11/14/2023 6:47 AM

This Word file provides email messages that have been sent to the email
address on the National Math Panel website (NationalMathPanel@ed.gov).
The authors of these email messages have granted their permission to
share their comments with the general public.

TABLE OF CONTENTS

  ---------------------- ---------------------- ------------------------------------------
  **Date**               **Author**             **Subject**

  January 27, 2007       Anonymous              [(No Subject)](#AnonymousB)

  December 29, 2006      Askey, Richard         [Suggestions](#RichardAskey2)

  December 22, 2006      Shacter, John          [Ideas for the National Math
                                                Panel](#JohnShacter5)

  December 18, 2006      Cotter, Joan           [Comments to NMP](#JoanCotter2)

  December 15, 2006      Jordan, Don M.         [Not Using Metric Is Costing the USC
                                                Classroom Teacher Time](#DonJordan)

  December 13, 2006      Askey, Richard         [Winter Mathematics
                                                Meeting](#RichardAskey1)

  December 03, 2006      Forman, Frank          [(No Subject)](#FrankForman)

  November 22, 2006      Johnston, Ron and      [The Role of English Instruction in
                         Linda                  Mathematics](#RonAndLindaJohnston)

  November 17, 2006      Stallcup, John         [National Math Panel Meeting_Public
                                                Comment](#JohnStallcup)

  November 14, 2006      Harte, Willis          [Math Book](#HarteWillis)

  November 9, 2006       Kohlberg, Gavi         [Comment from Palo Alto](#GaviKohlberg)

  November 8, 2006       Schaar, Richard        [Thank you and Comment](#RichardSchaar)

  November 5, 2006       Shacter, John          [How to Make MAJOR (not just Marginal)
                                                Educational Improvements](#JohnShacter4)

  November 2, 2006       Yang, Steven           [Public Written Comment for the 4th
                                                Meeting](#StevenYang)

  October 30, 2006       Moschkovich, Judit N.  [Statement for National Math
                                                Panel](#JuditMoschkovich)

  October 28, 2006       Janov, Lauren          [National Math Panel in Palo
                                                Alto](#LaurenJanov)

  October 28, 2006       Gilliland, Kay         [NCSM Public Comment](#KayGilliland)

  October 27, 2006       Treloar, TJ            [Nat\'l Math Panel](#TJTreloar)

  October 27, 2006       Goodkin, Susan         [Comments for National Math Panel, Palo
                                                Alto](#SusanGoodkin)

  October 26, 2006       Shacter, John          [Panel Composition And
                                                Mission](#JohnShacter3)

  October 25, 2006       Litvin, Gary           [RE: Written Comments For The Math
                                                Advisory Panel](#GaryLitvin)

  October 22, 2006       Dugan, Melissa         [Math Panel -- Public
                                                Comment](#MelissaDugan)

  October 22, 2006       Carthel, Chris         [Comments for the National Math
                                                Panel](#ChrisCarthel)

  October 21, 2006       Hayden-Smith, Rose     [Math Instruction Panel
                                                Comments](#RoseHaydenSmith)

  October 19, 2006       Santia, Julie          [Math Instruction for Gifted
                                                Students](#JulieSantia)

  October 17, 2006       Shacter, John          [Re: Ideas for the National Math
                                                Panel](#JohnShacter2)

  October 13, 2006       Grebow, David          [Math Panel Comment](#DavidGrebow)

  October 13, 2006       North, Joseph          [Calculators, Indeed!](#JosephNorth)

  October 12, 2006       Gill, Lisa Brady       [NatMathPanel_TIcomments.pdf](#LisaGill)

  October 09, 2006       Wyrick, Emily          [Concerned Teacher](#EmilyWyrick)

  October 07, 2006       Badgett, Angelique     [Math in Elementary
                                                School](#AngeliqueBadgett)

  October 06, 2006       Wetherbee, Ted         [NCTM Focal Points \>\> NMAP
                                                review](#TedWetherbee)

  October 02, 2006       Khatri, Daryao         [Educate Everyone](#DaryaoKhatri2)

  September 26, 2006     Simons, Jeanne M.      [Grant Management](#JeanneMSimons)

  September 24, 2006     Anonymous              [I Just Discovered Your
                                                Website](#AnonymousA)

  September 20, 2006     Boone, Delores         [I Need Specific Information, Please,
                                                ASAP](#DeloresBoone)

  September 19, 2006     Bladon, Philip         [President Bush's Executive
                                                Order](#PhilipBladon)

  September 19, 2006     Jay, Roger             [National Math Initiative](#RogerJay)

  September 12, 2006     Clements, WIC          [Math/Music](#WICClements)

  September 12, 2006     Khatri, Daryao         [Re: Registration for National Math Panel,
                                                Boston Meeting](#DaryaoKhatri3)

  September 11, 2006     Kra, Irwin             [Boston National Math Panel
                                                Meeting](#IrwinKra)

  September 08, 2006     Fretwell, Jack         [RE: June 29th Public
                                                Comment](#JackFretwell)

  September 07, 2006     Doore, Stan            [Re: Comments Follow-up](#StanDoore)

  September 06, 2006     Young, Lorelle         [U.S. Students Must Know the Metric
                                                System](#LorelleYoung2)

  September 05, 2006     Khatri, Daryao         [Re: Registration for National Math Panel,
                                                Boston Meeting](#DaryaoKhatri1)

  September 04, 2006     Marshall, John         [Some Views of US Math](#JohnMarshall)

  September 02, 2006     Brownridge, Dennis     [Teaching of
                                                Measurement](#DennisBrownridge)

  September 01, 2006     Bryant, Billy          [Mathematical Achievement](#BillyBryant)

  September 01, 2006     Marain, Dave           [Statement to the National Math
                                                Panel](#DaveMarain5)

  September 01, 2006     Alves, Michelle        [Re: Pre-Registration for Sept. Math
                                                Panel](#MichelleAlves)

  September 01, 2006     Beck, Bert             [REVISED Paper Submitted for National
                                                Mathematics Advisory Panel](#BertBeck)

  August 31, 2006        Kalinowski, Melissa    [RE: National Math Panel Meeting in
                                                Cambridge from
                                                9/13-14](#MelissaKalinowski)

  August 30, 2006        Weintraub, Ben         [National Math Panel
                                                Testimony](#BenWeintraub)

  August 29, 2006        Mowers, Kathy          [Re: Deadline for Math Panel
                                                Comments](#KathyMowers)

  August 29, 2006        Jaffe, Cheryl H.       [Comments for National Mathematics
                                                Advisory Panel](#CherylJaffe)

  August 27, 2006        DeBartolo, Joseph J.   [Comments to the National Math Advisory
                                                Panel Meeting](#JosephDeBartolo)

  August 26, 2006        Rusk, Richard W.       [National Math Advisory
                                                Panel](#RichardRusk)

  August 25, 2006        Abbat, Pierre          [National Math Panel
                                                Comments](#PierreAbbat)

  August 25, 2006        Carver, Gary P.        [Comments to NMAP](#GaryCarver)

  August 23, 2006        Elwell, Jim            [Letter to NMAP](#JimElwell)

  August 22, 2006        Brenner, William       [Teaching the Metric
                                                System](#WilliamBrenner)

  August 21, 2006        Gerke, Mary            [Metric Education](#MaryGerke)

  August 20, 2006        Hooper, William        [Comments to Nat'l Math Advisory Panel
                                                Meeting](#WilliamHooper)

  August 18, 2006        Pickar, Tony           [Public Input](#TonyPickar)

  August 03, 2006        Hu, Arthur             [Parent For Real Math](#ArthurHu)

  August 03, 2006        Marain, Dave           [Re: Questions to the Panel](#DaveMarain4)

  August 02, 2006        Marain, Dave           [Re: Questions to the Panel](#DaveMarain3)

  July 19, 2006          Young, Lorelle         [Teach Only the Metric
                                                System](#LorelleYoung)

  July 13, 2006          Shacter, John          [Teaching Math with the \"KISS\"
                                                Approach](#JohnShacter)

  July 10, 2006          Jordan, Don M.         [Teaching Metric in the US](#DonJordon)

  July 07, 2006          Groth, Randall         [Evidence Standards](#RandallGroth)

  July 06, 2006          Husemann, Tony         [Re: National Math Panel\'s
                                                Focus](#TonyHusemann)

  July 04, 2006          Lester, Frank          [Letter to Drs. Faulkner and
                                                Benbow](#FrankLester)

  July 03, 2006          Henschel, Mark         [The Need to Teach SI in the Early
                                                Grades](#MarkHenschel)

  July 03, 2006          Bergey, Michelle       [Best Practice for Math
                                                Instruction](#MichelleBergey)

  June 28, 2006          Trusten, Paul          [Metric System Should Be Sole Measurement
                                                System Taught In U.S.](#PaulTrusten)

  June 19, 2006          Cantrell, Marsha H.    [Comments for June 29th](#MarshaCantrell)

  June 15, 2006          Marain, Dave           [Re: Questions to the Panel](#DaveMarain2)

  June 15, 2006          Hobbs, Forrest         [Math Curriculum Review](#ForrestHobbs)

  June 14, 2006          Marain, Dave           [Questions to the Panel](#DaveMarain1)

  June 12, 2006          Johnson, Doug          [Math Ed](#DougJohnson)

  June 11, 2006          Avent, Kirk            [High School Math](#KirkAvent)

  June 09, 2006          Hirakawa, Diane        [Suggestions for Elem.
                                                Math](#DianeHirakawa)

  June 06, 2006          McCauley, Matt         [Constructivist vs.
                                                Traditional](#MattMcCauley)

  June 06, 2006          Good, Pamela           [Math Skills Commentary](#PamelaGood)

  May 29, 2006           Harbort, Bob           [Comment From a College
                                                Teacher](#BobHarbort)

  May 26, 2006           Naughtin, Pat          [Pat Naughtin Submission to National Math
                                                Panel](#PatNaughtin)

  May 25, 2006           Raeth, John S.         [Algebra Reform](#JohnRaeth)

  May 23, 2006           Jones, Laura R.        [Math Club for Girls](#LauraJones)

  May 21, 2006           Gray, Marta            [RE: Curriculum Directors](#MartaGray1)

  May 18, 2006           Gray, Marta            [Curriculum Directors](#MartaGray2)

  May 17, 2006           Cotter, Joan           [First Grade Mathematics
                                                Research](#JoanCotter)

  May 14, 2006           Socha, Susan           [Special Education Teachers and
                                                Mathematics](#SusanSocha)
  ---------------------- ---------------------- ------------------------------------------

\-\-\-\--Original Message\-\-\-\--\
[]{#AnonymousB .anchor}**From:** Anonymous\
**Sent:** Sunday, January 27, 2006 6:13 PM

**To:** National Math Panel

I work as a mathematics teacher and department chair at a high school of
about 500 students in the Lakes Region of New Hampshire. I graduated
from the University of NH in 1985 having taken courses up to Complex
Analysis. I have worked in various NH districts before settling in to my
present position for the last nine years.

The reason I am writing to this distinguished panel is to give my
perspective on the alarming changes that have transpired since the late
1980\'s. The current trend in education has over emphasized pedagogy
over content. Misguided principals and superintendents have pushed
constructivist methodologies on teachers and evaluated them on how well
they adhered to them. Content has taken a back seat. It is rare and
unusual to find a math teacher under 30 years old who has deep knowledge
of any math beyond high school. One of my colleagues had to have me
teach him what a logarithm is - he is certified in Secondary

Math.

Mathematics as a discipline has suffered as a result of a fanatic
emphasis on real-life, hands-on activities. Proofs have been
de-emphasized. It used to be that students would learn to prove the
square root of two is irrational or do a proof by induction for the

Binomial Theorem. Learning math for its own sake is discouraged. Respect
for rigor in mathematics has fallen by the wayside; most current
geometry texts introduce the Distance Formula before developing the
Pythagorean Theorem. It is sad because I have seen a fair share of
students who get a thrill out of seeing the beauty of pure mathematics
(taboo among education elitists). Yes, students still like being able to
derive the Quadratic Formula or seeing the Fundamental Theorem of
Calculus for the first time.

Now that\'s just high school, what has happened K-8? I can tell you that
with each successive year students are less and less fluent in
computation. There has been an undeniable erosion of skills. I find it
hard to blame the students or the teachers. They did not ask for the
programs that were adopted by their district. They did not write
standards that said paper and pencil computation was not important or
that quick recall of math facts was not necessary. They did not concoct
a pedagogy that said one should just hand students a calculator so that
their lack of computation skills does not get in the way of their
critical thinking, problem-solving skills. High school teachers cannot
continue to sustain this largesse of incoming ninth graders who are
incompetent in fractions, integers, decimals, percents\... We need
balance in curriculum overview, teacher training, state standards or
dare I say-we need national standards and national competency tests.
Please put more mathematics back into Math Education.

[]{#RichardAskey2 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Richard Askey\
Sent: Friday, December 29, 2006 3:20 PM\
To: National Math Panel\
Subject: suggestions

Dear Tyrrell and others,

I will not be able to stay over for the next meeting in New Orleans,

so would like to send a few suggestions to the Math Panel.

Teacher education and licencing: The National Research Council did

a study of exams for teachers and published it as \"Testing Teacher

Candidates\". They asked someone at the Univ. of Nebraska who

studies testing to do an evaluation of tests in five areas including

mathematics. In the report on the math test he looked at, he

wrote that the questions seem reasonable but a content expert

would have to look at them to be sure. The review was done for

the US Dept of Education. I suggest that the Dept of Education

ask NRC to do this again, but have content people heavily

involved. When testing experts look at exams they have a

completely different focus. They worry about whether the results

can be reproduced, which is important. ETS sets the Praxis Tests

at a level which is too low since the main concern is to keep

people who clearly do not know enough out of a classroom. To

do this they have questions at this level overused in comparison

to those at other levels. One trouble with this is that the

exam sets too low a level of knowledge which candidates and

people educating them and those hiring them expect. To put

this crudely, I expect that a one hour exam with 60 reasonable

questions will give a similar ranking to people taking it to

a one hour exam with 6 to 10 reasonable multiple step questions,

but students will have to have a much better knowledge of

mathematics to do well on the second than on the first. The

\"reliability \" of the first test will clearly be somewhat

better than the second, but to me, the trade of this for

less content knowledge is not worth it. This is an opinion,

but one which I know is shared by quite a few others. This

should be discussed seriously and as far as I know it has

not been. Clearly on a harder test the level for passing it

has to be lower initially, but should be raised in later

years.

When the National Board for Professional Teaching Standards was

starting to test candidates, I talked with two people involved.

I said that the tests were set at too low a level, as they

had to be since the program would die immediately if they were

set where they should be. They agreed and said that the passing

rate the first year was only 33%. I asked if they had done any thinking

about how to bring the level up to what it should be in say ten

years. They said NBPTS was too busy just running the program to

have done this. As far as I can tell, they still have not done this.

My question was asked almost 10 years ago.

The Presidential Award winning elementary school mathematics teacher

in Wisconsin for 2004 wrote a paper for the Wisconsin Teacher of

Mathematics. This appeared shortly after she won this award. The

article had may mathematical errors. I have talked with a couple

people involved in this type of decision, and they both said that

the primary emphasis was on innovation rather than what the content

was and what students were learning. This clearly should not be

in your report, but a private note to the people involved in this

would be appropriate.

There will likely be more comments coming. I wish you and the committee

the best and look forward to a serious report in a year. I am not

expecting much from the preliminary report since there has not been

enough time to work on it.

Sincerely,

Dick

Richard Askey

[]{#JohnShacter5 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Shacter\
Sent: Friday, December 22, 2006 12:39 AM\
To: National Math Panel\
Subject: Ideas for the National Math Panel

**[CHAIR AND MEMBERS OF NATIONAL MATH PANEL, WITH COPY TO SECRETARY OF
EDUCATION]{.underline}** (per Ms. Jennifer Graban):\
\
This may be my last attempted contact with you, since I have not had any
evidence that anyone is paying any attention.\
\
Please let me be as direct as I can:\
\
Through no fault of your own, I am persuaded that your assigned task may
well amount to \"a stacked deck.\"\
\
THE SECRETARY OF EDUCATION HAS BASICALLY ASKED A GROUP OF ADMITTEDLY
DEDICATED BUT RATHER NARROWLY EXPERIENCED SPECIALISTS (MOSTLY
MATHEMATICAL/EDUCATIONAL EXPERTS) TO FIX SOMETHING WITH WHICH THEY HAVE
BEEN INTIMATELY CONCERNED WITH OVER THE YEARS. WHEN SHE ALSO ADDS THE
ADMONISHMENT THAT ONLY RESEARCH-ESTABLISHED \"SOLUTIONS\" BE CONSIDERED,
SHE PLACES FURTHER RESTRICTIONS ON THE OUTCOME, SINCE MUCH IF NOT ALL OF
THAT RESEARCH WAS SELECTED AND GUIDED BY THE EXPERTS ON THE PANEL OR
THEIR COLLEAGUES.\
\
FORGIVE ME, BUT ALL OF EDUCATION IS OF COURSE A \"SERVICE.\" AND
NORMALLY, WHEN WE REVIEW THE MISSION, PRIORITIES AND PERFORMANCE OF A
SERVICE AND DETERMINE HOW EACH ONE OF THEM MIGHT BE IMPROVED, WE DON\'T
JUST ASK THE SERVICE PROVIDERS, THEMSELVES.\
\
IN THE SELECTION OF YOUR PANEL, WE SHOULD HAVE AT LEAST INCLUDED
REPRESENTATIVES OF THE INTENDED \"CUSTOMERS\" OR \"POINTS OF
DESTINATION\" OF THE GRADUATES WHEN THESE ITEMS ARE EVALUATED AND
REVISIONS OR REFORMS ARE DEVELOPED. AND IN THIS CASE THE INTENDED POINTS
OF DESTINATIONS ARE SUPPOSEDLY:\
\
1. QUALITY EMPLOYERS WHO HAVE TO ENGAGE IN INCREASINGLY TOUGH WORLD
COMPETITION FOR QUALITY JOBS AND COMPETITIVE WORLD POSITIONS;\
2. QUALITY UNIVERSITIES OR OTHER INSTITUTIONS OF ADVANCED OR HIGHER
EDUCATION; AND\
3. SOCIAL/POLITICAL LEADERS WHO ARE CONCERNED WITH THE STATUS AND NEEDS
OF OUR FAMILIES, COMMUNITIES, AND SOCIETAL/GOVERNMENTAL STRUCTURES.\
\
(From a practical point of view, it may be a bit easier to find a
consensus among leaders and representatives from areas 1 and 2 above
than from area 3.)\
\
As a semi-retired engineer & management consultant and still very active
practicing volunteer teacher of youngsters and adults, I have addressed
you a couple of times. As I stated above I have no evidence that anyone
has been paying any attention.\
\
Consequently, I have to conclude that your review and recommendations
may produce some marginal improvements, but is bound to fall short of
producing the truly MAJOR improvements and reforms that are so urgently
needed today \-- not only in math, quantitative reasoning and
communications, money management, etc. \-- but also in a number of other
vital subjects which are included in most current curricula, plus still
others which are at least equally needed but would have to be added to
the current curricula.\
\
Sorry I cannot be more optimistic. But the results from past expert
panels (math and beyond) have certainly failed to meet the most urgent
past, current, or future needs.\
\
I could expand on any of the above if I received some specific feedbacks
and were asked to do so.\
\
Best wishes and happy holidays

[]{#JoanCotter2 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Joan Cotter\
Sent: Monday, December 18, 2006 10:14 PM\
To: National Math Panel\
Subject: Comments to NMP

Dear Jennifer:

I am unable to attend the Fifth Meeting of the National Math Panel, but
I\'d to provide some comments.

·       Focus Area: Learning processes

·       Name: Joan A. Cotter, Ph.D.\
·       Title: Curriculum Developer\
·       Organization you represent: Activities for Learning

To get a good start in learning mathematics, children need the
following:

Group in Fives and Tens.

Grouping in fives, as well as tens, makes it possible to recognize
quantities and see them in one\'s mind. This the Romans (VIII for 8) and
composers (5 lines per staff) knew.

