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. The survey was addressed first to District Mathematics coordinators, but some members and advisors of NYC HOLD were also asked for their partial responses.
Some of the following responses were converted from DOC format to HTML using primitive and inadequate means (the wvHtml command on my Unix workstation). In those case a link is also supplied to the Word original. --BJB
Individual responses:
Marvin Bishop
Bas Braams
Sylvain Cappell
Elizabeth Carson
Ginny Donnelly
Jonathan Goodman
Fred Greenleaf
Leonie Haimson
David Klein
Christine Larson
Denise Matava Haffenden
Mike McKeown
Chuck Newman
Stanley Ocken
Marvin Rich
Martha Schwartz
Dear Mr. Rudall:
I am the father of two children in District 3 in Manhattan and a Professor of Mathematics/Computer Science at Manhattan College. Even though District 3 has adopted ?balanced? math both of my children are in special accelerated programs which use the constructivist approach of TERC (primary school) and CMP (middle school) only sparingly. The children in their programs get lots of ` traditional math' without relying on calculators; the standardized test scores of these children are mostly in the 4 range for the NYC and NYS math tests in all the grades.
While I am very glad that these programs are giving my children a solid basis for the further study of mathematics, I feel that the amount of constructivist approaches in other programs and schools is far too high. I have heard many stories from parents who have said that their children who used to love mathematics are now completely bored with the time wasting demands of cutting out boxes to find areas or being forced to draw pictures for every problem they solve. The accelerated middle school program director has told me that his teachers shouldn't have to teach long division (a topic which is left out of the TERC program). At the high school level the special science schools have begun to give a mathematics placement test and find that they now need about three classes of lower level mathematics.
My suggestion is to use the constructivist approaches as a 10% supplement to traditional mathematics. Topics such as multi-digit multiplication, long division, and division of fractions need to be part of the elementary school curriculum. Without these topics firmly in hand children will be ill-prepared for algebra and higher level mathematics courses. Calculator usage needs to be controlled.
Sincerely yours,
Marvin Bishop
marvin.bishop@manhattan.edu
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/~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
No answers to these three questions.
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?
District #
Students with Special Needs
No answers to these three questions.
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?
District #
Family Numeracy
No answers to these three questions.
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?
District #
Professional Development
No answers to the following questions.
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?
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/~braams/links/aps-ed0106.html
[2] The following references are all annotated at http://www.math.nyu.edu/~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.math.nyu.edu/~braams/nychold/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
--
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/~braams/
Response of Sylvain Cappell
This is a follow-up to a recent meeting with Diana Lam and Kristen
Kane.
Besides myself, there were two distinguished mathematical colleagues
participating, Prof. Charles Newman, Acting Director of the Courant
Institute of Mathematical Sciences at NYU and Prof. Robert Finerman,
long-term Chair of the Math. Dept. at Lehman College of CUNY and
long-term head of the Committee of Chairs of all the CUNY Math
Departments and also a member of his local school board. Also
participating was Elizabeth Carson, a parent activist with a
distinctive knowledge of what is going on in the math programs in the
NYC schools.
Please find my replies to some of the questions in your survey
below. I won't answer all of them as they don't all apply to my
professional context. You had also requested along with this a brief
narrative CV, which I include immediately below.
------------------------------------------------------------------------
Narrative CV of Sylvain Cappell
Sylvain Cappell was born in Brussels, Belgium in 1946 and immigrated
with his parents to New York City in 1950 and grew up largely in this
city. He is fluent in several languages, including French and Hebrew.
At Bronx High School of Science in 1963 he won the top National
Scholarship Award in the (Westinghouse, now Intel) National Science
Talent Search. At Columbia College he majored in math (but with
enough literature courses for a second major), graduating summa cum
laude in '66, and got his Ph.D. from Princeton in '69 (6 years out of
high school). He subsequently held faculty appointments there and
then came to NYU's Courant Institute of Mathematical Sciences in 1974,
becoming a full professor in 1978. He has been at NYU since then but
has also held visiting appointments at Harvard (several times), the
Weizmann Institute of Science, the Institut des Hautes Etudes
Scientifiques in Paris, the University of Chicago, the U. of Penn.
and the Institute for Advanced Study. He has been a Sloan Foundation
Fellow and a Guggenheim Foundation Fellow and has given invited
addresses to the International Congress of Mathematicians and to
national meetings of the American Mathematical Society and the
Mathematical Association of America.
Professor Cappell has had 16 Ph.D. students in mathematics and has
also helped several graduate students in mathematics education. Much
of his own research has focused on topology, but his about 100
research publications touch on many other areas of mathematics.
Prof. Cappell has edited several journals, including currently the
Communications in Pure and Applied Mathematics, and has served on and
chaired various national American Mathematical Society Committees and
on external review committees for many universities and foundations.
At NYU, Professor Cappell is the long-term Chair of the Courant
Institute's Faculty Appointments and Promtions Committee, the
long-term Chair of NYU's Research Challenge Fund Committee (in which
he evaluates research proposals in all academic areas), and serves on
the Faculty Council and the University Senate. He is a member of the
Educational Policy Committee and of NYU's highest-level administrative
committee, the new Committee on Academic Priorities and he chairs its
Sub-committee on Academic Program Review. Professor Cappell has over
the years mentored many New York area high school students interested
in math and several of these have won national honors, e.g., in the
National Science Talent Search. He has close professional and personal
connections to many mathematics teachers and math chairs in the city
schools and gives every year some lectures on mathematical subjects in
New York area high schools. He is deeply concerned about current
mathematical education issues and has discussed these extensively with
colleagues at CUNY, at Columbia University and at NYU.
------------------------------------------------------------------------
Math Questions
District #
Curriculum
1. Which curriculum materials are predominantly used in your district at
elementary, middle, and high school levels?
I live in District 2 which is known as a model sistrict. But in fact,
despite great expenditure of resources, it is witnessing a substantial
decline in the content of its math programs. Disaster has been largely
avoided so far only because the parents increasingly know all too well
that they have to send their children to get extensive (and expensive)
private tutoring in basic mathematical skills. Colleagues who teach
math in local high schools report that the tutoring business is
booming, but that among the kids who unfortunately hadn't yet received
such private tutoring they are witnessing a new phenomona; kids who
are smart, motivated and intrinsically talented in math but come out
of elementary school without standard arithmetic skills. (Parents in
nearby Chinatown who are very concerned but can't afford
individualized private tutoring are responding by widely using various
well-organized weekend private instructional programs in math.)
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?
The current curricular materials in District 2 are not working and
can't work because they reflect overly ideologically based views on
what mathematics is about and hence on what mathematics education
should be. We are in danger of repeating here in NYC an agenda in
math education that, on the record, failed in California several years
ago. Fortunately, in California, guided by capable and concerned
academics there (such as Professor James Milgram of Stanford
University and Professor David Klein of California State University at
Northridge) that decline has now been reversed. Indeed, there has
been a remarkably successful turn-around. My hope is that NYC will
avoid a lost decade in K-12 math education, such as California
experienced. Here's an article from the Los Angeles Times reporting
on what has happened there in math education:
>
>http://www.latimes.com/news/local/la-me-math22aug22.story
> Los Angeles Times
>
> Math Scores Equal Success
>
> Education: Uniform programs and improved teacher training are
>cited in L.A. elementary schools' improvement in standardized test
> scores.
>
>By SOLOMON MOORE and ERIKA HAYASAKI
>LA TIMES STAFF WRITERS
>
> August 22 2002
>
>Do the math: The Los Angeles Unified School District's math test scores
>are rising fast in elementary grades. For example, as many as 52% of
>Los Angeles third-graders placed at or above the national average in
>newly released Stanford 9 scores, up from 28% in 1998.
>
>Standardized elementary math programs and better teacher training led
>to those rises, district officials and education experts said. Efforts
>to improve reading also contributed to the higher math scores, with
>students better able to follow instructions and understand concepts.
>
>District elementary schools have moved away from a hodgepodge of more
>than a dozen math programs, some of which emphasized classroom
>interaction instead of following formal lesson plans in textbooks. Now
>only two state-approved math textbooks, stressing fundamental skills,
>are used for each of the lower grades across the district.
>
>Some elementary schools used to offer math two or three days a week,
>but now all are required to offer daily lessons of at least an hour.
>
>"Teachers are being trained to do the same thing with the same books,"
>said Sue Shannon, assistant superintendent for instruction. The
>district
>
>is trying to synchronize its math programs so that every elementary
v>school and every class is on the same lesson at the same time.
>
>Shannon said that such systematization makes teacher training more
>effective and tracks schools' progress more closely.
>
>In the last year, the district has trained 360 math coaches to
>spearhead math reforms at all elementary schools, said Dianna Masters,
>the district's director of math instruction. And 40% of all elementary
>school math teachers have participated in a 120-hour training course
>conducted by UCLA.
>
>Starting this year, elementary students will take quarterly diagnostic
>tests so that teachers will know which math skills need more emphasis
>and which students need extra help. Schools also are required to
>report, on a quarterly basis, how many teachers have volunteered for
>training workshops.
>
>However, high school math programs have yet to show the kind of gains
>achieved in lower grades. Most Los Angeles high school and middle
>school
>
>students still scored below the 35th percentile. (The national average
>is the 50th percentile.) But district math experts said upper grades
>will improve as students benefiting from the elementary school programs
>move up and the district focuses on high school math reform.
>
>Statewide standards adopted two years ago for math instruction are
>driving the training programs, the selection of textbooks and lesson
>plans in elementary math classes, said math education experts.
>
>"When California adopted world-class standards, it made a huge
>difference at the classroom level," said David Klein, a math education
>professor at Cal State Northridge. "And when you have good standards,
>success has very little to do with whether teachers are credentialed or
>uncredentialed." Half of L.A. Unified's teachers lack full credentials,
>district figures show.
>
>Klein also said good math instruction can overcome traditional learning
>barriers such as poverty and language. Stanford 9 test results show
>that African American and Latino elementary school students made
>greater gains in math scores--8% and 9.5% respectively--than in any
>other subject.
>
>"Math is a worldwide monoculture and has nothing to do with skin color
>or poverty," Klein said.
>
>In the last four years, the percentage of Los Angeles Unified students
>who placed at or above the national average on the Stanford 9 math test
>increased from 31% to 53% in second grade, 25% to 46% in fourth grade
>and 26% to 42% in fifth grade. Statewide scores will be released next
>week.
>
>"Just that they've sustained this rise over a four-year period is
>really
>
>impressive," said Gerald Hayward, co-director of the Berkeley-based
>Policy Analysis for California Education. Even accounting for the
>emphasis on exam preparation, Hayward said, the Los Angeles increases
>were significant. "Very few people would have predicted that by 2002
>over half the [elementary] kids would be exceeding the national norm"
>on the Stanford 9 test.
>
>Reading and language arts test scores have improved dramatically in
>elementary schools as well, and teachers said that helps to improve
>math performance.
>
>Stanford 9 test results show that the average second-and
>third-grader--who is most likely to have had two years in the highly
>structured Open Court reading program--scored above the national
>average in math.
>
>Karen Robertson, principal at Dena Elementary on the Eastside, said
>teachers now spend time making sure "children really understand words
>that the math series are using and understand what it means."
>
>Fourth-graders at the year-round Dena campus scored on average in the
>39th percentile in the recent Stanford 9 tests. In 1998, they scored in
>the 18th percentile nationally in math.
>
>Among the worst-performing schools in math in 1998 was South Park
>Elementary in South-Central Los Angeles, which scored in the 15th
>percentile nationally for math. This year, fourth-grade students at
>South Park scored in the 48th math percentile.
>
>Of the school's 1,263 students, 700 learned English as their second
>language.
>
>Karen Rose, principal at South Park for 10 years, said the Math Land
>program used there in the past was one of the causes of students'
>difficulties with math.
>
>Math Land "was terrible. It was terrible," she said. "It was
>disconnected; it wasn't standards-based. It was a mishmash."
>
>Education experts said Math Land was analogous to the now abandoned
>Whole Language approach in language arts in its emphasis on individual
>discovery and student interaction. Masters said Math Land relied on
>exercises using objects such as pickup sticks and marbles instead of
>formal drills.
>
>She recalled one lesson that had students invent their own mathematical
>formulas and discuss them in class.
>
>The new math programs and their texts consistently build on a few basic
>skills such as problem solving, estimates and measurements.
>
>High school math scores in L.A. Unified still lag behind the rest of
>the nation partly because programs are uncoordinated and use various
>texts, Masters said.
>
>There are fewer qualified teachers in upper-level math than in
>elementary grades, and the district hasn't been able to attract enough
>people to fill its high school math positions, she said. Next year, new
>professional development seminars will be offered at UCLA for math
>teachers in the higher grades.
>
>Teacher training workshops can help, said Cal State Northridge's Klein,
>but middle and high school math demands such specific knowledge that
>in-service programs alone will not be enough.
>
>The real solution will be to hire more teachers fully credentialed to
>teach high school math.
>
>"The nature of mathematics is that it's the most hierarchical of all
>human endeavors," Klein said. "You can't go to the top until you master
>the lower levels, and many teachers haven't even mastered the basics.''
3. What should be done to ensure a more coherent PK-12 numeracy approach
to curriculum?
Mathematical understanding and skills are highly cumulative and
require sustained efforts over many years to achieve satisfactory
mastery. Hence, there isn't - and can't be - enough time for
discovery based or constructivist based teaching to cover the
requisite material. Of course, students should be given a sense of the
fun and discovery in math but this has to occupy a comparitively small
part of student time in math classes. In practice, classes are now not
getting through even the thinned out curriculum. Moreover, in
practice every math class is leaving out different topics, which
ensures ongoing educational chaos.
District #
Instruction
1. Which instructional practices are predominantly used in your
district at elementary, middle, and high school levels?
The mathematics education is overly focused on ideologically motivated
pedagogical issues and not on substantive math content issues.
2. Which instructional practices are working and how do you know
(please cite student achievement data as evidence)?
See above:
3. Which instructional practices are not working and why?
See above:
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?
2. Besides the NYS and NYC assessments, what specific data is collected
to monitor student achievement in numeracy? How is this data used?
3. What are your suggestions to improve PK-12 assessment practices?
Use materials that work, such as those based on the Saxon books or the
Singapore series. Use curricula like those that are achieving
remarkable success in California. Let curricula be reviewed by
committees of educators for pedagogical practices and by
mathematicians for content.
District #
Support Structures
1. What are your district's intervention strategies and programs for
struggling students? How are struggling students identified?
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?
3. What else do you think needs to be done to support struggling
students in numeracy?
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?
One of the ironies about approaches to math education that
over-emphasize talking about math rather than really doing math is
that they work greatly to the disadvantage of students who are not
native speakers of English. They make progress in math overly
dependant on prior progress in English fluency. But in fact, and as
demonstrated by abundant exprience, for such students math achievement
can be an important source of access to the possibilities of American
society.
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?
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?
District #
Family Numeracy
1. How does your district engage with parents in relation to numeracy?
It commonly causes them to need to hire math tutors to make up for the
glaring deficencies of the content of the school math program.
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?
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?
This is the biggest waste of all. Money is being spent on training
teachers in the ideological approaches of programs like TERC, etc.
2. What do you think are the most pressing staff development needs in
your district? Why?
Resources could instead be used to have teachers learn to be more
comfortable with aspects of the math and math skills that they will be
teaching and e.g., what math the standard algorithms are based upon.
3. In addition to increased time, funding, and access to space, what
recommendations would you make to the DOE regarding professional
development?
See above:
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?
They are given a counter-productive ideological agenda.
(Back to Top of Page)
Response of Elizabeth Carson
(Please see here for the Microsoft
Word *.doc original version of Elizabeth Carson's reply. Also,
see here for the Microsoft Word *.doc
original of the table of CSD2 black and hispanic scores referenced
in the response below.)
Evan, Attached, please find my survey response and an addendum to my survey response. Several, who have not yet responded, have relayed to me their intentions to submit their survey response either later today or tomorrow at the latest. Thank you again for this seminal opportunity. Elizabeth Carson Co-Founder, NYC HOLD Honest Open Logical Debate on Mathematics Education Reform Phone 212.529.1302 FAX 212.529.0062 CELL 917.208.7153 www.nychold.com
Math Questions
District #
Elizabeth Carson, District 2 parent; Co-Founder, NYC HOLD Honest Open Logical Debate on Mathematics Education Reform. www.nychold.com
bio at
Curriculum
It is my understanding from individual communications with parents and teachers from a good number of community school districts, presentations and discussions at local and citywide meetings and Internet research over the past several years, that the math programs in NYC schools and districts vary widely. Schools and school district programs range from exclusive use of traditional college preparatory mathematics curricula (eg science high schools, top performing Queens District 26) to a combination of traditional and ?reform? NCTM Standards-based programs (eg Manhattan District 3 and Bronx District 8) to exclusive use of NCTM Standards-based programs (eg Manhattan District 2 and Brooklyn District 15) Some districts that offered entirely traditional college preparatory curricula in the past, are just now beginning to integrate pieces of an NCTM Standards based program (eg Queens District 26 ) Some districts that formerly adopted one or more NCTM Standards based programs have since chosen to drop the programs in favor of traditional skills based college preparatory materials ( eg majority of schools in Bronx HS Superintendency)
The public mathematics education policy and curricula reported in use in districts often does not match the realities of the instruction the children are actually receiving in the classroom. I am not alluding to the natural variation in the extent and nature of the use of the primary curricula or the natural variation in the quality of instruction, teacher to teacher, but rather to a most remarkable phenomenon in schools where strict adherence to NCTM Standards based programs is imposed: Individual teachers, among them usually the senior and most experienced teachers, who view the NCTM Standards based programs as seriously deficient and the mandated teaching approaches limiting, are making the decision to ignore the district directives, quietly close their doors, and teach what they deem in the best interest of their students - that includes use of non-sanctioned materials (eg workbooks, traditional texts) and non-sanctioned teaching strategies ( eg explicit instruction in standard algorithms, individual work in class, and inclusion of requisite of practice and drill) They do so at some perceived risk, privately expressing to colleagues, parents and others fear of retribution in the forms of personal or school sanctions. The phenomenon of doctrinaire implementation policies associated with NCTM Standards based program implementations and subsequent clandestine classroom teaching, is widespread (and not unique to NYC). In Manhattan Community School District 2, where strict allegiance to the NCTM Standards reform is the public policy, many classic examples of clandestine traditional instruction by senior teachers can be found.
