Several members of the Steering Committee of NYC HOLD met with Chair Evan Rudall of the Children First Numeracy Working Group on December 11, 2002, in the Department of Education's new Tweed building. The meeting was arranged by Evan Rudall and Elizabeth Carson as a follow-up to written presentations that some of us had made in response to working group questionnaire on mathematics instruction. In addition to Evan Rudall and Elizabeth Carson, the meeting was attended by Bas Braams, Sylvain Cappell, Bob Feinerman, Fred Greenleaf, Chuck Newman, Stanley Ocken, and Alan Siegel.
In preparation for the discussion our group had prepared some talking points. They follow here.
Curriculum Standards and Frameworks. New mathematics standards need to be adopted for New York City, based closely on the California and Massachusetts standards. We provide detailed critical comments on the NYC Scope and Sequence document.
Assessments. The current City and State assessments for grades 3-8 are at considerably too low a level, and public transparency is lacking.
Curricula. The present list of California approved curricula and the associated adoption reports should serve as the basis for approving curricula for use in the coming school year. Some curricula, including TERC, CMP, IMP and ARISE must be unequivocally banned.
Process. Curriculum approval should follow the model of the California textbook adoption procedures, which relies on evaluation by a panel of content experts -- i.e., mathematicians and scientists. More generally, the decision making body for NYC mathematics education should include expert mathematicians in addition to people whose expertise is mainly educational.
We appreciate the opportunity to advise members of the working group on issues of K-12 mathematics education in New York City. We understand that the role of the numeracy working group, within the Children First initiative, is to offer a blueprint for reform of mathematics instruction. We assume that this includes curriculum, standards, and assessment. We assume that the working group is interested in perspectives on specific curricula, standards, and assessments, and also in matters of policy with respect to selecting or specifying same. We were asked specifically to comment on the Scope and Sequence document for mathematics.
Many of us have used the Children First numeracy survey as a vehicle to express our views on mathematics instruction. These responses are, with a few exceptions, collected on a Web page [0]. Several themes recur throughout our individual responses, as noted in the Appendix.
New York City has multiple mathematics standards: the State standards, the NCEE/ACPS Performance Standards, and the City Scope and Sequence. Of these, the Scope and Sequence best approximates a useful set of standards, but it is insufficiently specific in many places and fails to indicate the weighting of topics needed to provide students with a proper grounding in mathematics. It is too vague to guide assessments and lacks the prioritizing needed as a basis for classroom planning. In contrast, the California and Massachusetts Standards are clear and balanced, and we recommend those standards as the basis for any future standards effort in New York City. [Addendum Dec 31, 2002: See this link for our detailed Commentary on the NYC Mathematics Scope and Sequence.]
In addition there is the New York State "resource guide" with classroom examples. This document is unrepresentative even of the State Standards, and too many of the activities, such as cutting cardboard in eighth grade, are devoid of grade-appropriate mathematical content.
We recommend for careful study the California content standards, the Massachusetts, standards, the Fordham reviews of State Standards, Bill Quirk's review of the NCEE standards, and the proceedings of the 1999 standards conference at UC Northridge. (References collected under [1]). For general guidelines on standards we refer especially to the introduction by Ralph A. Raimi and Lawrence S. Braden to their 1998 review of state standards [1.e], in which they explain what elements are to be included and excluded from such standards documents. The New York State standards and the NYC edition of the performance standards, and also the NYC Scope and Sequence, leave very much to be desired according to these criteria.
For the immediate future we recommend that curricula and assessments for New York City schools are to be evaluated simultaneously against the California and/or Massachusetts mathematics standards and the New York City Scope and Sequence document. We recommend that the NCEE America's Choice Performance Standards shall play no further role in NYC-DOE policy with regard to mathematics curriculum.
We endorse the role of yearly assessments for the purpose of maintaining standards and guiding instructional policy. However, we believe that the grades 3-8 assessments are at too low a level, and do not allow good students to display their achievement. We also believe strongly that the yearly assessments for the years in which they are controlled by the City (grades 3, 5, 6, 7) should be made public each year in order to have transparency and permit public review of the process.
We believe that NYC will need to start procurement of a new sequence of grade level tests for mathematics. In this procurement the DOE must find a way to balance some conflicting aims: integrity of the testing process, public openness of the tests each year, an alignment with new curricular standards and policies of which the effect will only gradually be felt throughout the grade levels, and a desire to maintain year-to-year comparability of results.
Another matter related to assessment, but independent of the content of the tests, is the use of value-added analysis (e.g., [2]), which looks at the evolution of individual student performance over time. We think that this is a very important tool for evaluating the success of individual schools, classrooms, and curricula, and we recommend that the NYC DOE adopt data collection procedures to allow value-added analysis of test results.
