This survey was developed and distributed by the Children First Numeracy Working Group of the New York City Department of Education (NYC DOE). Evan Rudall (ERudall@nycboe.net) is Chairman of the working group. My response was one of several produced by friends and associates of NYC HOLD around the period Nov 10-13, 2002, and which have been collected here.
Dear Mr. Rudall,
Following a meeting with Diana Lam and Kristen Kane, Elizabeth Carson asked me, a.o., to have a shot at the attached questionnaire. It is understood that the questionnaire was originally intended for District staff, and I should only provide a partial response.
By way of introduction, I am a physicist by training and am employed as a research associate professor in the Courant Institute, Department of Mathematics, at NYU. My educational background through the Ph.D. is from the Netherlands, although I spent my 4th grade and 11th grade years in the United States. I have had a serious interest in K-12 mathematics education for about two years now, and have paid particular attention to mathematics curricula and to education research. I maintain a personal education related web site at www.math.nyu.edu/mfdd/braams/links/, and this is my visiting card on education matters. Jointly with Elizabeth I am developing the NYC HOLD web site, which is found through www.nychold.com/ .
Math Questions
District #
Curriculum
1. Which curriculum materials are predominantly used in your district at elementary, middle, and high school levels?
The curricular materials that are widely used in NYC and with which I am most familiar are: TERC Investigations in Number, Data, and Space; Connected Mathematics Project (CMP); College Preparatory Mathematics (CPM); Interactive Mathematics Program (IMP); and Mathematics, Modelling Our World (MMOW, by the ARISE/COMAP consortium).
2. Which curriculum materials are working and how do you know (please cite student achievement data as evidence)? Which curriculum materials are not working and why? Which curriculum materials would you recommend elementary, middle, and high school levels and why?
I mentioned five curricula in response to question 1. Of these five, three are utterly degenerate; these three are TERC, IMP, and MMOW. One can be rated as awful; this is CMP. The fifth one, CPM, is bad.
None of these curricula can possibly be "working" in a sense in which this would be understood by mathematics professionals, including scientists and engineers. It is possible, however, to have highly verbal and non mathematical tests on which some false measure of success of any of these curricula could be demonstrated, and I believe that such assessments are in place in New York. Outside tutoring will also play a big role, and it is possible that there is even a Laffer curve effect via the mechanism of outside tutoring.
There are several curricula that I have studied and that have impressed me. For elementary school and early middle school these include Singapore mathematics and Saxon mathematics. They are quite different in nature, Saxon being much more focussed on practice and review, Singapore being more entertaining, but both can work well. For Saxon this is demonstrated in several California districts, and I point the reader to Ref. [0]. For Singapore this is demonstrated by the performance of Singapore students on international tests. Besides these two curricula I would trust, generally, the California textbook adoption process, and I believe that the Sadlier elementary curriculum is widely used in good schools.
For late middle school and high school I am impressed by the Dolciani series, Structure and Method (McDougal-Littell). Unfortunately the most advanced Dolciani, the pre-calculus Modern Introductory Analysis, has been allowed to go out of print. Saxon also seems a decent option for the late middle school and early high school years, as does Singapore's New Elementary Mathematics. There may be plenty of other good traditional choices, but I am not familiar with U.S. high school textbook series other than Dolciani. I don't know if the Japanese mathematics textbooks (Translated by UCSMP) could be an option; they are a very strong series for the highest grades. I don't know of U.S. studies that compare outcomes of various high school curricula. Internationally, of course, TIMSS especially has shown the superiority of typical curricula used in Korea, Japan, and Singapore.
3. What should be done to ensure a more coherent PK-12 numeracy approach to curriculum?
Curriculum in K-5 will focus on arithmetic in its many contexts, whereas algebra and geometry should make a serious introduction in middle school, together with continued review and practice in more basic numeracy. I see no reason to look for a single textbook series covering the entire K-12 spectrum. Of course the City and State should have good mathematics content standards that serve as a guide for curriculum selection and for assessment. The mathematics standards of California and Massachusetts can serve as a model, or either of the two can be adopted in full.
District #
Instruction
1. Which instructional practices are predominantly used in your district at elementary, middle, and high school levels?
The more influential and trend-setting districts, including my local District 2, are enamored by discovery learning. Mathematics textbooks are absent in K-5 (this is the TERC curriculum).