Avoid Counting for Adding and Subtracting.

Babies at 5 months can add and subtract up to 3 and they are not
counting. Japanese children learn to add 4 + 3 by first seeing both
quantities mentally; then taking 1 from the 3, combining it with 4 to
make 5 and 2, which they knew. They also learn to add 6 + 7 by seeing 6
as 5 + 1 and 7 as 5 + 2; the two 5s make 10, so the sum is 13. The
Japanese have research that shows the ability to count has little
correlation to math achievement or to progress in the Piagetian
conservation tasks. We must cease to make math attainment dependent upon
one\'s rote memory capabilities.

Name Numbers Explicitly.

All Asian children learn their math by saying \"ten-1\" for eleven,
\"ten-2\" for twelve, \... \"9-ten 9\" for ninety-nine. They understand
place value, the most important concept in arithmetic, early in first
grade. The average U.S. student does not comprehend place value until
the end of fourth grade. By using explicit naming for a few months (my
research shows), U.S. students will understand place value years sooner.

Teach the Thousands in First Grade.

The basic pattern\--math has been called the science of patterns\--that
10 ones equal 1 ten, 10 tens equal 1 hundred, 10 hundreds equal 1
thousand, and so on, cannot be gleaned when the highest number discussed
is 99.  Four- and five-year-olds work with thousands throughout the
world in Montessori classrooms.

Use Correct Vocabulary.

There is no rational reason to use \"number sentence\" instead of
equation. Scientists and engineers do not ponder number sentences. The
word* equation* emphasizes the equality between the two sides of an
equation, a fundamental algebra concept.

*\"*Take away\" limits understand of subtraction because subtraction it
is not always about \"going down.\" For example, when we make change, we
go up.

\"Regrouping\" is not a mathematical term and does not imply equality to
a child. Actually, it is what a military unit does after a defeat. But
every child understands \"trading\"; so, we *trade* 10 tens for 1
hundred.

Who\'s Teaching the Math?

Many teachers assign math homework that often requires a parent\'s help.
For a variety of reasons, over-burdened parents in many families are
unable to provide this help. The achievement gap will not disappear
until the teachers do the math teaching for every child.

Joan A. Cotter, Ph.D.

[]{#DonJordan .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Don Jordan\
Sent: Friday, December 15, 2006 11:02 PM\
To: National Math Panel\
Subject: Not Using Metric is costing the USC Classroom teacher time

Subject: Metric Education in the Classroom

Every Student who attends college must take chemistry. Each year I

hear Chemistry teachers talk about how much time they waste teaching

metric because it is not taught in the early years.

I recommend that the Math Panel issue a strong statement that metric

is primary language of measurement and should be taught first in grades

K-8. and

That Colleges of Education at our Universities should have somewhere in

the curriculum a strong and lengthy content on metric measurement. That

all teachers should be tested on metric measurement.

The teacher, especially the teachers in grades K-8, should feel very

comfortable teaching metric. Today they are not. When the doors are

closed the teacher will teach what she or he knows\... the old customary

language of measurement.

We are recycling the problem and your panel has a chance to do

something about it. I hope you will.

Thanks for taking the time to read my statement.

Don Jordan, Ph.D. Mathematics Linear Algebra, USC

Center for Science Education

![](media/image1.wmf)

[]{#RichardAskey1 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Richard Askey\
Sent: Wednesday, December 13, 2006 11:26 AM\
To: National Math Panel\
Subject: Winter mathematics meeting

Dear Jennifer and Tyrrell,

I just got the program for the winter meeting of some math societies in
New Orleans and noticed there would be a panel presentation from members
of the National Mathematics Panel. I was surprised to see two math
educators and no mathematicians speaking as well as the Chair of this
group. Can I assume by duality that the presentation at the annual NCTM
meeting will have the Chair and two mathematicians? Clearly not. There
is an underrepresentation of mathematics on this panel and on the
committee.

When the MET report (Mathematical Education of Teachers) was written,
three mathematics educators were asked to write the grade band parts.

All three drafts were terrible, so bad that three mathematicians were
asked to work with the authors to help draft something which was
appropriate both mathematically and for the audience intended. It is an
unfortunate fact that we cannot assume solid mathematical knowledge even
in elementary school mathematics by many people who write about it. I
have been seeing this while reading textbooks for a publisher, and
reading many other things. This is not the place to go into details, but
they can be provided if necessary.

I hold out hope that the National Mathematics Panel will come up with a
good report, but suspect that with Wilfred Schmid\'s family problem, the
already slight representation of mathematicians will

be inadequate for the job which needs to be done.

Sincerely,

Dick

Richard Askey

\-\-\-\--Original Message\-\-\-\--\
[]{#FrankForman .anchor}**From:** Frank Forman\
**Sent:** Sunday, December 3, 2006 5:22 PM\
**To:** National Math Panel

Frank Forman here:

Questions for the National Mathematics Advisory Panel

2006 December 3

Dear National Math Panel and Tyrrell Flawn,

I am both including the questions in the message body of this e-mail

and as a MS-Word attachment which is formatted.

I am not sure who is reading the NationalMathPanel@ed.gov mailbox.

Please reply to this at once, just to say that you have received this

set of questions. Tyrrell, when we met in the Secretary\'s meeting room

to celebrate Sarah Dillard\'s moving on to greener pastures, you showed

an interest about questions I would like the Panel to address and said

you would be in touch with me, though the rush of business evidently

prevented that. So here they are.

In no way should they be taken as constituting official policy of the

Department. As you know, I work in the Planning and Program Evaluation

Service, but to make certain that my questions are not confused with

any policy of the Department, I am sending them as a private citizen.

I hereby place them in the public domain. For the moment I shall not

diffuse them further beyond Sarah Jensen and Kenneth Thomson, who work

with me and with whom I have discussed asking questions of the Panel

and advised me about how to do so.

Being in the public domain, feel free yourself to steal, modify,

misrepresent, or distort the questions and ideas. If you want further

ideas or clarifications, I shall provide them.

You should also know that, before taking up economics in graduate

school, I was an undergraduate math major (both at the University of

Virginia) and have read on my own a good deal about logic, set theory,

metamathematics, and foundations. I can hardly be accused of not

liking the subject, even if I feel the Panel should address the issue

of usefulness.

I have aimed to be comprehensive in getting all the issues out.

Accordingly, it is quite long, but I hope not overly redundant or

verbose.

QUESTIONS FOR THE NATIONAL MATHEMATICS ADVISORY PANEL

Difficult questions may elicit deep answers, so the panel will better

articulate its aims and methods.

1\. The Usefulness of Mathematics

2\. The Crisis in Mathematics Education

3\. Truth to be Told to a Benevolent Despot

4\. The Structure of Educational Governance

5\. Treatment of the Gifted

6\. The Panel as a Sham

7\. Taboo Issues

Appendix 1: Charter of the National Mathematics Advisory Panel

Appendix 2: I Samuel 17

The Duchess\'s Epilogue

QUESTION 1. THE USEFULNESS OF MATHEMATICS (three articles)

ARTICLE 1. WHETHER MATHEMATICS IS USEFUL?

It would seem that mathematics is widely used.

Objection 1: Mathematics is mostly useless, except to those very few

who will become active scientists and engineers. Engineers use mostly

algebra, a very few formulae in geometry, and rarely calculus. For the

rest of us, not even algebra gets used. When I tried to put some

simple equations into something to be read by political appointees, I

was told to take it out, it would not be understood. It would have

been very nice, too, the time I represented the policy unit at some

technical discussions about regulations if the lawyers knew basic set

theory. I wanted to interrupt and get them to write out some simple

set formulas rather than long-winded phrases.

Objection 2. Even in the sciences, thinking is rarely as exact as it

is in mathematics, and engineers rest content with good rules of

thumb. Going down the ladder, the reasoning of advertisers,

politicians, preachers, and lawyers is horrendous. Deirdre McCloskey

told me a few months ago that Donald\'s estimate that a quarter of GDP

is devoted to persuasion should probably be increased to 30 percent.

Out with Euclid\'s Elements, in with How to Lie with Statistics and The

Art of Cross-Examination.

On the contrary, the Panel should ask businessmen to specify just what

they want, both for lower math skills for the bulk of their employees

and for those who will use math beyond the junior high school level.

Reply to Objection 1. Employers will know what skills they really

want, though they need to articulate what they want far better.

Reply to Objection 2. It is important that students realize what exact

reasoning is, the better to compare it with inexact reasoning and

bogus reasoning. Learning mathematics is essential to this goal.

ARTICLE 2. WHETHER THE NATURE OF MATHEMATICS THINKING IS UNDERSTOOD?

It would seem that we know generally enough about the general

principles of proofs, formulae, sets, and so on to get on with the

business of instilling the habits of exact reasoning that characterize

mathematics.

Objection 1. Attempts of specify more exactly just what mathematical

thinking consists of are failures. It is not enough to just teach the

same old math over and over again, but to envision what basically is

at foot. Such pronouncements, like the one below, of which I extract

the high points, are circular and not helpful.

http://www.qsa.qld.edu.au/yrs1to10/kla/mathematics/ppt/trw_mathematically.ppt

What is thinking mathematically?

\* making meaningful connections with prior mathematical experiences

and knowledge including strategies and procedures

\* creating logical pathways to solutions

\* identifying what mathematics needs to be known and what needs to be

done to proceed with an investigation

\* explaining mathematical ideas and workings.

What is reasoning mathematically?

\* deciding on the mathematical knowledge, procedures and strategies to

use in a situation

\* developing logical pathways to solutions

\* reflecting on decisions and making appropriate changes to thinking

\* making sense of the mathematics encountered

\* engaging in mathematical conversations.

What is working mathematically?

\* sharing mathematical ideas

\* challenging and defending mathematical thinking and reasoning

\* solving problems

\* using technologies appropriately to support mathematical working

\* representing mathematical problems and solutions in different ways.

Objection 2. Furthermore, there is there is a pitifully small subfield

in education called \"transfer of learning,\" the idea is that learning

one subject transfers to other subjects. Near transfer is algebra to

geometry or algebra to physics. Far transfer is what my English

teacher said when I asked him why we were reading fiction, that is,

books about things that were not true. \"To learn about life!\" he said.

I now agree that novels can get at human nature in a way that

biological and social scientists cannot. Far transfer is about Latin

or geometry or, well anything, that teaches one how to think.

In fact, little is known about the transfer of knowledge of

mathematics, specifically, to other fields.

On the contrary, while not nearly enough is known about the nature of

mathematical thinking and the transfer of that thinking to other

fields, our ignorance is not total. Accordingly, the Panel should

dwell upon this issue of transfer.

Reply to Objection 1. This will not do! There\'s an anthology collected

by Robert J. Sternberg and Talia Ben-Zeev, edd., The Nature of

Mathematical Thinking (Mawhaw, NJ: Lawrence Erlebaum, 1996). See the

review by John Mason, \'Describing the Elephant: Seeking Structure in

Mathematical Thinking,\" Journal for Research in Mathematics

Education, 1977 May. The title gives the gist of the review, but the

book\'s chapters should contain ideas for the members of the Panel.

Furthermore, informal characterizations of how mathematicians think

can also be illuminating.

Three men with degrees in mathematics, physics and biology are locked

up in dark rooms for research reasons.

A week later the researchers open the a door, the biologist steps out

and reports: \'Well, I sat around until I started to get bored, then

I searched the room and found a tin which I smashed on the floor.

There was food in it which I ate when I got hungry. That\'s it.\'

Then they free the man with the degree in physics and he says:

\'I walked along the walls to get an image of the room\'s geometry, then

I searched it. There was a metal cylinder at five feet into the room

and two feet left of the door. It felt like a tin and I threw it at

the left wall at the right angle and velocity for it to crack open.\'

Finally, the researchers open the third door and hear a faint voice

out of the darkness: \'Let C be an open can.\'

And this:

An engineer, physicist, and mathematician are all challenged with a

problem: to fry an egg when there is a fire in the house. The

engineer just grabs a huge bucket of water, runs over to the fire, and

puts it out. The physicist thinks for a long while, and then measures

a precise amount of water into a container. He takes it over to the

fire, pours it on, and with the last drop the fire goes out. The

mathematician pores over pencil and paper. After a few minutes he

goes \"Aha! A solution exists!\" and goes back to frying the egg.

Sequel: This time they are asked simply to fry an egg (no fire). The

engineer just does it, kludging along; the physicist calculates

carefully and produces a carefully cooked egg; and the mathematician

lights a fire in the corner, and says \"I have reduced it to the

previous problem.\"

These and many more from

http://www.xs4all.nl/\~jcdverha/scijokes/6.html. Go ahead and indulge

yourself. Keep going with 6_1.html and 6_2.html.These jokes should

inspire some thoughts, not that mathematicians come off best, but that

you might wonder (the beginning of wisdom, recall) just what is to

think like a mathematician.

Reply to Objection 2. Transfer of knowledge is certainly an important

issue. Shifting students from useless to useful math courses will

accomplish far more than all manner of improving teaching methods for

useless courses. But our ignorance on this issue is not totally bleak.

It\'s just that so little is known, esp. at the K-12 level, about

transfer of knowledge and most esp. from math to far fields.

ARTICLE 3. WHETHER GEOMETRY IS AT ALL USEFUL?

It would seem that learning the method of rigorous deduction is useful

to all in evaluating arguments of all sorts.

Objection 1. Geometry does indeed teach the art of making rigorous

deductions. (Forget that Euclid did not know that, if b is between a

and c, the b is between c and a.) The fact is that deduction is not

all that rigorous in physics. (What is the event space in which

special relativity operates? It is not a metric space, for two

distinct events, a photon leaving the sun eight minutes ago and its

arrival on earth now has a zero Minkowski metric. I could not find an

answer in the physics library when I was an undergraduate math major

at U.Va. and had to await Mario Bunge\'s Foundations of Physics (1967),

from which I have lifted the first sentence of the Duchess\'s Epilogue.

Even so, most physicists pay little attention to lack of rigor.)

Objection 2. Geometry is little used even by mathematicians. It is

enough for scientists and engineers simply to know various formulae,

like the Pythagorean theorem, which can be taught quickly using

algebra, and not burden them with a year long course in geometry,

which comes at the expense of studying probability and statistics.

Knowing how to spot bogus statistical arguments is helpful to

everyone, not just those few who will ever use the theorems of

geometry.

On the contrary, teachers should continue to acquaint students with

rigorous reasoning, though not necessarily through geometry. The Panel

should ask how this acquaintance might be accomplished more

effectively and efficiently. A balance should be struck between the

conservative principle of retaining the wisdom of the past (which

includes the teaching of geometry) as opposed to Mr. Jefferson\'s \"dead

hand of the past\" and Mr. Mencken\'s definition of tradition as \"the

cumulation of centuries of imbecilities.\"

Reply to Objection 1. Deduction isn\'t always so rigorous in

mathematics. Recall the ghosts of departed quantities, abolished by

Bolzano and Cauchy (see

http://www.maths.uwa.edu.au/\~schultz/3M3/Bolzano_v_Cauchy.html) in the

nineteenth century and reinstated rigorously by Abraham Robinson in

the 1960s.

Law is much, much worse. Get your students to read some Supreme Court

opinions. If you have gifted students and if you are a highly gifted

teacher yourself, your students will discover that these opinions fall

far short of the standards of rigor of geometry. How can such learned

judges come to opposite conclusions or issue concurring opinions? We

know what the Court actually decided (except of course that future

courts will have to interpret the decision). It is useful to know that

the law is much less rigorous than geometry (except that all those who

have suffered both geometry and law courses don\'t seem to fully know

it).

Reply to Objection 2. While perhaps an entire year of geometry now

comes at too high an opportunity cost of teaching probability and

statistics, experience with the \"New Math\" (basically the use of the

axiomatic method for algebra) shows that geometry is a far better and

more proven way to acquaint students with the method of rigorous

deductive thinking. Trigonometry has largely been eliminated as being

too costly, and so geometry might be scaled back also, but a working

experience with the deductive method is too important to forego.

(Admittedly, just what the transfer of knowledge to near and far areas

consists of is understood much too poorly.)

This Panel won\'t recommend scrapping math beyond the eighth grade, but

at least ask what would happen if students no longer had to suffer

from high school math. (Why is school so boring? Solve this, and the

education problem in the country is licked!)

+++++++++++++++++++++

QUESTION 2. THE CRISIS IN MATHEMATICS EDUCATION (four articles)

ARTICLE 1. WHETHER THERE WAS EVER A GOLDEN AGE OF LEARNING?

It would seem that education was much better in the past.

Objection 1. There never was a golden age of learning, and students

are doing about as well as they ever did. The legend about an

inordinately difficult eighth grade 1895 test in Salinas, Kansas, is

either bogus, not what it is claimed to be, covers a select

population, or misinterpreted. (Use Google on this. Quite

illuminating.) I did not find any long-term studies for mathematics,

but Sam Wineburg\'s delightful, \"Crazy for History,\" The Journal of

American History, 2004 March, argues this to be the case for American

history, at least since 1917, and Dale Whittington, \"What Have

17-Year-Olds Known in the Past?\" American Educational Research Journal

28(4) (1991): 759-80, details specific tests. (I can supply the

articles.)

On the contrary, whether there was ever a golden age of learning,

today\'s economy demands better learning than existed in the past.

Reply to Objection 1. Still, there has been a decline in test scores

starting in the 1960s, and this must be addressed.

ARTICLE 2. WHETHER ANYTHING NEEDS TO BE DONE?

It would seem that the failure of schools to adequately educate

students is an urgent matter.

Objection 1. The normal forces of supply and demand would ensure that

the numbers of mathematicians and yoga instructors would be set by the

market. If the demand for mathematicians should rise, the number of

students majoring in the field would also rise. There are no laws

limiting the number of courses in math one can take or the number of

math majors at a college.

On the contrary, there are certainly many ways the education system

does not work properly. It is not the failure of higher education that

is at issue but insufficient numbers of those prepared to profit from

studying mathematics after high school. The Panel needs to clarify

just what failures need to be addressed and how.

Reply to Objection 1. There are at least three kinds of failure at

work

A. Market failure. One reason there are public schools is that too

many parents do not meet the economist\'s criteria for rationality and

that the public wants to protect children from their irresponsibility.

Furthermore, we all tend to have short time horizons, optimal perhaps

for our hunting and gathering days, but suboptimal now. In implicit

recognition of this, voters regularly elect politicians to cope with

this suboptimality by mandating forced savings for adults and

compulsory education for children.

B. Government failure. Teachers\' unions make it mandatory that math

teachers get paid no more than English teachers. There is a shortage

of math teachers, since they command a larger salary in the market.

This is failure at the State level, failure to reign in nation-wide

rent-seeking by unions. The President introduced legislation to cap

medical malpractice settlements. The Democrats, who get the lion\'s

share of political contributions from the National Trial Lawyers

Association, blocked the law by filibustering in the Senate. The No

Child Left Behind Act, by contrast, went through, due to the extra

monies promised to the schools, more than enough to make up for

hypothetical withdrawal of Federal funds after 2013/14.

C. The abiding failure of human nature. The problem could be as old as

when an animal could first explore and learn from its environment and

so was no longer dependent on rigid genetic instructions. Perhaps in

the Old Stone Age, when our basic thought patterns were set, children

learned everything their parents wanted them to. Certainly by the

Bronze Age, this was no longer the case, when the Lord Himself had to

mandate instruction:

Deuteronomy 11:19. And ye shall teach them your children, speaking of

them when thou sittest in thine house, and when thou walkest by the

way, when thou liest down, and when thou risest up.

Our time horizons were at most those of a year in the Old Stone Age.

In today\'s world, learning is much extended, and lifelong learning

must be fostered by instilling the habits of learning and, moreover,

learning how to learn, early on.

ARTICLE 3. WHETHER MATH NOT LEARNED NOW CAN BE LEARNED LATER?

It would seem that self-interested individuals can pick up whatever

mathematics they come to realize they need at any time.

Objection 1. There are such things as critical periods for learning.

Objection 2. Businesses will not provide training, since trained

workers can move elsewhere and take with them the training a firm has

provided.

