is a key part of discussions about math education, and the NCTM standards themselves, and so, an article about "Project Follow Through" a research project on the relative merits of teaching strategies is included. A comparative overview profiling exemplary math education of differing philosophy and practice at the fourth and eighth grade level is included, parts are: the philosophy and units of our TERC and CMP curricula, the NCTM's "Summary of Changes in Content and Emphasis in K-4 and 5-8", the NYC BOEs math standards, the California Mathematics Content Standards, Virginia's Standards of Learning in Mathematics, the contents of the math curriculum developed by the Singapore Ministry of Education, and in the seventh grade comparative only, the Chinese International School's International Baccalaureate Higher Level Mathematics Syllabus.

We've included some information, not available online, which has been broadly distributed to District 2 parents: Superintendent Alvarado's letter to parents, the district's pamphlet for parents, "Parent's Guide to the New Mathematics Standards and Curricula in CSD#2" and an article on math reform, "The NCTM Standards for Mathematics, K-12."

It is hoped that the web site resource will guide parents in further research. A list of parent questions about the District's math education, is intended to inspire reflection, discussion and focus in dialogue between parents and educators.


Most would agree with what Dr Roger Howe, mathematics professor at Yale University wrote in his article, "The AMS and Mathematics Education: The Revision of the NCTM Standards," in Notices of the AMS: (included in your reference documents). "The relationships between computational expertise and conceptual understanding, and how each supports the other, is complex and requires careful study and thought."

The current disagreement and concern about math education is ,in great part, about those relationships. Questions have risen about how and to what degree creative and collaborative problem solving, discovery learning -constructing one's own knowledge through investigation and real world application should be integrated and balanced with what is termed the more traditional aspects of math education: direct instruction, mastery of basic skills through example, repeated practice of applications, drill, and an emphasis on the development of facility with the standard algorithms of arithmetic and algebra.

The sequence of learning is another point of disagreement. The traditional approach is hierarchical, involving the sequential mastery of basic skills followed by the development of conceptual understanding; which is in opposition to the progressive approach, where it is espoused that conceptual "big picture" learning comes first and foremost, and simultaneously or subsequently, the acquisition of math facts and facility with algorithms is developed.

There is thankfully, agreement that the goals in mathematics education are for our children to have both skills mastery and conceptual understanding.

One view held, and reflected in the basic concerns of some parents, is the view expressed by Dr H Wu, professor of mathematics at UC Berkeley, in his article, "The Mathematician and the Mathematics Education Reform Movement" " the question, does the NCTM reform improve on what is unsatisfactory in the so-called traditional curriculum - The answer is yes and no: the reform presents not an unalloyed improvement but a set of uneasy tradeoffs."

Unease is clearly expressed in the letter written and published in the Washington Post to Secretary of Education Richard Riley. The letter was written in response to the Secretary's endorsement of ten math curricula aligned with the NCTM standards, which include our middle school curriculum, CMP.

The letter was co-authored by five mathematicians and one scientist, and co-signed by more than 200 mathematicians and scientists, among them: seven Nobel laureates, several winners of the Fields Medal, the highest award in mathematics, department heads at more than a dozen universities, including Caltech, Stanford and Yale, two former presidents of the Mathematical Association of America, education administrators at the state and national level, education psychologists and education researchers.

The letter expresses concerns with, and in some cases opposition to, most of the curricula endorsed; and specifically alludes to several papers criticizing CMP. The letter also raises questions about the Expert Panel's process for determining which curricula were exemplary and promising (ie, faithfulness to the NCTM standards, being one criteria) and objection to the absence of the mainstream views of mathematicians and scientists in the evaluation process.

Frank Allen, Emeritus Professor of Mathematics at Elmhurst College, a high school teacher of mathematics for many years and past president of the NCTM, in his speech delivered before the NCTM Annual meeting in Chicago in 1989, just as the standards were being released said:

"I love school mathematics and still care about what is happening. According to my experience, students must know the mathematics before they can apply it. Or to say it differently, they cannot apply mathematics they do not know. It is like trying to teach people to play water polo before they know how to swim. Nor do I believe that students are necessarily motivated to study mathematics because it is useful." Dr Allen quotes the great mathematician Marshall Stone, "I hold that utility alone is not a proper measure of value, and would go so far as to say that it is, when shortsightedly applied, a dangerously false measure of value." Dr Allen continued, "We never hear anymore about the beauty of mathematics or about its structure and internal consistency - or about mathematics as an ideal arena for the application of logic to the thinking process - or indeed about any of the cultural values of mathematics that have been cherished by the race for generations."

There are a host of specific concerns and recommendations about the standards that have been offered by the mathematics community, and which in alignment with some of our District's parents' perspectives on our own NCTM standards based programs.

From the AMS (in Notices of the AMS, Feb, 1998): "We would like to emphasize that the standard algorithms of arithmetic are more than just 'ways to get the answer' - that is, they have theoretical as well as practical significance,".. "For one thing, all the algorithms of arithmetic 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." (see Dr David Klein's elaboration in his article "Math Problems..", published in the April issue of the American School Board Journal)

The (Mathematics Association of America Association Resource Group) MAAARG recommendations to the NCTM, provided during the revisions process, encompass parents' concerns as well. From the "General Comments" section of their report: "we want the revisions of the Standards to be more specific with regard to both skills and expectations for student' intellectual growth from one grade level to the next. Many teachers, both those teaching from reform materials and those who continue to use a more traditional approach, would like the Standards to specify what skills are really needed for each level of mathematics." ".. should offer direction for instruction of students who show more aptitude than usual in mathematics and the ability to absorb more mathematics and more sophisticated mathematics faster, not just those who eventually might study more mathematics," "...the mastery of skills is not addressed sufficiently," "...urge you to support the role of drill in school mathematics," "Learning of arithmetic facts and practice drills is discussed, but always in a negative light," "The standards are dead on arrival if they do not acknowledge the importance of arithmetic and algebraic skills and the deep concern that a significant portion of the population has about this issue," And, "In order to be successfully implemented in the classroom, many of the suggestions in PSSM Require a level of teacher knowledge, insight, and ability to reason logically that is simply not present in the general population of K-12 teachers. Our partial countermeasure is to make sure that curricular material are clear and complete enough to serve the needs of teachers as well as students."

These strong recommendations, combined with the fact that The NCTM standards (which our TERC, CMP and MMOW are closely aligned with), have been under revision over the past several years, indicate K-12 math education is, as in the past, a work in progress. During the recent revision process, the active engagement of many groups was solicited, which had not occurred during the process leading to the 1989 standards. In addition to the MAA and the AMS recommendations, input was provided by The American Statistical Association (ASA,) the American Mathematical Association of Two-Year Colleges (AAMATYC), the Association of State Supervisors in Mathematics (ASSM), the Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM)

There is always room for improvement in education. Perspectives and decisions about balance, emphasis and content will differ; struggle is a natural component in the evolution of education. Both content and performance standards will continue to vary curriculum to curriculum, district to district and state to state.

We have good reason in District 2, in our immediate educational community of teachers, staff developers, administrators, school board members, parents and students, to work together in the evolution and continuing improvement of our District's math education

The informed engagement of our parents is critical to ensuring excellence and assuring that a quality math education is to the greatest extent possible, an achievable goal for all of our students.

Thank you for you interest and consideration.

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