The public mathematics education policy and adopted curricula reported by districts can offer only a partial and sometimes seriously incomplete picture of the instruction students are actually receiving, absent comprehensive data on the nature and extent of home supplementation and private and institutional tutoring provided by students' parents. Of course, home support and enrichment is a natural and desired parental extension of school work, and should be encouraged and in concert with classroom instruction. A good picture of students' home supports should be considered an integral and reported part of the home- school continuum of mathematics instruction in a school and district. The absence of comprehensive information on home support becomes an even more critically important issue in instances where schools are using NCTM Standards based programs. Many parents find the NCTM Standards based programs to be deficient in important content and rigor and become soon aware of developing delays in mastery of skills and conceptual understanding they deem appropriate for their child's grade and ability level. As a result, parents with the means, choose to provide substantial tutoring outside the classroom, often assuming an unreasonably large share of the responsibility for their children's mathematics education, sometimes to the point where the tutoring literally becomes their children's primary mathematics instruction. The phenomenon of parental provision of outside tutoring in schools using NCTM Standards based programs is widespread ( and not unique to NYC) In Manhattan Community School District 2, where many parents have the educational background and/or means to provide outside tutoring, the practice is widespread.
Within the aforementioned contexts, issues of the absence of coherence and equity in students' opportunities for sound and adequate mathematics instruction across classrooms within schools, across schools within districts, and across districts within the city system are obvious and should be viewed as extremely serious.
Individual district changes in policy and curricula have often been made quickly, and without sufficient informed input and consent from classroom teachers or parents. Consultation with local university mathematics experts has been entirely absent.
Recommendation: Comprehensive survey and evaluation of mathematics programs and instruction students are presently receiving must include acquisition of experiences and expertise of classroom teachers, parents and university math experts. Survey and evaluation should include substantive open discussions with the key constituents, and should include public forums. Given the unfortunate ?closed? culture pervasive in the city system, one with a local climate of teacher and parent intimidation in some schools and districts, anonymous surveys of teachers and parents is advised.
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(note: I've placed additional questions listed under #2 and answers further below )
Given the absence of the important information articulated under #1, achievement data is of extremely limited value in evaluating mathematics programs in districts. There exists, too, concern among more knowledgeable parents and informed local mathematicians about the quality and integrity of the present city and state math assessments to reasonably evaluate the progress of college bound students. Further doubt is cast, given that in two separate years since the new CTB math and reading tests were initiated, reading scores have been thrown out for one entire grade. And, last year's (spring 2002) almost unbelievable math improvements on the citywide test at every grade (with a handful of exceptions) and in every district has raised again, questions about the integrity of the McGraw Hill CTB test and process.
2.Which curriculum materials are not working and why?
NCTM Standards based programs are deficient in important math topics and lack the rigor necessary in a college preparatory continuum and necessary to provide all students opportunity to fully explore and develop their interests and capabilities in K-12 math and science coursework. Additionally, they fail to provide adequate preparation for subsequent university level math-based courses and majors.
Test scores in District 2, where Investigations in Number, Data and Space (TERC), Connected Math (CMP) have been mandated in all K-8 schools since 1999 (with gradual implementation beginning in 1995) show extremely erratic patterns of increases and declines over the past four years since the CTB-M city and state assessments began ( 1999 through 2002), with marked declines in many schools, including the elite PS 6, both in the percentage passing (levels 3 and 4) and in the percentage reaching the top level 4 . The math achievement of students in schools with high concentrations of poor black and Hispanic students in the district is far too low, has declined in most cases since the new CTB-M was first administrated and indicates a very wide achievement gap. . (See attached chart) Many of those schools continued to show declines through last year's seminal citywide slight upswing in math scores. 22 NYC school districts showed greater improvement last year in mathematics achievement than District 2.
Recommendation: The NYC school system should establish a panel of math educators and math experts, with parent advisors, to review curricula, in use, and for consideration for use in NYC schools. The panel's analysis and recommendations could then be used to inform local school district curricular adoptions. This system would reflect the adoption process in place in California at the present time. The school and district community, most importantly classroom teachers and parents, should be fully informed and integrally involved in the local adoptions process. The citywide panel deliberations and local adoptions proceedings should be as open and democratic as possible.
Recommendation: NYC consider one or several of the programs on the California state adoptions (K-8) , Singapore Math (K-8) and several high school texts currently used in NYC, all recommended by NYC educators and mathematicians.
The California textbooks have been reviewed and approved by both Content Review Panels (CRP) comprised of mathematics experts and Instructional Mathematics Advisory Panels (IMAP) comprised of math educators; approved texts are aligned with the top rated ?world class? California state standards. See CA Mathematics Adoptions (2001) http://www.cde.ca.gov/cfir/math/2001adpr.pdf CA Academic Content Standards (1997) http://www.cde.ca.gov/board/pdf/math.pdf CA State Mathematics Framework (2001) http://www.cde.ca.gov/cdepress/math.pdf
Mathematicians' top pix from California adoptions: Saxon (K-3, 3-6), Progress in Math, California Edition, (K-6); Mathematics by Houghton Mifflin (K-5); Structure and Method, by Dolciani (6-8) Marked improvements in California student achievement particularly among poor urban student populations in recent years provides strong evidence California reforms are on the right track, and should be considered for replication here in NYC and NYS. California provides a very hopeful picture of what is possible with sound mathematics programs and effective instructional practices. See: They Have Overcome: High-Poverty, High-Performing Schools in California by Lance Izumi with K. Gwynne Coburn and Matt Cox (Sep 2002) at www.pacificresearch.org/pub/sab/educat/they_have_overcome.pdf and High Achievement in Mathematics: Lessons from Three Los Angeles Elementary Schools, by David Klein (Brookings, Aug 2000) at http://www.brook.edu/dybdocroot/gs/brown/bc_report/2000/LosAngeles.PDF
Singapore Math (in English) and with several US distributors is based on the Singapore Ministry of Education math syllabus. See www1.moe.edu.sg/syllabuses/ Singapore continues to be the highest achieving country in international comparisons. Informed mathematicians and educators view Singapore Math as an excellent, rigorous, balanced program that properly addresses computation and problem solving skills and conceptual understanding. see http://www.singaporemath.com/
High school program adoptions should provide the greatest choice possible in order to fulfill the wide range of interests, aspirations and abilities, and reflective of the quality and nature of previous preparation of NYC students, as per the recommendations of former Chancellor Levy's Math Commission report (2001).
Central review panel (described above) recommendations and district considerations of high school math programs should be subject to review and recommendations by senior NYC high school teachers representing schools from a broad spectrum of the city's student population.
High school texts: Algebra: Structure and Method Book 1, by Brown, Dolciani , Sorgenfry and Cole (McDougal Littell); Geometry, by Jurgensen, Brown, Jurgensen (Houghton Mifflin) Algebra and Trigonometry (Larson & Hostetler (Houghton Mifflin
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A standing committee of mathematics educators (K-12) and university mathematics experts and parent advisors should together develop a NYC mathematics framework, with grade by grade specificity, reflective of the NYS Standards and assessments, and the skills and knowledge necessary for a college preparatory K-12 continuum. The framework should then be used to inform district and school based curricular adoptions and implementation, professional development, and in-house assessment systems. An exemplary NYC math framework should serve as the basis for the development of a better system of city standardized assessments. San Diego developed a fine example of a city mathematics framework, which may be found at http://www-internal.sandi.net/standards/Math-eng/mathstand.htm
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District #
Instruction
In District 2 and other districts using primarily NCTM Standards based programs, constructivist teaching practices are enforced and supported with professional development.
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Teachers must be skilled in, and given the freedom to use, a broad range of teaching approaches including provision of inquiry-based learning experiences associated with a constructivist approach as well as explicit instruction, within the context of coherent, content -based college preparatory programs, in order to effectively engage, challenge and support, at minimum, an adequate level of student mathematics achievement, and optimally, to support students' reaching their full potentials.
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Not working: Discovery learning to the exclusion of explicit instruction in standard arithmetic algorithms; absence of clear explanations of mathematical rules and procedures and concepts.
Why? Discovery learning is extremely time consuming and in the end, many children simply are left behind, many children require explicit instruction to master skills and develop understanding
Not working: Too much emphasis on writing exercises and art projects as extensions of math lessons
Why? Very time consuming, small requisites for explanatory passages of solutions goes a long way. ELL students are particularly vulnerable to disenfranchisement, forced to struggle with language issues in addition to the math topics. Where language and literacy needs arise, teachers are compelled to initiate literacy instruction in math class, and effectively robbing students of precious instructional time in mathematics. Art projects most often have extremely limited relevance and highly questionable value in teaching mathematical topics.
Not working: Too much class time devoted to small group work (some collaborative work and group discussion is fine) Too often, one student performs the lion's share in small group work; group work assignments also rob students of the opportunity for individual achievement and can diminish students' desire toward personal excellence. Clustering of students at tables for periods of time where the teacher can not possibly be at all times immediately available opens opportunity for silliness and misbehavior.
Not working: Complete omission of requisites for memorization, practice and drill.
Why? Students require a degree of repetition, practice and drill to master arithmetic facts and standard procedures critically necessary to advance into Algebra and subsequent level math courses.
Not Working: Anti- algorithmic approach generally, encouragement of personal solutions well beyond the early primary grades, that do not work for more complex problems or in all cases; too much emphasis on ?real world applications,? a de-emphasis of traditional goals that include fluency and accuracy with foundation skills, rules and procedures of arithmetic and algebra necessary to begin to engage in real mathematical reasoning
Why? Its obvious why
Not working: absence of regular objective assessment
Why? So-called ?authentic assessment?(ie portfolios of class and home work and teacher and student journals with narratives about progress) is strongly advocated in NCTM based programs, and often effectively to the exclusion of regular objective assessments. Alternative assessments certainly have value to teachers and parents, however, used solely, limit teachers' means to monitor and support student progress and their means to assess their teaching practice. Parents, without the absolute indicators of progress or deficiencies, that regular objective assessment provides, are left unable to adequately monitor their child's mathematics education or advance their child's learning at home
see : A Mathematical Manifesto, by Ralph A. Raimi for NYC HOLD at http://www.math.nyu.edu/~braams/nychold/#issues-mm
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District #
Assessment
NO ANSWER
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NO ANSWER
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The development of a coherent, detailed, grade specific and rigorous college preparatory NYC math framework must be developed first to inform district and school level decisions on in-house assessments. San Diego developed a fine example of a city mathematics framework, which may be found at http://www-internal.sandi.net/standards/Math-eng/mathstand.htm (see my response to question #2)
In addition to regular objective measurements based on a high quality city framework, alternative assessments (ie portfolios of student class and home work, and teacher journals documenting student work and progress) could be very usefully employed if grounded in the context of the goals and objectives articulated in the city framework.
An exemplary NYC mathematics framework should be used toward the development of a better system of city standardized assessments
Ongoing professional development in the content and various purposes of school-based and city and state standardized assessments should be provided.
The experience and expertise of senior NYC mathematics educators and university mathematics experts and with consultation with parents, should be employed in assessment development and use.
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District #
Support Structures
NO ANSWER
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No Answer
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Based on personal communications with parents and teachers of struggling students, a student textbook, a structured curriculum with very specific goals and objectives , individual and closely monitored class work, , explicit instruction including explanation, requisite for practice and drill, regular objective assessments, optimal home support and foremost, skilled and inspired teaching are the necessary components to reach and raise the achievement level of the struggling student
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District #
ELL Students
I have heard repeated laments from Chinatown instructors of the inadequacy of the Whole Language approach with, particularly, new immigrant ELL students and the crippling effect of the literacy based constructivist math programs. Chinatown teachers' views and expertise appear absent or ignored in the process by which literacy and mathematics education programs and policies are chosen and developed for their ELL students.
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No Answer
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No Answer
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District #
Students with Special Needs
No Answer
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No Answer
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No answer
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District #
Family Numeracy
In school districts where NCTM based programs are used, school-based math nights are sponsored at which parents are introduced to the overarching NCTM philosophy and are introduced to mock classroom lessons and activities. Some schools host parent seminars where parents are given instruction and support in how to help their children with home work assignments.
Parents have found these math nights initially informative as an introduction to the thrust of the NTCM Standards-based reform programs, but egregiously inadequate as a forum for deeper discussions that would include the broaching of parental questions and concerns with the materials, teaching approaches and their children's progress.
The math nights offered to parents in schools using NTCM based programs fail to provide either the support necessary to expedite the constructivist methodologies at home, or to quell the widespread parent dissatisfaction with the programs. See news and reports under NYC HOLD web site/ NYC Issues at http://www.math.nyu.edu/~braams/nychold/#nyc-issues and press articles under NYC HOLD web site/NYC Mathematics Education at http://www.math.nyu.edu/~braams/nychold/#nyc-news-math
I am not aware of the parent supports in districts with traditional mathematics instruction.
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Provision of clearly articulated goals and objectives and ongoing support and resources to promote home extension and enrichment of classroom instruction would be most useful. Direct and regular communication between classroom teacher and parent is critically important. Email is fast becoming the best means of communication. Individual class web sites which provide class goals and objectives, class work, homework assignments, test schedules, and web based resources are very useful, in order to keep parents connected and informed and to allow opportunity for questions and input
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For parental concerns regularly raised in districts with the NCTM Standards based programs, see NYC HOLD Mission Statement/ ?We are Parents? at http://www.math.nyu.edu/~braams/nychold/who-we.html#intro and District 2 Parent Questions and Comments, under NYC Issues/District 2 at
District and school staff must show more respect for parents' values and standards for their children's mathematics education, by soliciting and supporting open dialogue, by comprehensive research of home supports, by building coherence between class and home instruction, by seeking to develop viable means to inform policy decisions with the experiences and values held by members of the school community; rather than actively seek to quash questioning or critical voices in public discourse and school and district-wide paper and electronic systems of parent communication, and effectively bar any substantive parental participation in math education policy decisions, as is now, unfortunately, most often the case.
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District #
Professional Development
Professional Development
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?
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NO ANSWER
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I am concerned with the fact that some district math coordinators lack an adequate mathematics background themselves, as was the case with the former District 2 Director of Mathematics, Lucy West.
Recommendation: A minimum level of college mathematics education should be determined by a panel of math educators and mathematicians, to be consistent with the new NYS credentialing requirements and strictly enforced.
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Addendum
CSD2 Black and Hispanic Schools, Scores. See here for the Microsoft Word *.doc original of same.
Response of Ginny Donnelly
(Please see here for the Microsoft
Word *.doc original version of Ginny Donnelly's reply)
Dear Mr. Rudall:
I was sent a copy of your survey by Elizabeth Carson of NYC HOLD.
Thank you for your interest in soliciting our opinion.
My background:
I am the mother of a daughter who attended 9 years of District 2
elementary and middle schools. For 8 of those years I volunteered at
least one day a week in the classroom (usually not the class my child
was in), often helping students with math. I was also a School
Leadership Team member for 3 years. While I am not a professional
mathematician, every position I have held - in insurance, accounting,
banking and as inventory manager for a major educational publisher - has
required a thorough knowledge of math. My daughter's K-2 math program,
Miquon workbooks supplemented with a variety of interesting activities,
gave children a solid foundation. Then District 2 schools were forced
to adopt TERC and CMP. I observed not only how much my daughter hated
having the math she enjoyed replaced by writing, but also how the other
students I worked with fell farther behind the more years of
constructivist math they had. Now that she is a freshman at Bronx
Science (she managed to score well enough to get in thanks to her own
innate ability and a lot of tutoring from me), I can see how poorly
District 2 prepared her and her schoolmates for high school math.
Ginny Donnelly
Math Questions
District # 2
Curriculum
Unfortunately, TERC, CMP & Arise
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These programs as stand-alones are not working. Good schools and teachers supplement with a variety of more traditional materials. Parents hire tutors and enroll their children in prep courses to make up the deficiencies. Even gifted children need these supplements to score well enough on 4th grade standardized tests to be accepted into SP programs in middle schools.
I recommend Miquon Math Lab Materials from Key Curriculum Press for the lower grades. These were used successfully when my daughter was in K-2 before TERC was mandated. They do what TERC only claims to do: really teach kids math concepts. Up through high school I'd recommend the University of Chicago School Mathematics Project series, published by Scott Foresman Addison Wesley. This series does a good job of combining traditional math with real-world problems.
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Find out from master teachers - not from staff developers with preconceived programs they're pushing - what really works in the classroom, and use this info to shape curriculum. Make sure the curriculum is aligned with the standardized tests that unfortunately determine so much of our children's academic standing. Communicate among elementary, middle and high schools to make sure students are taught in elementary school what they're expected to come into middle school knowing, and are taught in middle school what they're expected to come into high school knowing. Find out what colleges expect incoming freshmen to know.
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District #2
Instruction
Constructivist discovery learning.
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Focused test prep improves test scores.
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Reliance on constructivism alone. Kids can't be expected to discover on their own principles that it took centuries for humanity's most gifted minds to work out. Children, parents and honest teachers complain that more direct instruction is needed.
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District #2
Assessment
Yes. Seem like a good idea - don't know how well they're working. Parents should see them too.
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Portfolios, class grades, teacher assessments. Teachers use student reflections to plan and assess progress and instruction.
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Pay more attention to teacher evaluations. Perform item analysis of test material by grade to make sure curriculum covers all areas that will be tested.
Families should be sent the results of all tests their children take. In particular, we are not given their 8th grade test results.
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District #2
Support Structures
In schools I know, extra periods of math during the school day and after school math when funding was available.
Identified by test scores and class marks.
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When teachers can provide the instruction the students need - not simply more of the unsuccessful programs - test scores do improve.
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Free teachers to teach what they know works. Make sure they don't have to keep looking over their shoulders to avoid trouble with principals and district staff developers when they do this. Use more direct instruction. While discovery learning may have a limited place, it wastes a lot of time and very often students don't discover what they're supposed to. As my daughter said, "You spend a lot of time figuring how to solve a problem, and your way doesn't work, or it takes a long time. But because you spent so much time on it, you remember that way and not the easier way."
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District #2
ELL Students
In the middle school I'm familiar with, special classes in Eng. and math. As far as I know, school administration and staff.
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Test scores improve.
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It's heartbreaking to see ELL students struggle with the excessive reading and writing required by TERC, CMP, etc. Often these students are competent in math, and their faces light up when they are given a number problem that they know how work out. Making math a subdivision of English deprives these children of one of the few areas in school where they can shine academically.
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District #2
Students with Special Needs
IEP's, specialists, inclusion classes, special classes, etc. Per DOE guidelines.
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More time on task. Inclusion classes with regular teacher plus well-trained special ed teacher. Improved test scores.
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If students with special needs are put into inclusion classes with untrained paras, they can be too disruptive. Paras need to have enough training to handle situations that arise.
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District #2
Family Numeracy
The district wants schools to have a yearly math night for parents, where staff developers tell parents how wonderful TERC, CMP & Arise are and disregard parents' real questions and concerns. They also want teachers to send home photocopies of sheets from these programs telling parents not to teach their children any traditional math.
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Since most parents I know care more about their children really learning math than about them serving as guinea pigs for failed math programs, they ignore these instructions and tutor their kids or pay for tutoring.
Some suggestions for using everyday situations to teach math are useful.
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District staff developers tell parents that they're wrong to have concerns that their children can't get the right answer to math problems in a reasonable amount of time. Good schools tell parents what they're doing to supplement the programs, as well as pointing out the good aspects of the programs, so their students will learn math and be able to succeed on standardized tests.