We are convinced that nothing that the NYC-DOE can do can be more cost-effective and beneficial than controlling the choice of curriculum. We do not think that the working group should propose a single curriculum for any grade. Rather, the working group should identify several curricula that it judges to be effective in content-oriented mathematics instruction. The choice should then be left to the schools.
We want to emphasize that New York City could have much better math curricula if the Department of Education would rely on content evaluation by subject matter experts -- professional mathematicians and scientists -- in a process similar to what is used for California textbook adoptions for grades K-8. That process results in expert panel content reviews of all considered programs, and these documents are public. Failure to conduct vigorous debates including content experts has led to a series of poor curriculum choices. The Sequential Mathematics sequence is an example that predates the even worse NCTM motivated curricula.
For identifying effective curricula in short order we advise the working group to start from the most recent outcome of the California textbook adoptions process for grades K-8: the CFIR document [3].
We recognize that there may be good reasons for some schools or classrooms to deviate from the approved list, and the DOE will have some waiver process. In that connection we would advise that the DOE also adopt a short list of curricula that are currently popular and for which waivers will not be granted. This list of unequivocally banned curricula should include at least TERC, CMP, IMP and ARISE. These curricula are fatally flawed because they implement in the most extreme way the 1989 NCTM Standards' wrongheaded call for de-emphasis of algebraic and formal skills. Absent outside tutoring, students forced to take these curricula will be totally unprepared for college mathematics.
We note that years of curricular neglect have created a situation where in many schools and classrooms children start the year at an achievement level that may be three years behind desired standards. So, although the curricula in the California adoptions document are listed by corresponding grade level, we recommend that initially schools will have much flexibility in matching the intended and the actual grade level on a per classroom basis. We recognize that this is going to be a sensitive process, since no-one likes to face up to the need to teach in the first year in the higher grades perhaps several years below proper grade level. We hope that the DOE will face up to this need.
We imagine that the DOE might permit in the 2003-2004 school year any school to start the year in some of its classes in grades 2-3 using a textbook that is one year behind grade level; in some of its classes in grades 4-5 a textbook that is up to two years behind grade level; and in some of its classes in grades 6-8 a textbook that is up to three years behind grade level. In these cases the schools will strive to reduce the gap by about one year by the end of the year (i.e., cover two years of learning in one); students for which this is not possible can be held back.
At the same time, we would insist that already during the 2003-2004 school year every school must offer its pupils in grades 1-5 that are ready for it the opportunity to learn at grade level. (Unfortunately we can not think it realistic to insist on this for grades 6-8.) Schools could achieve this in different ways: by creating disparate classes or by nonstandard placement of pupils.
We would anticipate that in the 2004-2005 school year all pupils in grades K-2 will start the year at grade level, in grades 3-5 no classroom will start more than one year behind grade level, and in grades 6-8 no classroom will start more than two years behind grade level.
Some recurring themes in our responses to the Children First numeracy survey.
The fatally flawed prescriptions of the 1989 NCTM Standards underlie many if not all reform curricula. Of these, the ones mentioned most often in our responses, and always in the negative, were TERC for grade school, CMP for middle school, and IMP and ARISE for high school. It is unacceptable that these curricula in particular are employed in NYC public schools.
Many parents cope via expensive and intensive outside tutoring.
The District (CSD 2, in particular) has never engaged in an honest interaction with parents with regard to mathematics curriculum.
The professional development that is in place in support of TERC and other curricula is at best an expensive waste of time. Teachers need education in mathematics content and not training in the pedagogy of discovery learning.
Several of us stressed the need for clear, coherent, grade by grade standards to guide curriculum and assessment, with reference to the experience in California.
The Saxon and Singapore curricula were both mentioned several times as good alternatives, frequently used for home schooling or to supplement NYC reform curricula.
Many of us mentioned the additional unfair burden that the highly verbal reform curricula place upon English language learners, for whom mathematics might otherwise be the subject in which they could excel.
Several of us expressed deep distrust of the claimed research base in support of the reform curricula.
[0] www.math.nyu.edu/~braams/nychold/quest-0211.html
[1.a] www.nycenet.edu/dis/standards/math/NYCMath.pdf
[1.b] www.cde.ca.gov/be/st/ss/
[1.c] www.cde.ca.gov/ci/cr/cf/
[1.d] webdev1.doe.mass.edu/frameworks/current.html
[1.e] www.edexcellence.net/standards/math/math.htm
[1.f] www.edexcellence.net/library/soss2000/2000soss.html
[1.g] wgquirk.com/NCEE.html
[1.h] www.csun.edu/~hcbio027/standards/conference.html/
[2] www.mdk12.org/instruction/ensure/tva/tva_1.html
Wednesday December 11, 2002
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