2. Which instructional practices are working and how do you know (please cite student achievement data as evidence)?
The teacher teaches and the student practices. This has to be the core of effective instruction. This effective instruction is embedded in settings of exploration, classroom interaction, and entertainment. We don't expect pupils to concentrate on hard work for seven hours per day, and fortunately it isn't needed. For miscellaneous supporting references, also concerning the next question, see [2a-2v].
3. Which instructional practices are not working and why?
Discovery learning cannot work. To be sure, student exploration has a legitimate limited role in instruction, but ultimately students will learn what is taught.
In science education I'm persuaded that nothing of any value at all happens in K-8 in District 2. About discovery learning in science, a retired teacher wrote: "I would just like to point out that District 2 has already begun the process in science. All science is to be taught as `Project-Based'. ... [T]eachers are not supplied with any materials or plans. They are to develop three projects each year (life science grade 6, physical science grade 7, earth science grade 8.) Instead of development lessons (with demonstrations and laboratory exercises) most students now simply sit in groups and read trade books -- then they make lovely posters and give a presentation on something they know little about." (cited in [1]).
District #
Assessment
1. Does your district use the GROW reports? What are the limitations of these reports? How should they be modified to be more useful?
No answer.
2. Besides the NYS and NYC assessments, what specific data is collected to monitor student achievement in numeracy? How is this data used?
No answer.
3. What are your suggestions to improve PK-12 assessment practices?
A very easy and very valuable improvement would be to adopt a more skills and content oriented assessment. I would think of the Iowa Test of Basic Skills (ITBS) or the SAT-9 or the newer components of the California STAR. These also allow a wider benchmarking against the performance of other localities.
District #
Support Structures
1. What are your district's intervention strategies and programs for struggling students? How are struggling students identified?
No answer.
2. Which of these strategies work and how do you know (please cite student achievement data as evidence)? Which of these strategies do not work and why?
No answer.
3. What else do you think needs to be done to support struggling students in numeracy?
It seems obvious that many students have no chance, without tutoring or other outside help, to achieve basic numeracy on the basis of NYC's chosen curricula. The key is to select good curricula at all grade and performance levels.
District #
ELL Students
1. What support structures exist in your district to ensure the achievement of ELL students? Who makes the decisions around support structures?
2. Which of these strategies work and how do you know (please cite student achievement data as evidence)?
3. Which of these strategies do not work? Why?
No answers to those three questions.
District #
Students with Special Needs
1. What support structures exist in your district to ensure the achievement of students with special needs? Who makes the decisions around support structures?
2. Which of these strategies work and how do you know (please cite student achievement data as evidence)?
3. Which of these strategies do not work? Why?
No answers to those three questions.
District #
Family Numeracy
1. How does your district engage with parents in relation to numeracy?
2. Which of these strategies work and how do you know?
3. What issues do parents raise and how do you address those issues? What else should your district be doing around family numeracy?
No answers to those three questions.
District #
Professional Development
1. What are the professional development structures that are in place in your district? Which of these are effective and how do you know?
2. What do you think are the most pressing staff development needs in your district? Why?
3. In addition to increased time, funding, and access to space, what recommendations would you make to the DOE regarding professional development?
4.
How many mathematics specialists/staff developers are in your district
at the elementary school level?
How many elementary schools do you have?
How many mathematics specialists/staff developers are in your district
at the middle school level?
How many middle schools do you have?
How many mathematics specialists/staff developers are in your district
at the high school level?
How many high schools do you have?
5. What percentage of the time are math specialists/staff developers in classrooms or with teachers?
6. How are math specialists/staff developers selected? By whom? Using what criteria?
7. What training do math specialists/staff developers receive?
No answers to those questions.
References:
[0] High Achievement in Mathematics: Lessons from Three Los Angeles Elementary Schools, by David Klein (Brookings, Aug 2000). http://www.brook.edu/dybdocroot/gs/brown/bc_report/2000/LosAngeles.PDF
[1] NSES - The National Science Education Standards, by Bas Braams. A letter to the Education Committee of the American Physical Society (June, 2001). http://www.math.nyu.edu/mfdd/braams/links/aps-ed0106.html
[2] The following references are all annotated at http://www.math.nyu.edu/mfdd/braams/links/
[2a] E. D. Hirsch Jr., The Schools We Need - And Why We Don't Have Them (Doubleday, New York, 1996).