The district should introduce good math programs that teach computational fluency as well as understanding concepts (which the current programs don't do well anyway) and let parents know how they can help with good programs.
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District #2
Professional Development
As of last year, professional developers came around to schools and went into classrooms. This was only occasionally helpful. What was helpful was when the district math teachers could get together and trade experiences so they could edit lessons and use only what works. I know this is effective because good teachers told me so.
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Developing a curriculum that will teach kids math without average and gifted children needing outside tutoring to succeed. Sharing teachers' experiences of what actually works in the classroom.
Parents are transferring their kids to private schools solely because of the district's poor math curriculum Children who cannot afford private tutoring are being shut out of the specialized science high schools because they can't do the math required for the admissions test.
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Professional development should be done primarily in the classroom. Less experienced teachers should have plenty of opportunity to observe master teachers at work, and master teachers should go into classrooms to observe less experienced teachers and make helpful suggestions. All staff developers should spend a good portion of their time teaching classes of their own.
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Professional Development
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?
Too many staff developers. Not enough master teachers.
As a parent, I don't have the info to give specific answers to the questions in this section.
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It seems that the main criterion is adherence to stand-alone constructivist programs.
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Input on math practices and reform curricula in New York City public
schools, particularly District 2.
Jonathan Goodman, Professor of Mathematics, Courant Institute of
Mathematical Sciences, New York University. goodman@cims.nyu.edu, (212)
998-3326
Reform curricula: These are curricula and teaching practices
inspired by or aligned with the NCTM standards. Specific curricula
used in District 2 include TERC, CMP, and ARISE. I have studied
curriculum materials from these curricula and studied the Mathematics
Standards of New York City. I have attended seminars and studied
materials on reform mathematics education practice and observed
classroom instruction using CMP and ARISE in a District 2 school.
Conclusions: The reform curricula and teaching practices used
by District 2 are far inferior to other available curricula based on
more rigorous standards. This is my expert opinion as a professional
mathematician and a parent of two kids who attended District 2
schools. It is also the opinion of a vast majority of university
mathematicians who have studied K-12 educational issues in the past
decade.
Quality: TERC, CMP, and ARISE have clearly been created mostly
by people with little understanding of mathematics or interest in
correctness. They are full of mistakes and misunderstandings.
Appropriateness: Reform curricula do not give students the
knowledge and skills they need to succeed in college mathematics and
science.
Research: Most of the so-called research supporting reform
curricula is inaccurate or invalid. Detailed critiques of this
research are available.
Value: The goals of reform curricula, teaching problem solving
skills and understanding of fundamental mathematical principles, are
not realized by the actual curricula. Instead, TERC, CMP, and ARISE
are basically dumbed down versions of earlier curricula.
Recommendation: The New York City Board of Education should launch a
serious investigation of its mathematics curricula by a broad panel of
independent experts. These experts should not be selected by the
current mathematics curriculum staff of the Board of Ed, but by an
independent group with no existing position in curriculum issues. The
experts should include representatives from the large and active group
of New York City university mathematicians who oppose reform
curricula.
Math Questions
District # 2
Curriculum
Response of Jonathan Goodman
Response of Fred Greenleaf
Remarks Fred Greenleaf
Professor of Mathematics, NYU/Courant Institute
Dear Mr. Rudall:
Thank you for your invitation to reply to your questionnaire. I
welcome the opportunity because during the past 2 years I have spent
quite a bit of time talking to parents and to math teachers in NYC,
and examining curricular materials for various math programs based on
NCTM (National Council of Teachers of Mathematics) recommendations
which have been heavily promoted in District 2 of NYC and are now
being implemented on a broader scale throughout the City. These are
TERC (Investigations in Number and Space)
CMP (Connected Math Project)
ARISE (Mathematics: Modeling Our World)
IMP (Interactive Math Program)
It is my opinion that these programs are based on an extreme and
misguided "constructivist" educational philosophy that will have
disastrous consequences for the many students who aspire to 2-year or
4-year college level programs having significant math requirements,
such as those in Business, PreMed, Engineering, etc. This sense of
alarm is shared by many of my colleagues at the Courant Institute, and
at other institutions, who have followed the rise of these
NCTM-promoted programs. It is also shared by many teachers in the NYC
school system with whom I conducted extensive interviews in order to
find out how these programs looked to those in the trenches. My
edited summary of those interviews is appended as a plaintext
attachment to this message. You might find it interesting to hear
comments from rank and file math teachers that have not been filtered
through the the "math experts" of the Board of Education, who have a
vested interest in making the new programs sound worderful -- their
professional advancement (not to mention the flow of grant money)
depends upon it. Beware of what you hear from the beauraucracy.
As for my background in math education, I append a short cv as another
attached plaintext file, but it suffices to say that I've had a lot of
experience with development of math curricula, and that includes
serious efforts on programs for entering freshmen who are not
necessarily going to be math majors. (For instance, I led the team
that developed the 3 course math/science component of the NYU Core
Curriculum, required of all students). Whether we're talking about
core programs in math and science literacy, or regular math courses
for science majors, business majors, and premed students, I have found
that the single greatest obstacle to success for entering college
students -- even in courses for non-majors -- is lack of PROFICIENCY
in algebra. That means: being able to DO it, not just talk about it.
Most of the NCTM-promoted programs I reviewed strongly downplay
symbolic manipulation skills (which lie at the heart of real
mathematics) in favor of ad hoc "visualization" techniques, and
lengthy unguided projects in which students are supposed to "discover
math principles for themselves". Now there is something to be said for
including in a math curriculum some projects in which students are
encouraged to "learn by discovery" -- I have often done this the
courses I have developed. The problem is that most NCTM-promoted
programs being suggested for use in NYC are quite extreme in their
emphasis on the process of "discovery", at the expense of mastery of
basic content and proficiency in basic skills. The NCTM based programs
are quite unbalanced in their emphasis, and as a result are totally
inadequate as preparation for eventual college level courses.
In a recently completed review of math programs being implemented in
NYC, the Levy Commission conceded that the NCTM-promoted high school
program ARISE and IMP, that were to be mandated throughout the Bronx
as of Fall 2000, were not an adequate preparation for college level
work. The Commission went on suggest that "choice" be allowed
beginning in grade 9, so college bound students might take courses
with stronger content.
THAT IS TOO LATE! The underpinnings of proficiency in algebra are
laid in middle school, and even at the elementary level. For
example, learning to work with fractions, AS FRACTIONS, is the
precursor of later algebra. It is not enough to deal with them as
numbers punched up on a calculator, or by comparing lengths of
paper strips.
Doors will be closed to students who aspire to any college level work
unless students are allowed to elect courses with stronger content
BEGINNING IN MIDDLE SCHOOL AT THE LATEST, but preferably throughout
the early grades.
Now I would like to present some excerpts concerning the view from the
trenches, extracted from the more detailed attached plaintext file
labeled "Edited Teacher Interviews".
What do teachers think? In my interviews I found many math teachers
willing to speak, as long as their anonymity was assured. I spoke to
teachers at grade-, middle- and high school levels. Many complained
that the NCTM based courses tend to be quite "dumbed down". Here are
some quotes:
"I've been teaching math for a long time, and am struck by how much
less math actually gets covered under the new programs, compared to
what got accomplished just a few years ago"
"Weaker students may benefit from these programs, but the effect on
the better students is going to be disastrous. The only ones who
will really benefit from these programs are the Stanley Kaplan
tutorial centers -- for them it will be a godsend!"
One teacher described an hour-long training session in which kids
colored an array of numbers. She asked the trainer, what was the point
of spending so much time on this? What math concepts did it lead to?
The reply:
"Concepts don't matter. What counts is how the kids feel about it."
I can't think of a better illustration of what the phrase "dumbed
down" might mean.
Skilled teachers' hands are being tied by overzealous administrators
and NSF-funded "trainers", who know about pedagogy but have very
little knowledge of math CONTENT. Indeed some of the more zealous
proponents of these constructivist programs have claimed that one
doesn't really need to be proficient in content, one simply has to
know how to teach. Experienced math teachers are chastized -- even
threatened with reprisals -- if they deviate from the mandated
constructivist scripts. As one teacher put it:
"There is no longer any classroom autonomy. Teachers are being
treated as if expertise in one's subject, and personal teaching
skills, are irrelevant. Everyone is being forced to work from the
same fairly ridiculous script".
This atmosphere of micromanagement and intimidation is alienating many
of the experienced teachers. Older, experienced teachers are
contemplating early retirement; younger ones look to other locations
where ability to teach math content is appreciated, and probably
better paid.
The constructivist philosophy is flawed at its core. Zealous
"constructivist" educators posit that really meaningful learning takes
place only when students teach each other in small peer-led group
discussions, with teachers confined to roles as mere "facilitators" of
this process. To me, as a working mathematician, it is absurd to
expect students to invent major portions of math on their own, through
extensive aimless and time-consuming group projects (aka the "crayola
curriculum"). Discovery based learning has a valid place in the
classroom, but the constructivist programs are extremely biased in
this direction, and student progress is very slow. In fact, many
teachers report that:
"In our school, using program xxx, no teacher has ever managed to
cover more than 60% of the year's material".
The District replies "We never expected to cover all of it". Yet the
District has repeatedly failed to offer guidance on WHICH 60% is to be
covered. Furthermore, if these curricula are to provide an adequate
preparation for the State Regents exams (as specified in the NY State
Resource Guide with Core Curriculum), one would have to cover ALL of
the NCTM course materials, and that is impossible.
It is time to acknowledge the serious flaws in the NCTM based programs
being promoted so zealously in District 2 and a few other venues, so
we can get on with the task of creating programs of math preparation
adequate for today's world. What we really need is programs with some
sense of balance, created with the involvement of MATHEMATICIANS as
well as educators.
My colleagues, whose responses you have also solicited, will certainly
offer many suggestions about what can be done, so I defer comment
along those lines. I think you will find particularly detailed
responses from Professors Bas Braams, David Klein, and Mike McKeown,
whose views I share. My sense is that the Board of Ed must first
become aware that there is a problem before there can be any
solutions. In this respect, you may be interested in a third plaintext
file attached to this commentary, "Why we question the NCTM-approved
math programs being promoted by District 2" (4 pages), which
summarizes the concerns of myself and my colleagues .
As for the questionnaire, it is clearly directed toward teachers,
administrators, or parents with children in the NYC school system, and
so I find it difficult to respond line-by-line. I have addressed some
of your issues in the comments above, and in more detail in the
attached files.
Fred Greenleaf
Math Questions
District #
Curriculum
1. Which curriculum materials are predominantly used in your district
at elementary, middle, and high school levels?
District 2: TERC, CMP, ARISE
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 and my colleagues have spent a lot of time reviewing the course
materials for TERC, CMP, and ARISE. I would NEVER recommend their
use in any K-12 math program, except for
.Possible use in grades K and 1
.Possible use of a few better projects as occasional supplementary
projects at the higher levels.
To harried parents, desperate for materials to supplement the
incoherent and inadequate programs now in place in District 2, I
recommend
. The Singapore Curriculum, a time-tested English language
curriculum available in inexpensive paperback editions. These
excellent and lively materials are appropriate for U.S grade
levels K-6. Soon we should have revised versions of the higher
level curriculum adapted to US grade levels 7-12. Materials are
available through www.singaporemath.com
. The Saxon curriculum (see response of Bas Braams for more
details on this).
3. What should be done to ensure a more coherent PK-12 numeracy
approach to curriculum?
Kill all NCTM-promoted math curricula. Replace with math texts that
give serious attention to content, a coherent overview of math
concepts, and adequate attention to development of basic math skills
-- eg easiy facility with things like fractions and symbolic
manipulations.
Instruction
1. Which instructional practices are predominantly used in your
district at elementary, middle, and high school levels?
The most doctrinaire versions of constructivist math curricula
2. Which instructional practices are working and how do you know
(please cite student achievement data as evidence)?
NA
3. Which instructional practices are not working and why?
None of the constructivist NCTM-base programs are working, despite
protestations of Lucy West. Alarmed parents are paying enormous sums
for supplemental tutoring (those who can afford it, at least), in far
larger numbers than a decade ago. Why? Because by 5th grade, after
having been immersed in TERC, their kids are functional illiterates
in math and their parents realize how detrimental this will be to
their childrens' futures. The kids can't add, can't multiply, can't
do simple fractions, without lengthy trial and error gamesmanship.
Perversely, all this expensive outside tutoring keeps District 2
grades from falling abysmally (because District 2 is relatively
wealthy) and revealing these programs for the sham they are. Other
less affluent districts may not fare as well.
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?
NA
2. Besides the NYS and NYC assessments, what specific data is
collected to monitor student achievement in numeracy? How is this
data used?
NA
3. What are your suggestions to improve PK-12 assessment practices?
NA
District #
Support Structures
1. What are your district?s intervention strategies and programs for
struggling students? How are struggling students identified?
NA
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?
NA
3. What else do you think needs to be done to support struggling
students in numeracy?
NA
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?
NA
2. Which of these strategies work and how do you know (please cite
student achievement data as evidence)?
NA
3. Which of these strategies do not work? Why?
NA
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?
NA
2. Which of these strategies work and how do you know (please cite
student achievement data as evidence)?
NA
3. Which of these strategies do not work? Why?
NA
District #2
Family Numeracy
1. How does your district engage with parents in relation to numeracy?
Mostly it tries to keep them as quiet as possible, and hand them a
lot of reassuring propaganda about how "wonderful" all these new
NCTM-based programs are. This technique is well illustrated by a major
parents' forum held by the District in April 2000, supposedly to let
parents' concerns be heard. The panel of District "math experts",
which included NO PRACTICING MATHEMATICIANS only MATH EDUCATION
experts, spent 2.5 of the alloted 3 hours time telling everyone how
wonderful their pet programs were. And then -- whoops! We're
unfortunately almost out of time so we can only hear one or two
parents questions from the floor.
2. Which of these strategies work and how do you know?
This strategy certainly works to keep parents from raising embarassing
questions about why their kids are mathematically incompetent and why
the kids' homework projects are so moronic.
3. What issues do parents raise and how do you address those issues?
What else should your district be doing around family numeracy?
For this you should consult the response of Elizabeth Carson, who has
been working intensively with distressed parents for the past 4 years
(and has children of her own in the system).
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?
Mostly NSF-funded teacher training that is almost devoid of math
content, since its purpose is really to indoctrinate teachers in the
new NCTM-promoted programs. The trainers themselve know little math;
their only concern is pedagogical correctness (eg stamping out the
word "algortihm").
Since these training programs focus on ideological purity and
indoctrination, they are no help in getting teachers better prepared
to teach math content and skills. They are useless.
Much more effective (but untried) would be programs to enlist skilled
senior, or recently retired, math teachers and pay them to devise and
conduct training programs for in-service teachers whose math is not so
strong. This could be particularly effective if senior math teachers
were to engage with K-6 teachers, most of whom exit School of
Education teacher training programs almost devoid of serious math
content.
Call me a curmudgeon if you will, but I believe you should know some
math content in order to teach it well, even at the lowest grade
levels.
2. What do you think are the most pressing staff development needs in
your district? Why?
NA
3. In addition to increased time, funding, and access to space, what
recommendations would you make to the DOE regarding professional
development?
See above
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?
NA
7. What training do math specialists/staff developers receive?
NA
BRIEF CURRICULUM VITAE
FREDERICK P. GREENLEAF
Current Position:
Professor of Mathematics
New York University/ Mathematics Department
Courant Institute of Mathematical Sciences
251 Mercer Street
New York, New York 10012
Contacts:
Office: (212) 998-3173 FAX: (212) 995-4121
E-mail: greenlea@cims.nyu.edu
Personal Data:
Birthplace: Allentown, Pennsylvania; January 8, 1938
Citizenship: U.S.
Education:
1. Pennsylvania State University: B.S. (Chemistry/physics) 1959
2. Yale University: M.A. (Math) 1961; Ph.D. (Math) 1964.
Fellowships/Awards:
1. Westinghouse Science Talent Search: Grand Prize, 1955.
2. Alumni Scholar, Pennsylvania State University, 1956-59.
3. NSF Graduate Fellow, Yale University, 1959-63.
4. Golden Dozen Award (Distinguished Teaching), NYU 1990.
5. Golden Dozen Award (Distinguished Teaching), NYU 1998.
Research Grants (as Principal Investigator):
1. NSF Research Grants in Functional analysis and geometry of groups,
1971-1984; 1985-1996.
2. NSF Math/Science Curriculum Development Grant (DUE 92-54301).
A large-scale Science Core Program for the non-science student,
March 1993 - August 1996, $357,190.
3. NSF Math/Science Curriculum Development Grant (DUE 96-52081).
Reform of science and math education at NYU, August 1996 -
September 1998, $199,993.
Previous positions:
1. Yale University: 1963-1964, Instructor
2. University of California (Berkeley): 1964-1968, Asst. Professor
3. New York University: 1968 - present.
4. University of California (Los Angeles): Visiting Professor/Math,
1979-1980; 1981-1982.
5. University of California (Berkeley): Visiting Professor/Math, 1985
Administrative Experience:
1. Course coordinator: Business Calculus program, Math Department;
September 1975 - present.
2. Director of Undergraduate Studies/Mathematics, New York
University, September 1989 - August 1992.
3. Chairman: Science Education Policy Committee, New York University.
Led development of 3-semester core math/science curriculum
Foundations of Scientific Inquiry (FSI), now required of all
non-science majors at NYU. September 1990 - August 1995.
4. FSI Steering Committee, New York University, New York University:
overseeing progress of FSI program; active development of new
courses in the program. September 1995 - 2000.
Major Course Development Initiatives (NYU):
1975: One semester calculus course designed for students in Stern School
of Business. Designed program, produced text and course materials;
liason with Stern School of Business. (Scope: approx 400 students
annually).
1991-2000: Development of lab projects and course text materials for
first course "Quantitative Reasoning: Understanding the Mathematical
Patterns in Nature" in NYU science core program Foundations of
Scientific Inquiry. (Scope: about 600 students annually).
1991 - 2000: Development of lab projects and course text materials for
second course "Natural Science I: Cosmos and Earth" in NYU science
core program Foundations of Scientific Inquiry. (Scope: about 200
students annually).
1996 - 1998: Development of computer interfaces and computer-enhanced
lab projects to accompany the first course Quantitative Reasoning
in NYU science core program (FSI).
Spring 2000: Development and supervision (with Andre Adler of FSI
Program) of summer seminar "Quantitative Reasoning in the College
Curriculum " for the NYU Faculty Resource Network, a consortium
involving NYU and various other colleges throughout the eastern U.S.
Seminar focused on integration of math and science in the teaching
of non-science majors math courses.
Community Service:
1. 1970 - present. Referee for innumerable math research journals and
National Science Foundation research grant proposals.
2. March 2000 - present. Mentoring students from Stuyvesant High School
(Manhattan): advising students participating in the Intel
Competition, and leading tutorial sessions on advanced topics.
