In Chronological Order:

1. The NCTM 1989 __Curriculum and Evaluation Standards__,
generally known as the “NCTM Standards”, see http://standards.nctm.org for access to
the full text, but for members of NCTM only.
Out of print but available in university libraries.

2. The NCTM 2000 Principles and Standards for School Mathematics, generally known as “PSSM”, http://standards.nctm.org for access to the full text, but for members of NCTM only. For sale by NCTM, and available in university libraries.

3. __Ten Myths About Math Education And Why You Shouldn’t Believe
Them__, generally referred to as “The Ten Myths”, a statement found at http://www.nychold.com/myths-050504.html, made public on May 4, 2005, by Karen Budd,
Elizabeth Carson, Barry Garelick, David Klein, R. James Milgram, Ralph A.
Raimi, Martha Schwartz, Sandra Stotsky, Vern Williams, and W. Stephen Wilson,
in association with the advocacy groups NYCHOLD and Mathematically
Correct. Each “Myth” is followed by a
statement called “Reality”, explaining how or why it is false, i.e., a myth,
and then by some research references in support of that statement. Many of the Myths are intended to be
recognizable as doctrines of the National Council of Teachers of Mathematics,
or closely allied with or support for their curricular and teaching
recommendations. For example, Myth #1
is “Only what students discover for
themselves is truly learned.”

4. __Ten Myths (Maybe) About Learning Math__, by Jay Mathews, a
column printed in The Washington Post, May 31, 2005, in which he reprints the
Ten Myths themselves and a brief reply (unsigned) to each from a representative
from NCTM, as he had asked it to provide for publication in his column. (Full text at http://www.math.rochester.edu/people/faculty/rarm/Mathews_myths.htm.)

5. __Reaching for Common Ground in K-12 Mathematics Education__,
generally known as “Common Ground”, a paper publicized in June, 2005 as a
working document in a project still underway; find it and sequels at http://www.maa.org/common-ground, a
web site maintained by the Mathematical Association of America. __Common Ground__ was written by Deborah
Ball, Jeremy Kilpatrick, Joan Ferrini-Mundy, R. James Milgram and Wilfried
Schmid, assisted in their deliberations by Richard Schaar as moderator. (Ferrini-Mundy as chief editor of NCTM’s
PSSM and Milgram as a leader in the writing of the 1998 California Mathematics
Standards thus may be seen as representing the two poles of the recent
controversies.)

6. The NCTM ** Curriculum Focal Points for Prekindergarten
through Grade 8 Mathematics: A Quest for Coherence**, generally known at
the “Focal Points”, is an official document of NCTM, released on September 12,
2006 and available at http://nctm.org/focalpoints
for free download. For each of the ten
grades mentioned in the title the paper lists three major topics for emphasis
in mathematics, with some elaboration and some reference to earlier NCTM
Standards publications. There has been
some dispute over whether the wording of the Focal Points represents a
departure from those earlier NCTM recommendations, some mathematicians and
journalists interpreting them as a reversal (see Documents 7, 8, and 10 below)
and President Francis Fennell of NCTM disagreeing (Documents 9, 11, and 12).

** **

**7. New Report Urges Return to Basics in Teaching Math: **

From the text:

The nation's math teachers, on the
front lines of a 17-year curriculum war, are getting some new marching orders:
Make sure students learn the basics.

In a report to be released today,
the National Council of Teachers of Mathematics, which represents 100,000
educators from prekindergarten through college, will give ammunition to
traditionalists who believe schools should focus heavily and early on teaching
such fundamentals as multiplication tables and long division.

The council's advice is striking
because in 1989 it touched off the so-called math wars by promoting open-ended
problem solving over drilling. Back then, it recommended that students as young
as those in kindergarten use calculators in class.

Those recommendations horrified
many educators, especially college math professors alarmed by a rising tide of
freshmen needing remediation. The council's 1989 report influenced textbooks
and led to what are commonly called "reform math" programs, which are
used in school systems across the country…

Infuriated
parents dubbed it "fuzzy math" and launched a countermovement. The
council says its earlier views had been widely misunderstood and were never
intended to excuse students from learning multiplication tables and other
fundamentals.

Nevertheless, the council's new
guidelines constitute "a remarkable reversal, and it's about time,"
says Ralph Raimi, a University of Rochester math professor…

Nearly 80 teachers and
other experts spent 18 months writing and reviewing grade-by-grade guidelines,
which cover preschool through eighth grade. The panel aims to give a roadmap to
instructors, schools systems and states about exactly what children should be
learning -- and to start a debate that could put the math wars to rest…

Supporters of the council's
previous views worry that the new report may lead to a return to the kind of
rote learning they say left many children without any understanding of
concepts. ..