Objection 3. Later in life, workers have too many other objectives to

accomplish, while kids have time on their hands. Furthermore, the

brain is more supple at earlier ages.

Objection 4. Workers have short planning horizons set in the

Environment of Evolutionary Adaptation (EEA), generally the Lower

Paleolithic.

On the contrary, the Panel should investigate the genuine barriers to

adult education and the extent to which mathematics education should

be directed toward enable adults to learn math later, or \"learning how

to learn.\"

Reply to Objection 1. This may very well be the case, but none of the

articles in the Journal for Research in Mathematics Education that I

spotted go into the matter.

Reply to Objection 2. This is too general a problem and looks like

rent-seeking on the part of businesses to get the taxpayer to foot the

bill for training.

Reply to Objection 3. This could merely mean that further education is

not all that it is cracked up to be.

Reply to Objection 4. This again is too general, as witness what is

supposedly \"too low\" as savings rate (never mind that most investment

comes from retained earnings by businesses), and says nothing about

how big this molehill is.

ARTICLE 4. WHETHER THE NEED FOR MATHEMATICIANS CAN BE KNOWN?

It would seem that no one can say how many mathematicians there

\"ought\" to be, since we can\'t even count them. There were, for

example, between 4 and 15 million scientists and engineers in 2003,

depending on how they are counted

(http://www.nsf.gov/statistics/seind06/c3/c3s1.htm). International

data is even less reliable. Such projections as do get made do little

more than draw straight lines on logarithmic paper.

Objection 1. We very well know that mathematics, whether at the level

of basic numeracy to that of pure mathematicians, is going to become

so much more needed as computerization of basic work through the

ability to make sophisticated new products as product cycles continue

to shrink that it is pointless to demand quantification. School reform

will lag so far behind the trends toward computerization and global

competition that there is no chance that there will be too much

mathematics taught in schools. This is what Mr. Jefferson called \"the

common sense of the matter.\"

On the contrary, the Panel should strive to find a proper balance

between requiring certain courses for all and making others available.

Reply to Objection 1. It is not at all clear that far too much math is

required in schools already. Furthermore, courses are indeed available

for those who want to further their mathematical learning.

+++++++++++++++++++++++++

QUESTION 3. TRUTH TO BE TOLD TO A BENEVOLENT DESPOT (two articles)

ARTICLE 1. WHETHER THE PANEL BASICALLY WANTS TO TELL A BENEVOLENT

DESPOT WHAT TO DO?

It would seem that there is a inbuilt bias toward saying \"this is how

I want the world to be\" and then advising a benevolent despot about

what to do. This \"truth model,\" as James M. Buchanan calls it is

entirely different from his \"exchange model,\" which says that voters

simply have different desires about what public goods they want

provided, whence the basic problem become how to design a constitution

so that voters get what they want for themselves without having to pay

for too many things they don\'t want.

Objection 1. There is such a consensus about what students should

learn in mathematics that there is really no difference between the

truth and exchange models. The only real differences are over how best

to achieve these aims, and finding out is the principle task of the

Panel.

On the contrary, there are serious divisions about the aims of

education, and they play into the culture wars. This war, according to

James Davidson Hunter, The Culture Wars, is all about the existence of

transcendental source of (absolute) morality vs. the contextualist

(whom the absolutists call relativist) approach, which denies this.

The Panel should strive to bring this conflict out in the open, for no

one takes an extreme position on these matters.

Reply to Objection 1. This is just not true, as argued above, if only

due to differences on what mathematics is good for, to the extent that

this have even been thought about in the first place. Beyond this,

there are four principle philosophies of education:

A. Perennialism, which urges the study of the classics, be it the

Bible, the Koran, or the Little Book of Chairman Mao, whose principle

task is that of moral education. Largely vanished from the public

schools in America, a look at Ministry of Education websites in East

Asia shows that specific time periods in Japan and Korea are set aside

for moral education, specifically so named. Conservatives generally

regard moral education as a good thing. This not specifically related

to mathematics, however.

B. Essentialism. This, also called \"Back to the Basics,\" holds that

education should be organized around specific subjects and around the

specifics of knowledge to be learned in each of these subjects. This

approach also appeals to conservatives, as well as to expert panels

who strive to draw up curriculum standards.

C. Progressivism. This approach envisions not so much a body of

materials to be learned but rather the formation of habits of thought.

(Dewey\'s concentration on training students to serve the common social

good can be detached from this overall vision). This appeals to

liberals.

D. Existentialism. This says that students should build their own

course of study by following their various blisses. This also appeals

to liberals, even if they characteristically are concerned with

society-wide problems, and it assumes that young students both know

their \"particular circumstances of time and place\" (Hayek, see below)

about what paths to take to achieve whatever they want to achieve,

regardless of how well they are prepared to cope in the world after

they leave school. It assumes that education is as much about the

self-construction of personalities as anything else. It is the

ultimate in free-market choice.

ARTICLE 2. WHETHER THE PANEL\'S ADVICE IS ARBITRARY?

It would seem that are chosen by a Darwinian selection process. Those

that deviate from the median by more than seven percent are deemed

over the top, off the wall, and out to lunch. (The worst case is that

of bio-ethicists.) The consensus changes over time: one can join a

panel today without insisting that trigonometry be mandated or even

taught. Probably not so with geometry and certainly not so for anyone

insisting that no math be required after junior high school. Any

consensus will lag behind reality.

Objection 1. There is an objective, external world out there, and the

process of deduction, induction, and abduction results in closer and

closer approximation to this reality.

Objection 2. Cultural literacy does not require much knowledge of

mathematics. Eric Donald Hirsch, a top expert in the subject, did not

give Gödel\'s Incompleteness Theorem, certainly the most celebrated

result in mathematics in the last century, among his 6,900 entries.

See http://www.barlelby.com/59/ for an online version of The New

Dictionary of Cultural Literacy, third edition, 2002)

On the contrary, the Panel should think instead about what level of

mathematical literacy can be achieved in popular culture as well as

about what students should take in school and how the courses should

be taught. General familiarity with statistics would benefit the

citizens, as consumers and as voters alike, in helping them spot bogus

arguments. This is hardly an arbitrary claim.

Reply to Objection 1. Whether or not it would be arbitrary to demand

knowledge of this particular item, surely a broader appreciation (his

definition of mathematics is just \"The study of numbers, equations,

functions, and geometric shapes (see geometry) and their

relationships. Some branches of mathematics are characterized by use

of strict proofs based on axioms. Some of its major subdivisions are

arithmetic, algebra, geometry, and calculus.\"

Reply to Objection 2. It would be remarkable if students should

remember the quadratic equation! I have asked countless folks to

recite it to me; only those who had majored in math remember it. (I

actually had an occasion to use it, once, when I was fooling around

with some data and came up with a quadratic equation.) The most that

might be hoped for is that equations be presented, along with graphs,\^

in popular culture, such as non-science television shows and pamphlets

that get handed out on street corners. Yet I am reliably informed that

even in Japan, where students score well on international math tests

and who are driven hard by themselves, their parents, and their

society, equations are absent in popular culture.

\^(The first graph was drawn about 1340 by Nicole Orésme of the

Universities of Paris and Oxford and was unknown to mathematicians of

ancient Greece, Rome, China, and India. There may be examples of early

graphs representing continuous change, but since this concept did not

fit into their deep cultures, it was not developed. This is my

favorite example of a second-nature notion that is so prevalent around

the world that it seems like first nature.)

=====================

QUESTION 4. THE STRUCTURE OF EDUCATIONAL GOVERNANCE

It would seem that the present policy of letting the States do

whatever they will to improve education, under the prospect of no

longer getting all the Federal monies they would have if educational

progress is not adequate constitutes the right mix between central and

local control.

Objection 1. The main issue is not what supposedly should be taught

and how but why these reforms and strengthenings have not already been

done. Teachers in America are so bound by bureaucratic rules that they

cannot rely their own \"the knowledge of the particular circumstances

of time and place\"\^ and adopt their teaching accordingly. Liberate the

teachers from the educrats!

\^(The reference is to Friedrich Hayek\'s article, \"The Use of
Knowledge

in Society\" (1945) American Economic Review 35(4): 519-530,

http://virtualschool.edu/mon/Economics/HayekUseOfKnowledge.html, which

all Panelists are strongly urged to read.)

Objection 2. Research is directed too heavily toward \"one size fits

all,\" even as this is hotly denied. When NCLB gets reauthorized, care

should be taken to allow experimentation and not punish trying out

promising practices that eventually fail. A superior form of

educational governance would view failures positively, as being

necessary to learn from experience. Henry Petroski\'s engaging Success

through Failure shows this for engineering, but it is applicable

everywhere. Education reform is as much about setting up a learning

network among educators as it is in achieving immediate results on

standardized tests. The plain reality is that humans communicate

largely by stories, meaning that a teacher will pay the greatest

attention to a fellow teacher that has gained his respect and less to

empirical studies no matter how good.\^

\^(The Panelists are also strongly urged to browse, if not read, Paul

H. Rubin\'s Darwinian Politics: The Evolutionary Origin of Freedom

(Rutgers UP, 2002). Paul is a professor of economics and law at Emory

University and is well-versed both in Public Choice economics and

socio-biology, whose respective paradigms of utility and fitness

maximization conflict with each other. On page 177, he recounts the

case of Ford Motor Company using statistical analysis to defend itself

in the Pinto liability case, as deliberately including a dangerous

feature in its design of the Pinto on grounds of its over-all

cost-effectiveness, as the law indeed explicitly allowed. The

prosecutors paraded the injured in front of the jury, and the jurors

awarded huge damages to the injured.)

Objection 3. The largest (though unintended) effect of NCLB is to take

control from teachers, schools, districts, and counties and

concentrate them in the States. By mandating State-wide curriculum

standards, any previous drift toward increasing critical thinking in

the school curriculum, has been halted.

Objection 4. It is \"thinking outside the box\" that is more needed than

simply feeding back answers on tests. No National Panel can possibly

reach any consensus on what such \"lateral thinking\" consists of, to

say nothing about how to foster its development. The only way to

foster lateral thinking is to let teaching innovations bubble up from

the bottom, even at the expense of failing to make Adequate Yearly

Progress in some instances.

On the contrary, the Panel should pay the greatest attention to the

structure of educational governance, along with thinking about what

mathematics is good for and how better to teach it. How much

within-State variation should be allowed is something for the Panel to

dwell upon and about which to make representations to the

reauthorizers of NCLB. Every mathematician (and economist) knows that

It is rarely the case that optimum = maximum (which would lead to

irresponsibility ) or optimum = minimum (which would stifle

innovation). Indeed, establishing a learning network about successful

and unsuccessful innovations could well lead to better (though not

immediately measurable) improvements in math education than any

implementing of what are now regarded as better methods of teaching.

Reply to Objection 1. This would lead to irresponsibility. The choices

are 1) choice (free market), 2) irresponsibility, and 3)

accountability. There being no real prospect of privatizing education,

the No Child Left Behind Act strengthens accountability, and

strengthens it beyond what the States are capable of.

Reply to Objection 2. Such a learning network can indeed be set up,

but it should still be up to the States to try only those reforms that

ensure that the basics still be learned and that Adequate Yearly

Progress continue to be made.

Reply to Objection 3. There is nothing that precludes changes in NCLB,

when it is reauthorized, to allow different standards varying by

school. Students at some schools could be assessed partly on the basis

of better and better mastery of higher-level thinking skills. There is

no need for this to come at the expense of failing to improve on the

mastery of basic skills.

Reply to Objection 4. It will be well enough for States to define and

measure these higher-level skills (which need to be applied only to

certain schools or selected students within those schools.) If a

learning network, that reaches across the States can be set up, more

and more States can join in as they themselves see fit. Thought should

be given to flexibility within counties, districts, and individual

schools, but within the overall framework of making Adequate Yearly

Progress according to State-wide standards that apply to all schools.

It is not clear that there are genuine trade-offs to be made.

===============

QUESTION 5. TREATMENT OF THE GIFTED (two articles)

ARTICLE 1: WHETHER IT IS ASSUMED BY DEFAULT THAT ALL CHILDREN ARE

GIFTED?

It would seem that the Panel members, all being gifted themselves,

design curricular practices that work mostly for the gifted and pass

over the heads of normal kids.

Objection 1. The Panel members have all been careful to realize this

problem.

Objection 2. As an example of correcting this bias, the \"new math\"

axiomatic approach has largely been abandoned, for introducing

concepts too early, though it lives on math instruction. I was a new

math guinea pig in 1959-60 but find that post-new math students manage

to know, for example, what the intersection of sets are and what the

distributive law states. It\'s just that these \"New Math\" ideas are

introduced only later and are not subject to axiomatic treatment. Yet

the much more recent \"constructivist\" approach to mathematics (also

called the problem solving approach) has been subject to the same

criticism as being inappropriately advanced conceptually for most

students.

On the contrary, the Panel should scrutinize all studies they have for

differential effects on different students of various programs, search

the universe and its attics for other studies, and that future studies

pay attention to this issue. They should bear in mind what the great

sociologist of science, Robert King Merton, dubbed the Matthew effect,

viz.:

For vnto euery one that hath shall be giuen,

and he shall haue abundance:

but from him that that not

shal be taken away

euen that which he hath.

\--Matthew 25:29 (original 1611 spelling) (Parable of the Talents)

The Panel should be acutely aware of the intrusion of the culture wars

into the writing of articles and their evaluation. The notion of a

transcendental and absolute source for morality that dominates on one

side (what was in the 1950s called the \"squares,\" as opposed to the

\"mods\") manifests itself psychologically in standing firm and not

caving in. Both sides accuse the other side of caving in with great

regularity . The \[Henry\] Petroskian virtue of \"success through

failure\" is more needed than ever before. (This is also called

\"openness to experience\" and is among the \"Big Five\" Personality

Factors, clusters determined through factor analysis, the others being

conscientiousness, agreeableness, extroversion, and neuroticism).

Reply to Objection 1. The bias toward assuming everyone is like

oneself is so powerful that it creeps in despite the best intentions.

Reply to Objection 2. There are arguments that the problem-solving

approach (that is, the pedagogy of presenting real-world problems to

students rather than drilling them on formulae, whereby they construct

their own understanding of mathematics on the fly) works at least as

well as more traditional back-to-the-basics approach. See, Alan H.

Schoenfeld, \"Problem Solving in The United States, 1970-2007: Research

and Theory, Practice and Politics\" (Draft H, October 14, 2006. To

appear in: G. Törner, A. H. Schoenfeld, & K. Reiss (Eds.). Problem

Solving Around the World\--Summing up the State of the Art. Special

issue of the Zentralblatt für Didaktik der Mathematik/International

Reviews on Mathematics Education: Issue 1, 2008 (which I can supply).

ARTICLE 2: WHETHER THE SPECIAL NEEDS OF THE GIFTED ARE BEING IGNORED?

It would seem that the gifted are basically no different from the rest

of the population and that they will flourish in any atmosphere.

Objection 1: Penny Van Deur\'s study, \"Gifted Reasoning and Advanced

Intelligence,\" from the Australian Association for the Education of

the Gifted and Talented, of which I can supply a copy,\^ , argues that

gifted children are able to negotiate and construct meta-mental maps,

that is several diverse ways of approaching problems and, moreover

begin to do so at the earliest ages.

\^The essay was at http://www.nexus.edu.au/teachstud/gat/vandeur.htm,

but many or most of its files have been moved to

http://www.dete.sa.gov.au. Lots of articles on the gifted are still

there.

Objection 2: Gifted children commonly get bored with school and even

drop out. They do not achieve their potential.

On the contrary, it is crucial to resolve these issues, especially to

bring out the full creative powers of the gifted, for America will

increasingly rely on the special contribution of their gifted in an

increasingly competitive world.

Reply to Objection 1: The opportunity costs of specially catering to

the gifted, as argued in Mara Sapon-Shevin\'s Playing Favorites:

Gifted Education and the Disruption of Community should not be

slighted.

Reply to Objection 2. Gifted children, in fact, are better off in

mainstream classrooms: \"Many gifted programs, for example, focus on

counseling able students or developing their social skills through

activities such as leadership training and small-group interaction

(e.g., Parker, 1983). In the name of improving gifted students\'

creativity, many programs forego substantial academic content and,

instead, teach problem-solving skills in isolation from any particular

academic content. These \'skills\' are easily acquired and applicable

only to narrowly-structured problems; they are, in consequence, of

doubtful merit (McPeck, 1981). As Borland (1989, p. 174) notes,

special instruction for the gifted often consists of \'an array of

faddish, meaningless trivia\--kits, games, mechanical step-by-step

problem-solving methods, pseudoscience, and pop psychology.\' Moreover,

educators frequently dissuade students from attempting intellectually

challenging programs by exaggerating the emotional and social risks of

strategies like acceleration and early college attendance (Daurio,

1979).\" From Aimee Howley, Edwina D. Pendarvis, and Craig B. Howley,

\"Anti-intellectualism in U.S. Schools, Educational Policy Analysis

1(6) (1994). http://epaa.asu.edu/epaa/v1n6.html

=====================

QUESTION 6. THE PANEL AS A SHAM (two articles)

ARTICLE 1. WHETHER THE PANEL IS A SHAM?

It would seem that the Panel is basically a sham. No real new research

will be undertaken, any more than the Institute for Education Sciences

has come up with substantial research in the several years of its

existence. Reform is going to take place. Absent research, it will

take the tried and true path of increasing test scores in line with

conservative ideology (essentialism mostly) of drill, drill, drill,

discipline, discipline. It is risky to do actual research, which might

threaten the entrenched positions of ideologues. (This is all but

argued by Edward A Silver: \"Improving education research: Ideology or

science?\" Journal for Research in Mathematics Education, 34(2) (2003

March) , p. 106f, of which a copy can be furnished.)

Objection 1. These charges are so predictable that they will be hurled

regardless of the facts of the situation and therefore should be

ignored. The Panel members do indeed represent a wide variety of

points of views.

On the contrary, the Panel should address the matter of the culture

wars up front and relate them to various philosophies of mathematics

education.

Reply to Objection 1. The culture wars are nevertheless real.

Reply to Objection 2. In an ideal world, these relationships would be

better known, but in any case doing well on tests is important for

morale, and doing well encourages students and citizens alike to to

continue to strive.

ARTICLE 2. WHETHER SCORING WELL ON TESTS IS AN END IN ITSELF?

It would seem that the Panel is a sham, for winning the symbolic

competition in irrelevant tests of irrelevant courses has become an

end it itself and is at best weakly related to becoming economically

\"competitive,\" itself a dubious notion.

Objection 1. Good preparation in mathematics is increasingly important

in a world where production is becoming more and more based upon

applying science and using engineering skills.

Objection 2. The tests we have are good measures of the skills that

will be more and more needed in the future economy.

Objection 3. Being better prepared in mathematics will enable American

workers to do better in international economic competition.

On the contrary, while scoring well on tests is not without its

symbolic value, and even if test scores are imperfect indicators,

having indicators is indispensable. Those who rail against them are

nevertheless quite willing to use them in support of their ideas.

Reply to Objection 1. However true this is, and still only a small

number of workers will be engaged in jobs that actually utilize

mathematics beyond arithmetic, wee know from biology that animals

engage in ritualized combat, that when beta-male challenges alpha-male

the winner does not kill the loser but accepts a ritual sign of

submission. In human warfare, representatives from two parties can be

chosen to engage in one-to-one combat rather than the winning side

exterminating the losing side. An appendix contains the original

description of a very well-known instance of symbolic competition.

Reply to Objection 2. Since the relationship between mathematics

education and national \"competitiveness\" is nearly unknown, and since

\"competitiveness\" has no operational definition anyhow, except

GDP/capita (just like \"access\" to education winds up getting measured

by enrollment), it is well enough that U.S. students score high on

these tests. For the same reason, the Iron Curtain countries thought

it so important that they win in the get a large number of medals in

the Olympic games that they cheated. They thought it tremendously

important that their very best athletes run a fraction of a second

faster than other countries\' best athletes, even though this says next

to nothing about the average speed of the members of these countries,

since the distribution of running speeds is not normal at the extreme

ends.