3. 1999-2000. Member of advisory panels on K-14 math/science
education policy, organized by Woodrow Wilson Foundation.
4. March 2000 - present. Member of a working group of professors
from NYU and other universities, advising parents' groups in
District 2 (Manhattan K-12) regarding the "constructivist" math
programs being imposed in District 2, and elsewhere in NYC.
Consulting
1. Editorial consultant to W.H. Freeman Co, (development of
mathematics texts), 1982 - 1984.
2. Consultant in mathematical analysis, IBM Thomas J. Watson Center,
on mathematical models in MRI and radar imaging,
September 1983 - December 1984.
Professional Societies:
1. American Mathematical Society
2. American Association for the Advancement of Science
Current Research Interests:
1. Research on Lie groups, noncommutative harmonic analysis, and
the interplay between analysis, geometry, and algebra.
2. Curriculum reform of math/science offerings for non-science majors,
in connection with Foundations of Scientific Inquiry program at NYU
and related NSF curriculum development grants.
Publications related to math/science education.
1. Introduction to Complex Variables, W.B. Saunders Co.,
Philadelphia, 1972, 588 + (xii) pp.
2. Calculus: A short course with applications to business,
economics, and the social sciences (written with G. Freilich),
W.H. Freeman Co., San Francisco, 1976, 395 pp.; 2nd Edition,
Harcourt-Brace-Jovanovich, 1985, 436 pp.
3. Algebraic methods in business, economics, and the social sciences
(written with G. Freilich), W.H. Freeman Co., San Francisco,
1977, 312 pp.
4. Quantative Reasoning: Understanding the Mathematical Patterns
in Nature, Course 1: NYU Integrated Math/Science Curriculum,
McGraw-Hill, New York, 1994, 550 pp.; revised 1997, 605 pp.;
2nd Edition, 2000, 654 pp.
5. Quantative Reasoning: Understanding the Mathematical Patterns
in Nature (Workshop Projects): NYU Integrated Math/Science
Curriculum, McGraw-Hill, New York, 1994, 119 pp.; 2nd Edition
2000, 227 pp.
6. The Analysis of Starlight, Course 2: NYU Integrated
Math/Science Curriculum, McGraw-Hill, New York, 1995,
206 pp.; revised and expanded 1997, 308 pp.
7. Atoms, Molecules, and the Chemical Bond (with N. Kallenbach),
Course 2: NYU Integrated Math/Science Curriculum,
McGraw-Hill, New York, 1996, 186 pp.
February, 2001
Note: This is a preliminary draft of concerns voiced by the group of
NYU and other New York City college math faculty regarding new math
programs being implemented in District 2 of New York City.
Why we question the NCTM-approved programs being promoted by District 2
We believe that the math programs currently being put in place by
District 2 suffer from severe deficiencies, and in the long run will
work to the detriment of students and families in the district. All
of these programs -- TERC, CMP, ARISE, and others -- are based on a
single radical educational philosophy and all share the following
deficiencies.
1. They are Unbalanced.
Any reasonable program of math instructions should achieve a
balance between
. mastery of basic skills and extensive practice in problem
solving techniques,
. acquiring a firm grasp of mathematical concepts,
. direct instruction and guidance by teachers knowledgeable in
their subject, on the one hand and
. individual and group activities involving discovery-based
learning, on the other.
The programs being implemented in District 2 (TERC and CMP) in their
pure forms focus entirely on having children learn math by discovery
in group activities. Practice on basic problem solving skills is
actively discouraged, and little meaningful homework is assigned that
might strengthen those skills. Algebra and symbolic manipulation
skills are strongly de-emphasized in favor of ``visualization'' and
use of manipulables, leaving students ill-prepared for higher level
courses. The use of supplementary materials covering these topics is
strongly discouraged, though a few principals allow supplementation,
apparently in defiance of District orders. Teachers are strongly
discouraged, and in some schools forbidden, to ``instruct'' or
actively guide the discussions resulting from group activities.
Students are left with poor basic skills, and without a coherent
understanding of what they have done, or the larger picture into which
their activities fit.
All this is in accord with standards for new K-12 math curricula
issued in 1989 by the National Council of Teachers of Mathematics
(NCTM). Those standards firmly embraced the ``constructivist''
philosophy that the role of the teacher is not to teach, but to act as
a mere ``facilitator'' for group efforts in which students are
supposed to ``discover math for themselves'' and construct their own
understanding of the subject. They strongly downplayed work on basic
math skills and paid little attention to development of algebraic
concepts. The District programs, based on the 1989 Standards, reflect
those attitudes.
The 1989 NCTM Standards were substantially revised in year 2000, in
response to rising criticism of the 1989 Standards by professional
mathematicians, college teachers, and education authorities in states
such as California. The year 2000 NCTM Standards placed much more
emphasis on mastery of skills, but none of the programs now in place
reflect those recent changes. Spokespersons for NCTM attempt to
justify the existing programs by insisting that the original standards
were ``misinterpreted'', and that the revised standards merely
``clarify'' what was intended. A comparative reading of both Standards
suggests otherwise. The 1989 Standards were very clear in their
de-emphasis of basic math and algebra skills, and in their zeal to
replace traditional programs with new ones focused entirely on
``learning by discovery''.
The programs TERC, CMP, ARISE being introduced in District 2 were
created in the spirit of the 1989 Standards, and are inconsistent with
the more moderate and realistic revised year 2000 Standards. Our
District is being saddled with a set of programs that are already
outmoded because they embody the serious faults of the 1989 Standards.
2. The Programs are Unworkable.
The educational philosophy on which the District 2 programs are
based appears to be fundamentally flawed. These programs are unable to
meet their own objectives, let alone the larger objective of providing
sound training in math.
A certain level of discovery based learning in group activities
is desirable, and can help students understand math concepts and make
them feel more comfortable about math. However, this mode of
``discovery based learning'' is painfully slow. After all, it took the
best thinkers of their times centuries to get algebra straight; do we
want to have students spend enormous amounts of time re-inventing the
wheel?
Typical District 2 programs consist of modules, between 9 and 11
units to be covered in a year. Because of the time required to
``rediscover mathematics'', students do not in fact get to complete
their yearly programs. Based on our own interviews with in-service
teachers in the District it appears that
No teacher in any school has ever managed to cover more than 60%
of the units in the 1-year packages they have been given. The
TERC and CMP programs cannot meet their own professed goals,
because the pace of these activities is so very slow.
That means: EACH YEAR, students fall about 40% behind the materials
they are supposed to cover. Moreover, what does get covered varies
from school to school. Thus when students move from elementary to
middle school, or to high school, there is no assurance they arrive
with knowledge of any particular set of math concepts. The result can
only be chaos.
All this should not surprise anyone who has been involved in discovery
based projects. The remarkable thing is that proponents of the
District 2 programs -- which in their pure (unsupplemented) forms are
100% group activity -- have never acknowledged this gap between their
professed goals and reality. We doubt that these programs can ever be
made to work without radical restructuring and a move away from
instruction based on a single educational ideology.
3. The Programs are Inconsistent with NY State Standards.
A grade-by-grade comparison of the New York State math standards,
on which the new Regents A and B exams are based, shows that TERC
(program for grades 1-5) and CMP (grades 6-8) give short shrift to
more than 30% of the topics specified in those Standards -- especially
those related to basic math concepts and skills, and competence in
algebraic reasoning. That would be bad enough, if teachers using the
TERC and CMP programs could in fact cover the materials in each grade
level program. They have not been able to do this much in real life.
Failure to cover the mandated TERC and CMP materials is hardly
the teachers' fault, as we have noted in (2.) Developers of the
NCTM-approved programs have never acknowledged fundamental problems
inherent in curricula that focus entirely on ``discovery'' projects.
It is impossible to master mathematics without serious attention
to CONTENT and PRACTICE OF SKILLS. The deficiencies of the
``constructivist'' programs in these areas will have a serious impact
on families who hope to see their children advance through educational
opportunities. We can expect children subjected to these programs to
be at a disadvantage in: (i) statewide tests (grade 4) which are used
for admission to desirable middle schools, (ii) citywide placement
tests (grade 7) for admission to desirable high schools, (iii) the
citywide specialized science high school entrance exam, (iv) achieving
well in the NY State Regents tests, (v) succeeding in high school AP
courses, (vi) performing well in college-entry SAT tests.
4. These Programs Promote Inequities.
About 75% of all high school students go on to college of some
sort, even if not to a four-year program, and math is -- after
literacy -- the most troublesome ihurdle to entrance and to
success. In college they will face quantitative math and science
requirements in a vast number of programs, including business,
economics, biosciences and premed, computer science, math, physics,
chemistry, and engineering. District 2 curricula downplay basic
problem solving skills and mastery of math concepts needed to gain
entry to and succeed in such programs. Because group work procedes so
slowly, and because so much time is devoted to repetetive ``math
game'' projects, constructivist programs cover fewer math concepts
than earlier programs did, and their coverage of these concepts is
often superficial. As a result, many parents in the district have been
resorting to extensive tutoring at their own expense. The District 2
programs will have a devastating effect on students from low-income
families who cannot afford these extras.
Parents in a public school system deserve a level playing field,
regardless of their economic circumstances. No parent should have to
go to great expense to compensate for the built-in deficiencies of the
math programs being promoted in District 2. The inadequacies of the
District 2 curricula are widening the gap between haves and have-nots.
The Programs Promote a Failed Ideology.
In the early 1990s TERC, CMP, and several other NCTM-approved
``constructivist'' math programs were implemented on a large scale in
the state of California. There they proved such failures that in 1997
all NCTM-approved programs were decertified and new statewide math
standards were formulated, this time with input from concerned
mathematics professionals as well as members of the education
establishment. Yet in District 2, and throughout New York City,
school authorities seem determined to implement the same failed
programs as if nothing ever happened.
In California the failure of these programs was evidenced by a
steady decline in statewide math test scores, and by a dramatic
increase in the need for math remediation among students entering the
state college system. Furthermore, well documented nationwide studies
extending overq several years have demonstrated that direct
instruction -- allowing teachers to teach instead of relegating them
to the role of ``facilitators'' of group investigations -- is by far
the most effective means of improving math skills, especially among
low-income and minority K-12 students [1].
6. These Programs Ignore Proven Alternatives to NCTM-Based Curricula.
The recent international TIMSS study of math instruction,
involving over 500,000 students worldwide, demonstrated that by the
time they reached 8th grade students from Singapore and Japan rate
highest in math ability, while the U.S. students ranked 28th among 41
countries. By 12th grade U.S. students ranked near the bottom, 19th
out of 21 nations surveyed at that grade level, with performance
comparable to that found in underdeveloped countries. Proponents of
the NCTM-approved programs claim that their curricula are closely
modeled on the programs used in Singapore and Japan. They are not. In
fact, the NCTM-approved programs have distorted key tenets of the
Asian programs beyond recognition, by focusing exclusively on just one
aspect of those programs -- discovery based learning by students
working in groups.
The Singapore, Japanese, and European K-12 math curricula
recognize the primary importance of a skilled teacher in math
instruction. Their course materials strike an excellent balance
between work on problem solving skills, direct instruction to convey
math concepts, as well as group investigations designed to illuminate
those concepts. As a result the Singapore materials, at every grade
level, are far superior to those in the programs now being promoted in
District 2, and student performance is far better. How could it be
otherwise, when the District programs so thoroughly denigrate the role
of the teacher?
The Singapore curriculum is particularly interesting. Singapore has a
system of universal education, in English. Rich and poor alike were
included in the TIMSS survey that placed Singapore first in the
world. This curriculum consists of a series of English language texts
and workbooks (including group projects), one for each grade level,
that have been refined through more than a decade of use. These
materials are issued in inexpensive paperback editions, and are
commercially available [2]. Why have these programs been so ignored by
American educators?
We have carefully examined videotapes of eight grade math classes
in Japan and Germany, created as part of the TIMSS study. Proponents
of NCTM-approved curricula often point to these tapes, claiming that
they demonstrate the similarity between those successful programs and
the ``constructivist'' programs being promoted in the United
States. However, close examination of those tapes reveals startling
discrepancies between the Asian and European programs, and those being
implemented in the U.S.
The tapes show very skilled teachers at work; all have a firm
grasp of the mathematical concepts they are teaching, and their
classroom presentations are superb. On the tapes one sees those
teachers spending more than 50% of their time in DIRECT
INSTRUCTION. Although classes involve a certain amount of group
and individual effort on the day's project, classes always begin
with the teacher reviewing basic skills and concepts needed to
solve the problems of the day; teachers actively intervene in
guiding group discussions; finally, they spend considerable time
at the end providing an overview of what has been accomplished,
and reviewing the math concepts illustrated by the day's project.
Teachers in the successful programs are hardly passive ``guides on the
side'' -- the role to which teachers have been confined in virtually
all NCTM-approved programs.
Conclusions
The cornerstone of the constructivist philosophy of education, upon
which the District 2 programs are based, is that more meaningful
learning is supposed to take place when students teach each other in
small peer-led groups and thereby ``construct'' their own
knowledge. We working mathematicians know it is absurd to expect
students to invent all of mathematics on their own, unaided, through
the exclusive use of time consuming and wasteful group projects. The
NCTM-approved programs in District 2 are a recipe for disaster,
although this may not become clear until a generation of students NYC
has failed. That was the pattern in California, and will be the
pattern here unless something is done to modify these programs and
acknowledge their flaws.
District 2 could begin to address these issues by recognizing
that there may be serious problems with the ``constructivist''
curricula they have so ardently been promoting. What is needed is a
meaningful dialog with teachers and concerned citizens about
modifications and alternatives to these flawed curricula.
Many things could be done. As a first step, the best of the
projects in the present curricula -- those with substantial math
content -- could be kept, while the rest are discarded in favor of
supplementation that restores some balance among the goals listed at
the beginning of these remarks. California has already endured the
effects of the unadulterated constructivist programs (including TERC
and CMP), and state authorities have now developed approved lists of
more balanced instructional materials. We could take advantage of
their experience by examining the texts on the California approved
list. Portions of the English-language Singapore Curriculum might also
be a useful resource. The Singapore texts are currently being used by
a few school in New Jersey and Maryland, and it would be interesting
to learn more about their experience with these materials. (The entire
Singapore text series is inexpensive and commericially available, and
a new edition is being prepared that conforms to U.S. grade levels.)
There is no lack of resources for supplementing the present programs,
if the District has the will to acknowledge the deficiencies of those
programs.
Finally, the most important step would be cease confining
teachers to the role of passive ``facilitators'' of unworkable
programs. Let knowledgeable math teachers exercise their initiative
in getting math concepts across, and shift the District's focus toward
getting more such teachers into our schools. Finally, instead of
harassing experienced math teachers who chafe at the vacuous nature of
the District 2 programs, the District might be better served if it
listened to those teachers and enlisted them to help train newcomers
in math content (with which they have little contact if they are
products of typical School of Education teacher training programs,
especially in grades K-5).
REFERENCES:
[1] For example, Project Follow Through was conducted from 1967-1995,
initially as an adjunct to the Head Start program. These studies were
large scale and statistically sound, involving 700,000 students
nationwide, and they compared direct instruction with various programs
based on the same ``discovery'' philosophy employed by TERC and
CMP. Direct instruction methods proved clearly superior to all
``constructivist'' modes of instruction examined in this study. These
studies have been largely ignored by the education establishment which
showed, and continues to show, little interest in results counter to
their ``constructivist'' prejudices.
[2] Texts for a single grade level of the Singapore Curriculum cost
about $20. Further information about the texts can be found on the
internet: www.singaporemath.com Various U.S. organizations are working
to prepare versions of this curriculum that conform more closely to
U.S. grade levels; there is already a pretty close match for grade
levels K-6.
Response of Leonie Haimson
(Please see here for the Microsoft
Word *.doc original version of Leonie Haimson's reply)
I was asked by Elizabeth Carson to respond to your math survey, which
is attached. I am a public school advocate and consultant, and until
recently worked for the Educational Priorities Panel. More
importantly, I was a long-time public school parent, as my daughter
attended three public schools in D2 from K-6th grade. This fall, I
took her out of the NYC public school system, in large part because of
the inadequate math instruction she received in the public schools.
I would be happy to discuss further my concerns about the math being
provided by District 2. Please feel free to email or call me at the
number below.
thanks,
Leonie Haimson
124 Waverly Pl.
New York, NY 10011
212-54-1491
leonie@att.net
TERC, CMP, IMP
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None of the constructivist curriculum materials appear to be working well, and the TERC curriculum is particularly inadequate, as many D2 principals will point out if they're directly asked. This is evidenced by the dropping math scores at most schools - see particularly the precipitous drops in 2001 in the percentage of students at level 4 in the higher-achieving schools in the district. Both principals in the largest middle schools (Wagner and Baruch) are openly negative about TERC because they've seen the negative results at their schools; the Wagner principal opened a school tour two years ago by saying that ?CMP is not as bad as TERC.?
On a more personal level, my daughter's test scores dropped yearly from 3rd grade onwards, and by the end of 5th grade, she was scoring below grade level. After that, we spent the entire summer doing Singapore math, so that in 6th grade she did better. Nevertheless, I have now taken her out of the public school system, and the inadequate math curriculum was one of the two major reasons for this. (The other was the class size - 32 per class last year, compared to 16 this year.) This year, in 7th grade, she is doing algebra, and though she is still catching up, she is doing remarkably well - but only because we work with her extensively at home.
It is no wonder TERC has been so unsuccessful - and is so widely detested among most parents. As implemented in D2 schools, there is no textbook, no workbooks, no internal system of assessment, no way to remediate if students don't understand the material or are absent for a few days. The children never learn conventional algorithms and over the years have been discouraged from using these methods in class if taught them by their parents. The homework is often unintelligible to students and parents (even to me, who had two years of calculus in HS, and my husband, who has a Ph.D in physics and teaches science at Princeton.)
The process of teaching and learning with the prescribed methods are so time-consuming and confusing that teachers never cover much of the material (or ?units?) that they are supposed to - and the material covered, like fractions, percentages, etc., is so badly taught that most of middle school is taken up w/material that should be review. Moreover, the middle school curriculum is similarly indirect and inefficient, and students never get to learn traditional algebra, which is a necessity if they are to have careers in many fields that necessitate solid training in math. This is why the few D2 students lucky enough to get into Stuyvesant, Brooklyn Tech etc., need tutoring and have to be placed in remedial programs.