"The risk is that we end up
with students who have no idea what math is all about or how to use it,"
says Joseph Rosenstein, a math professor at Rutgers University in New Jersey …

8. ** Report Urges Changes in the Teaching of Math in the U.S.
Schools**, by Tamar Lewin in The New York Times, September 13, 2006. (Full text at http://www.math.rochester.edu/people/faculty/rarm/nyt_focal1.htm.)

From the text:

“In a major shift from its influential recommendations 17 years ago, the National Council of Teachers of Mathematics yesterday issued a report urging that math teaching in kindergarten through eighth grade focus on a few basic skills. If the report, “Curriculum Focal Points,” has anywhere near the impact of the council’s 1989 report, it could signal a profound change in the teaching of math in American schools… [The 1989 Standards] was incredibly influential,” said Chester E. Finn Jr., a Department of Education official in the Reagan administration… “This report is a major turnaround.” Dr. Finn added, “This is definitely a back-to-basics victory…”

In a way, the new report stands as a plea for consensus … And consensus may be at hand. Some of the same math professors who last year released a chart – aimed directly at the National council of Teachers of Mathematics – detailing the “10 myths” of “N.C.T.M. (Fuzzy)” math now find themselves generally in line with the new report. “It represents an enormous evolution from the 1989 standards, from the perspectives and attitudes that were present in both camps then,” said R. James Milgram of Stanford, one of the “10 Myths” signers.

9.
__An email letter to the entire membership of NCTM, from the
President, September 15, 2006__

[Reprinted here in full except, in the last
paragraph, a list of links to related documents on the NCTM web site, http://www.nctm.org.]

From: Francis (Skip) Fennell (president@nctm.org)

Subject: Curriculum Focal Points Released

Date: Fri, 15 Sep 2006 22:19:47 -0400

Dear NCTM
Members:

I am pleased to announce that ** Curriculum
Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for
Coherence** as released on September 12.
The Curriculum Focal Points are the next step in the implementation of
the Standards. The focal points fully
support the Council's

** Curriculum Focal Points** presents the most important mathematical
topics for each grade level. A focal
point specifies the mathematical content that a student needs to understand
thoroughly for future mathematics learning.
The focal points are compatible with the original Standards and
represent the next step in realizing the vision set forth in

Unfortunately, some of the media coverage has
raised questions and caused concern among our members. Despite several conversations with a
reporter from the Wall Street Journal explaining what the Curriculum Focal
Points are and are not, a September 12 Wall Street Journal article did not
represent the substance or intent of the focal points. The focal points are not about the basics;
they are about important foundational topics.
The Council has always supported learning the basics. Students should learn and be able to recall
basic facts and become computationally fluent, but such knowledge and skills
should be acquired with understanding. Unfortunately, some of the other news
media have followed the Wall Street Journal's lead and have similarly
misrepresented the Curriculum Focal Points.

The Council's goal is to support teachers in
guiding students to learn mathematics with understanding. Organizing a curriculum around a set of
focal points can provide students with a connected, coherent, ever expanding
body of mathematical knowledge. The
focal points describe what should be the focus of what students should know and
understand thoroughly.

I encourage you to explore the complete …Curriculum Focal Points section of the NCTM Web site.

Sincerely,

Francis (Skip) Fennell

President

10. ** Teaching Math, Singapore Style**, Editorial in The
New York Times, September 18, 2006.

Excerpt: “Many people trace this unfortunate
development to a 1989 report by an influential group, the National Council of
Teachers of Mathematics. School districts read its recommendations as a call to
reject rote learning. Last week the council reversed itself, laying out new
recommendations that will focus on a few basic skills at each grade level.”

11. ** A letter to the
New York Times**, from Francis Fennell
[President of NCTM], dated September 18, 2006. (Full text at NCTM web site, http://www.nctm.org/focalpoints/nyt_letter.asp.)

Excerpts:

To the Editor:

…

Forty-nine of our 50 states have developed
state curricular frameworks. Most of these have been influenced by the National
Council of Teachers of

Mathematics' "Curriculum and Evaluation
Standards" (1989), or the more

recent "Principles and Standards for
School Mathematics" (2000). Close to 30 of the states have revised their
curricular frameworks since 2003.

What some refer to as basic skills (for
example, multiplication facts, and

fluency with the addition, subtraction,
multiplication and division of whole

numbers) have always been a fundamental core
of elementary school

mathematics. Always.

But we want more. We want children to
understand the mathematics they are

learning and we want them to be able to solve
problems, which is, in the

long run, why we do mathematics.

Our recently released "Curriculum Focal
Points" identifies important

mathematical topics in each grade, from
prekindergarten through eighth

grade. It identifies the mathematical content
students need to understand

deeply and thoroughly for future mathematics
learning.

It offers a framework to guide states and
school districts as they design

and organize revisions of their expectations,
standards, curriculums and

assessment programs.