Reply to Objection 3. Spokesmen for education in countries in the Far

East, such as Japan, China, and Singapore regularly complain that,

while their students do very well on math tests, they cannot think,

that is think creatively. There aren\'t any really good tests of

independent thinking, and no one know how to foster it.

++++++++++++

QUESTION 7: TABOO ISSUES

This page intentionally blank.

++++++++++++++

APPENDIX 1: CHARTER OF THE NATIONAL MATHEMATICS ADVISORY PANEL

\[added to remind the panel members of their original purposes, even if

my suggestions may, in some instances, go beyond the original

charter.\]

http://www.ed.gov/about/bdscomm/list/mathpanel/charter.pdf

Authority

The National Mathematics Advisory Panel (Panel) is established within

the Department of Education under Executive Order 13398 by the

President of the United States and governed by the provisions of the

Federal Advisory Committee Act (FACA) (P.L. 92463, as amended; 5

U.S.C. App.).

Background

In order to keep America competitive, support American talent and

creativity, encourage innovation throughout the American economy, and

help State, local, territorial, and tribal governments give the

Nation\'s children and youth the education they need to succeed, it

shall be the policy of the United States to foster greater knowledge

of and improved performance in mathematics among American students.

Purpose and Functions

The Panel shall advise the President and the Secretary of Education

(Secretary) on the conduct, evaluation, and effective use of the

results of research relating to proven-effective and evidence-based

mathematics instruction, consistent with policy set forth in section 1

of the Executive Order. In carrying out its mission, he Panel shall

submit to tthe President, through the Secretary, a preliminary report

not later than January 31, 2007, and a final report not later than

February 28, 2008.

The Panel shall obtain information and advice as appropriate in the

course of its work from:

1\. Officers or employees of Federal agencies, unless otherwise

directed by the head of the agency concerned;

2\. State, local, territorial, and tribal officials;

3\. Experts on matters relating to the policy set forth in section 1;

4\. Parents and teachers; and

5\. Such other individuals as the Panel deems appropriate or as the

Secretary may direct.

Structure

The Panel shall consist of no more than 30 members as follows:

1\. No more than 20 members from among individuals not employed by the

Federal Government, appointed by the Secretary for such terms as the

Secretary may specify at the time of appointment; and

2\. No more than 10 members from among officers and employees of

Federal agencies, designated by the Secretary after consultation with

the heads of the agencies concerned. The Secretary shall designate a

Chair of the Panel from among the group of 20 members who are not

employed by the Federal Government. Non-Federal members of the Panel

shall serve as Special Government Employees (SGEs). As SGEs, the

members will provide personal and independent advice based on their

own individual expertise and experience.

Meetings

Subject to the direction of the Secretary, the Chair, in consultation

with the Designated Federal Official (DFO), shall convene and preside

at meetings of the Panel, determine its agenda, direct its work, and,

as appropriate, deal with particular subject matters, and establish

and direct the work of subgroups of the Panel that shall consist

exclusively of members of the Panel.

The Secretary or her designee shall name the Designated Federal

Official (DFO) to the Panel. The Panel shall meet at the call of the

DFO or the DFO\'s designee, and this person shall be present for all

meetings. The DFO will work in conjunction with the Chair to convene

meetings of the Panel.

Meetings are open to the public except as may be determined otherwise

by the Secretary in accordance with Section 10(d) of the FACA.

Adequate public notification will be given in advance of each meeting.

Meetings are conducted and records of the proceedings kept as required

by applicable laws. A majority of the members of the Panel shall

constitute a quorum but a lesser number may hold hearings.

Estimated Annual Cost

Members of the Panel who are not officers or employees of the United

States shall serve without compensation and may receive travel

expenses, including per diem in lieu of subsistence, as authorized by

law for persons serving intermittently in Government service (5 U.S.C.

5701-5707), consistent with the availability of funds.

Funds will be provided by the Department of Education to administer

the Panel. The estimated annual person-years of staff support are four

\(4\) Full-Time Equivalents. The estimated two-fiscal-year cost will be

approximately \$1,000,000.

Report

The Panel shall submit to the President, through the Secretary, a

preliminary report not later than January 31, 2007, and a final report

not later than February 28, 2008. Both reports shall, at a minimum,

contain recommendations, based on the best available scientific

evidence, on the following:

1\. The critical skills and skill progressions for students to acquire

competence in algebra and readiness for higher levels of mathematics;

2\. The role and appropriate design of standards and assessment in

promoting mathematical competence;

3\. The processes by which students of various abilities and

backgrounds learn mathematics;

4\. Instructional practices, programs, and materials that are effective

for improving mathematics learning;

5\. The training, selection, placement, and professional development of

teachers of mathematics in order to enhance students\' learning of

mathematics;

6\. The role and appropriate design of systems for delivering

instruction in mathematics that combine the different elements of

learning processes, curricula, instruction, teacher training and

support, and standards, assessments, and accountability;

7\. Needs for research in support of mathematics education;

8\. Ideas for strengthening capabilities to teach children and youth

basic mathematics, geometry, algebra, and calculus and other

mathematical disciplines;

9\. Such other matters relating to mathematics education as the Panel

deems appropriate; and

10\. Such other matters relating to mathematics education as the

Secretary may require.

The Secretary may require the Panel, in carrying out subsection 2(b)

of Executive Order 13398, to submit such additional reports relating

to the policy set forth in section 1 of the Executive Order.

Termination

Unless extended by the President, this Advisory Panel shall terminate

April 18, 2008.

This charter expires April 18, 2008.

Approved:

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Date Secretary

Filing date:

+++++++++

APPENDIX 2: I Samuel 17

(a well-known instance of the use of symbolic competition)

1 Now the Philistines gathered together their armies to battle, and

were gathered together at Shochoh, which belongeth to Judah, and

pitched between Shochoh and Azekah, in Ephes-dammim.

2 And Saul and the men of Israel were gathered together, and pitched

by the valley of Elah, and set the battle in array against the

Philistines.

3 And the Philistines stood on a mountain on the one side, and Israel

stood on a mountain on the other side: and there was a valley between

them.

4 And there went out a champion out of the camp of the Philistines,

named Goliath , of Gath, whose height was six cubits and a span.

5 And he had an helmet of brass upon his head, and he was armed with a

coat of mail; and the weight of the coat was five thousand shekels of

brass.

6 And he had greaves of brass upon his legs, and a target of brass

between his shoulders.

7 And the staff of his spear was like a weaver\'s beam; and his spear\'s

head weighed six hundred shekels of iron: and one bearing a shield

went before him.

8 And he stood and cried unto the armies of Israel, and said unto

them, Why are ye come out to set your battle in array? am not I a

Philistine, and ye servants to Saul? choose you a man for you, and let

him come down to me.

9 If he be able to fight with me, and to kill me, then will we be your

servants: but if I prevail against him, and kill him, then shall ye be

our servants, and serve us.

10 And the Philistine said, I defy the armies of Israel this day; give

me a man, that we may fight together.

11 When Saul and all Israel heard those words of the Philistine, they

were dismayed, and greatly afraid.

12 Now David was the son of that Ephrathite of Bethlehem Judah, whose

name was Jesse; and he had eight sons: and the man went among men for

an old man in the days of Saul.

13 And the three eldest sons of Jesse went and followed Saul to the

battle: and the names of his three sons that went to the battle were

Eliab the firstborn, and next unto him Abinadab, and the third

Shammah.

14 And David was the youngest: and the three eldest followed Saul.

15 But David went and returned from Saul to feed his father\'s sheep at

Bethlehem.

16 And the Philistine drew near morning and evening, and presented

himself forty days.

17 And Jesse said unto David his son, Take now for thy brethren an

ephah of this parched corn, and these ten loaves, and run to the camp

to thy brethren;

18 And carry these ten cheeses unto the captain of their thousand, and

look how thy brethren fare, and take their pledge.

19 Now Saul, and they, and all the men of Israel, were in the valley

of Elah, fighting with the Philistines.

20 And David rose up early in the morning, and left the sheep with a

keeper, and took, and went, as Jesse had commanded him; and he came to

the trench, as the host was going forth to the fight, and shouted for

the battle.

21 For Israel and the Philistines had put the battle in array, army

against army.

22 And David left his carriage in the hand of the keeper of the

carriage, and ran into the army, and came and saluted his brethren.

23 And as he talked with them, behold, there came up the champion, the

Philistine of Gath, Goliath by name, out of the armies of the

Philistines, and spake according to the same words: and David heard

them.

24 And all the men of Israel, when they saw the man, fled from him,

and were sore afraid.

25 And the men of Israel said, Have ye seen this man that is come up?

surely to defy Israel is he come up: and it shall be, that the man who

killeth him, the king will enrich him with great riches, and will give

him his daughter, and make his father\'s house free in Israel.

26 And David spake to the men that stood by him, saying, What shall be

done to the man that killeth this Philistine, and taketh away the

reproach from Israel? for who is this uncircumcised Philistine, that

he should defy the armies of the living God?

27 And the people answered him after this manner, saying, So shall it

be done to the man that killeth him.

28 And Eliab his eldest brother heard when he spake unto the men; and

Eliab\'s anger was kindled against David, and he said, Why camest thou

down hither? and with whom hast thou left those few sheep in the

wilderness? I know thy pride, and the naughtiness of thine heart; for

thou art come down that thou mightest see the battle.

29 And David said, What have I now done? Is there not a cause?

30 And he turned from him toward another, and spake after the same

manner: and the people answered him again after the former manner.

31 And when the words were heard which David spake, they rehearsed

them before Saul: and he sent for him.

32 And David said to Saul, Let no man\'s heart fail because of him; thy

servant will go and fight with this Philistine.

33 And Saul said to David, Thou art not able to go against this

Philistine to fight with him: for thou art but a youth, and he a man

of war from his youth.

34 And David said unto Saul, Thy servant kept his father\'s sheep, and

there came a lion, and a bear, and took a lamb out of the flock:

35 And I went out after him, and smote him, and delivered it out of

his mouth: and when he arose against me, I caught him by his beard,

and smote him, and slew him.

36 Thy servant slew both the lion and the bear: and this uncircumcised

Philistine shall be as one of them, seeing he hath defied the armies

of the living God.

37 David said moreover, The Lord that delivered me out of the paw of

the lion, and out of the paw of the bear, he will deliver me out of

the hand of this Philistine. And Saul said unto David, Go, and the

Lord be with thee.

38 And Saul armed David with his armour, and he put an helmet of brass

upon his head; also he armed him with a coat of mail.

39 And David girded his sword upon his armour, and he assayed to go;

for he had not proved it. And David said unto Saul, I cannot go with

these; for I have not proved them. And David put them off him.

40 And he took his staff in his hand, and chose him five smooth stones

out of the brook, and put them in a shepherd\'s bag which he had, even

in a scrip; and his sling was in his hand: and he drew near to the

Philistine.

41 And the Philistine came on and drew near unto David; and the man

that bare the shield went before him.

42 And when the Philistine looked about, and saw David, he disdained

him: for he was but a youth, and ruddy, and of a fair countenance.

43 And the Philistine said unto David, Am I a dog, that thou comest to

me with staves? And the Philistine cursed David by his gods.

44 And the Philistine said to David, Come to me, and I will give thy

flesh unto the fowls of the air, and to the beasts of the field.

45 Then said David to the Philistine, Thou comest to me with a sword,

and with a spear, and with a shield: but I come to thee in the name of

the Lord of hosts, the God of the armies of Israel, whom thou hast

defied.

46 This day will the Lord deliver thee into mine hand; and I will

smite thee, and take thine head from thee; and I will give the

carcases of the host of the Philistines this day unto the fowls of the

air, and to the wild beasts of the earth; that all the earth may know

that there is a God in Israel.

47 And all this assembly shall know that the Lord saveth not with

sword and spear: for the battle is the Lord\'s, and he will give you

into our hands.

48 And it came to pass, when the Philistine arose, and came and drew

nigh to meet David, that David hasted, and ran toward the army to meet

the Philistine.

49 And David put his hand in his bag, and took thence a stone, and

slang it, and smote the Philistine in his forehead, that the stone

sunk into his forehead; and he fell upon his face to the earth.

50 So David prevailed over the Philistine with a sling and with a

stone, and smote the Philistine, and slew him; but there was no sword

in the hand of David.

51 Therefore David ran, and stood upon the Philistine, and took his

sword, and drew it out of the sheath thereof, and slew him, and cut

off his head therewith. And when the Philistines saw their champion

was dead, they fled.

52 And the men of Israel and of Judah arose, and shouted, and pursued

the Philistines, until thou come to the valley, and to the gates of

Ekron. And the wounded of the Philistines fell down by the way to

Shaaraim, even unto Gath, and unto Ekron.

53 And the children of Israel returned from chasing after the

Philistines, and they spoiled their tents.

54 And David took the head of the Philistine, and brought it to

Jerusalem; but he put his armour in his tent.

55 And when Saul saw David go forth against the Philistine, he said

unto Abner, the captain of the host, Abner, whose son is this youth?

And Abner said, As thy soul liveth, O king, I cannot tell.

56 And the king said, Inquire thou whose son the stripling is.

57 And as David returned from the slaughter of the Philistine, Abner

took him, and brought him before Saul with the head of the Philistine

in his hand.

58 And Saul said to him, Whose son art thou, thou young man? And David

answered, I am the son of thy servant Jesse the Bethlehemite.

It should be noted that there are contrary happenings, recorded later

in the same book and in two books following it:

1 Samuel 25:22

So and more also do God unto the enemies of David, if I leave of all

that pertain to him by the morning light any that pisseth against the

wall.

1 Samuel 25:34

For in very deed, as the Lord God of Israel liveth, which hath kept me

back from hurting thee, except thou hadst hasted and come to meet me,

surely there had not been left unto Nabal by the morning light any

that pisseth against the wall.

1 Kings 14:10

Therefore, behold, I will bring evil upon the house of Jeroboam, and

will cut off from Jeroboam him that pisseth against the wall, and him

that is shut up and left in Israel, and will take away the remnant of

the house of Jeroboam, as a man taketh away dung, till it be all gone.

1 Kings 16:11

And it came to pass, when he began to reign, as soon as he sat on his

throne, that he slew all the house of Baasha: he left him not one that

pisseth against a wall, neither of his kinsfolks, nor of his friends.

1 Kings 21:21

Behold, I will bring evil upon thee, and will take away thy posterity,

and will cut off from Ahab him that pisseth against the wall, and him

that is shut up and left in Israel.

2 Kings 9:8

For the whole house of Ahab shall perish: and I will cut off from Ahab

him that pisseth against the wall, and him that is shut up and left in

Israel.

++++++++++++

THE DUCHESS\'S EPILOGUE

When all was over\--that is, when it became clear that nothing

important is ever over in mathematics education\--in came the Duchess

and drew her morals.

Giftedness Moral: Neither suppose everyone is gifted nor ignore their

special needs, for they are America\'s future.

Anthropological Moral 1: Our time horizons were set during the Old

Stone Age.

Anthropological Moral 2: Contests are highly ritualized, in animal and

human societies alike. Beware of elevating scoring well on tests to an

end in itself, even as doing well on these tests will certainly boost

the morale of Americans.

Cultural Moral: Bring the Culture Wars out in the open. There will be

less dissension and more openness to pick the best from both sides.

Polarization is only apparent.

Economics Moral 1: The forces of supply and demand will solve most

problems. If they do not, consider whether the cure is worth its cost.

Economics Moral 2: Beware of using terms like competitiveness that

have no operational meaning. What would happen if the United States

ceased to be \"competitive\"?

Economic Moral 3: Always consider the cost of lost opportunities, such

as the neglect of education for the gifted.

Epistemological Moral: Do not fall back on ideological beliefs where

knowledge is not firm. Rather, sponsor further research.

Ethical Moral: Do not just say \"this is how I want the world to be\"

and pretend to be giving advice to a benevolent despot.

Metaphysical Moral: Learning comes from within; it does not come from

without. \"Lead a horse to water, but you can\'t make him drink.\" To be

sure, rare teachers can inspire a willingness to learn, but in

practice only 10-15 percent of the variation in learning comes from

variation in methods of course instruction, less if learning is

learning habits of thought, rather than just doing well on tests. Free

will is hard to measure, even to proxy, so it is rarely considered in

research in mathematics education.

Pedagogical Moral 1: How mathematics education is transferred to other

realms is more important that the math itself, since few students will

ever use math beyond what they learn in junior high school.

Pedagogical Moral 2: Realize that shifting students from less useful

math courses to more useful ones will do more for general mathematics

education than improving teaching techniques for less useful courses.

Political Moral 1: The structure of educational governance is the

overriding one. Always ask why reforms have not been implemented. What

are the institutional barriers?

Political Moral 2: Heed the conservative admonition to learn from

tradition, but do not be afraid to propose different approaches.

Finally, the moral of this set of moral is: Check your Premises.

\-\-\-\--Original Message\-\-\-\--\
[]{#RonAndLindaJohnston .anchor}From: Ron and Linda Johnston\
Sent: Wednesday, November 22, 2006 2:00 PM\
To: National Math Panel\
Subject: The Role of English Instruction in Mathematics\
\
\
Dear Panel Members,\
\
Please accept my paper on what I believe to be the missing link in\
mathematics education. The two page paper is being submitted as an\
attachment in PDF format. Thank you for this.opportunity to bring so\
important a matter to your attention. .\
\
Sincerely, Ron Johnston

## ![](media/image2.wmf)

[]{#JohnStallcup .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Stallcup\
Sent: Friday, November 17, 2006 6:42 PM\
To: National Math Panel\
Subject: National Math Panel Meeting_Public Comment

**Public Comment to** *"The National Math Advisory Panel"*

**Palo Alto, California November 5,6 2006**

**Presented by: John Stallcup**

**Co-Founder APREMAT/USA**

Mr. Chairman and panel members welcome to California, I thank you and
the Panel for this opportunity to speak today. I am the initiator and
Co-Founder of APREMAT/USA. APREMAT is the most effective Spanish
language early elementary math program in existence and is in use today
by over two million first, second, and third grade students in a number
of Latin American countries. APREMAT/USA as a program of the Heritage of
America Foundation will be providing the APREMAT program free to the two
million Spanish speaking first, second, and third grade students in the
US who by and large are failing to become proficient in mathematics.

I want to point to four areas of opportunity that need the Panel's
attention:

[First:]{.underline} There is a lack of focus, attention, energy or
concerted effort, on effective early elementary math education in
general and specifically for English language learners. Not only is
there no one person or entity in charge of early elementary math
education at the federal, or state level but no major grant making
authority either public or private funds early elementary math programs
that reach large numbers of students even though efforts to improve
reading are well funded across the board at all levels and by
corporations including Toyota and State Farm.

The lack of effective early elementary math instruction creates the
pervasive lack of computational skills in the middle grades and is a
primary cause of future problems learning algebra and higher math. You
cannot reasonably expect the average student to be able to master
Algebra without having learned their computational skills to the level
of automaticity.

There is a National Institute for Literacy, a National Science
Foundation, a Reading First initiative, support from all levels of
government and non profits for reading programs large and small. Not
only is there no National Institute for Mathematics, or a National
Mathematics Foundation, there isn't even a Mathematics **Second**
Initiative. There are no governmental organizations or initiatives
(present company excluded) focused exclusively on mathematics education
let alone elementary mathematics.

Symbols and hero's matter a great deal. Laura Bush and many other
celebrities champion reading. Who will champion mathematics? Without
focus you get failure. Without funding you flounder. Without attention
there is no energy.

If Mathematics education is ***"Mission Critical"*** you sure can't tell
by where the attention, energy and resources are going.

[Second:]{.underline} Math is a world language and a fungible skill set.
There are a number of proven well researched early elementary math
instructional programs being effectively employed to teach literally
millions of less academically fortunate students around the world that
could be effectively employed here with little funding or iteration and
are not. I would be surprised if anyone in the room had ever heard of
APREMAT before today and that is emblematic of a key problem in our
attempt at improving math education in the US. Cost effective, easy to
implement early elementary math instructional practice and programs have
been developed, researched and fielded around the world, and all but
completely ignored in the US to our continuing detriment.