(For the importance of taking algebra in middle schools, see the NCES report "Coming of Age in the 1990s: The Eighth-Grade Class of 1988 12 Years Later" : [http://nces.ed.gov/pubs2002/2002321.pdf]:
?Taking algebra in eighth grade is for most students an indicator of both having strong skills in mathematics and preparing to take high-level mathematics courses in high school...There is reason to believe that the effects of high school course taking choices continue into the future and influence students' performance and persistence in higher education........Horn and Nuñez (2000). Mapping the Road to College: First-Generation Students' Math Track, Planning Strategies, and Context of Support. (NCES 2000-153). looked at the impact of algebra at eighth grade in NELS:88. They found that taking algebra in the eighth grade was associated with substantially higher rates of participation in advanced mathematics courses, even while controlling for mathematics proficiency and parents education... In turn, the rate at which students completed advanced-level high school mathematics courses had a direct bearing on whether or not they enrolled in a 4-year college within 2 years of graduating from high school. )
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The students in D2 are crying out for a math curriculum that balances understanding with fluency and provides enough practice in both problem solving and computation. Schools and teachers are now apparently being given more latitude to devise their own approaches by the District leadership, apparently because they realize the widespread dissatisfaction, but this leaves too many teachers on their own, without direction and the ability to adopt a better curriculum.
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District #
Instruction
See above. The instruction is constructivist, ?discovery-based?, which in practice leaves too many students (and teachers) confused and without the ability to do basic math.
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The students who were the most successful at my daughter's elementary school and tested highest in math were those who had teachers who had resisted the TERC curriculum and had resorted to smuggling in Xeroxes etc. of workbook materials that they had used in the pre-TERC era.
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See above.
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District #
Assessment
I don't know what these are and never saw them. If they are ?value-added? data - or data about individual students followed through time -- I never saw evidence of this at D2.
On a much simpler level, when I asked both my child's teacher and principal about what the different categories on the 4th grade (state) assessments indicated, because my daughter had tested high on some of them, but abysmally low on others, they had no idea what any of the diagnostic categories meant. I also tried contacting the relevant personnel at NYSED, who never responded. If these categories are provided for diagnostic help, they should be explained to both teachers and parents.
In addition, the state assessments, unlike the city tests, seem to mask some of the deficiencies of the elementary school curriculum and instruction, because computation and getting the right answer is less important on these tests. I imagine a District-wide analysis of the summary data of the 4th grade assessments, broken down according to some of these different categories, by someone who understands what they mean, might provide evidence of the specific weaknesses of the constructivist methods.
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None, as far as I know of. Especially in elementary school, there is no internal system of assessment. When I asked the district staff developer about this in 2001, she responded that they were still in the process of designing such a system, with the help of some experts from the Netherlands!
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Whatever new curriculum or method of instruction that is adopted needs to have its own internal assessment system, so that students can be tracked as to comprehension and fluency, starting in the first grade. Otherwise, there is simply no way that teachers and parents can ever figure out what it is that their children have or have not been learning, and no way to address these gaps.
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District #
Support Structures
I imagine for the students who are so behind that they are in danger of being retained (testing at Level 1), some extra help is given in the afternoon. I know that there is no assessment made before 3rd grade to identify these students in advance in order to give them additional help before this.
For students like my daughter, teachers never even identified her as needing more help, even after I had complained repeatedly that she was struggling, and even after she had dropped below grade level at the end of 5th grade. When I asked about how she could be helped, they suggested I hire a private tutor, which is the most common response, particularly among schools that serve a largely upper middle class clientele.
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Tutoring helps, but not as much as having good, solid math instruction in the first place, because it is too expensive to provide more than once a week, compared to the math they receive at school, which occurs every day.
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An entirely different curriculum and method of instruction needs to be provided. I found that the Singapore Math books are especially easy to use, inexpensive, and provide a good balance between understanding and computational fluency. There is a reason that Singapore students test highest in the world on math.
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District #
ELL Students
The constructivist materials are especially counterproductive with ELL students, because they based on verbal skills and the ability to read and write rather than compute. Their use also hampers many English speaking students who have natural strengths in numbers rather than words, and who traditionally have found math one of their best ways to excel.
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District #
Students with Special Needs
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District #
Family Numeracy
They give parent workshops in the evenings, ostensibly to engage parents and teach them how to help their children in the TERC methods. After three years of going to these workshops, however, I feel that they were really designed to blunt parent criticism by confusing them so much that they would feel stupid, and would feel that they had no right to protest because they really didn't understand math.
Over the years, D2 parents have organized a counter-movement with math professors at NYU and elsewhere (who could not so easily be made to feel that they too stupid to protest), to try to reach out to the District leadership with their parental and professional concerns, and to ask them to provide a more balanced curriculum. The District leadership has been openly contemptuous of this organization and their efforts.
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Many of the most-involved parents in D2 are fed up with TERC and want a significant change. There have been countless attempts to communicate this to the district leadership, who refuse to address these concerns. Instead of simply hosting more ?parent workshops?, the district should listen to the parents and institute a new curriculum in math, with a traditional textbook, workbooks, and a better balance between understanding and computational fluency.
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District #
Professional Development
There is a very expensive structure of professional development to train teachers in the TERC methods. My daughter had the ?school leaders? in TERC math for four years in a row - those teachers who had been trained in TERC and were supposed to reach out to other teachers to help train them in the methods. The result was that my daughter's test scores in math, and her ability to successfully do math, dropped steadily the longer she was in their classes.
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There needs to be an alternative that encourages and trains teachers in other methods than TERC and CMP - with a more solid grounding in basic math. I think teachers would welcome this, as many of them are as frustrated as parents with the constructivist training that the District provides.
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Professional Development
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?
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Response of David Klein
(Please see here for the Microsoft
Word *.doc original version of David Klein's reply)
Math Questions
District #
Curriculum
My name is David Klein. I am a professor of mathematics at California State University, Northridge, and a national advisor for NYC HOLD. I have been asked by Elizabeth Carson to respond to this questionnaire. Some of my answers are based on my experience as a full time consultant and trainer for the Los Angeles County Office of Education during a 12 month period beginning in July 1999.
In Los Angeles Unified School District (my local school district), California state approved math books are used in K-8 in accordance with CA state policy. At the high school level, textbooks for Algebra I, Geometry, Algebra II, precalculus, and beyond are selected by local school districts largely on the basis of their alignment with California's rigorous and demanding mathematics standards.
More specifically, in grades K-5 in LAUSD, two series in wide use are Scott Foresman CA Mathematics Copyright © 2001, and Harcourt Math Copyright © 2002. Other California state adopted programs used by districts in the state are listed at: http://www.cde.ca.gov/cfir/pl/math/math2001pub.html (For a concise listing, see also: http://mathematicallycorrect.com/adopt.htm)
Three textbook series are in wide use at the middle school level in Los Angeles and throughout California. These programs are listed at: http://www.csun.edu/~vcmth00m/mmath.html
Detailed evaluations by a committee of mathematicians appointed by the CA State Board of Education are also available at the above site. Many high schools use textbooks that are part of a series of books that begin with the middle school texts listed at http://www.csun.edu/~vcmth00m/mmath.html.
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Student achievement has increased significantly in California with the classroom use of state approved math books. The site below provides a useful data summary, following cohorts of students from 1998 to 2002.
http://www.cde.ca.gov/statetests/star/charts/2002math.pdf
More detailed data is available at: http://star.cde.ca.gov/
Because of the hierarchical nature of mathematics, and the strong dependence at any grade level on prerequisites, the greatest gains have been made by students who were in elementary school starting in 1998. This is because those younger students have benefited the most from coherent and structured instruction in mathematics.
Curricular materials that claimed alignment with the National Council of Teachers of Mathematics (NCTM), such as MathLand, TERC, Quest 2000, Connected Math, IMP, CPM, and others of this type left California students poorly prepared and resulted in state policy changes currently underway.
At the high school level, data for Los Angeles students indicates that students of all backgrounds fare better under classical mathematical treatments rather than the so-called integrated programs. This data is available at: http://mathematicallycorrect.com/la.htm
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I was commissioned by the Brookings Institution to write a report on Los Angeles elementary schools successful in teaching mathematics. That report, High Achievement in Mathematics: Lessons from Three Los Angeles Elementary Schools, will be published in the near future, but it is currently available at: http://brookings.org/dybdocroot/gs/brown/bc_report/2000/LosAngeles.PDF
This report identifies policies of schools that contribute to higher achievement in mathematics, with particular attention given to the role of the principal of the school. Also identified are policies of school districts that impede mathematics achievement.
It is particularly important for school administrators to identify successful, and mathematically knowledgeable teachers to serve as mathematics education advisors and coaches. It is all too typical for mathematically weak teachers to be placed in such positions as a reward for their willingness to follow education fads. This tendency is discussed in the above referenced report. It is a matter of great importance for student achievement in mathematics.
I also suggest the abandonment of weak mathematics programs such as TERC and Connected Math. These programs have been strongly criticized by mathematicians across the country for lack of intellectual content, including lack of basic skills development and poor explanations of mathematical concepts.
A number of better programs are available. Among these are the California approved math books and the Singaporean math books. Singapore was the top ranked nation worldwide for mathematics achievement of students, and the textbooks used there are excellent.
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District #
Instruction
Los Angeles Unified School District is so large that there are many different kinds of instructional strategies. However, in recent years and concomitantly with rising test scores, there has been a greater focus on direct instruction and teaching coherently to the state standards.
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Please see my responses to questions above.
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Discovery learning in mathematics can easily interfere with coherent instruction. It is time consuming and inefficient at best. In the hands of teachers who don't have absolute mastery of the subject, discovery learning projects can cause educational damage to children.
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District #
Assessment
I'm not qualified to answer this question.
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I'm not qualified to answer this question.
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One of the dangers of assessment is doing it too often. Too many assessments takes time away from instruction. An even greater danger is that poorly designed assessments can drive instruction negatively. Assessments should focus on knowledge of mathematical content, facility in calculation and problem solving. Unfortunately, some faddish project-oriented assessments focus on the process of problem solving and include poorly worded, open ended questions.
The California STAR exam is an example of a good assessment. Achieve, Inc. also has some good sample problems for middle school students.
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District #
Support Structures
The basic strategy in Los Angeles is to try to help students complete Algebra I starting in 8th grade. For struggling students, Algebra I is stretched out as a two year course (whereas for other students it is a one year course). Struggling students are identified by test scores and grades.
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The strategy described for the previous question does not work well. The main reason students have difficulty with algebra is that they never learned arithmetic properly. Teaching the algebra at a slower rate without the arithmetic prerequisites does not succeed for obvious reasons. Unfortunately, ideology drives this policy much more than common sense. The goal of "algebra for all" by 8th grade sounds good, but it is essential to provide the prerequisites for algebra before students study algebra. The district is providing elementary school students with those prerequisites now, but a generation of students, now in middle school and high school, were deprived of essential arithmetic skills when NCTM style math programs like TERC, Connected Math Project, MathLand, Everyday Math, etc. were imposed on teachers.
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An excellent resource for struggling students is the Saxon Mathematics series of textbooks. While the Saxon books are used in some elite private schools for high achieving students, those books are particularly helpful to struggling students because of the constant review imbedded in the exercises. The Saxon mathematics program includes materials specifically designed for struggling students.
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District #
ELL Students
I'm not qualified to answer this question.
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I'm not qualified to answer this question.
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I'm not qualified to answer this question.
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District #
Students with Special Needs
I'm not qualified to answer this question.
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I'm not qualified to answer this question.
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I'm not qualified to answer this question.
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District #
Family Numeracy
I can provide only limited information on this question. Parents are expected guide their children to do homework assignments. In some cases, including assignments for students in gifted classes, homework projects are extensive and of necessity involve parents for procurement of materials to complete assignments. This is more often the case in science classes than math classes.
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There are approximately 20,000 homeless children who are students in Los Angeles Unified School District. A child's capacity to deal with homework is partially dependent on circumstances in the home (or lack of a home). While homework is an essential part of mathematics education, aimless projects can cause great distress and damage for these children. It is important that basic skill instruction be addressed during class time and not relegated solely to parents.
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I have no response for this question.
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District #
Professional Development
My comments on professional development appear in response to question 3 below.
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My comments on professional development appear in response to question 3 below.
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Most professional development programs for math teachers are of such low quality that they can cause more harm than good. When teachers are directed to use poorly designed discovery learning methods (as is typical), it is the students in the end who are harmed. Professional development is best focused on mathematics content for teachers, rather than on pedagogical fashions popular in education colleges. Using sound textbooks can go a long way in providing teachers with stronger content knowledge. One reason for poorly designed inservices for teachers is that the designers/coordinators of the inservices are often mathematically incompetent. For further explanation on this phenomenon, see
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Professional Development
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?
I do not know the answers to these questions.
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I do not know.
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I do not know.
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I do not know.
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Response of Christine Larson
(Please see here for the Microsoft
Word *.doc original version of Christine Larson's reply)
November 13, 2002 Evan Rudall, Manager Children First Numeracy Working Group NYC Department of Education Dear Mr. Rudall: I have completed a copy of a math survey developed by the NYC DOE's Children First Numeracy Working Group distributed to certain members of NYC-HOLD by Elizabeth Carson. It is attached to this e-mail. Please excuse the tardiness of response. I am a parent of two children who have attended CSD#2 primary and middle schools, respectively. My younger son is now in a CSD#2 Middle School, my older son now attends Bronx High School of Science. I was actively involved in my sons classrooms in the early grades, an officer of my sons' elementary school PTA, and that PTA's representative to CSD#2 Parents Council, for a few years in their later elementary years. My sons attended the primary school which piloted use of both Marilyn Burns' materials and TERC. I have been fortunate in that I have been able to erratically, though substantially, supplement my sons math education - through financial investment in tutoring and through working with them in home-schooling math programs. I am a co-founder of NYC-HOLD. I became involved in the issue of CSD#2 math curricula as a result of at least four things. First: I became aware of district policies through my involvement in the C37 process necessitated by Tony Alvarado's departure to San Diego. Second: I became aware that the vast majority of parents became disenchanted with their child's CSD#2 math education around the 4th grade. Third: I recognized that my sons, though deemed competent math students, not only were at least two years behind their cousins in other school systems, they also struggled with what I considered simple math calculations. Fourth: I was haunted by the extreme frustration and discouragement my older son was experiencing with CMP. And, finally, I was acutely aware of the fact that I (similar to many other parents in the well-off area in which I live) could ensure my children's success through heavily supplementing their math education while most parents whose children are subjected to TERC, CMP, ARISE, etc., in the public system could not similarly redress the math curricula failings for their children. I maintain full-time, paid employment as a budget analyst so I have some facility with simple arithmetic and spreadsheets - and some sense of the everyday uses of math. Thank you for this opportunity, Christine Larson
Math Questions
District # 2
Curriculum
In CSD#2 the elementary curriculum is TERC (?Investigations in Number, Data and Space?), ?supplemented by? materials such as those developed by Marilyn Burns (e.g., Math-in-the-City), the Middle School curriculum is CMP (Connected Math Program) and, the high school curriculum, in the CSD#2 high schools, is ARISE (?Mathematics: Modeling Our World?).
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To my knowledge these curricula are not working as materials for teaching math. Student Achievement Data at the higher scoring schools is deceptive as a measure of the effectiveness of these curricula for a few reasons not least of which is that, at the higher scoring elementary and middle schools in CSD#2, such as PS234, PS6, Upper Lab, Wagner, etc. - a vast number of parents supplement through outside tutoring and/or use of home-schooling curricula and/or commercial workbooks. Such supplementation invalidates the such scores as indicators of program effectiveness.
These curricula do not provide coherent and explicit instruction in math nor require necessary practice in key math skills. Such curricula waste time on peripheral activities. Further, they rely too much upon students' facility with language such that, particularly in the higher grades and for those with less facility with words and written expression, an excess of effort is exerted on describing how one ?solved? a problem or the steps one took in an exercise. Time is then required of the teacher to parse the written work and, hopefully, determine whether the math content has been grasped. There is insufficient time to evaluate students work given the amount of written material and - in some cases - weeks go by before students work is checked undermining the value of such work for the timely accretion of student understanding.
In supplementing my children's math education I've found, in grades three through six, Saxon materials have been helpful as they are explicit and easy to follow. I have looked at the Singapore Math textbooks and would endorse their use as a comprehensive K-12 curriculum - however, because the Singapore Math curriculum is much more advanced, it could be used only if it were introduced in the early grades and taught by persons with adequate math knowledge. I've found the California's list of adopted programs useful as a guide (see: http://www.cde.ca.gov/cfir/math/2001adpr.pdf or http://www.cde.ca.gov/sfir/math/ab2519adpr.html).
I would endorse programs in which the concepts and skills are taught explicitly and practice is required. ?Discovery? activities should be extensions only of a sound, basic program.
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I am not sure I understand the question but I am assuming that the question goes to the matter of how one would ensure a unified PK-12 math education for students in the NYC public schools.
First: a coherent set of measurable objectives and content standards should be established Citywide. The California framework is useful as an example of such content standards as it is explicit and understandable (see: http://www.cde.ca.gov/board/pdf/math.pdf). These standards should be developed by a team consisting primarily of those who understand math content (i.e., mathematicians) with assistance from those who are expert in PK-12 instruction (i.e., PK-12 teachers with extensive and diverse teaching backgrounds), PK-12 math instruction (i.e., grades 6-12 math teachers with diverse math program backgrounds) and those who are expert in child development (i.e., parents). It is probably also necessary to involve those from the education schools though PK-12 instructors are preferable as they know what works.
Second: identify PK-12 programs that align with the standards and implement those programs Citywide. Make sure such programs use textbooks which can be used as reference materials and for review purposes in children's homes - it is absolutely crucial that parents are involved in their children's educations.
Third, and as part of the implementation effort, strengthen math content knowledge of teachers - possibly through instituting centralized (given the Tweed building is such a lovely facility) math content ?refresher? courses for teachers by grade. |
District #2
Instruction
Primarily some approximation of ?discovery? learning as dictated by the identified curricula. |
Achievement improves and children's sense of their own skill development grows (which enhances ?self-esteem?) as a result of directed practice. With these curricula, this sense of achievement and skill development generally occurs only during directed test preparatory sessions for the NYC/S Assessments - i.e., during direct instruction and practice on explicit math content.
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Discovery learning consumes too much time and does not, contrary to its claims, provide the ?opportunity? for students to develop a ?deep? understanding of the concepts the discovery exercises are purportedly intended to develop. Further, and as noted above under ?Curriculum, Question 2,? much of the written work is not helpful in advancing understanding and competence as too much effort is expended on writing without adequate review and critique by the teacher of what was written (and thus what was understood) and insufficient effort on math content.
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District #2
Assessment
Don't know.
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Not sure.
In elementary school and, in one case, middle school, my children's quarterly reports were broken down by specific performance standards - a few of which addressed math content. I am not sure what ?data? was collected to assess student achievement according to these standards as tests were rarely administered. It seemed that class work - which constituted a math portfolio of sorts - and the children's regular self-assessments were the primary sources for teacher assessments of student achievement.
Middle school tests are more frequent but I think assessment continues to be much like what's noted above.
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Math content and skill tests should be administered frequently and graded promptly. (Homework also should be reviewed promptly.) Parents/guardians should be made aware of test performance, possibly through having to sign tests or periodic test reports.
My older son is now at Bronx HS of Science and is thriving under direct instruction, regular homework and tests. He appreciates being able to evaluate his progress through the results of his efforts rather than reflection on his efforts.