This is not a change, but reflects what has
been the council's commitment to

teaching and learning for more than 80 years.

Francis Fennell

President, National Council of Teachers of
Mathematics

Reston, Va., Sept. 18, 2006

12.
Francis Fennell’s ** Letter
to the Wall Street Journal** (Abridged; full text at NCTM web site http://www.nctm.org/focalpoints/wsj_letter.asp.)

Reading, Writing and Troubled Arithmetic

September 27, 2006; Page A19

The Curriculum Focal Points released by the
National Council of Teachers

of Mathematics are the next step in
implementing the group's "Principles

and Standards for School Mathematics,"
published in 2000 ("Arithmetic

Problem: New Report Urges Return to Basics in
Teaching Math," page one,

Sept. 12). Based on the NCTM standards, the
Curriculum Focal Points

identify the most important mathematical
topics from pre-kindergarten …

Contrary to the impression left in your
article, learning the basics is

certainly not "new marching orders"
from the NCTM, which has always

considered the basic computation facts and
related work with operations

to be important. Nor is the new focal-points
approach to curriculum

development a "remarkable reversal"
for NCTM. As stated in NCTM's 1989

and 2000 standards, conceptual understanding
and problem solving are

absolutely fundamental to learning
mathematics. The council has never

promoted estimation "rather than precise
answers." Estimation is a

critical component to the overall
understanding and use of numbers.

Organizing curriculum around a set of focal
points can provide students

with a connected, coherent, ever-expanding
body of mathematical

knowledge. This isn't a change, but reflects
what has been the council's

commitment to the teaching and learning of
mathematics for more than 80

years.

Francis (Skip) Fennell

President

National Council of Teachers of Mathematics

Reston, Va.

*************************************************************

** Footnote to the Twelve Documents**:

To anyone
reading this it should be well known that Documents 1 and 2 are the backbone of
the current debate, for they are the stated policy of The National Council of
Teachers of Mathematics (NCTM) on the subject of school mathematics curriculum,
and #1, the 1989 “Standards”, is the genuinely seminal document. The influence of the Standards was
manifested over the following five to ten years by the textbooks and “programs”
for elementary, middle and high schools written in their wake. Elementary school mathematics doesn’t
usually feature textbooks as such, but the published program material is given
to the teacher, who has a book with exercises and other materials that can be
reproduced and distributed to the students to take home or use in class; hence
the word “program” rather than “textbook” in such cases, though “program” can
apply even in cases where textbooks used by students exist, and at higher grade
levels. However presented, the math
programs written to accord with the 1989 Standards all intend to inculcate a
certain manner of teaching and learning (often called “constructivist”) in
addition to the mathematical information
(“content”) to be learned.

In 2006 some of
the more widely used reform programs, all written under NSF grants though
published and sold commercially, books and materials continually being revised
under subsequent NSF grants, are:

For primary
grades, __Everyday Math__ and the
TERC __Investigations__ (sometimes merely called “TERC”);

For the middle
schools, CMP (the __Connected Math Program__; and

For high
school, __Core-plus__ and IMP (the __Interactive
Math Program__.

There may be a
few reform programs that outsell these – I don’t really know the sales figures
– but these are known to me as having generated the major outbursts of parents’
(and mathematicians’) indignation over the period since the 1989 Standards were
published. Yet the parents who have
carried their objections to their school board meetings and their local
newspapers have, except rarely, never heard of, let alone read, NCTM’s
Standards and PSSM, the founding documents lying behind those programs, and
only when they really began to engage their local school systems in debate over
changing the curriculum have they become aware of the linked interests of NCTM,
the publishing industry, and,
ultimately, national professional educational bureaucracy, aided by the
National Science Foundation, that has been denying to their children what they
expect of school math instruction.

Two
such parents’ advocacy groups have become much more than that since their
founding, in that they operate web sites crowded with manifestos, statistics,
opinions, reprinted newspaper and magazine articles and so on in support of
their cause. They are “Mathematically
Correct” in California, with web site http://mathematicallycorrect.com
and NYCHOLD in New York City, with web site http://www.nychold.com. There is much overlap in the things posted
on these two, and cross-references, and they both espouse the same
anti-“reform” point of view, but neither is superfluous and both serve as
sources of material for smaller, local groups, mainly formed since about 2000,
when disaffected parents in such places as Penfield, NY and Bellevue, WA have,
in the course of their local fights with their local school districts,
discovered they had company in other parts of the country.