-   There is near universal employment of the Abacus in parts of China
    to enable their five year old students to acquire number sense, and
    compute large columns of figures easily. Chinese students are
    getting a two year head start over our best math students because
    they employ a simple, easy to use, inexpensive, tool. In practice a
    near system wide ***"advanced placement"*** program. Chinese
    educators understand the positive impact of the manipulative aspects
    of the abacus on brain function for learning more complex subjects.
    All we need to get started is a set of well produced Utube training
    pod casts, a few million dollars for a supply of Abacus and the will
    to use them.

-   Many countries in Latin America use the APREMAT program. First
    initiated in 1998 by a Honduran foundation APREMAT is already
    effectively used by over two million first, second, and third grade
    students to learn mathematics because it works. Unlike the US, if
    you don't pass the math exam for your grade level in Latin America
    you do not advance to the next grade. If you think we have problems
    finding qualified math teachers willing to work in harsh
    environments, imagine the problems educators have in the jungles of
    Latin America (no roads, no windows, dirt floors, no college
    degrees, no money, etc). Yet the second poorest country in Latin
    America, Honduras created an effective easy to use, consistently
    administered, inexpensive, research based, instructional practice
    for teaching math on the radio in Spanish.

> Two thirds of the three and a half million Hispanic k-3 students in
> the US speak Spanish at home and are by a large margin not
> *"proficient"* in math by any definition. Hispanic students taking the
> California high school exit exam fail to pass the math portion more
> often than the reading portion. The word's "destination disaster" come
> to mind.

[Third:]{.underline} We can choose to use the internet to empower math
education or not. But we cannot claim there is not an effective,
inexpensive way to do so. The greatest potential opportunity to advance
the level of mathematics instruction occurred a few weeks ago when
Google bought Utube. The internet is already an effective, albeit
disorganized "force multiplier" for education. The future of math
education may in large part be determined by how well educators,
organize and integrate online distance learning with the classroom.

Imagine if someone had bothered to video tape a years worth of Jaime
Escalante teaching calculus. India and Singapore are collaborating on
[www.heymath.com](http://www.heymath.com/) a math instruction website
for high school students. A great deal of math instructional content is
already available online, whether The Math Forum at Drexel University or
MIT's Open University. The opportunity is ***"here and now"*** to
organize both existing and new content into easy to use, effective math
education ***"toolsets"*** for students and teachers. The content is not
well organized or easy to navigate but I suspect the Googleplex down the
road could fix that in very little time.

[Fourth:]{.underline} Mathematics needs a new narrative. Mathematics as
a brand needs to be repositioned. When you listen to the majority of
Americans, discuss mathematics you get the distinct impression that
something in our bottled water or our Starbucks coffee has given us a
mass case of math phobic ***"dyscalculia*"**. This includes many
educators. In America we are ashamed when we are illiterate but it is ok
to be innumerate. The far too common and universally acceptable refrain
*"I am just no good at math"* implies a cultural belief in ability over
effort. This debilitating belief combined with the general acceptability
of being innumerate are two of the biggest impediments to increasing the
level of math achievement in the US.

In order to change the narrative two things must occur.

-   Parents must understand ***"How high is up".*** The ***"fraud of
    proficiency"*** that now exists due to NCLB, must be exposed
    publicly to enable parents to understand what mathematics problems
    their child needs to be able to solve. This could be accomplished in
    part by providing an online quiz based on the NAEP math questions
    with the national version of ***"proficiency"*** as the yardstick.
    You could encourage daily newspapers to publish the NAEP and TIMSS
    questions as well.

-   The Gross Rating Points (GRPs) of mathematics in the media
    (electronic & print) need to be significantly increased. The number
    of hours available of high quality, excellent, relevant, "Sticky"
    television programming that either directly (Discovery Channel) or
    indirectly (CSI) teaches science and history are in the thousands.
    The number of hours of mathematics programming is to low to mention.
    Ask Madison Avenue and Hollywood for help.

I suspect no more proficient group of mathematics professionals has ever
been assembled. Expectations for this panel are high. Educators across
the country are hoping your work will result in actionable concrete
recommendations that work for all students no matter their income,
origin, or genotype.

Although the Federal budget only provides about 8% of education funding,
you will set the mathematics education agenda for at least the coming
decade. The ability to identify, clarify and help initiate fundamental
positive changes in mathematics education is in your hands.

I hope you create a clarifying focus on all levels of mathematics that
isn't there at the state or federal levels. I hope you encourage more
foundation support for early math education. I hope you will benchmark
and borrow proven effective mathematics instructional programs from
other nations. I believe if you leverage the internet today thru public
private collaborations you will accelerate the process of improvement
and last but not least please begin the process of changing the present
negative, exclusive debilitating, narrative to the positive, empowering,
inclusive, story that is mathematics. Thank you and good luck.

\-\-\-\--Original Message\-\-\-\--\
[]{#HarteWillis .anchor}**From:** Harte Willis\
**Sent:** Tuesday, November 14, 2006 2:29 PM\
**To:** National Math Panel\
**Subject:** math book

Dear National Math Panel,

Greetings from Iowa!  After seeing the piece in today's Times about math
teaching, I wanted to bring your attention to a Russian middle school
math book I translated and adapted several years ago.  The response to
the textbook has been, as they say, overwhelming, and reviews uniformly
positive.  You may see the book at
[http://www.perpendicularpress.com](http://www.perpendicularpress.com/)

Thanks,

Will Harte,

George Washington High School,

[]{#GaviKohlberg .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Gavi Kohlberg\
Sent: Thursday, November 09, 2006 11:36 PM\
To: National Math Panel\
Subject: Comment from Palo Alto

**Public comment for meeting of National Mathematics Advisory Panel**

**November 6, 2006**

**Gavi Kohlberg**

**Stanford School of Medicine**

**Former CEO of Digi-Block**

I strongly urge the National Mathematics Advisory Panel to examine
scientific evidence related to **innovative** teaching and learning
methods and tools. While evaluating long-practiced teaching techniques
is clearly valuable and necessary, evaluating innovations in math
education is of utmost importance. Innovations should have tremendous
importance to us in math education, just as they have tremendous
importance to us in fields such as medicine. Innovations let us do
things that we couldn't do before, or let us do things better than
before. For example, the advent of imaging technology allows us to see
within the human body without opening it up. Perhaps an advance in math
education could allow us to teach place value so well we would not have
to teach it over again each time we introduce a new procedure!

Just to make clear the potential benefits of innovation. Note that
identifying an advance that can teach a segment of mathematics 20%
"better" would lead to huge benefits if it were identified and applied
to a significant portion of our students. I strongly believe that such
innovations currently exist and are underutilized.

To ground this public comment in reality, I'd like to briefly give an
example of an innovation that I believe is underutilized that could have
a tremendous effect on our ability to teach students the foundations of
mathematics.

The Digi-Block teaching method, invented by my father, mathematician
Elon Kohlberg, and honed by many dedicated individuals and teachers over
the last several years has the potential of increasing students'
understanding of number sense dramatically (both in terms of depth of
understanding as well as in efficiency of learning).

The great advance of Digi-Block is its merging of theoretical
mathematical ideas (like the elegance and complexity of base-10) with
educational realities (for example, that young children benefit from
tactile experiences) to build an effective framework for children to
learn and explore mathematics. This framework gives young children the
ability to do such things as proof their answers to problems, or even
proof the algorithms themselves.

Yesterday Mr. Williams deplored the recommendation to take away time
from geometry teaching, noting that it was the lone course that
emphasized proofs in the K-12 curriculum. Here is an innovation that
allows proof to be an integral part of elementary school math.

So far there has been very positive feedback from teachers who have
successfully implemented Digi-Block. In addition there is currently a
research study over a year underway with students with significant
cognitive disabilities in Phoenix, Arizona led by Dr. MaryLou Cheal at
Arizona State University. The preliminary results of this study show
tremendous improvement in number sense in a cohort that is believed to
have extremely limited mathematical potential. Hopefully, similar
improvement will be shown through a study in a broader cohort in the
near future.

In my opinion, one of the weaknesses of math education, particularly at
the foundation, the elementary school level, is that very few of the
individuals involved, from teachers to policy makers, have a strong
background in both elementary school education and higher level
mathematics. This severely hurts our ability to identify and evaluate
innovations, like Digi-Block, that make important advances that must be
appreciated both mathematically and educationally. Yet this is a
potential strength of this panel, where as a whole, these abilities are
present. So I respectfully urge you to make sure that important
innovations are recognized and, if effective, recommended to be
incorporated into mainstream mathematics education now and in the
future.

Thank you.

[]{#RichardSchaar .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Richard Schaar\
Sent: Wednesday, November 08, 2006 12:44 PM\
To: National Math Panel\
Subject: Thank you and comment

Tyrrell and Jennifer, I wanted to thank you for the opportunity to speak
to the National Math Panel.  I hope that I was able to answer
the members\' questions.  If they seek more information, most of my
points were from the document submitted by Texas Instruments to
the Panel.  The history of TI and Instructional Calculators and TI\'s
experience in elementary school is not so if the Panel has further
questions in that area, please contact me.  If there is a question on TI
written materials, you can contact any of us. 

 

In addition, I would like to thank you for letting us attend the day\'s
sessions which we did.  There was a great deal of very helpful
information presented during the day.  It caused me to reflect on my
experience with National work in math and science education so I would
like to make a personal comment on the topic of a National Curriculum. 
Texas Instruments has supported many National efforts to solve our K-16
math education problems, the Glenn Commission, Susan Sclafani\'s Summit,
and now this Panel.  We also were deeply involved in the business
communities efforts in getting No Child Left Behind through the
Congress. 

 

At each step, we were told that a National Curriculum was politically
impossible.  I have even been told by some that we do not want a
National Curriculum because we cannot get it right. 

 

Frankly, I look to this Panel to get it right.  However, once it does,
with all decisions about books, curriculum, and standards made
locally, the Panel\'s recommendations maybe impossible to apply.. 
Each recommendation will have to be modified for the local district, and
who knows what will happen after the modification to the efficacy of the
intervention. 

 

We see it on a small scale with the successful Richardson program.  It
cannot be applied in the same way in the District next door because they
use different materials in a different way even though the state test is
still the metric.  I think that the Panel needs to take this issue into
consideration as it deliberates and consider it for inclusion in its
recommendations.

 

Once again, thank you and if you need any more information from us,
please feel free to contact us anytime.  You are doing critically
important work.

 

Regards,

Richard

[]{#JohnShacter4 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Shacter\
Sent: Sunday, November 05, 2006 1:28 AM\
To: National Math Panel\
Subject: How to Make MAJOR (not just Marginal) Educational Improvements

Dear Members of National Math Panel -\
\
I wonder whether you shouldn\'t make your math-teaching recommendations
in the context of the following, somewhat broader challenge.\
\
After all \-- how can we decide what and how to teach **anything
(including math)**, except in the context of an accepted mission and of
specific performance criteria.\
\
I have sent you several more specific memos on the teaching of math,
money management, savings and stock investments, etc.,\
and I shall be glad to try to answer your questions or expressions of
interest.\
\
Best wishes - John Shacter\
\
=========================

## HOW TO MAKE MAJOR (not just MARGINAL) EDUCATIONAL IMPROVEMENTS

Drafted by John Shacter, 11-04-06, for public consideration and,
hopefully, action.\
\-\-\-\-\-\-\-\-\-\-\-\-\-\--\
I shall begin by listing five rather basic assumptions for the reader\'s
consideration and approval.  \
\
To start: \-- Organizations without declared and accepted missions are
condemned to flounder and misallocate their always limited, precious
resources.\
There must be some reason for having ANY educational system.\
In order to develop and implement an acceptable reform package, it is
thus essential that we first agree on the basic mission for
\"education.\"\
\
**1. I PROPOSE THE FOLLOWING OVERALL MISSION FOR \"EDUCATION\":**

## TO FACILITATE AND PROVIDE THE MEANS FOR STUDENTS (YOUNGSTERS AND ADULTS) TO ENJOY QUALITY LIVES AND CAREERS IN TODAY\'S AND TOMORROW\'S \"SHRINKING\" AND EVERMORE DEMANDING AND COMPETITIVE \"OUTSIDE\" WORLD.

(We shall elaborate on that mission statement, below. I don\'t claim any
originality for this draft-statement. However, there has been
demonstrably a surprising amount of confusion or outright bypassing by
the experts on this essential, basic point.)\
\
\-\-\-\-\-\-\--

## 2. FROM NOW ON, WE SHOULD ALL AGREE THAT THE REAL COMPETITION IS NO LONGER AMONG OUR DOMESTIC SCHOOLS, SYSTEMS OR STATES. IT IS BETWEEN OUR NATION AND A DIVERSE AND RAPIDLY DEVELOPING GROUP OF LEADING NATIONS, SUCH AS CHINA, INDIA, AND \-- YES \-- FINLAND.

\-\-\-\-\-\-\--

## 3. AS PART OF EDUCATION, \"SCHOOLING\" IS A \"SERVICE\" \-- AND AS ANY SERVICE \-- WHEN WE REVIEW ITS PERFORMANCE, OR HOW IT COULD BE IMPROVED, WE SHOULD ALWAYS ASK THE INTENDED CUSTOMERS OF THE SERVICE, ALONG WITH THE PROVIDERS OF THE SERVICE.

## AND IN THE CASE OF \"SCHOOLING,\" SOME OF THE MOST IMPORTANT CUSTOMERS HAVE GIVEN US THEIR ANSWERS. FOR EXAMPLE, QUALITY EMPLOYERS, PROFESSIONALS AND LEADERS OF QUALITY UNIVERSITIES HAVE BEEN TELLING US THAT TOO MANY OF OUR GRADUATES NEED \"REMEDIAL\" EDUCATION BEFORE THEY CAN BE FURTHER TRAINED OR EDUCATED. 

(We educators don\'t like the term \"remedial.\" We prefer the term
\"developmental\" education.)\
\
\-\-\-\-\-\-\--

## 4. BECAUSE OF WHAT THEY READ OR HEAR IN THE MEDIA, MOST OF THE PUBLIC IS FAIRLY SATISFIED WITH THEIR OWN LOCAL SCHOOLS, ALTHOUGH THEY MAY EXPRESS SOMEWHAT VAGUELY CRITICAL VIEWS OF THE NATIONWIDE STATUS OR PERFORMANCE OF \"EDUCATION\" AS A WHOLE.

## THEREFORE, ANYONE WHO IS FAMILIAR WITH THESE CONDITIONS SHOULD AGREE THAT MAJOR IMPROVEMENTS IN OUR SCHOOLING WILL CONTINUE TO BE VIRTUALLY IMPOSSIBLE TO ACHIEVE, UNLESS A COALITION OF PROFESSIONAL GROUPS, ET AL. IS FORMED AND WAYS ARE FOUND TO LAUNCH AN EFFECTIVE PUBLIC INFORMATION AND MOBILIZATION INITIATIVE.    A BASIC MESSAGE AND SET OF RECOMMENDATIONS WILL THUS ALSO HAVE TO BE DEVELOPED AND AGREED UPON. MOST OF THE SPECIFICS WILL OF COURSE HAVE TO BE ADDRESSING VARIOUS APECTS OF ENRICHED AND UPDATED CURRICULUM AND TEACHING APPROACHES.

\-\-\-\-\-\--

## 5. FINALLY, IT IS ESSENTIAL THAT THE MESSAGE AND THE WHOLE REFORM PROGRAM BE CONSTRUCTIVE AND FUTURE-ORIENTED, NOT CRITICAL AND PAST-ORIENTED. WE SHOULD NOT BLAME TEACHERS FOR ANYTHING, BUT INDICATE HOW THEY CAN BE FURTHER DEVELOPED. AFTER ALL, TEACHERS AS WELL AS STUDENTS HAVE BEEN AMONG THE VICTIMS OF OUR INSTITUTIONAL INADEQUACIES. 

\-\-\-\-\-\-\--\
\
Please allow me to elaborate on these points.\
\
\
It has become obvious that \-- for the sake of our quality lives and
careers, if not survival \-- we shall have to prepare most of our
public-school (and college) students more fully for quality jobs,
careers, and any meaningful and enjoyable participation in the ever
wider open and competitive \"flat outside world.\"\
\
So far, we have been losing ground to old and new foreign competition.
For example, whereas the Chinese and Indians turn out hundreds of
thousands of engineers per year, the U.S. is preparing only about
70,000, and a substantial portion of them are either foreign-born or the
children of foreign born parents. (However, we are by far the world\'s
undisputed number-one producer of LAWYERS per capita!)\
\
We must also meet this challenge to our school systems, communities, and
homes if we wish to prevent serious slippages in our economic, political
and security positions, as well as in our share of the world\'s quality
jobs. And we need to provide effective \"catch-up\" and \"enrichment\"
programs for interested adults, as well.\
\
However, this time \-- before we \"invent\" another round of educational
planning and improving \-- let\'s all commit to the following
proposition:\
\
IT SHOULD BE THE CORE MISSION OF OUR PUBLIC SCHOOLS TO PROVIDE THE
FULLEST POSSIBLE PREPARATION OF OUR GRADUATES FOR THE \"OUTSIDE
WORLD.\"\
\
Other interests can be added. However, they should not be allowed to
compete with this core mission.\
\
With 13 years of mandated schooling, not counting any pre-K programs, we
should be able to include the following three target areas as key parts
of the \"outside world\":\
\
A. QUALITY EMPLOYMENT AND CAREER\
B. QUALITY HIGHER EDUCATION OR ADVANCED CAREER TRAINING, AND\
C. QUALITY PARTICIPATION IN FAMILY, COMMUNITY AND SOCIETY.\
\
Once we can assume agreement on the above, let us reconfirm and resolve
that the public-school curricula of all states should include the
following basic and \"spice-up\" categories of knowledge and skills. I
have not attempted to tie each of the following items to just one of the
above three mission targets. Rather, I feel that many of the following
items would meet the requirements of more than one of the above mission
targets:\
\
1. EFFECTIVE COMMUNICATIONS \--\
INCLUDING EFFECTIVE LISTENING AND READING, WITH UNDERSTANDING AND
CRITICAL EVALUATION, FOLLOWED BY CLEAR AND EFFECTIVE SPEAKING AND
WRITING.\
\
Without effective communication, there can be hardly any expression or
payoff for any level of education. We currently list some \-- not all
\-- of these topics under titles like reading, vocabulary, spelling,
language arts, and writing. All too frequently, any or all of these
topics are inadequately presented, appreciated, and practiced. A very
simple spot interviewing process \-- say of customers in a mall \--
could quickly establish the existing gaps among the youngsters and
adults of any community.\
\
(I have in fact developed a list of rather simple questions which could
be applied in this kind of sampling process on this topic and any the
following ones. For example, one or a couple of the earliest questions
should test for effective LISTENING. Obviously, students should be
evaluated for levels of understanding and reasoning, and for clarity and
effectiveness of expression \-- not for the particular views they
express. Some teacher development will undoubtedly be required.)\
\
2. EFFECTIVE QUANTITATIVE OPERATIONS AND REASONING (MATH), including
\"numbers sense\", and including sound choices involving the development
and selection of preferred alternatives for a future with uncertainties
or \"probabilities,\" as well as with facts and data. (See also the next
topic.)\
\
In today\'s rapidly advancing and highly competitive world, this second
category of teaching and learning is almost as essential as the first
area.\
\
3. MONEY MANAGEMENT, including understanding budgeting, determining
profit or loss, assets and liabilities, savings versus stock
investments, etc.\
\
Properly presented, this and the following categories can be also
regarded as highly interesting and challenging \"spice-up\" areas. They
can be combined or interspersed with any current curriculum.\
\
4. INNOVATION, including scientific, technical/engineering, business,
societal/government, and artistic innovations, and successful project or
business startup requirements.\
\
5. PERSONAL SUCCESS REQUIREMENTS, including reliability, punctuality,
consideration for laws and morals, consideration for members of the
family, work-teams, neighborhood, society at large \-- and a willingness
to insist on the adoption of these personal qualities on the part of all
responsible individuals and groups.\
(This item to be applied at once, including a spirit of collaboration
and proper behavior in our schools, buses, etc.)\
\
6. AWARENESS OF THE BASIC ELEMENTS OF OUR COMMUNITY, STATE, NATION AND
WORLD, including key constitutional, political, societal, economic and
cultural factors, and current events, issues, and choices.\
\
7. AWARENESS OF MAJOR, PAST WORLD-WIDE AND U.S. DEVELOPMENTS from
ancient to current times.\
\
8. REPEATED REVISITATIONS OF CHALLENGING CAREER CONSIDERATIONS AND
PLANNING, starting in the elementary grades, with clusters of careers,
interesting and well informed outside volunteers, self-evaluation, etc.\
\
This outline of the proposed next round of educational planning and
improving will be continued in the form of additional memoranda.\
It is not intended to formulate an entirely new curriculum to take the
place of the current state or local curricula, BUT IS INTENDED TO
\"SPICE UP\" THE RATHER BORING AND SEEMINGLY PIECEMEAL OR OVERLY COMPLEX
APPROACHES THAT WE ARE TAKING IN SO MANY OF OUR TEXTBOOKS AND
CLASSROOMS, TODAY!\
AND IT IS ALSO INTENDED TO RELATE THE CURRICULUM AND TEACHING TO THE
REAL, OUTSIDE WORLD.\
\
More complete success will also depend upon the existence of ADULT
LEARNING PROGRAMS, of early PRE-K PROGRAMS, and of enriching AFTERNOON
AND SATURDAY PROGRAMS (like boys and girls clubs), particularly for
children who are in need of community subsidies and support.\
\
Obviously, current and future teachers will have to be introduced to
some new topics and approaches which would greatly broaden their
preparation in today\'s teachers colleges. Until these colleges enrich
their own staff and curriculum, this further development could be
arranged in combination with experienced, perhaps retired, local
volunteer-professionals or military retirees in communications, in the
sciences, in engineering, in enterprise and innovation planning and
management, etc. At least hundreds of age-appropriate, introductory
videos are also available. They should be prescreened and accessible to
every teacher at every public school. (If youngsters know anything, they
know how to watch television, and teachers can push the \"pause\" button
for discussion purposes. Most teachers or supervisors would want to
preview the videos before introducing them to the class. A considerable
fraction of the materials may be almost as \"new\" to the teachers as to
the students.)\
\
The professional volunteers could also assist the teaching process by
participating in teachers workshops as well as in regular classrooms.
Current certification requirements need to be broadened for this
purpose.\
\
The whole program is intended to be implemented in a positive and
constructive \-- not critical \-- school and community environment.
Let\'s make our teaching and learning as exciting, challenging,
profitable and enjoyable, as possible. One of the aims should be to make
our teachers and students look forward to their next day of \"work.\"\
\
©2006 John Shacter; semi-retired engineer, management-and-technology
consultant, and still very active volunteer-teacher and educational
consultant.\
Additional background information can be found in the Who\'s Who volumes
of Science and Engineering, and of Finance and Business.\
(By the way, John received his early primary and secondary education in
Vienna, Austria.)