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District #2
Support Structures
In some cases, after- or before- school sessions have been used.
Not sure how ?struggling? students are identified.
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The sessions considered most effective by parents I know were those which briefly utilized direct instruction rather than extensions of the discovery program - such sessions were short-lived in the one circumstance I'm aware of.
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As noted through-out, explicit instruction in math content, regular practice and regular content tests, appear the most effective strategies in improving the performance and understanding of all, and most especially, struggling, students.
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District #2
ELL Students
Don't know.
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As I don't know what's used, I don't know what's effective though I would think that ELL students would benefit greatly by explicit instruction of math content, regular practice and regular tests.
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Literacy, discovery based instruction does not work - for obvious reasons. At least one of the previously better performing schools in Chinatown has drastically deteriorated in its math performance since the introduction of the noted curricula.
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District #2
Students with Special Needs
Don't know.
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Don't know.
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Don't know.
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District #2
Family Numeracy
CSD#2 does not ?engage? with parents: it allows parent involvement only where such involvement is limited to supporting the district's implementation of TERC, CMP, ARISE.
Supposedly, parents are ?engaged? in the following ways:
CSD#2 Math Office helps schools in running Math Nights which generally are occasions in which a representative from the Math Office undertakes a public relation exercise in which he/she gives a talk, supposedly on how the district chose these math curricula, tells the parents they will not understand what their children are learning, and then breaks the parents break up in to groups to ?experience? what their children experience in a ?discovery learning? exercise. These nights sometimes involve the distribution of some Math Games, articles on the advantages of Constructivist teaching, and, in the past, copies of what was the BOE ?What Your Child Learned...? pamphlets (i.e., a listing of the math skills and content knowledge expected by grade).
In elementary school, parents are ?discouraged? from engaging in their children's ?numeracy? development through parent letters which implicitly (or, in some instances where schools write their own letters, explicitly) discourage parents from teaching their children traditional math (e.g., algorithms) and encourage parents support of their children in whatever exercise is assigned. Parents are periodically encouraged to play games with their children without adequate information as to the underlying concepts the game reinforces.
Please see the ?Parents? section of the CSD#2 Math Office website http://www.nycenet.edu/csd2/math. You will note that it is primarily a PR piece on the curricula.
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None of the noted strategies are successful in productively engaging parents in their child's math education and sound ?numeracy? development. These strategies are sometimes effective in making parents of children in the early grades believe that said parents do not understand math, thus cannot help (and should not try to help) their children and the programs implemented are creative outlets for their childrens innate ?math? abilities. As the children reach the higher grades, though, parents who are able - who have the time and knowledge and/or money to pay for tutors - ignore the school's advice and supplement their child's math education.
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Parents regularly question the soundness of the curricula, the opaqueness of assignments, the frustration experienced by their children and themselves in that they are unable to assist, etc. The district does not address the issue as family math knowledge and substantive parental involvement appears to be anathema - these curricula are protected ?black boxes? beyond parental comprehension and ability.
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District #2
Professional Development
CSD#2 has a Math Office which appears to focus its effort on improving teachers' instructional practices. These sessions may improve teachers' use of the noted curricula; however, such sessions do not improve teachers' math knowledge so if math education is the issue here the staff development is not effective.
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The most pressing math education staff development need relates to math knowledge and curricula that teaches math content and develops math skills. Many of the teachers - even the more generally effective teachers - have insufficient math knowledge and staff development sessions should address knowledge deficiencies. Curricula should set forth the content to be taught.
Few if any of the Math Staff Developers in CSD#2 have degrees or even training in mathematics - or, even, mathematics education.
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Not sure I'd recommend increased time, funding and access to space as I am unaware of the current resources - many of which currently may not be used effectively (e.g., as in CSD#2) so simply to increase such resources is not necessarily sensible particularly given the substantial budget cuts faced by the DOE.
Professional development should focus on math knowledge and could be undertaken centrally. Locally, mentoring by master teachers and in-school meetings amongst teachers within grades, possibly could address matters of instruction.
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Professional Development
How many mathematics specialists/staff developers are in your district at the elementary school level?
Not sure. The Math Office website lists 18 staff developers and 4 administrators. I haven't been keeping track. This is an area in which I am ignorant.
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?
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Don't know.
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Don't know though many of them, in CSD#2, were, at one time, elementary school teachers at PS234. Instructional practices in discovery learning, not mathematics, seem to be their expertise.
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Don't know.
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Response of Denise Matava Haffenden
(Please see here for the Microsoft
Word *.doc original version of Denise Matava Haffenden's reply)
Mr. Rudall: I am attaching the survey you sent to Elizabeth Carson through Kristen Kane. She also asked that we send a short bio. Denise Matava Haffenden 7 Peter Cooper Road NYC 10010 212.260.6453 I have worked in the Board of Education for the last 23 years. I hold an undergrad degree in art and elementary education, my speciality being math, and a masters in guidance and counseling. For the last 14 years I have been an educational evaluator in Manhattan HS. My home base is LaGuardia HS, but I work in a variety of District 2 high schools and Alternative HS sites. This has allowed me to see many changes going on involving curricula and environment. In addition, I have taken my son out of public school based on extremely low standards in one of the higher ranked districts (District 2) Hope the survey helps. Denise Matava Haffenden
Math Questions
District # 2
Curriculum
District 2 has mandated TERC in elementary school, CMP in junior high school, and ARISE in high school. These programs are not considered college preparatory by Levy's Math Commission.
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According to TIMS, Singapore's curriculum put that country first in the world in mathematics. I have used Saxon and Addison Wesley, in a supplementary way to Singapore math curricula books and had excellent success with students in Chinatown Saturday cram schools. I know that the students who come out of District 2 math programs are not succeeding based on my job as an educational evaluator for Manhattan HS. I very often receive referrals for students who are considered "learning disabled" in math (as well as writing or phonics) when the problem is they were never taught math in the first place. At LaGuardia HS, where I do special education evaluations, referrals regarding math has increased significantly and usually these students have been exposed to non-traditional methods of math instruction (not learning division for example)
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My first suggestion would be the banning of grants to place curricula in the schools. District 2 has made curricula decisions based on how much money they receive as opposed to the success of a curricula. This reliance on money fosters lack of communication and defensiveness on the part of the grantee's.
While I am against strict adherence to one curricula (based on the one size fits all), I do believe that we must ensure that all students, especially in the early grades, be taught traditional, universal methods for approaching math. In addition, trying to fit special education students into a "one size fits all" approach goes against the philosophy of IDEA.
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District #
Instruction
As an educational evaluator who travels to at least 20 different schools, I notice that collaborative teaching is more the norm than in the past. I find that this means, if the teacher is not interacting with a group of students, then they are usually gossiping. When the teacher gets close to the group, they go back on task. I find many of the classes are chaotic and unfocused and often students leave a class not knowing what to do. Since many teachers are newer teachers, these are the people least able to control a class and work in groups. Schools, such as LaGuardia H.S. and some alternative schools (Satellite Midtown) rely more on lecture and discussion in communicating information.
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As said previously, I don't believe collaborative teaching works, especially with students who are deficient in skills as well as teachers who are new to the profession. Discipline, focus, organization are all put on the back burner in place of carrying out a philosophy that does not allow students to learn. Many students cannot concentrate in a noisy environment, others don't have self motivation. And others, rely on others work, because they get a group grade rather than individual merit.
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District #
Assessment
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In my experience, as both a parent of an elementary school student, as well as an employee of the Board of Education, they rely totally on NYS and NYC assessments. Tests given by teachers are not usually graded, rather having comments or evaluations which are high subjective and difficult to compare.
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Use grades so that teachers and students have a more objective way of judging performance. Also, portfolio and subjective assessment allows for too much flexiblity and not enough information about how the student is really performing. Each individual teacher is allowed to use their language to convey the same and different ideas, which makes it difficult to compare students and organize information.
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District #
Support Structures
It appears to me that support services tend to be more of the same curricula, rather than using different approaches. When students don't respond well to more of what is being done in the classroom, then they are referred for special education, as if it is the student' fault, rather than the choice of curricula and teaching methods.
I have noticed that students referred for resource room, tend not to be learning disabled rather they don't respond to the approach that has been chosen by the District. Then the resource room uses more of the techniques and curricula mandated by the District, and wonder why the student doesn't learn. In contrast, some students in the resource room do very well because of excessive test modifications that don't fit their disability.
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Use a more traditional, structured curricula that focuses on basics.
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District #
ELL Students
With the new guidelines governing LAB scores and category X, much is being done to ignore the plight of students with bilingual issues.
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District #
Students with Special Needs
The insistence of moving away from the IEP and issuing waivers for inclusion has diminished much of the support structures available to students. The guiding factor is, once again, "one size fits all" which is in direct violation of IDEA. In addition, students from higher performing schools are using the special education support services and 504 to ensure extra benefits to those students who are performing average or above, with no disabilities. Special education services have deteriorated significantly in the last three years, especially the erosion of separate location resource room and the elimination in most schools of self contained classes.
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I know inclusion for most learning disabled students doesn't work, because they miss what they're learning in class, feel different and on the high school level, don't use it or can't benefit from it. At one school, Legacy HS, students who are quite handicapped and are functioning on very low elementary levels (Grades Kindergarten through fourth) are sitting in regular mainstreamed classes, as an example of a working inclusion program. In most of the schools I enter, only one or two have resource room scheduled as a separate class, so that students do not miss regular classes. I rarely see an IEP that is followed by the Board of Education anymore. Everything involves waivers and inclusion.
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District #
Family Numeracy
If you agree with their methods, they will engage you. If you don't you are labeled crazy and ignored.
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Parents use to go to school board meetings and raise their concerns. Most have stopped at this point and taken their children out of the public schools or, if not possible, use private tutoring to do what the district doesn't do. My district should stop being forced to dance to the grantor's rules and pick curricula based on its worthiness and sound, scientific research, not research done by the curricula publishers or endorsers.
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District #
Professional Development
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Professional Development
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?
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They receive training by the curricula supporters rather than traditional mathematicians. In addition, up until this year, our Director of Mathematics in District 2 had no degree in math, but was a theatre major. It was a very good act!
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Response of Mike McKeown
(Please see here for the Microsoft
Word *.doc original version of Mike McKeown's reply)
Evan Rudall Manager Children First Numeracy Working Group Mr.Rundall, Enclosed are my responses to your questionnaire on mathematics education, as transmitted to me by Elizabeth Carson. I am a Professor of Medical Science at Brown University in Providence, RI. I am also vice-chair of the Molecular Biology, Cell Biology and Biochemistry Department and Director of the Molecular Biology, Cell Biology and Biochemistry Graduate Program. I have used my college mathematics in scientific publications, in particular, I have used differential equations to model a biochemical process as a way of designing the most sensitive possible experiments. I have been actively involved in mathematics education issues since my older, twin children were in seventh grade. They are now juniors in college. I am a co-founder of Mathematically Correct, and have reviewed elementary school, middle school and algebra textbooks. Some of these reviews are listed in my response. I was part of the committee that wrote the California Mathematics Program Advisory. I was an active member of the committee that wrote the San Diego Mathematics Standards. I worked on the early stages of writing the California Science Standards. I was an active consultant to a member of the California Standards Commission during the time when the California Mathematics Standards were written. I have been invited to speak on math issues in a number of venues. I was flown to Washington, DC by the US DOE to discuss mathematics education with then Education Secretary Riley. I was twice an invited speaker at the Education Leaders' Council annual meeting. I was named an Unsung Hero by the Center for Education Reform. I recently gave the lead talk in a discussion on math education at the American Enterprise Institute. I refer to data from my presentation in the attached text. In addition, my wife was a mathematics major at the University of California, San Diego who went into math teaching and tutoring. She has seen students from schools throughout the San Diego and Providence areas, and knows how students do with a wide array of curricula. My comments include her insights. Thank you for your time, Michael McKeown, PhD Molecular Biology, Cell Biology and Biochemistry Box G-J363 Brown University Providence, RI 02912 401-863-9807 FAX 401-863-1348
Math Questions
District #
Michael McKeown, Ph.D
Professor of Medical Science
Molecular Biology, Cell Biology and Biochemistry Department
Brown University
Providence, RI
Curriculum
The district in which I live uses Chicago/Everyday Math for K-6 and the UCSMP Transitions series for 7 and 8.
Providence City Schools uses TERC/Investigations in Number Data and Space for K-5 and Connected Math for middle schools.
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My son has used Everyday Math and Transitions, and I my wife, a long time math tutor, have examined these in detail. The K-6 Chicago program does a poor job of building essential mathematical skills, especially those that give a clear understanding of the place value system. In particular the methods used, e.g. lattice multiplication, obscure rather than clarifying the power of the decimal system for mathematical problem solving. The favoritism toward unusual, invented or non-standard methods robs students of valuable understanding of general methods and of valuable skills that generalize in later mathematics. My wife tutors students stuck in this program and reports that they have all the difficulties mentioned.
Transitions is mixed program. Some aspects of it have appropriate content, but it fails to explain how to do anything, including key concepts and methods such as solving equations by transformation. In many cases, there will be a relatively simple set of problems and then a giant leap to a problem of much greater difficulty without covering the any of the missing and essential steps in between. The books also suffer from an alteration of good, important content (e.g. building the skills in fractions, decimals, percents and exponents, plus introduction to the analytical methods of algebra), with relatively unimportant or even stupid lessons that are neither important educational end points nor necessary building blocks for later learning. Because of errors such as this, this program is extremely dependent on the teacher. A teacher who is highly knowledgeable about mathematics and where things are going in the future can pick what is important and ignore what is not important. Other teachers, especially the mathematically weak, will fail to include what is important and do the unimportant instead. My wife tutors a number of students using this program and must often make up for the deficiencies in the book and the teacher errors that it encourages.
I have examined and reviewed the second grade TERC and looked at other grades as well. I have examined and reviewed the seventh grade Connected Math Program and carefully examined the grade 6 program.
TERC is the single worst math program I have personally examined. There are few content goals that are clear to an outsider, and there is little real content, period. The only explicit teaching is as to how to use a calculator. There is no development of skills, nor is there development of logical clarity. Further comments can be found at http://mathematicallycorrect.com/books2f.htm . Based on what is covered in these books, it is virtually impossible for a student to succeed in mastering algebra or any course requiring post-algebra mathematics. The only option for children who use this book without a complete supplementary course at home or from a tutor is to give up any hope of a science or engineering career. Schools can hide this with watered down courses, but they can't change the fundamental problem. If further evidence is needed, TERC was one of the most highly rated programs in California from 1992 to 1998, when California adopted high level, clear, grade by grade mathematics standards, in part in backlash to the excesses of TERC and other similar programs. Now it is off the state approved list.
Connected is better than TERC, but that is judging the quality of different cancers http://mathematicallycorrect.com/books7a.htm . Some appropriate topics are in the program, but careful examination reveals that coverage is at a very low level, mastery is not required, and skills are not built. Even when it seems that students might need to understand and apply some concept such as arithmetic with signed numbers, the seeming sophistication disappears when one realizes that all calculations are done with calculators such that the only skill needed is to punch in the numbers in the right order. |
Adopt a coherent set of explicit, grade-by-grade set of standards in which the material of each grade grows in depth and complexity from year to year with clear connections between years. Especially important is directing the K-7 curriculum, above all, to preparing students for algebra, and then teaching algebra courses that stress the powerful analytic and problem solving concepts and techniques of algebra. The best public example I know of for this is the California Math Standards. Other sets of standards, notably the NCTM Standards (PSSM) and the New Standards Performance Standards, fall short in terms of content-specificity, grade-specificity, emphasis on analytical methods, and reliance on a particular, and not well supported, instructional strategy.
Once good standards are chosen, use books closely aligned to the content of the standards. For K-8 math, California has done exactly this.
Note that bad standards and bad exams drive bad instruction. My home district and state use the New Standards Reference exam. This stresses invented methods and wordy essays rather than broadly examining student skills and knowledge. Districts are now buying teach to the test booklets (Exemplars), to teach students the particular types of problems favored by New Standards and, at least as importantly, to make them realize that good grades depend on essays of a particular wordy style, especially if accompanied by something other than an effective but standard methods. |
District #
Instruction
Chicago and Transitions are a mix of relatively poorly designed discovery learning methods and some direct teaching, especially by better teachers. The long period spiral of Chicago weakens the program as students never master anything, and thus must redo second and third grade stuff in fifth and sixth grades. As noted above, about half of Transitions is relatively poorly designed and misdirected material which is mostly done by discovery. Other parts, even with good content fail to teach students essential skills or expect them to make unreasonable leaps.
TERC is a disastrous mix of discovery learning methods, and a draconian insistence on not using or learning standard methods.
Connected is also dedicated, almost exclusively, to discovery learning. This leads to a failure to discover many of the important aspects of pre-algebra and real problem solving.
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As part of a conference on mathematics education, I looked into high performing schools that have a high proportion of at risk students < http://www.aei.org/past_event/mc.pdf >. I used the Education Trust's search engine < http://64.224.125.0/dtm/ > , and looked for high minority, high poverty schools that score as well or better than 75% of the schools in their state. I chose California because of the large data set (large population, many schools, students are tested every year, etc.) Four schools are at the top:
School %AA+H % poverty Relative Rank Kelso, Inglewood 98 86 83
Bennet Kew, Inglewood 98 74 77
Robert Hill Lane, LA 93 97 75
Payne, Inglewood 98 91 75
Year SAT9 98 99 00 01 Scores in percentile Kelso 3 66 78 82 84 4 64 77 69 75 5 67 74 73 67
Bennett-Kew 3 80 84 83 86 4 57 69 65 73 5 54 49 58 69
Lane 3 62 71 72 78 4 40 64 64 68 5 53 56 67 65
Payne 3 55 78 76 79 4 43 61 67 66 5 44 51 57 68
All of these schools use favor teacher directed, whole class instruction, with an emphasis on mastery. For at least part of the time, some of these have used, with success, Saxon Math. During the period of TERC ascendancy, at least Kelso and Bennett-Kew used older Silver Burdett programs. See also
This emphasis on direct teaching and mastery helps students to master the material they need to solve problems, and indeed, direct teaching in terms of how to deal with different types of problems also strengthens student skills in solving other problems.
California has switched to content rich books in recent years and has seen an improvement in student mathematics performance. To some extent, the level of improvement has been held back by districts fighting to continue bad practices, but improvement is happening.
I have personal experience with the Saxon program as it is what we have used to make sure our youngest child gets the math he needs even if the district uses Everyday and Transitions. As a tutor, my wife recommends it to parents who ask for a book that works well for building the kinds of knowledge and skills not covered in current school math programs. The instruction is clear, the lessons are well structured and the homework is designed, over time , to build mastery.
In addition, at one point our older twin children found themselves in a discovery learning, watered down algebra/geometry program called College Prep Math. To make sure that no permanent damage was done, she taught both of them Algebra and Geometry. The book of choice of Algebra was Dolciani, Structure and Method, which was one of the top two books in our review of Algebra I texts < http://mathematicallycorrect.com/algebra.htm >. The Foerester Algebra I should work as well, but may not be in press any more.