Most if not all
of the more local uprisings take place in affluent suburbs of cities where the
parents are by no means ignorant of mathematics and its uses. Penfield is a suburb of Rochester, home of
Kodak and Xerox; Bellevue, next to Seattle, has Boeing; Palo Alto is the
intellectual center of “Silicon Valley”; and Montgomery County, Maryland is across
the river from D.C. These towns now
have web sites of their own (Palo Alto’s was in fact the pioneer), detailing
local problems and local education news but with internet links to relevant
materials found on the two major sites, links that the local teachers and
parents can use to educate themselves concerning the wider battle in whatever
degree they have time for. The material
contained on the two major sites, from book reviews of reform math programs to
advice on the political strategies of local education, is often, indeed
usually, written by mathematicians and teachers, from knowledge and experience
beyond what a local parents’ group could bring to its campaign unassisted.

Only in
California, where HOLD (for “honest, open, logical debate”), the pioneer group
in Palo Alto, soon followed by Mathematically Correct in San Diego, managed to
bring the full weight of California’s education law, via extraordinary
authority it grants to the California Board of Education and its subsidiary
committees, onto their side – the anti-NCTM side – of the “math wars”, have
local parents’ groups had any substantial success in changing the direction of
math education in their districts. Not
even in New York City’s famed District 2, where with the aid of NYCHOLD they have
gathered a most impressive team of mathematicians from CUNY and NYU to argue
their case, first to the District authorities and then to the councils of the
city itself, all without effect.

A major obstacle to all such efforts has been the continuing financing, by the National Science Foundation’s division of Education and Human Resources (NSF-EHR), of the further spread of the reform curricula, far beyond what the publishers could have achieved by mere advertising, and certainly not the intrinsic values of their books and materials. The NSF participation in the commercial success of the “reform” programs has been via the major schools of education, whose professors have applied for and received multi-million dollar grants for programs called “systemic initiatives” in earlier years and “math-science partnerships” (“MSTs”) more recently.

A typical MST,
entitled __Deepening Everyone’s Mathematics Content Knowledge: Mathematicians, Teachers, Parents, Students,
& Community__, is described in its abstract at the NSF site

http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0227603.

Under the terms of this grant, a
small team of professors in the Graduate School of Education of the University
of Rochester cooperates with several small school districts in the Rochester,
NY area “to develop effective ways to foster the mathematical content knowledge
necessary for a successful implementation of reform mathematics curricula. The three suburban Rochester districts are
in various stages of the adoption and implementation of curricula while the
rural districts are in the early stages of a curricular reform process.”

The grant money
is used to pay teachers’ coaches, to buy curricular materials, to reimburse
professors and teachers for the expense of travel to conferences, to invite
visiting lecturers and to help defray the University’s costs in having a school
of education that can do such things.
It – and far from incidentally – makes it attractive to the school
districts themselves, financially attractive, to adopt the programs being urged
by the education professors, for they consequently obtain at no cost to the
school district the services of these education professors in educating or
re-educating the participating teachers (“professional development”, this is
called) in both mathematics and pedagogy, all as a byproduct of showing them
how to use these particular programs, which they are all assured, by both
grant-holders and publishers, are the very finest of research-proved,
“Standards-based”, modern math curricula for their children.

The publishers’
salesmen sometimes like to call them “NSF-approved”, or “NCTM-approved”. Certainly the acronyms “NSF” and “NCTM”
appear largely in the publishers’ printed leaflets, flyers, and web-page
descriptions, some of which are used by school districts to distribute to
parents of children who will be affected by a new adoption of one of these programs.
The CMP pamphlets, for example, offer easy-to-read graphs showing the
improvement in math skills certain other districts have enjoyed, which have
adopted CMP in earlier years. In strict truth, however, NSF does not formally
approve the programs written with its financial aid, and NCTM __says__ it
never approves or disapproves any programs whatever. A matter of principle.
However, see http://www.math.rochester.edu/people/faculty/rarm/endorse.htm
for a brief account of an occasion,
during a public dispute seven years ago between NCTM and its present
adversaries, when NCTM found it convenient to violate this principle.

Also
in strict truth, there is __no__ body of valid research literature showing
that __any__ of these programs is an improvement on any competing, “traditional”,
program. (See http://newton.nap.edu/books/0309092426/html/1.html,
and pages 2 and 3 that follow, which form the Executive Summary of the
Mathematical Sciences Education Board’s study, __On Evaluating Curricular
Effectiveness: Judging the Quality of
K-12 Mathematics Evaluations__, published by the National Academies’ Press in
2004. In the full report is given
detailed evidence on the absence of such research literature, despite the
blizzard of publishers’ propaganda that would have you believe these programs
have a valid claim to superior performance.
In the time of these programs numerous mathematicians have pointed out
the visible absence of good mathematics contained in them, but their advocates
have cited studies showing that despite the absence of content (something
merely denied) the programs produce good results. It is now known that these studies, which have been so persuasive
to those already persuaded, and so unpersuasive to the parents of children
undergoing the reform programs, should in all honesty not be used against the
latter.

Ralph A. Raimi

11 December 2006