[]{#StevenYang .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Steven Yang\
Sent: Thursday, November 2, 2006 4:41 PM\
To: National Math Panel\
Subject: Public Written Comment for the 4th Meeting

**A Simple and Duplicatable Math Solution for the United States**

by Steven Yang, CEO and Founder, MathScore.com

I believe that the National Math Panel should emphasize a solution that
can ***easily be duplicated*** across every school within the United
States, regardless of teacher talent, access to computer technology, and
budget. Although proposals to hire staff, train teachers, entertain
students, and integrate technology all have merit, none of those types
of proposals will effectively scale to meet the needs of every school in
the United States.

According to the findings in TIMSS, Asian countries, such as Singapore,
China, and Japan greatly outperform the United States. They consistently
outperform us without having made any significant adjustments to the way
they teach math for well over 100 years. What they do differently is so
basic that it surprises me to see such confusion in the United States.

In Asian countries, students are forced to focus on math facts by
regularly doing timed tests. By the end of 4th grade, nearly 100% of all
students in these countries have complete mastery over their
multiplication and addition math facts. Kindergarteners are typically
exposed to addition, and by 2nd grade, addition math facts have already
become second nature. By the end of 4th grade, without question, these
kids know their multiplication facts. Furthermore, these students
typically demonstrate superior critical thinking skills. This is because
students who know their basics have a proper foundation on which to
build critical thinking skills.

According to student usage at MathScore.com, less than 1 in 5 of our 5th
grade users start the school year with mastery over multiplication math
facts! The root cause of failure of United States math students is an
inadequate foundation in basic math skills, caused by the failure to
memorize math facts at a young age. Nearly every Algebra I teacher in a
low performing school will agree with that statement. If you would like
some details regarding our analysis, I would be happy to supply you with
anonymous usage data.

As the solution, I believe the National Math Panel should suggest a
mandate on regular timed math tests starting with first graders. There
should be a standard on the number of problems, difficulty of the
problems, and the time allotted at each grade level. This way,
regardless of school resources, every teacher in the country can
unambiguously adhere to this approach. I also believe knowledge of math
facts should be tested on state tests. **This solution is simple,
measurable, and can be implemented easily in every school in the United
States.** It even supports the NCTM Focal Points.

For schools with computers, I believe technology can help. MathScore.com
provides customizable, printable math facts worksheet generators at no
charge. I believe these generators can make the process of producing
appropriate math facts worksheets as painless and efficient as possible.
We can also provide a patent-pending, adaptive learning system for
schools that have Internet access. I believe the proven improvement in
test scores seen by users of our system validates the approach of
starting with math basics before focusing on critical thinking skills.

If there is anything I can do to help, please feel free to let me know.

Sincerely,

Steven Yang

CEO and Founder, MathScore.com

[]{#JuditMoschkovich .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Judit N. Moschkovich\
Sent: Monday, October 30, 2006 3:55 AM\
To: National Math Panel\
Subject: statement for National Math Panel

Dear Ms. Graban,

I am attaching a statement I wrote to represent TODOS at the November

6th session. Please let me know that you have received this document

and were able to open it.

Thank you for time and consideration,

Dr. Judit N. Moschkovich

Associate Professor

Education Department

University of California

![](media/image3.wmf)

[]{#LaurenJanov .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Lauren Janov\
Sent: Saturday, October 28, 2006 3:26 PM\
To: National Math Panel\
Subject: National Math Panel in Palo Alto \-- Material You Might Like to
Consider as Part of Your Program

Ms. Graban\--

 

Please see the attached compilation of current research and practices re
the benefits of teaching math in ability groupings.  Hopefully this will
be of interest to your panelists during their November 5th and 6th
discussions at Stanford as you try to discern the \"processes by which
students of different abilities or backgrounds learn math.\" 

 

It was prepared for California elementary school audiences, but the
concepts and findings are applicable to larger audiences too (secondary
schools and schools in other states).

 

It is presented in a myth-reality format to make it less dense and
more accessible to any one interested in the subject matter. Several
individuals created this document, each of whom was interested in
improving the delivery of math to elementary students.  None worked
under the auspices of any school or program.

 

\-- Lauren Janov

![](media/image4.wmf)

[]{#KayGilliland .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Kay Gilliland\
Sent: Saturday, October 28, 2006 1:05 AM\
To: National Math Panel\
Subject: NCSM Public Comment

Here is a copy of the remarks I hope to make. Please include them in the
meeting materials of the Panel. Thank you, Kay

![](media/image5.wmf)

[]{#TJTreloar .anchor}\-\-\-\--Original Message\-\-\-\--\
From: TJ Treloar\
Sent: Friday, October 27, 2006 7:53 PM\
To: National Math Panel\
Subject: Nat'l Math Panel

As a speech-language pathologist in the Ventura Unified School District
in Southern California, I work with special ed children every day.  I am
aware of how much energy and funding is spent on these children. 
However, as a mother of two children identified as gifted, I have a
vested interest in the energy and funding spent on their education. 

 

My daughters love math and science, and I am pleased with how excited
they are to learn these subjects!  They need to have teachers who are
well able to keep them interested.  We need my little girls to grow up
to be scientists and leaders of our world. 

 

Please fund programs for gifted education.  As much as we need to raise
the bar for our lower functioning students, it is equally important to
inspire our children who love to learn and are capable of excelling
academically!

 

Thank you,

TJ Treloar

[]{#SusanGoodkin .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Susan Goodkin\
Sent: Friday, October 27, 2006 6:12 PM\
To: National Math Panel\
Subject: Comments for National Math Panel, Palo Alto

Dear Ms. Graban, 

 

Attached please find comments submitted for the National Math Panel
hearing in Palo Alto.  I have submitted the comments both as an
attachment and as text below, in case you have any problems opening the
attachment.

 

Thank you.

 

Susan Goodkin

 

Comments Submitted to the National Math Panel

 

I am a lawyer, Rhodes Scholar, and advocate for gifted children. I am
writing to strongly urge this panel to address the needs of gifted math
learners in its final recommendations. \
Far too frequently, gifted learners are simply ignored in the
classroom.  Not only is this detrimental to our gifted students, it is
detrimental to our country's continued leadership in science and related
fields.  As I am sure you are well aware, recent international
assessments establish that an embarrassingly small percentage of our
students have mastered advanced math compared to their peers in
countries such as Singapore and Japan.

 

At best, our teachers are simply too overwhelmed by other demands,
particularly NCLB pressure to focus on low-achieving students, to meet
the needs of gifted students. Too many educators also lack the training
and/or curriculum resources to adequately teach gifted students even if
they try to find the time to do so.  At worst, far too many parents
(myself included) have encountered teachers and administrators who are
unabashedly hostile to the notion that high-ability math students are
not adequately served by a curriculum geared to bringing all students up
to mere proficiency.

 

Below, I have included two of my op-ed pieces that have been published
in newspapers across the country. I submit these pieces for two reasons.

First, I believe the pieces raise issues \-- the impacts of NCLB on math
instruction for gifted children, and the problems with the prevailing
use of whole-group instruction, rather than ability-grouping, to teach
math \-- that need to be considered and addressed by this panel.

More importantly, in response to these pieces, I have heard from
educators and parents across the country. Almost without exception, they
have expressed dismay at the abysmal failure of our public schools to
provide an appropriate education for our gifted math students.

If this panel truly aims to improve math instruction for all students,
it must ensure that teachers are provided with the training, resources
and incentives to appropriately educate their gifted students. Without
these prerequisites, the needs of our gifted students will continue to
be ignored.

Thank you for your consideration of these comments.

Susan Goodkin\
9452 Telephone Road #188\
Ventura, CA 93004\
805-642-6686\
<SGoodkin@aol.com>\
 

**Philadelphia Inquirer, October 17, 2006:**

 

**Whole Group Instruction Drags Good Math Pupils Down\
By Susan Goodkin and David G. Gold**

Given the math training our gifted elementary students receive in public
schools today, America\'s recent sweep of the Nobel prizes in science
and economics is a feat unlikely to be duplicated by younger
generations.

Frustrated parents nationwide will attest that the predominant method of
elementary-school math instruction holds back our top young math minds,
and, as practiced under the No Child Left Behind Act, stultifies them.
Remedying this requires the political will to implement a solution that
is obvious but runs afoul of both liberal and conservative political
agendas.

Research consistently shows, and common sense dictates, that the best
way to nurture high-ability math minds is to group these children
together and give them a curriculum geared to their abilities. Rather
than implementing such \"ability grouping,\" however, most elementary
schools nationwide take exactly the opposite approach: \"whole-group
instruction.\"

In whole-group instruction, all children are taught the same lesson at
the same time, without regard to their ability or mastery of the
subject. Education experts have long recognized that such instruction
impedes high-ability students. Karen B. Rogers, author of Re-Forming
Gifted Education, unequivocally states, \"If educators should want to
level the playing field of achievement so that all become mediocre in
their output, then whole-group instruction is the answer!\"

In contrast to math, primary teachers almost universally teach reading
through ability grouping. Educators clearly understand that without
differentiated reading groups, Harry Potter readers would spend their
time listening to the teacher help those students struggling to sound
out *Hop on Pop*. Whole-group instruction is the mathematical
equivalent. As an acquaintance recently recounted, when his child
requested harder math work, his teacher responded that he must \"wait
until the others catch up.\" This is, unfortunately, a refrain heard
across the country.

The problems have increased under the No Child Left Behind Act. NCLB
threatens draconian sanctions for failing to bring all children up to
minimum proficiency but no penalties for failing to advance those
children who already meet the standards. Thus it pressures math teachers
to aim the discussion at the least skilled, and to ignore our future
math and science leaders.

Math-ability grouping encounters resistance from across the political
spectrum. Many liberals oppose expanded use of any instruction method
that acknowledges students differ in their abilities. Their attitude is
partly a response to the rightly discredited practice of tracking. As
widely employed in the 1960s, tracking inflexibly placed students in a
fixed learning tier, and frequently did so in a racially biased manner.

Liberals, while appropriately rejecting tracking, threw out the baby
with the bath water. They concluded that recognizing any differences in
ability is elitist. Yet a truly equitable education system would provide
all children, including the most advanced, the opportunity to learn at
their own level - a goal that cannot be met through whole-group
instruction.

Conservatives are also reluctant to champion ability grouping. To admit
that the current approach holds students back, conservatives would have
to admit that NCLB is a substantial obstacle, not a solution, to
improving math instruction to gifted children.

Ability grouping can serve all students without the flaws of tracking.
It is much more fluid, allowing students to move easily between groups,
depending on their mastery of the subject and unit being taught.
Moreover, evidence suggests that when unbiased assessment procedures are
used, the group that benefits most from this approach is high-ability
minority students.

Secretary of Education Margaret Spellings has declared that this
administration\'s educational efforts will \"make sure we continue to
lead the world in Nobel Prize winners.\" However, if President Bush
truly wants our public schools to develop math and science leaders, the
federal government must provide incentives for teachers to group math
students by ability. This is the only way we can strive to bring all
students up to proficiency - and produce Nobel laureates.

 

**Washington Post, December 27, 2005:**

 

**Leave No Gifted Child Behind\
By Susan Goodkin**

Conspicuously missing from the debate over the No Child Left Behind
(NCLB) Act is a discussion of how it has hurt many of our most capable
children. By forcing schools to focus their time and funding almost
entirely on bringing low-achieving students up to proficiency, NCLB
sacrifices the education of the gifted students who will become our
future biomedical researchers, computer engineers and other scientific
leaders.

The drafters of this legislation didn\'t have to be rocket scientists to
foresee that it would harm high-performing students. The act\'s laudable
goal was to bring every child up to \"proficiency\" in language arts and
math, as measured by standardized tests, by 2014. But to reach this
goal, the act imposes increasingly draconian penalties on schools that
fail to make \"adequate yearly progress\" toward bringing low-scoring
students up to proficiency. While administrators and teachers can lose
their jobs for failing to improve the test scores of low-performing
students, they face no penalties for failing to meet the needs of
high-scoring students.

Given the act\'s incentives, teachers must contend with constant
pressure to focus their attention simply on bringing all students to
proficiency on grade-level standards. My district\'s elementary school
report card vividly illustrates the overriding interest in mere
proficiency. The highest \"grade\" a child can receive indicates only
that he or she \"meets/exceeds the standard.\" The unmistakable message
to teachers \-- and to students \-- is that it makes no difference
whether a child barely meets the proficiency standard or far exceeds it.

Not surprisingly, with the entire curriculum geared to ensuring that
every last child reaches grade-level proficiency, there is precious
little attention paid to the many children who master the standards
early in the year and are ready to move on to more challenging work.
What are these children supposed to do while their teachers struggle to
help the lowest-performing students? Rather than acknowledging the need
to provide a more advanced curriculum for high-ability children, some
schools mask the problem by dishonestly grading students as below
proficiency until the final report card, regardless of their actual
performance.

Perhaps these schools, along with the drafters of NCLB, labor under the
misconception that gifted students will fare well academically
regardless of whether their special learning needs are met. Ironically,
included in the huge body of evidence disproving this notion are my
state\'s standardized test scores \-- the very test scores at the heart
of the No Child Left Behind Act. Reflecting the schools\' inattention to
high performers, they show that students achieving \"advanced\" math
scores early in elementary school all too frequently regress to merely
\"proficient\" scores by the end. In recent years the percentage of
California students scoring in the \"advanced\" math range has declined
by as much as half between second and fifth grade.

Many gifted students, of course, continue to shine on standardized tests
regardless of the level of instruction they receive. But whether these
gifted students \-- who are capable of work far above their grade level
\-- are being appropriately educated to develop their full potential is
not shown by looking at test scores measuring only their grade-level
mastery. Nor do test scores indicate whether these students are being
sufficiently challenged to maintain their academic interest, an issue of
particular concern in high school. Shockingly, studies establish that up
to 20 percent of high school dropouts are gifted.

When high school faculty members face the prospect of losing their jobs
if low achievers do not attain proficiency, what percentage of their
resources will they devote to maintaining the academic interest of
high-level students? How much money will administrators allocate to
providing advanced courses? How many of the most experienced teachers
will teach honors, rather than remedial, classes?

Surely we can find a way to help low-achieving children reach
proficiency without neglecting the needs of our gifted learners. If we
continue to ignore gifted children, the NCLB may end up producing an
entire generation of merely proficient students \-- a generation that
will end up working for the science leaders produced by other countries.

[]{#JohnShacter3 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Shacter\
Sent: Thursday, October 26, 2006 5:54 AM\
To: National Math Panel\
Subject: PANEL COMPOSITION AND MISSION

Dear Math Advisory Panel Members -\
\
I am aware that you must be getting quite a bit of advice on your
assignment.\
\
You therefore may not recall \-- but I have shared several e-mail
summaries of some of my conceptual and implementation ideas to you
before.\
\
I assume that you are basically a panel of math and education professors
and practitioners.\
\
As a semi-retired engineer and management consultant, as well as a still
very active volunteer-teacher I wonder whether you may wish to receive
more of my basic ideas about the mission and performance of
\"schooling\" and particularly of \"math\" in that context? (Preparing
students for quality lives and careers in a shrinking and evermore
competitive \"outside world\".)\
\
(My background descriptions are in the Who\'s Who Volumes of Science and
Engineering, and of Finance and Business.)\
\
Do you have any engineers or managers in your panel?\
\
Thank you for your response(s) -\
\
Best wishes - John\
John Shacter

[]{#GaryLitvin .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Gary Litvin\
Sent: Wednesday, October 25, 2006 8:21 PM\
To: National Math Panel\
Subject: RE: Written comments for the math advisory panel

Dear Jennifer,

Thank you very much for your timely response. I have attached our brief

comment; we hope it will find its way to the Panel.

With best wishes,

Gary Litvin

President

Skylight Publishing

![](media/image6.wmf)

\-\-\-\--Original Message\-\-\-\--\
[]{#MelissaDugan .anchor}**From:** Mel\
**Sent:** Sunday, October 22, 2006 5:56 PM\
**To:** National Math Panel\
**Cc:** Carolyn Triebold\
**Subject:** Math Panel - Public Comment

Good day -

 As the parent of an elementary-school child who is gifted in
mathematics and language arts, I wanted to remind the panel that while
establishing curricula and standards for lower-ability children is
important, it is equally important to develop and implement programs
which benefit those children at the gifted end of the spectrum. 

The \"No Child Left Behind\" Act often achieves its mission at the
expense of gifted children, lowering classroom standards by slowing the
pace and focusing repetitively on basic skills.  Gifted children are an
important resource for our future, one which requires special attention
and a broader curriculum to target their needs and skills.

