Survey responses for Children First Numeracy Working Group

Response of Marvin Bishop

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

Response of Bas Braams

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.

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. 

                     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.