My wife, working as classroom teacher and as a long time tutor has seen students from many public and private schools in San Diego County, California as well as from many schools in the Providence, Rhode Island area. Students using high content books with clear instructions and clear examples come to her with better skills and problem solving ability than those who are in alternative discovery learning programs. As she has long noted, students come to her either to turn a B into an A, or a D/F into a C. In either situation, the students who come to her from a content rich course are better off than those coming from a discovery learning course, such as TERC, Connected, College Prep Mathematics or any others.
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Discovery learning, exploratory math courses have less content, covered in less depth to lower levels of mastery. They work less well. Programs like the Integrated Math Program (IMP) have a record of failure when evaluated independently. It has reached the point where the authors/publishers won't give outsiders a list of schools using the program.
TERC, MathLand and related programs were dropped by California as soon as rigorous content standards were adopted. Students using these books could not learn the content, because it was not there.
College Prep Math and its ilk left many Californians ill prepared. The state math exams are broken down into subject-specific tests at the high school level. There is a ?traditional? order set of tests and an ?Integrated? style set of tests, each with the same content, although parts are differently arranged. Comparison of Traditional school scores and integrated math school scores shows a consistent advantage for traditional schools.
Students with high ability do not develop their potential, and those who have weak mathematics aptitude simply get nothing of any value. They are left helpless.
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District #
Assessment
NA
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Adopt clear, high, grade-by-grade standards such as those in California. Get a good nationally normed test and write a separate test that covers, broadly and in depth, the material of the standards for each grade. Test each student on each test every year. Breadth and depth of testing across the standards, plus fairness and rapid response probably indicate the need for a machine scored, standardized test. Other forms of assessment for diagnosis and checking student progress on a regular basis can use other methods as well.
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District #
Support Structures
Don't know
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Bennett-Kew, noted above as a high performing at risk school, regularly assesses students relative to its own internal standards at least once a month and begins remediation as soon as a student falls behind. The principal knows where each student stands relative to the standards each month.
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Direct teaching, focus on building toward algebra in grades K-7 or 8. Use effective textbooks. Hire teachers who know mathematics and where it is going, even at elementary grades. If necessary, use math specialists to do all math teaching.
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ELL Students
Providence probably follows a discredited Bilingual Ed approach, but I am not sure.
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Some recent evidence suggests that the best thing to do is to teach kids English immediately, then teach them math in English. This has been reported in a number of newspapers in response to ballot measures dealing with Bilingual Education.
Then move on the effective strategies discussed above.
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Students with Special Needs
Don't know
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Don't know
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Don't know
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District #
Family Numeracy
The districts I am familiar with have family math nights, not a one of which has been worth a second of my time.
Districts are relatively uninterested in parent input with respect to math teaching. Indeed, San Diego has become downright hostile to comments from parents and teachers. Providence has that reputation as well.
It is now common for teachers to tell parents that math is different now so the parents should not try to help or teach their children any math. Indeed, I was once told by a teacher that nobody uses the math I regularly use in my lab. The strategy of making math seem too esoteric for parents certainly solidifies the teacher/school position in implementing TERC-like programs, but does not help the child actually learn math and creates great friction at home, particularly if the child has trouble with any one of the ill designed lessons.
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One thing that would help immediately is to use math programs with MATH BOOKS. Something tangible and solid that parents and children can read, together or apart, with clear descriptions and summaries as to what the student was to have learned, what the conclusions are, what the big picture is, and how to do problems.
Districts and teachers can stop telling parents that teaching the children math at home will only interfere with their building `conceptual understanding' and learning the new math for the modern world.
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Parents raise many issues and the response of administrators involves first trying to convince the parent that there is no problem, the parent just didn't quite understand what was going on. The next is deception, to try to convince the parent that an apparent problem is really a case of agreement once we redefine various elements of the complaint and play on the parent's desire to be friendly. Next, if the parent still has a problem, the plan is to discourage the parent to the point where he or she gives up.
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District #
Professional Development
Most professional development in Providence is directed at implementation of TERC and Connected. In my home town, it is toward using the Exemplars, which are teach to the test practice for the New Standards Exam. Teaching TERC well is not teaching well, so those programs are not effective. Most of the Exemplars training sessions are loathed by teachers and viewed as yet another waste of their time outside of classrooms.
An additional kind of in service is to bring in an outside consultant, most of whom are cheerleaders for discovery learning methods. An example of the work of one such snake oil salesperson, and the flaws in what she does, is at http://www.intres.com/math/turkey.htm .
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Mathematically knowledgeable teachers, at all levels. Elementary teachers should be competent, now, at the level of Algebra I, at least. If they can't do real algebra, they can't know where the K-5 math they teach will lead.
Middle school teachers are particularly weak relative to the level of math they need to teach. Many have moved up from a general K-8 credential rather than having a single subject math credential. The consequence of this that they do not know where post Algebra math goes and in fact are not necessarily that great with algebra. No clear path the college math and science in the teacher's mind means no clarity on what is really needed.
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Make sure teachers know math well above where they teach. Test them for competence in mathematics. Teach them the math they don't know. Include serious math in the teachers' editions of text books.
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Professional Development
How many mathematics specialists/staff developers are in your district at the elementary school level? ?? How many elementary schools do you have? 5 How many mathematics specialists/staff developers are in your district at the middle school level? ?? How many middle schools do you have? 1 How many mathematics specialists/staff developers are in your district at the high school level? ?? How many high schools do you have? 1 |
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Don't know
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My local district has a single asst super for curriculum. She does not seem to have much knowledge of mathematics, but certainly is capable of following the latest fads.
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Don't know
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Department of Mathematics
November 8, 2002
Dear Mr. Rudall,
I'm the CCNY math professor who has been in contact with Kristen Kane
and Barbara Taragon: both have invited me to meetings at Tweed,
possibly at your behest. Elizabeth Carson asked me to fill out and
submit the questionnaire that follows. Since the questions are
directed to district superintendents, I can offer useful responses
only to some of them.
I'll begin with personal information. My interest in NYC K-12
education goes back to 1971, when I joined the CCNY Math Department,
where I remain to this day. For three decades, my colleagues and I
have been puzzled by the failure of many otherwise intelligent
students to arrive in college with even a modicum of basic math
skills. I acquired insight into this contradiction about two years
ago, when I began attending the NYC HOLD meetings, initiated by
Elizabeth Carson and involving parents, K-12 teachers, and university
mathematicians and scientists.
Since that time I have become chair of the CCNY Math Department's
working committee on precalculus mathematics education and have
studied K-12 mathematics education issues. In particular, I am
teaching and reshaping the CCNY Math Department's introductory math
content course for undergraduate education majors. Most of the
students in that course are NYC high school graduates. In many cases,
their mathematics knowledge is profoundly deficient.
For example, at the beginning of the semester, only 3 out of the 20
students correctly converted 3 7/8 to a decimal. To my dismay, I have
found that similar deficiencies are shared by some in-service
teachers: DOE personnel observed a fourth grade teacher giving two
independent explanations purporting to show that =BC is greater than
=BD.
In this introductory letter it is inappropriate to point the finger of
blame toward groups or individuals involved in K-12 education.
Indeed, the problems of mathematics education are national in scope.
There are, however, specific issues in New York City that must be
addressed if we are to help our students achieve the goals of
Chancellor Klein's Children First Initiative and President Bush's No
Child Left Behind program.
As I have indicated to Linda Curtis-Bey, Ms. Kane, and Ms. Taragon, I
believe that a well-designed NYC grant proposal for the NSF's
Math/Science Partnership initiative could play an important part in
addressing local problems. I look forward to working with you, your
DOE colleagues, and Chancellor Klein.
Best regards,
Questionnaire: general observations
The questionnaire is directed to district supervisors, and so many of
my responses will refer to a larger context, informed by the following
principles:
The success of the K-8 curriculum should be measured by the
percentages of students who go on to complete successfully Math A and
Math B.
The success of the K-12 curriculum should be measured primarily by the
percentages of NYC high school graduates who
The difficulty of gathering the indicated data does not diminish their
relevance.
I have been careful to indicate that success in college mathematics is
not the only goal of the K-12 curriculum. If, however, the Children
First goals of excellent education for a maximum number of students
are to be achieved, it seems to me that K-12 graduates' ability to
choose to pursue mathematics-related careers (science, mathematics,
medicine, finance, economics, mathematics education, computer
programming, and many more) should be a very significant part of the
desired outcome. Unfortunately, the NCTM-inspired curricula, in my
opinion and that of the draft report of Chancellor Levy's Math
Commission, fail to provide students with the tools for choosing such
careers.
In this regard, I believe that the single worst failure of mathematics
education, nationally and locally, has been the lack of communication
between K-12 and college math/science faculty for at least the last
thirty years. In particular, graduate schools of education and
curriculum developers have lost sight of the need to examine the
college mathematics and science curriculum as a means of informing
sound K-12 curriculum design that will propel students toward later
success.
Math Questions
1. Which curriculum materials are predominantly used in your district
at elementary, middle, and high school levels?
I have examined closely TERC Investigations and Connected Mathematics
Project materials. To a lesser extent I am familiar with the ARISE
curriculum.
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?
TERC Investigations seems to provide the opposite of the mathematical
foundation required for college-bound students. Practice with
grade-appropriate skills-based problems is totally absent. More
important, the thrust of the pedagogy is to get students to adopt
trial and error approaches to straightforward computational problems.
Particularly insidious is that the problems are carefully chosen to be
susceptible to trial and error solutions. In sum, both content and
pedagogy are profoundly at odds with what students should be getting.
Connected Mathematics contains some decent material, but it seems
impossible that teachers could cover enough of the material to provide
a coherent 6-8 foundation for high school mathematics. The
development of fraction arithmetic rules is left largely to the
student; furthermore, the first edition omitted fraction division
completely. As in the case of TERC, there is excessive emphasis on
trial and error methods.
I spent about an hour looking through the ARISE textbooks: I could see
almost nothing that remotely related to the mathematics content
knowledge and skills that students will require in college. In
particular, it seemed that algebra, in the sense of formulating and
manipulating symbolic expressions, is virtually absent from the
curriculum.
The best K-8 English-language curriculum I know about is Singapore
Mathematics, which actually runs from K-6 but covers a fair amount of
more advanced material. The USDOE has signed an agreement with the
Singapore Education Ministry to exchange views on math education. I
believe that Federal funding would be available for implementing that
curriculum.
3. What should be done to ensure a more coherent PK-12 numeracy
approach to curriculum?
I suggest that skills-focused analysis of TERC (K-5), CMP(6-8), and
ARISE(9-12) will reveal little if any coherence. Of course, it's
always possible to compile a list that suggests correspondence between
each of these curricula and the NYC Performance Standards, but that is
in large part because the Performance Standards are insufficiently
specific.
In order to assure curriculum coherence, K-12 educators and
representatives of CUNY math department should formulate a master list
of specific skills at each grade level that will allow students to
succeed in Math A, Math B, and college level mathematics. It is
critical to assign relative weights for the importance of, and the
time that should be devoted to, the development of, specific skills.
The greatest defect of the Performance Standards is their lack of such
weighting.
Instruction
1. Which instructional practices are predominantly used in your
district at elementary, middle, and high school levels?
The nearly exclusive thrust of recent curriculum innovations has been
to indoctrinate teachers with a false doctrine of skills versus
understanding. Teachers are being told that they are avoiding ``rote
learning'' and ``drill to kill'' and that they should focus on ``big
ideas,'' ``higher-order thinking,'' ``conceptual understanding,'' and
so forth. The practical outcome, in too many cases, is to produce
students who are totally bereft of both skills and understanding.
It is of course necessary for students to have a sense of the many
real-world situations that mathematical symbols can be used to
represent. However, it's at least as important for eighth-grade
students to know six different ways of writing the fraction 4/5 as to
know six different ways to draw pictures using that fraction. If
students are ignorant of multiple symbolic representations, they won't
have the tools for solving non-trivial problems.
2. Which instructional practices are working and how do you know?
I strongly suggest that the DOE solicit answers to these questions by
distributing anonymous questionnaires to all teachers. It seems
unlikely that district supervisors committed to specific
programs/curricula can respond objectively to these questions.
I can address these questions only on the basis of what I see in
pre-calculus and calculus courses at City College. Students don't
know the basic symbolic moves needed for success in high school
algebra, a fortiori in college mathematics.
and so on, ad infinitum (well, ad large finitum).
Assessment
3. What are your suggestions to improve PK-12 assessment practices?
I think it crucial to determine how well current testing instruments
emphasize material appropriate for college bound students. I am
particularly disturbed by the fact that only a small percentage of
questions on the New York State 8th grade exam deal with fraction
arithmetic. Is it possible that students can score in Level 4 without
knowing anything about fractions?
Here are some specific recommendations.
K-12 educators and representatives of CUNY mathematics departments
should collaborate to devise skills-focused grade-by-grade tests that
will assess grade-appropriate mathematical skills critical for
college-bound students.
Based on the tests so devised, the DOE, with the support of the
college math/science community, should petition New York State to
revise the emphasis of its 4th and 8th grade exams. The same analysis
should be applied to the New York City exams in grades 3,5,6, and 7,
but I have not seen these tests and so cannot comment on the
appropriateness of their current emphasis.
All assessments should include data on family income and educational
support, and especially on time spent helping with homework and money
spent on outside tutoring. Absent such data, it is irresponsible to
suggest that some instructional programs are more effective than
others.
Family Numeracy
1. How does your district engage with parents in relation to
numeracy?
One of the most disturbing features of some K-12 curricula, or at
least in the way they are implemented in some New York City School
Districts, is their attempt to control or to exclude parent
involvement. Of course, parents are horrified, and rightly so, when
their children fail to learn a core of basic arithmetic and symbolic
skills. Instead
Professional Development
3. In addition to increased time, funding, and access to space, what
recommendations would you make to the DOE regarding professional
development?
An important goal of professional development is to help teachers help
their students perform well on mandated testing instruments. If,
however, the DOE wants to achieve the goal of preparing students for
college, it is critical to involve college mathematics and science
faculty in discussions of, and in programs for improving, K-12
mathematics content and pedagogy.
For the first time, the National Science Foundation, via the
Math/Science Partnership (MSP) initiative, has called for partnerships
between universities and school districts that emphasize the
contributions of university math and science faculty. I presume that
NYCDOE is thinking seriously about how to co-ordinate the two
five-year proposals,
Poor student performance in mathematics adversely impacts performance
in science. Furthermore, it is clear that math instruction must be
repaired from the bottom up. As a result of these considerations, =95
the targeted proposal should be directed toward improving K-8
mathematics instruction and student performance.
7. What training do math specialists/staff developers receive?
Suggestion:
University mathematics faculty and K-12 math specialists/staff
developers should work together to identify the math content and
pedagogy
needs of K-12 teachers.
Math Questions
District # 2
Curriculum
1. Which curriculum materials are predominantly used in your district at elementary, middle, and high school levels?
Connected Mathematics, TERC and Arise
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 started teaching at IS131 in 1988. At that time the school was one of the top in the city in mathematics. The textbooks used were from the Dolciani and Sadlier series. Because of changes in school population mathematics scores dropped during the 1990's, although they remained far above the citywide average until the Connected Mathematics program was introduced. After 3 years of using the program the school was well below 50%. I have been told that there has been some improvement in test scores during the past year-- a result of intensive test preparation (including Saturday workshops for students).
Below are my experiences with Connected Mathematics.
1) Constructivist programs work best with small class size and with students that already have the 'social skills' needed for intensive cooperative activities. I found most students from IS131M worked best in a structured, teacher-centered environment.
2) Connected Mathematics does not teach math in a logical sequence. Instead it uses booklets that tend to present the curriculum in a disjointed way.
3) The curriculum is confusing for parents to comprehend and therefore makes it difficult to help their children with homework assignments.
4) Connected Mathematics assumes the student is competent in basic math skills, something lacking by students who use TERC prior to Connected Mathematics.
5) Although I must give a low grade for the Connected Math Program when used for teaching mathematics, I found several of booklets very useful (as a supplement) with science laboratory exercises I had developed.
3. What should be done to ensure a more coherent PK-12 numeracy approach to curriculum?
#1 A unified citywide curriculum should be developed that includes daily lesson plans. A starting point should be either the mathematics curriculum from the early 1970's or those being worked on in California and Massachusetts. Daily lesson plans should be easily accessible to all teachers via the Internet.
#2 Bring back citywide midterm and final exams in Mathematics (and all major subjects). For the past 20 years teaching math and science has become more problematic with less emphasis on a meaningful 'final exam' given at the end of the school year. Students know that grades are turned at the end of May. Teachers know that the state and citywide tests are finished at the end of spring. As a result, the end of May and all of June have become very unproductive months for learning (with the exception of classes taking regents exams, where June becomes a real power month!) We need to implement citywide final exams the last week of school (in all major subjects). If it can be done for regents' classes, it can be done for all classes.
#3 Make use of university mathematicians in preparation of curriculum and citywide exams. In the 1970's most math teachers and administrators majored in math or related fields. This is no longer the case. Those in decision-making roles in the NYC schools no longer have the background in mathematics or science to understand what the deficiencies of their various programs are. It is crucial to allow university mathematicians a role in the design of both curriculum and tests in NYC.
District #2
Instruction
1. Which instructional practices are predominantly used in your district at elementary, middle, and high school levels?
There is a major emphasis on constructivist mathematics and project-based learning approaches in all subjects.
2. Which instructional practices are working and how do you know (please cite student achievement data as evidence)?
The demographics in District 2 make actual assessment difficult since many students have outside help. Even in Chinatown there is a large increase in after-school and weekend learning centers.
District #2
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?
The GROW report started after I retired.
3. What are your suggestions to improve PK-12 assessment practices?
There is presently too much emphasis on the NYC and NYS exams, which leads teachers to spend more time on test preparation and less on a daily curriculum.
I suggest the following:
Citywide midterm and final exams that clearly access material from the citywide curriculum. By linking these exams directly to the daily curriculum, teachers will spend more time on day-to-day teaching and less on test preparation for the NYC and NYS exams. In addition a final exam given the last week of school would ensure that real learning takes place till the end of the school year.
District #2
Support Structures
1. What are your district's intervention strategies and programs for struggling students? How are struggling students identified?
The same as throughout the City.
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?
It has always been easy to identify a struggling student. The problem is what to do next! Small help sessions for students work, if those most in need show up. The major problem here is how to get those students most in need to attend. (See below).
3. What else do you think needs to be done to support struggling students in numeracy?
Bring back a strong after school sports (and other interesting activities) program and link it with after school tutoring. After school tutoring for struggling students whether by teacher or another student `must' be made mandatory. For next year the city should attempt to implement a structured after-school tutoring program tied to the extended school day. I strongly feel that this is far more effective than extending each class 3 minutes.