Thank you for your attention -

Sincerely, 

Melissa Dugan

\-\-\-\--Original Message\-\-\-\--\
[]{#ChrisCarthel .anchor}**From:** Chris Carthel\
**Sent:** Sunday, October 22, 2006 10:36 PM\
**To:** National Math Panel\
**Subject:** Comments for the National Math Panel

Dear Sir or Madam:\
\
I am a parent of two math students who are both in high school now. In
addition, I recently completed the mathematics necessary for a Bachelor
of Science degree in Chemistry. I experienced some difficulties in my
earlier math classes, including classes prior to (and including)
algebra, partly because of what I believe were shortcomings in the way
the courses were organized (i.e., curriculum) and taught (i.e.,
pedagogy).\
\
**Problem-Solving: Point A to Point B**\
\
One of the most frequent complaints I hear from my children and college
peers is \"I don\'t see how you got from point A to point B in that
solution.\" I have also had this compliant myself, and I see this as a
recurring problem in both teaching and textbook design.\
\
The better math textbooks (and teachers) I have seen include annotated
solutions that provide a clear explanation of how a problem progressed
to a solution through each intermediate step (e.g., what rule was
applied, what manipulation was performed, etc.). Good annotations of
solution steps provide not only an explanation of how to progress from
step to step, but can even serve as a sort of built-in remediation in
some cases. For example, a step in a calculus problem may require the
utilization of a trigonometric identity. Identification of this in an
annotation not only explains the transition but can also provide a
remedial effect. Annotations are universal in that they can serve every
student's needs. The advanced students can simply ignore them, while the
struggling students can use them to build up their skills. In fact, a
web-based textbook could even be configured so that every student could
decide for themselves whether to turn on or turn off the annotations.\
\
**Use of Technology to Enhance Math Education**\
\
I have seen some truly impressive web-based technologies, such as Java
applets, living graphs, etc., that could enhance the learning of
mathematics. But I have been surprised by the slow infusion of these
technologies into classrooms and textbooks. The value of these new
technologies is that they permit the student to make real-time, two- or
three-dimensional observations of the behavior of equations at different
values and limits. It makes the learning experience more real and
understandable. Although I am aware of some copyright concerns regarding
the use of electronic (e.g., PDF format) textbooks, students badly need
the ability to search and retrieve information as quickly as possible in
an electronic format.\
\
We are, in my opinion, long overdue for an electronic textbook approach
that resembles a web page. I am not necessarily advocating the complete
abandonment of physical textbooks, but perhaps an approach where the
textbook is bundled with an electronic version available via perhaps a
web account that contains the ability for word searches; quick linking
from tables of contents, glossaries, and indexes; interactive JAVA
applet-based figures and graphs where appropriate, etc. (e.g.,
<http://mathworld.wolfram.com/>).\
\
**The Need for National Math Standards**\
\
It is my sincere hope that by defining what is meant by "competence in
algebra" and "readiness for higher levels of mathematics" as described
in Executive Order 13398, Sec. 4.(a), the Panel will be in a position to
provide meaningful guidance for developing national math standards.\
\
The American Chemical Society (ACS) publishes national standards
(including testing standards) for chemistry. I have been surprised to
discover that there is not, at least to my knowledge, an analogous set
of national standards for mathematics.\
\
**Teacher/Student Diligence**\
\
I have seen several brilliantly knowledgeable math teachers who
displayed only mediocre skill at *conveying* their knowledge in an
absorbable way. I have come to realize that student achievement in
mathematics is not simply a function of the teacher's knowledge of
mathematics, although teacher knowledge is certainly important. In my
opinion, the real magic of student achievement occurs as a result of a
teachers' *skill* at *conveying* their knowledge in an interesting and
organized way that can be easily absorbed by engaged students.\
\
Note that I limited my statement to engaged students. There is a
obviously a certain degree of diligence required of math students
themselves. This is what I think of as the \"you can lead a horse to
water, but you can\'t make him drink\" syndrome. The best teacher,
textbook, and curriculum in the world are all worthless to a student who
is not making the conscious choice of engaging themselves in the
learning process by showing up, paying attention, and absorbing,
applying, and practicing as much as they can. Students cannot be
overlooked as participants in the process.\
\
I mention students because I have seen some evidence in our American
culture, in particular K-12 math classes, of what I refer to as
"glorification of mediocrity" or "antagonism of success." In other
words, a peer pressure environment sometimes exists that utilizes
harassment and embarrassment to prevent some promising students from
achieving their full potential. I have seen potentially excellent
students make a conscious choice to perform badly in order to "fit in"
with their less engaged peers. It seems to fit with the old maxim
"misery loves company" This is perhaps better described as "laziness
loves company."\
\
Every child deserves to be freed from the bondage of what President Bush
has described as the "soft bigotry of low expectations," regardless of
whether that bigotry arises from a teaching institution, a specific
teacher, or a fellow student.\
\
Thank you for the opportunity to comment. I look forward with great
anticipation to the panel's conclusions and recommendations.\
\
Chris Carthel

[]{#RoseHaydenSmith .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Rose Hayden-Smith\
Sent: Saturday, October 21, 2006 7:08 PM\
To: National Math Panel\
Subject: Math Instruction Panel Comments

Dear Ms. Graban:

 

My name is Rose Hayden-Smith, and I am the parent of a GATE-identified
student at Loma Vista Elementary School in Ventura, California.  I would
like these comments to be added to the record, as I am unable to attend
the meeting in Palo Alto.

 

My daughter is gifted in mathematics, but her standardized test scores
have not always reflected this. In an effort to get all students to a
proficient level, advanced students are neglected.  We have seen our
school\'s standardized test scores drop, as students previously scoring
advanced in mathematics have dropped to the proficient category.  The
effects on youth morale and potential are disasterous.

 

This is wrong, and more attention needs to be paid to accelerating and
affirming the work of students who are gifted in mathematics.  Focusing
entirely on improving the performance of lower-ability students
is unfair, and ultimately hurts all students.  The United States has
become less competitive in the sciences and mathematics, and I believe
that much of this is due to the stulifying effects of whole-group
instruction in mathematics.  Ability-grouping in the language arts is an
accepted educational strategy, but this has not been widely adopted as
an instructional strategy in mathematics, at least not in my district,
and math scores are low, as a result.   Resources need to be provided to
teachers to teach them how encourage the talents and academic
development of higher-abilty students, and this panel needs to include
in its recommendations an acknowledgement that higher-ability students
warrant attention, too.

 

To feed my daughter\'s desire for learning (and to counteract the
boredom she has often felt in school), we are now supplementing her in
an after-school enrichment program.  The cost to our family is
significant, about \$1,000 a year, but we feel it essential to maintain
her enthusiasm for learning, and to prepare her to contribute to a
healthy and effective American society and economy.

 

I hope that this panel will consider a well-balanced approach to math
instruction that will consider the learning needs of ALL students. 
While raising all students to proficiency in math is a worthy goal,
supporting the talents of gifted students is equally important.  Failing
to foster and develop the potential of ALL students is wrong.

 

Sincerely,

 

Rose Hayden-Smith

[]{#JulieSantia .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Julie Santia\
Sent: Thursday, October 19, 2006 4:22 PM\
To: National Math Panel\
Subject: Math Instruction for Gifted Students

Math Panel:

I just heard about this panel today. It is important that your panel
consider math instruction for gifted students as important as the
curriculum for average and under-achieving students. Our high achievers
in math are our future scientists and doctors. We need to let our
talented math students advance and not hold them back as they are now
with today\'s standard math instruction practices. Don\'t let anyone
fool you into thinking there is differentiation within math instruction.
Advanced math students are such because of the supplementation they do
at home, not anything that is happening in the classroom.

The advanced math students really could use more attention. They should
be celebrated and rewarded for their abilities. Allowing them to do work
at their level instead of holding them back, is a good start.

Thank you for your time,

Julie Santia

Engineer

Ventura, CA

[]{#JohnShacter2 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Shacter\
Sent: Tuesday, October 17, 2006 11:07 AM\
To: National Math Panel\
Subject: Re: Ideas for the National Math Panel

Hi Jennifer -\
\
Thanks a million for your info. on the above.\
Could you distribute my memo (below) to the participants and to Sec.
Spellings?\
\
Thanks, John\
\
John Shacter\
Semi-retired engineer, management-and-technology consultant, and still
very active volunteer-teacher & educ. consultant\
===========================\
\
Hi Folks -\
\
Let me try once more:\
\
(This is not limited to just \"math\") \--  but I cannot agree that we
can discuss what and how to teach without first agreeing on the \"what\"
and then on the \"how.\"\
\
Overall, I believe we tend to omit or play down some of the most
interesting and useful topics and then seem to be succeeding in making
too much of the rest of \"studying\" too boring and laborious.\
\
\-\-\-\-\-\-\-\-\-\-\-\-\-\--\
\
Generally, students also get too little opportunity to help in the
understanding and explanation process, or to express themselves more
generally \-- orally or in writing.   \
\
As teachers, we should be also able to illustrate to the students WHY we
are teaching them the things that we are teaching them.\
\
We should do a lot of teaching by asking a series of leading and teasing
questions (\"Socratic Method\").\
\
Use of common sense, the KISS principle (Keep It Simple, Stupid), a
light touch or sense of humor, and introduction of some competition can
also help to engage the students in the teaching and learning process.\
\
\-\-\-\-\-\-\-\-\-\-\-\-\-\--\
\
Let me illustrate the approach with the teaching of some basic math:\
\
Effective teachers require their 3rd-grade students to memorize the
multiplication table. For example, they want their students be able to
tell them \-- eyeball to eyeball \-- what 7x8 is. But the best teachers
teach more. They might want the students to tell them also what 56
**[DIVIDED BY]{.underline}** 7 or 8 is. And then, when they receive
correct answers, they might also ask the students to tell them what
5**[7]{.underline}** divided by 7 or 8 is \-- EXACTLY, AND STILL
EYEBALLING THEM. (Today, most **[COLLEGE GRADS]{.underline}** and
professors might not know the answer to that one! Chances are, they
might ask for permission to use their calculators!!)\
\
Or the best teachers might ask their students whether integers or whole
numbers could be treated as decimals, as well. (The answer is of course
that they CAN. All you have to do is to place a decimal point at the
right end of the number. After that you can use the decimal rule of
moving the decimal point, say, a couple of places to the right, when you
wish to multiply the number by 100, or to the left, if you want to
divide the number by 100. It takes a movement of six places if you
multiply or divide by one million. And if you don\'t have enough digits,
just add a sufficient number of zeros on either end of the number\....)\
\
Or the best teachers might introduce their students \-- also in third or
fourth grade \-- to the use of question marks or letters along with
numbers in equations \-- without scaring them by the use of the word
\"algebra.\"\
\
\-\-\-\-\-\-\-\-\-\-\-\-\--\
\
Many additional examples could be given in such areas as \"societal and
character education\", \"money management\", \"starting your own
business\", \"U.S. form of government\", \"current events and issues\",
etc. etc. which should be (but are not always) taught and discussed
during the 13 long years of primary- or secondary-school curricula.\
\
In my view, today\'s U.S. teachers aren\'t taught what and how to teach
in more interesting, challenging and effective ways because their
professors in the colleges of education are often themselves lacking in
their selections and understanding of the topics \-- and they are likely
to practice too much \"pseudo-psychology\", and tend to take themselves
much too serious.\
\
In any case, it is my guess that few of them would dare to face an
average primary or secondary classroom and try to demonstrate their own
proposed, conceptual approaches to \"effective teaching\" in qualitative
or quantitative (student-gains) terms.\
\
Fortunately, there are effective answers to these challenges, and there
are some teachers who have taught themselves to apply them.\
\
Cordially, John\
\@2004 John Shacter\
Semi-retired engineer, management-and-technology consultant, and still
very active volunteer-educator.

[]{#DavidGrebow .anchor}\-\-\-\--Original Message\-\-\-\--\
From: David Grebow\
Sent: Friday, October 13, 2006 4:39 PM\
To: National Math Panel\
Subject: Math Panel Comment

Dear Jennifer:

 

The issue of mathematics readiness needs to being at the Pre-K level.
Mathematics needs to be regarded as a language. And the current research
points to the fact that languages are best learned early, practiced as a
part of one\'s daily life, i.e. made relevant and heard at home as well
as at school. I would throw technology into the mix since many parents
do not know and would not learn basic or advanced math. So the \'in loco
parentis\' in this case would be the mathematics website where math
would be \'spoken\' and, like learning a language, be incorporated into
age and grade appropriate songs, games and other enjoyable activities.

 

I am an educator and have worked at the intersection of education and
technology for many years. Since I know this will work, and that the
technology and pedagogy are in place, all that\'s missing is the will to
make it happen. Hopefully the meetings of the National Math Panel and
their final recommendations will look at the issue from this perspective
and programs will be started to see if this is a good path to travel.

 

Sincerely,

 

David Grebow

CEO, KnowledgeStar. Inc. 

\-\-\-\-\-\-\-- Original Message \-\-\-\-\-\-\--

\> Subject: \"Calculators\", Indeed!

\> []{#JosephNorth .anchor}From: Joseph North

\> Date: Fri, October 13, 2006 12:58 pm

\> To: \<jennifer.graban@ed.gov\>

\>

\>

\> Dear Ms. Jennifer Graban:

\>

\>

\> I would have some comments to share about \"Calculators\",

\> et caetera.

\> Now, when I attended Elementary School and High School

\> in the primitive country to the north of US, known as Canada,

\> circa 1952 - 1962, I never had an Electronic Calculator, and

\> I got a score of 800 / 800 in my SAT Achievement Mathematics

\> test in 1962, just allow me to assure you!

\> At McGill University, circa 1962 - 1966, I was allowed a

\> Slide Rule, even in exams!

\> Now, when I took the GRE in 1973 in Grad School, again up in

\> primitive Canada, intending to be admitted for Ph.D. in Physics

\> and Astronomy at UNC Chapel Hill, NC, my Aptitude Test,

\> Quantitative Ability acore was 720 / 800, just allow me to

\> again assure you! Oh, and I still have my ETS score mailings,

\> just in case you might like to examine same!

\> Now, when I lived in Fairfax County, Northern VA - \[w\]one of

\> the most affluent in America - I would quiz the young adults at

\> the swimming pool where I lived, circa 1999. They could not

\> correctly mentally convert the Fahrenheit temperature of 68

\> degrees to its equivalent Celsius temperature of exactly 20

\> degrees, saying they needed their Calculators to do that!

\> Now, fast forward to about 2 weeks ago at the swimming pool

\> where I live here in North Austin. I was talking with 2 young

\> College age adults, and we got into Math., WOW! So, I asked

\> them what this number was, 0.434294481903\.... They had no idea,

\> however, the young lady told me she had Mathematica installed on

\> her boyfriend\'s 64-bit computer. So, we went to the boyfriend\'s

\> father\'s apt., and they fired up Mathematica, and tried to find

\> out together whatever that crazy number was! And, they worked

\> hard for about 30 minutes before giving up - well, the football

\> game - Ohio State & our Longhorns - was about to begin, and that

\> was also important to them.

\> I asked if I could try it out, after the game had started.

\> They said I could. Now, I hadn\'t used Mathematica for about 20

\> years, and it employs some weird syntax, differing from that of

\> bc, PARI/GP, Maple, maxima, et caetera. So, I looked at the most

\> extensive online help provided by Mathematica, and, within \~ 10

\> minutes, I showed them what it - 0.434294481903\... - was! They

\> were all (including Dad) happy, and so WAS I!!

\> So, what lessons might we glean therefrom?! The use of

\> complicated \"Calculators\", Graphing \"Calculators\", as well as

\> vastly more powerful Computer Algebra software does a disservice

\> to students who have NOT had a chance to really explore numbers -

\> with mind, pencil, and paper - as I HAD up in primitive Canada

\> so long ago, I believe!

\> Penultimately, then, what was that crazy number, please???!!!

\> \"And ye shall know the truth, and the truth shall make you free.\"

\> (ref.: John 8:32, KJV, 1611) therefor!

\> Tempus fugit et ad augusta per angusta.

\>

\>

\>

\>Nil desparare (Gauss),

\>

\>

\>Joseph Roy D. North

[]{#LisaGill .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Lisa Brady Gill\
Sent: Thursday, October 12, 2006 6:59 PM\
To: National Math Panel\
Subject: NatMathPanel_TIcomments.pdf

Hi Jennifer:\
TI and Melendy Lovett were pleased to receive the invitation to provide
written comments to the National Math Panel.  We are very supportive of
the work of the National Math Panel and appreciate the took the
opportunity to support their work. 

I\'ve enclosed our written comments for your review.  In addition, we
are sending 22 hard copies by Federal Express this evening to you at the
U.S. Department of Education for distribution to the National Math Panel
members.  Can you let me know if they will receive them prior to the
November meeting?

In addition, you were kind enough in your letter to Melendy to suggest
she might have the opportunity to give oral remarks at the November
meeting and we\'d like to formally request that she be able to do so.  I
mentioned this to Tyrrell at the meeting in Boston and let her know
we\'d be following up with this request. 

TI is honored that Richard Schaar has been invited to share
effectiveness research related to graphing calculators at the November
meeting, as well.  And look forward to working towards our shared
missions of improved mathematics education for all students in the
future. 

Thank you for your consideration of these written comments and of our
request for Melendy to give oral remarks for the Math Panel members to
consider as they prepare their report.  And please don\'t hesitate to
contact me should you have further questions or need more information.

Best Regards,\
Lisa Brady Gill

Lisa Brady Gill\
Executive Director, Office of Education Policy and Practice\
Texas Instruments, Incorporated

![](media/image7.wmf)

[]{#EmilyWyrick .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Emily Wyrick\
Sent: Monday, October 09, 2006 10:52 PM\
To: National Math Panel\
Subject: concerned teacher

please help me in my pursuit of voicing the concerns of math teachers.\
 \
Thank you for your time,\
 \
Emily Foster\
(middle school math teacher in NM)

![](media/image8.wmf)

[]{#AngeliqueBadgett .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Angelique Badgett\
Sent: Saturday, October 07, 2006 4:00 PM\
To: National Math Panel\
Subject: math in elementary school

I am a second grade teacher in Wichita, Kansas, USD 259.  We have been
mandated to use a curriculum that is inferior in teaching mathematics. 
We use \"Investigations\" and have been told that we are to use it as
our primary math resource.  I am very concerned about this program and
the ineffective way it teaches math to students.  I have decided, at the
risk of being reprimanded or fired, to discontinue using this program
again.  (I had tried to use it two years ago when we were told to the
first time.)

 

I need your organization\'s help.  I have been told that Investigations
is researched based, however many states are finding that in actuality,
the scores on state tests are dropping drastically.  I have been told
that I am not self-employed and that I will teach what I am told to
teach.  I have heard from them that spiraling, an approach where
students who do not understand a concept the first time, will get an
opportunity to try again at the same concept later.  I have been told
that we have to follow the guidelines and pacing guide given to us, even
if no one in the class understands the concept.  I know that this is not
sound advice but my district is deaf to teachers.

 

I have tried to mobilize elementary parents and teachers as well as
teachers in middle and high school so that together we can fight the
unfortunate decision made, by a hand-selected few, to the detriment of
all.  I am at my wit\'s end.  I have been trying to find an organization
that can help me present my case to my district.  I read about your
group in an article called \"Miracle Math.\"  I understand that there
are members who are fighting \"fuzzy math\" in elementary school.  I
need to know what I can do to rectify an already out of control
situation.

 

Is there any research proving that this math is inadequate?  Is there an
advocacy group that would be willing to help me and my fellow teachers
and parents in this fight?  Do you have any resources that would be
helpful to me?

 

I appreciate, but more importantly the elementary children of Wichita
appreciate, all of the help you can give us.

 

Sincerely,

Angelique Badgett

[]{#TedWetherbee .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Ted Wetherbee\
Sent: Friday, October 06, 2006 1:51 PM\
To: National Math Panel\
Subject: NCTM Focal Points \>\> NMAP review

Dear NMAP Members,

NCTM Focal Points (September 2006, K-8) strikes me as clear and

reasonable, and I\'m curious to see the September 13-14 NMAP meeting

transcripts on how it was received. I doubt that Math Wars would have

occured had Focal Points (and a similar quality document for grades

9-12) been available, promoted, and used over the past twenty years.

I also hear from NCTM people that Focal Points represents no NCTM change

whatsoever, none. This is posturing as an infallible authority, e.g.

those who see change in doctrine are ignorant. However, this is about

math education, and this should be treated as a displine which admits

the possibility of error and, thus, hope for improvement.