[2b] Diane Ravitch, Left Back: A Century of Failed School Reform (Simon and Schuster, New York, 2000).
[2c] Jeanne S. Chall, The Academic Achievement Challenge: What Really Works in the Classroom? (Guilford Press, New York, 2000).
[2d] Williamson M. Evers (Ed.), What's Gone Wrong in America's Classrooms (Hoover Press, Stanford, 1998).
{2e] They Have Overcome: High-Poverty, High-Performing Schools in California, by Lance Izumi with K. Gwynne Coburn and Matt Cox (PRI, Sep 2002). http://www.pacificresearch.org/pub/sab/educat/they_have_overcome.pdf
[2f] Education in Singapore, by Chester E. Finn Jr. (Feb 2002). http://www.edexcellence.net/gadfly/v02/gadfly06.html#checker1 http://www.edexcellence.net/gadfly/v02/gadfly07.html#checker1
[2g] Telling Lessons from the TIMSS Video Tape, by Alan Siegel (2002). http://www.cs.nyu.edu/faculty/siegel/ST11.pdf
[2h] A Brief History of American K-12 Mathematics Education, by David Klein (2001). http://www.csun.edu/~vcmth00m/AHistory.html
[2i] Romancing the Child, by E. D. Hirsch, Jr (2001). http://www.educationnext.org/2001sp/34.html
[2j] Progressivism's Hidden Failure, By Louisa C. Spencer (2001). http://www.edweek.org/ew/ewstory.cfm?slug=24spencer.h20
[2k] The Math Wars, by David Ross (2001). http://www.objectivistcenter.org/articles/dross_math-wars.asp
[2l] Whole Language Lives On, by Louisa Cook Moats (2000). http://www.edexcellence.net/library/wholelang/moats.html
[2m] What About Rote Memorization?, by Ralph Raimi. http://www.math.rochester.edu/u/rarm/memory.html
[2n] In Defense of "Mindless Rote", by Ethan Akin (Mar 30, 2001). http://www.nychold.com/akin-rote01.html
[2o] No Excuses: Lessons from 21 High-Performing, High-Poverty Schools, by Samual Casey Carter (The Heritage Foundation, 2000). http://www.noexcuses.org/pdf/noexcuseslessons.pdf
[2p] No Excuses: Seven Principals of Low-Income Schools Who Set the Standard for High Achievement, by Samual Casey Carter (The Heritage Foundation, 1999). http://www.noexcuses.org/pdf/noexcuseslessons.pdf
[2q] Why Traditional Education Is More Progressive, by E. D. Hirsch, Jr (AE, 1997). http://www.taemag.com/issues/articleid.16209/article_detail.asp
[2r] Developmentalism: An Obscure but Pervasive Restriction on Educational Improvement, by J. E. Stone (EPAA, Apr 1996). http://epaa.asu.edu/epaa/v4n8.html
[2s] Reform Mathematics Education: How to "Succeed" Without Really Trying, by Paul Clopton (2000). http://mathematicallycorrect.com/reform.htm
[2t] Blackboard Bungle: Why California Kids Can't Read, by Jill Stewart (LA Weekly, Mar 1996). http://www.kidsource.com/kidsource/content/whole.1.html
[2u] What was that Project Follow Through? A focus issue of Effective School Practices (Winter 1995-96) with articles by Grossen, Bereiter, Becker and Engelmann, and others. http://www.uoregon.edu/~adiep/ft/151toc.htm
[2v] What Is Changing in Math Education?, by Mathematically Correct (Feb 1996). http://mathematicallycorrect.com/what.htm
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Bastiaan J. Braams (Research Associate Professor)
Dept. of Mathematics - Courant Institute of Mathematical Sciences
New York University - 251 Mercer Street - New York, NY 10012-1185
Email: braams@math.nyu.edu
Web: www.math.nyu.edu/mfdd/braams/
See other Survey responses for Children First Numeracy Working Group; return to Links, Articles, Essays, and Opinions on K-12 Education; or to the BJB Essays page; or to the