District #2
ELL Students
1. What support structures exist in your district to ensure the achievement of ELL students? Who makes the decisions around support structures? 3. Which of these strategies do not work? Why?
NA
District #2
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?
NA
2. Which of these strategies work and how do you know (please cite student achievement data as evidence)?
NA
3. Which of these strategies do not work? Why?
NA
District #2
Family Numeracy
1. How does your district engage with parents in relation to numeracy?
As a teacher I saw little engagement with parents dealing with either the science or mathematics curriculum.
2. Which of these strategies work and how do you know? What issues do parents raise and how do you address those issues? What else should your district be doing around family numeracy?
NA
District #2
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?
Professional development in District 2 emphasizes pedagogy and does not promote teacher understanding of the content material. This is especially true in the early grades.
2. What do you think are the most pressing staff development needs in your district? Why?
Teachers, especially K-5, need a solid understanding of basic mathematics and science. They need to understand what they are teaching `before' they teach it. Too many teachers learn with their students.
3. In addition to increased time, funding, and access to space, what recommendations would you make to the DOE regarding professional development?
Staff development as presently used in NYC is basically unproductive, a fact that few educators will admit to.
I would recommend:
1) Increase the emphasis on math and science content-oriented workshops at local universities (there is substantial grant money available for this purpose).
2) Internalize staff development within schools and districts. We need more teachers observing other teachers and exchanging ideas.
3) Remove all outside consultants from schools. There are more than enough highly-qualified teachers (and retired teachers) willing to work for a fraction of the costs.
4) Increase the use of retired teachers as mentors and curriculum planners.
Professional Development
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?
AT IS131M there are 2 or 3 teachers (staff developers) with half-time teaching programs (staff development). I cannot comment on the selection process although
it does not seem to be cued to their understanding of basic mathematics or experience in the classroom.
There are extensive training sessions for math teachers and staff developers in District 2 as part of an NSF grant. These are specifically designed to provide staff developers with skills to teach Connected Math.
Dear Mr. Rudall,
I am pleased to respond to your survey questions as forwarded to me by Elizabeth Carson. I apologize for the lateness of this response; I have been out of town until late last night and unable to access my computer.
Ms. Carson indicates that you would appreciate a short biographical sketch. I will make it very brief due to the near deadline. I hold a BS in mathematics and a lifetime teaching credential in California to teach secondary mathematics and physical science and have several years experience teaching grades 7-12. I also hold a MS in geology and Ph.D. in geophysics and have taught science courses and remedial math in the California State University system for around fifteen years. I was a member of the committee which drafted the California mathematics framework and served on two panels to evaluate instructional materials on the state level. For the last few years I have worked professionally as a mathematics specialist for (and contracting with) our county office of education. In this last capacity I am not employed by any ?my district? but have helped in various capacities in several districts, one school extensively (Eshelman Avenue in LAUSD) and several other schools briefly, visited many schools, and served on county and state external (high stakes) evaluation teams at ten elementary schools, three middle schools, and four high schools. I will respond to your questions, as I am able, with reference to several districts and sites which I have observed.
Curriculum #1: California is an adoption state for grades K-8 and the state book adoption list is enforced by requirements for expenditure of state instructional materials funds. There is a short list of adopted books aligned to the rigorous and specific state standards and framework and many, but not all districts have adopted recently from this list. The report of the 2001 CA book adoption may be downloaded from http://www.cde.ca.gov/cfir/math/mathrpt.pdf. Note that most of these are special editions to meet CA specifications and are not the same programs marketed nationally by the publishers. I have seen many of the adopted materials in use in classrooms. The districts and sites which have made the most significant gains in the last couple of years adopted the most prescriptive listed materials, the modified direct instruction program from Saxon Publishers.
Curriculum #2: I have seen good results from the CA school mathematics reform program, although the best test score gains have been in the elementary grades, and the high schools are more or less static. I believe the stagnation at secondary grades to be primarily due to two factors: the lack of a state materials adoption past grade eight, and the relatively deep holes (relative to early grades where it is easier to catch up to the level of the standards) in prerequisite skills and concepts created by the previous decade of incoherent mathematics educations driven by progressivist education reform. The successes are due, I believe, to our clear and specific standards and the straightforward teacher-friendly adopted materials. Here are a few examples generated by the CA mandatory testing program:
California SAT-9 Math Ave NPR
Grade 1998 1999 2000 2001 2002
2 43 50 57 59 63
3 42 49 57 61 64
4 39 44 51 54 58
5 41 45 51 55 58
6 48 52 57 60 62
7 45 47 51 53 54
8 45 48 50 51 52
9 50 51 54 54 54
10 43 45 47 47 48
11 46 48 50 50 50
Los Angeles USD SAT-9 Math Ave NPR
Grade 1998 1999 2000 2001 2002
2 32 36 41 44 53
3 30 35 42 49 54
4 27 30 35 39 47
5 28 31 35 39 44
6 30 34 37 39 42
7 29 32 33 34 35
8 30 33 34 34 35
9 37 38 39 39 39
10 33 36 36 36 37
11 37 41 41 41 43
(LAUSD adopted the Scott Foresman books for K-5 in half the district and the Harcourt Brace in the other half. Progress has been acceptable, but would possibly be more if instructional practice had not been confounded by inappropriate professional development and improper pacing in the district.)
Baldwin Park USD SAT-9 Math Ave NPR
Grade 1998 1999 2000 2001 2002
2 19 30 43 48 57
3 22 29 49 53 59
4 23 24 36 45 50
5 25 29 34 46 51
6 38 42 48 52 59
(Baldwin Park is a high poverty district which adopted the Saxon materials)
Manhattan Beach USD SAT-9 Math Ave NPR
Grade 1998 1999 2000 2001 2002
2 74 82 89 93 92
3 79 81 87 92 93
4 81 82 82 87 92
5 83 85 88 87 92
(Manhattan Beach is a highly affluent district which adopted Saxon materials and showed that high performance could be improved by better instruction.)
Torrance Unified School District
Response of Chuck Newman
Dear Evan,
I'm writing to you, as a follow-up to the Oct. 30 meeting of Diana
Lam, Kristen Kane, Elizabeth Carson, Bob Feinerman, Sylvain Cappell and
me. Elizabeth asked me (and a number of others) to respond to a survey
originally designed for NYC district math personnel.
Rather than send a bio, let me give the URL of my NYU homepage:
http://www.math.nyu.edu/faculty/newman/index.html I am currently acting
director (equivalent to a dean) of the Courant Institute of Mathematical
Sciences (http://www.cims.nyu.edu/), home of NYU's departments of
Mathematics and of Computer Science, which includes the number one
Applied Mathematics program in the world.
With a Ph.D. in Physics, and as a university administrator and (for
30 years) a mathematics professor, I think I fairly represent the
consensus views of mathematicians, scientists, engineers and those
involved in their education at the college level in our alarm at the
effect we perceive on the students arriving in college from the use of
constructivist/discovery learning/child centered/... K-12 mathematics
curricula. Just so you don't misperceive this concern as directed
primarily at "elite" students, let me insert a few paragraphs I wrote
(Feb., 2001) to Matthew Goldstein (no direct response ever received
although the report of his commission ended up somehwat improved from
early drafts), CUNY Chancellor, when he was chair of the Levy Math
commission, studying NYC math curricular issues at the time. Here are
those paragraphs to Goldstein from 2001:
---------
"I hope you'll excuse me for using some blunt language in the rest
of this message, but I fear that you and CUNY are about to be set up
by the Board of Ed. for the eventual blame of approving an approach to
K-12 (fast being converted into K-16) mathematical education doomed to
disaster. The rosy picture you have probably been told about the
pilot programs in District 2 reminds me of the joke about the guy who
jumps off the roof of a 30 story building; as he passes the 15th
floor, someone standing by the window hears him say, `So far, So
good!'
A number of Courant faculty have gotten involved in these math
education issues and recently had a discussion (together with Lucy
West, the District 2 math. coordinator and John Thorpe of NCTM) with
the CUNY Math. Chairs. That discussion, together with seeing the
Board of Ed. pre-prepared conclusions of your committee, have I think
led them to appreciate the pickle CUNY is about to get into if your
committee acquieses in the Board of Ed. charade that all is going well
with the new math curricula, and it's only the retrograde
mathematicians at elite institutions like Stanford and NYU who cause
problems in the public perception. The truth of course is that we'll
manage fine even if most city school graduates can't add fractions,
but CUNY will suffer a great deal [NOTE ADDED: it's of course really
the NYC public school students who will suffer the most, when they
arrive at college after having been told for 8 years that they're
doing fine in mathematics and discover that they are unequipped for an
increasingly large number of careers]. And that would be a terrific
shame, considering how seriously it seems to now be on the upswing."
----------------------
Clearly, given my background, I will not respond in detail to most of
the questions on your survey. But let me make some general comments.
Indeed after seeing a little bit on the web about Roxbury Prep., which I
believe you co-founded (my wife's first teaching job, in 1966, was in
Roxbury), I have the feeling that you have some pretty good ideas of
your own about what kinds of curricula and instruction NYC's students
really need and the hope that you won't be taken in by the
unsubstantiated claims about the efficacy of the latest fads that you'll
hear from many representatives of the "old guard" of the Board of
Education (I know it's now DOE), schools of education, foundations, ...
Curriculum: I know something about TERC and a bit about CMP and IMP.
They should be discarded as fast as possible and replaced by Saxon or
Singapore or something similar. You should rely on people like Ralph
Raimi and David Klein (Elizabeth sent you their contact info.) in
deciding on the best replacement curricula
Instruction: Discovery learning is fine (even desirable, time
permitting, which it often is not) as a modest supplement to instruction
based on content and much practice. It should not occupy more than a
small percentage of the time (I would say 10%; in TERC it seems to be
somewhere around 90%).
ELL students: Mathematics curricula that require writing skills
(replacing use of formulas) can be disastrous for many ELL students, who
otherwise might excel in mathematics.
Special Needs Students: many apparently do much better with
structured more traditional approaches.
Family Numeracy: The inability of parents to work with their
children because of the extreme difference of such curricula as TERC
compared to the curricula they had had themselves has been one of the
many negative features of these curricula.
Professional Development: For many teachers, the crying need is for
more mathematics content for themselves, rather than indoctrination
programs into the intricacies of such curricula as TERC.
Sincerely,
Chuck Newman
Response of Stanley Ocken
The City College of CUNY
138th Street at Convent Avenue
New York, N. Y. 10031
Stanley Ocken
Dept. of Mathematics
The City College of CUNY
3. Which instructional practices are not working and why?
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?
that can be submitted by NYCDOE. In the past, similar proposals have
been fragmented among many interested players. The result has been to
split the pot with no real benefits to students. That shouldn't be
allowed to happen this time around, for only a focused and large-scale
effort can have a reasonable hope of improving math/science education
in New York City.
Response of Marvin Rich
(Please see here for the Microsoft
Word *.doc original version of Marvin Rich's reply)
Dear Mr. Rudall,
I have been asked by Elizabeth Carson of NYC HOLD to complete the
attached questionnaire form and provide a short bio.
I started my career as a teacher in 1969 after graduating as an
engineer from Rensselaer Polytechnic Institute. My first school was
JHS17 in District 2 where I started as a math and science teacher. I
was extremely impressed with the quality of science and math being
taught in the early 1970's. The science lab was full of great
equipment -- enough to allow weekly laboratory exercises and quality
demonstrations to complement daily lessons. The Bureau of Curriculum
Development from the Board of Education provided all math and science
teachers with daily lesson plan books that made life a lot easier for
a beginning teacher. These books, in my opinion, remain superior to
most of what is presently being produced by most school
districts. Sadly, as changes occurred in the State Curriculum, NYC
chose not to update the books. As a result of this and the lack of a
meaningful citywide curriculum plan, many schools and districts tend
to do whatever (if anything) they feel like in math and science.
I went on to obtain a Masters in Biology (NYU, 1977), and a Ph.D. in
Biophysics (NYU, 1982). Enjoying both scientific research and teaching
I decided to remain in the classroom and pursue my scientific research
endeavors on a part-time basis. As it turned out my research work and
contacts with NYU greatly assisted me as a teacher for the remainder
of my 30-year career (all of which was in District 2-- split between
math and science). My research at NYU allowed me to develop several
innovative science, and integrated math/science laboratory modules
which I used in my classes.
Since retiring 18 months ago, I spend a great deal of time working at
NYU, assisting in the development of The Molecules of Life Course for
the MAP Program, a science program for non-science majors, and
pursuing my research interests in Molecular Modeling. I continue to
maintain ties with many of my colleagues at IS131 and am aware of the
present work being done in science and mathematics in the district.
I maintain two education related web sites: Project MathMol
(Mathematics and Molecules) http://www.nyu.edu/pages/mathmol and
Edinformatics, http://www.edinformatics.com (a general education site
for all educators and students).
Sincerely,
Marvin R. Rich
Response of Martha Schwartz
(Please see here for the Microsoft
Word *.doc original version of Martha Schwartz's reply)
|
Grade |
98 |
99 |
00 |
01 |
02 |
|
2 |
61 |
70 |
74 |
77 |
82 |
|
3 |
62 |
69 |
76 |
79 |
81 |
|
4 |
64 |
67 |
72 |
77 |
79 |
|
5 |
62 |
67 |
74 |
76 |
81 |
|
6 |
66 |
68 |
73 |
75 |
77 |
|
7 |
65 |
68 |
68 |
74 |
75 |
|
8 |
65 |
68 |
69 |
69 |
70 |
|
9 |
71 |
71 |
72 |
74 |
72 |
|
10 |
58 |
64 |
63 |
65 |
65 |
|
11 |
60 |
62 |
67 |
65 |
64 |
(TUSD is a relatively high SES district which adopted the traditional Houghton Mifflin books for K-5 and a variety of other state-adopted materials for 6-8. Gains are modest in high school where older materials are still in use. This is a common issue statewide.)
Eshelman Ave El SAT-9 Math Ave NPR
Grade 1998 1999 2000 2001 2002
2 39 39 48 57 71
3 48 52 61 66 74
4 27 52 50 61 67
5 41 25 48 44 62
(There are many other examples which could be given. I chose with Eshelman School, a maverick in LAUSD, which uses Saxon materials. This is a Title 1 school, 75% Free and Reduced Lunch, with about 25% English Language Learners.)
I will close this listing of examples with a general note: The most effective classrooms I have seen rely and clear and precise instructional materials and not the creativity of individual teachers. Coherent and coordinated programs are the best and indeed only way I have seen to raise performance more than one classroom at a time.
Curriculum #3: The groundwork for a more coherent approach to numeracy has been laid in California. If politically possible, adopt the CA standards, frameworks, book adoption list, and testing program.
Instruction #2: I have of course observed in several districts and done a formal evaluation (using test scores) in one. The practices which seem to be most effective (in those places where scores are increasing the most) are in no particular order:
Instruction driven by student assessment, including proper placement in the curriculum
Teacher-led instruction
Significant amounts of guided practice
Significant amount of distributed practice (e.g. 25 multiplication problems are best practiced five per day for five days than given as 25 examples of the same thing for one night homework)
Frequent assessment and reteaching where necessary
Aggressive remediation of basic skills, such as learning number facts to automaticity
Material introduced in small increments and mastered before being built upon
Brief daily repetition of basic skills
I note that the Saxon materials provide all of this automatically if used as recommended, but the other CA materials lend themselves to lesson planning incorporating all of the above.
Instruction #3: In the district I evaluated formally, negative correlations to student achievement were found for block schedules, use of a computer program for instruction, and reliance on extensive homework assignments. Also, the previous poor performance in California as a whole was connected to the widespread use of ?discovery learning? practices.
Assessment #3: At the most successful sites assessments in constant and constantly cumulative. This is automatically done in Saxon math - there is a ?final? every week. This allows teachers to keep tabs on every student's growth, mastery, and retention of all topics and intervene immediately when necessary. Such a system may be standardized and computerized to allow a site or even a district to monitor the progress of every child.
Support for struggling students: I have seen a great many attempts at this, most of them unsuccessful. Some of this I commented on earlier with respect to the formal evaluation I just completed. Many of the CA adopted materials come with ?intervention systems? which are assessment driven and meant to be implemented in extended time slots, beyond the regular hour per day for math. I have anecdotal reports only of the efficacy of these approaches. For young students, the implementation of coherent basic programs has significantly cut down on the need for remediation. For older students, such as many of my struggling university students, strong student consequences turn out to be important. Student outcomes improved markedly when students were threatened with expulsion if they didn't pass the developmental math classes. The fewer students who failed even in the face of this threat needed considerable one-on-one assistance. All of them had significant gaps from elementary school. In my fifteen years experience in this, I found that those students who could be made reasonably fluent in the arithmetic of fractions were ultimately successful in algebra and even beyond, but none of those who could not do simple fraction operations could be easily helped.
ELL #2: I have no special expertise on language acquisition other than my observations at Eshelman School, where test scores of these students are remarkably high. The staff there credits the unexpected efficacy (for ELL students) of a direct instruction academic English program for kindergarten (and grade one?) called Language for Learning, marketed by SRA McGraw Hill. This might be worth an informed look, as might their related program Español to English. Asian students seem to do fine (in math) with English immersion alone. Here are reading SAT9 scores for Eshelman, which has a significant number of Spanish only kindergartners (I have already cited their math growth):
Reading
|
Grade |
1998 |
1999 |
2000 |
2001 |
2002 |
|
1 |
36 |
34 |
56 |
77 |
|
|
2 |
30 |
35 |
38 |
56 |
63 |
|
3 |
34 |
36 |
48 |
52 |
56 |
|
4 |
23 |
37 |
37 |
58 |
54 |
|
5 |
38 |
31 |
46 |
41 |
57 |
Special Needs: Again, I am not expert but have observed much at Eshelman. They use the same programs for special and general education, but students are placed at the levels needed. The upper grades SE teacher assures me that all her students leave knowing their times tables. Most of them also leave with decent reading skills. I humbly suggest those interested visit the school.
Family numeracy (general): I just spoke last week with the principal of a previously underperforming elementary school. At my suggestion, the initiated a ?math facts test? after school program run by moms and coordinated by the ELL coordinator, who just happened to be interested and took up my suggestion for such a program. The after-school testing, and the little rewards offered, quickly captured the imagination of the students and caused them to request help at home. This greatly bolstered math facts recall among the students and appropriate to the CA math standards for their grades. It had the interesting and unexpected side effect of boosting parent participation in general and support for academics, which are much improved this year over last.
Professional development (general): I have had considerable experience delivering a mathematics PD program for teachers, developed for California. This five-day program is called ?The Winning Equation? and targets math content for grades 4-7 but taught with an adult perspective - absent much advice on pedagogy. Pedagogical issues do come up occasionally in that context, but I have found that most teachers appreciate and almost all need the in-depth exposure to the content, which they never had as students themselves. They find this immediately helpful in the classroom, as it provides them multiple ways to understand and explain the material. This material is reasonably well edited and quite simple to deliver with a trainer-of-trainers model.