I think that the NCTM made a serious improvement with Focal Points, a

straightforward content endorsement which is remarkably clear, concise,

and potentially useful. To say it is no change at all is to limit its

usefullness. Most states had math standards designed with NCTM

documents first and foremost as The Standard and with among the best of

people available who truly believed in NCTM Standards. If Focal Points

is what was really intended and within prior NCTM documents, it has

taken a very long time to make these intentions known and realized.

It is good science as well as commendable integrity to admit error (even

the slightest error in this case of math education) along with any

correction. I think that Focal Points could used as intended to revise

state math standards\--as Minnesota is currently doing. It is a change

indeed, and I commend the NCTM for making it. They have regained my

respect by this change.

I am curious as to NMAP views of NCTM Focal Points because revision of

Minnesota math standards is beginning next week through committee

meeetings, and public comment will likely be part of the process. It

appears that NCTM Focal Points directly closely addresses the new

Minnesota state law requiring revision of math standards to include

algebra 1 by 8th grade.

Respectfully yours, Ted Wetherbee

\--

Ted Wetherbee

Mathematics & Computer Science

Fond du Lac Tribal & Community College

[]{#DaryaoKhatri2 .anchor}\-\-\-\--Original Message\-\-\-\--\
**From:** Daryao Khatri\
**Sent:** Monday, October 02, 2006 12:00 PM\
**To:** National Math Panel\
**Subject:** Educate Everyone

Dear Members,

 

Rick Stiggins in his paper on assessment writes, "Society has seen fit
to redefine the role of its schools. No longer are they to be places
that merely sort and rank students according to their achievement. Now,
they are to be places where all students become competent, where all
students meet pre-specified standards and so are not left behind."

 

I agree with this statement and this should form the basis of teaching.
The same message is evident in "*Color-Blind Teaching: Excellence for
Diverse Classrooms*." By Daryao Khatri and Anne Hughes.

 

A child is crying for milk and there is no milk. It can eventually lead
to death. The parents and students are in a similar situation. Both
groups are screaming for help, but the teachers and the institutions
that prepare them to teach do not seem to have any answers.

 

At the September 13-14, 2006 meeting, a parent from an affluent
neighborhood complained that her three-year-old boy who used to love
math all of a sudden hates math because he is not learning anything in
math in his school. A panel member mentioned that at one place in an
affluent neighborhood, an explosion has occurred in the number of
tutoring schools because teachers are not teaching what students are
expected to know for their homework. She reported that this has happened
because of an imposition of some arbitrary curricula.

 

Welcome to the world of entrepreneurship. If you want to see tutoring
schools in action, just visit some of the Asian countries including
India where several tutoring schools are operational in almost every
neighborhood because children are [not]{.underline} taught what they
need to learn in their schools.

 

I heard Curriculum Developers pushing for a change in school curriculum
and asking the panel to recommend such curriculum changes at the
national level. Textbook publishers, who could not provide satisfactory
answers to the question raised by the panel regarding the size of the
books and the irrelevant pictures that are included in them, were also
pushing for the adoption of their books.

 

Come on and please give students a break from back pains!

 

Because we have looked for answers in similar places all along, the
situation with math education has gotten worse. We all know that neither
the books nor the curriculum teach students; it is the teacher and
teacher alone who is responsible for teaching. Books and curriculum are
only materials to be used by the teachers. Therefore, the problem does
not lie with selection of new textbooks or new curriculum, it lies in
the preparation of teachers. The colleges and/or departments of
Education at the higher education level should take responsibility for
this failure and do something about it. But these schools do not know
how to.

 

Let me put this problem in a mathematical form. After all this is a
National Math Panel.

 

Student Performance = Teacher + Books + Curriculum + School
Infrastructure + Parents + Neighborhoods + Others

 

Where student performance is a dependent variable and all others to the
right of the equal sign are independent variables. Researchers need to
study the impact of independent variables on the dependent variable.
*The problem has been that many researchers treat the dependent variable
as if it is an independent*.

 

Dr. Hughes and I have been researching this problem for decades and
finally we have [a]{.underline} solution. What is not under our control
and what we cannot change needs to be left alone, i.e., if some student
has mother only, we cannot provide that student a father, can we! If you
look at the equation, we will have a strong relationship between a
teacher and student learning. Therefore, we looked at the teacher and
the college professor who train these teachers. The problem lies with
the college professor and therefore with the schools and/or departments
of education. To remedy this situation, therefore, we need to look at
both the professor and the teacher.

 

We have documented this research in two books: "*American Education
Apartheid---Again*" And

"*Color-Blind Teaching: Excellence for Diverse Classrooms*." Based on
these books and our own experiences, we have [researched, documented,
and tested]{.underline} a model in faculty development that is working.
This model uses one-week to two-week workshops and mentoring. The
comments from two workshops for math faculty are attached with this
email. The second phase of mentoring started during the Fall Semester
2006 in Mathematics and Organic Chemistry. Results will be available at
the end of the semester.

 

If you looking for meaningful faculty development and training for
teachers, then we invite you all to the campus of the University of the
District of Columbia and witness it for yourself.

 

Thank you all.

 

Dr. Daryao S. Khatri

Professor of Physics

University of the District of Columbia

\-\-\-\--Original Message\-\-\-\--

[]{#JeanneMSimons .anchor}From: Simons, Jeanne M

Sent: Tuesday, September 26, 2006 10:27 AM

To: National Math Panel

Subject: Grant Management

Although I realize that the Math Panel is primarily concerned with
curriculum and other issues directly related to instruction, I have
found, in my work offering targeted assistance in mathematics in urban
schools in Massachusetts, that many of the issues schools are facing are
related to a lack of a systems approach to reform.

I would like to suggest that the Math Panel consider reevaluating the
structure of federal grants programs with the following issues in mind:

\* Every grant program has a different purpose or cause and although
these, for the most part, address important issues, they do not
encourage a systems approach at the school level where reform efforts
should be driven by the needs of the school or district level.

\* Grants usually last for only a year or two, after which the school is
left looking for new funding which usually takes them in a different
ideological direction in order to follow the funding. We know that most
programs take about three years to move past the implementation dip and
to show results. The structure of our grants programs do not allow
schools the luxury of sustaining programs for this length of time.

I would propose a system where the needs of the schools drive the grants
programs. For example, perhaps there could be a single national grant
application linked to the school and district improvement plans. For
example, instead of the grant program defining that a school\'s coaching
program should support differentiated instruction, grants in this area
would be awarded to schools with coaching in this area already defined
in their plans and in their unified grant application.

The unified grant application would have to be long term and subject to
minimal changes on an annual basis. Obviously this would be a complex
document to write and would require significant introspection and long
term planning by each school and district. This introspection and the
financial incentive of grants being rewarded to schools with well
written plans would hopefully drive schools to create quality plans. To
offset concerns about the difficulty of writing such a complex document,
it must be considered that the work involved in writing the grant
proposals normally written by districts would be substantially reduced,
with the narrative portions eliminated in favor of this universal
document.

In order to guide districts, there should be a guiding document giving
an outline of the important components of math reform that the
Department of Education would be willing to fund. For example, a few
might be:

Data driven instruction (with a description of what this might look
like)

Content PD for teachers

Math coaches

Math specialists

Or whatever the Math Panel deems critical to math reform.

We all know the major issues and the most promising leverage points, the
key is getting the districts and schools to implement these different
programs in a thoughtful, whole school manner. My suggestions provide a
financial incentive for pulling all of the reform programs in a school
together into what would hopefully be a more effective system of reform
from the federal level right down to the school level.

I have attempted to give a brief summary of my thoughts in an effort to
respect your time. I realize this represents a dramatic change across a
number of programs, but I truly believe that something of this magnitude
is necessary if we are going to see substantial changes in our
educational system. This change must be done at the federal level if it
is to be effective. Please feel free to contact me if you need further
information.

Thank you,

Jeanne Simons

Massachusetts Department of Education

> \-\-\-\--Original Message\-\-\-\--\
> []{#AnonymousA .anchor}**From:** Anonymous\
> **Sent:** Sunday, September 24, 2006 7:03 PM\
> **To:** Flawn, Tyrrell\
> **Subject:** I just discovered your website
>
> I am currently pursuing a Bachelor\'s degree in Biotechnology. I
> possess a degree from France where I was born and grew up. The biggest
> challenge that I must face in my science classes (beside having to
> learn all the terminology in English) is the fact that I must convert
> my answers to the English system which I find difficult to master for
> its lack of practicality.
>
>  
>
> I have sometimes challenged my teacher as far as the usage of the
> English system in scientific applications is concerned.
>
>  
>
> I am sending you these words to share with you my support for your
> organization.
>
>  
>
> Sincerely,
>
> Anonymous

[]{#DeloresBoone .anchor}\-\-\-\--Original Message\-\-\-\--

From: Delores Boone

Sent: Wednesday, September 20, 2006 7:36 PM

To: National Math Panel

Subject: I need specific information, please, ASAP

I see are vague \"we need to\" comments on ED.gov in

regards to math for 7th graders.  What I want to know is

this:

 

What is the national minimal standard that a 7th grader

student for Math? 

 

What should the schools (minimally) be trying to teach

each student? 

 

My son was doing basic fractions and touching on some

algebra ideas when I home schooled him in 3rd grade. This

he did not have until the end of 6th grade in public schools

and now in 7th grade his \"review\" work is subtraction and

back to the basics ! 

I want to know what the USA  Ed.gov  says the minimal

standard should be and what it was in the past:  1960\'s -

1970\'s.  

WHY  are we going backward instead of forward?  Where

are the academics of yesteryear that showed children how

to do math without \"cheat sheets\" and other \"fun\" things

that create busywork in math problems that takes kids

twice as long to do it?

Please,  respond to the questions as soon as possible and

think on why our country is behind so many others.  As

much as I think we have too much government interference

in some areas,  I think the government is not doing its job

when it comes to education.  We need NATIONAL standards

and UNIFORM curriculum.  Three of learning about PNW

fisheries and salmon is NOT  three years of science !  It is

causing out children to be idiots in everything except salmon.

 

Respectfully,

 

Delores Boone, R.N.

\-\-\-\--Original Message\-\-\-\--\
[]{#PhilipBladon .anchor}**From:** Philip Bladon\
**Sent:** Tuesday, September 19, 2006 7:16 AM\
**To:** National Math Panel; Flawn, Tyrrell; Graban, Jennifer; Kelley,
Ida Eblinger\
**Subject:** President Bush\'s Executive Order\
**Importance:** High

Dear Sir

With reference to [President Bush\'s Executive Order to improve
performance in mathematics]{.underline} I am pleased to have the
opportunity to provide recommendations to your panel.

1\. A major part of the solution to solve the problem would be to teach
and fully adopt the SI / Metric system as quickly as possible throughout
all schools and colleges.

2\. The vocabulary of the SI / Metric system with units, prefixes, and
symbols should be fostered across the curriculum (all subject areas not
just math and science). My book\* is one \'tool\' to help that. (\* ref
below)

3\. This major task to improve mathematics can be assisted by the Metric
Associations in the USA and the United Kingdom.

4.I also recommend adoption of SI units wherever possible and avoid
using confusing metric units such as calorie, kilocalorie, etc. These
units should be archived. The SI unit for \'energy in food\' is
kilojoule (symbol:  kJ )

Please do not hesitate to contact me for more information. I am willing
to attend one of your meetings.

Yours faithfully

Philip Bladon

[www.simetricmatters.com](http://www.simetricmatters.com/)

\-\-\-\--Original Message\-\-\-\--\
[]{#RogerJay .anchor}**From:** Jay, Roger\
**Sent:** Tuesday, September 19, 2006 2:13 PM\
**To:** National Math Panel\
**Subject:** National math iniative

>  

I would certainly hope that you access the expertise of the NCTM and
AMATYC, two organizations whose interest in the proper education of our
students is uppermost! They have both done extensive work in developing
guidelines for math instruction at the K-14 level, where most of your
attention should be focused. Please don't 'reinvent the wheel'.

>  

Roger L Jay

Math Professor

Tomball College

[]{#WICClements .anchor}\-\-\-\--Original Message\-\-\-\--

From: WIC Clements

Sent: Tuesday, September 12, 2006 7:25 PM

To: National Math Panel

Subject: Math/Music

National Math Panel Members;

Consider my work in math and music, all original. For years I have tried
to

have my work read with an open mind, solely for the purpose of advancing

music and math. Wolfram Research (Mathematica), Walter Hewlett (Stanford

University), Boulez (IRCAM), the list goes on. Last week, after speaking
to

Gary Garratin of Garritan Orchestral Libraries, \"Gary\" seemed very

interested, that is until he looked at the math.

My intention has always been to advance the understanding of math and
music

through education using the concept of Cartesian Algebra and the hidden
2-D

nature of music theory, The Cartesian Music System, which is based on a

unique dicovery and a software routine I wrote for Dr. Dika Newlin in
1979.

Therefore, I have forwarded last weeks overview to \"Garritan Orchestral

Libraries,\" including the response from Garratin, Which reads as
follows:

\"Wow, that looks very involved! It seems to be a bit over my head

(mathematically), but the music examples do sound quite interesting. Not

sure if it could fit into our product line and what we do.

This looks like it could develop into a composer\'s tool.

Good luck in pursuing this work further.

Gary\"

I can show you a way to bring math and music to the forefront of our
culture

if you\'ll go through these e-mails I sent to Garratin in order to get
an

idea of what I do. Gary needs mathematics lessons (music lessons too).

WIC Clements

[]{#DaryaoKhatri3 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Daryao Khatri

Sent: Tuesday, September 12, 2006 9:17 PM

To: National Math Panel

Subject: Re: Registration for National Math Panel, Boston Meeting

Dear Jennifer,

We just completed a six-week (five-week instruction) summer intervention
for 12 students from District Public High Schools who have been admitted
to UDC as freshmen for Fall 2006.  The results compel us to question the
wisdom of offering remedial math courses at the college level.  A copy
of the draft report is attached for you and for the Math Panel.

Thank you.   Hope to see you in Boston.

![](media/image9.wmf)

[]{#IrwinKra .anchor}\-\-\-\--Original Message\-\-\-\--

From: Irwin Kra

Sent: Monday, September 11, 2006 6:55 PM

To: National Math Panel

Subject: Boston National Math Panel Meeting

Jennifer,

 

Attached is the written version of the remarks that I may get to make on
Thursday. I know that the written version is longer than what is needed
for 5 minutes, and I will keep any oral remarks to 5 minutes or less.
Sorry that I could not get it to you earlier. I will bring three copies
of the written version to the meeting. Do you need in addition a disc
that contains the attached file?

See you on Wednesday.

![](media/image10.wmf)

[]{#JackFretwell .anchor}\-\-\-\--Original Message\-\-\-\--

From: Jack Fretwell

Sent: Friday, September 08, 2006 2:51 PM

To: National Math Panel

Subject: RE: June 29th Public Comment

Hi Jennifer,

I can\'t make the Boston meeting and I know it\'s late, but  will you be
able to do anything with the attached comment?

 

Jack Fretwell

Starboard Training Systems

![](media/image11.wmf)

[]{#StanDoore .anchor}\-\-\-\--Original Message\-\-\-\--

From: Stan Doore

Sent: Thursday, September 07, 2006 12:15 PM

To: National Math Panel

Subject: Re: Comments followup

Hi:

I mailed a copy of the recommendations to Dr. Olsen at the NAS last
week.  I then thought I should email a copy to you all.  I hope this
didn\'t confuse you too much.  A copy of the letter is attached in PDF
format.

 

Regards, Stan Doore

![](media/image12.wmf)

[]{#LorelleYoung2 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Lorelle Young

Sent: Wednesday, September 06, 2006 3:40 AM

To: National Math Panel

Subject: U.S. students must know the metric system

National Math Advisory Panel:

 

I believe this article should be brought to the attention of
the National Math Advisory Panel members.  If our schools do not
produce metric-literate graduates, how can the U.S. compete globally if
companies must spend money on metric training that should have been
accomplished in U.S. schools?  Companies in foreign countries do not
have to make this investment in metric training.  These countries
graduate students who know and can use the metric system with facility
while we confuse our students by trying to teach both the outmoded
inch-pound system and the metric system, with the result that they
master neither system. 

 

Thank you for your attention.

 

Sincerely,

 

Lorelle Young, President

U.S. Metric Association, Inc.

[]{#DaryaoKhatri1 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Daryao Khatri

Sent: Tuesday, September 05, 2006 9:30 AM

To: National Math Panel

Subject: Re: Registration for National Math Panel, Boston Meeting

Dear Jennifer,

Thank you very much again.  Following this email from you,

 Jack Hughes has asked us to share this information regarding Faculty
Workshops for Math Faculty at the University of the District of Columbia
(UDC) that were conducted during the Spring and Summer of 2006.

 

Please share this email with the members of the National Math Panel. 
Two files are attached.

 

The retention rate nationally in the STEM disciplines hovers around
25-35%. This is no different in HBCU\'s. At UDC, the retention rate in
math courses is also around 30-35% in many of the courses at the
remedial and introductory levels.

 

Dr. Hughes, professor of Sociology/Education and teaches social science
statistics, and I, professor of Physics, however do have retention rates
around 95% and higher in all of our courses. We attribute this success
to the way it is taught, the pedagogy used in the teaching of these
courses. We wanted to test this first for Chemistry and Physics faculty
and then for faculty in the Math department. Following a phenomenal
success in the workshop for Chemistry and Physics faculty (14 Ph.D.\'s
faculty), we conducted two workshops for the math faculty.

 

The objectives were two fold: First, can we bring a change in the
attitude of those professors who teach these courses in terms of
recognizing the need of sound pedagogy for professors. Second, do we
need to provide follow-up mentoring for those who have attended the
pedagogy workshop(s).

 

The first workshop was conducted for 9 full-days (10:00-4:00) every day
from May 2-12, 2006 and then a mini workshop from June 13- 27, 2006 (5
full-days) for those who missed out on the first because of conflicts in
their schedules. A total of 13 math faculty members attended these
workshops on a volunteer basis.

 

In regard to change in their attitudes, the comments are attached in two
separate files. As far as follow-up mentoring for some of these faculty
members is concerned, two attempts are under way during the Fall
Semester, 2006; one in math and the other one in organic chemistry.

 

Thank you very much.

![](media/image13.wmf)![](media/image14.wmf)

\-\-\-\--Original Message\-\-\-\--\
[]{#JohnMarshall .anchor}**From:** John Marshall\
**Sent:** Monday, September 04, 2006 4:44 PM\
**To:** National Math Panel\
**Subject:** Some views of US math

 

I would like to make a comment about Mathematics teaching in the USA but
before I do I should introduce myself. My name is John Marshall and my
main residence is in England where I spent the majority of my working
life in the field of mathematics. For my sins I was a teacher, college
lecturer and inspector of schools. More recently I was a 'visiting
lecturer' at the University of South Florida. In recent years I
contributed to the Minnesota K-12 Mathematics Framework as an expert
reviewer, keynote speaker and author. The American magazine Phi Delta
KAPPAN has published four articles of mine, the most recent being in the
January 2006 edition - *Math Wars 2: It's the Teaching, Stupid*. The
NCTM journal Teaching Children Mathematics also published *Educating
Hannah: It's a What?,* in the Geometry special of February 1999, done
with Sir Wilfred Cockcroft.  My wife, of 45 years, and I have a home in
Oldsmar, Florida. Our son spent a year at an American high school before
his University course in the UK.

 

In terms of the colloquial Math Wars I would be seen as being on the
reform side but I have to say at the outset that I do not recognize much
of what I see as 'reform based mathematics' in the USA as being
compatible with my experience. As I said in my KAPPAN article of
November 2003; "I find myself in complete agreement about the need for
reform. Let there be no doubt about that. We cannot go on killing so
many young minds like we have for they will grow up and replicate the
problems we now have and nothing will have changed. And yes, the aims
and aspirations of current NCTM Standards are to be commended. I just
don't see how many of the exemplars offered match up with those aims. To
me they just do not seem to reflect the attitude to the
teaching/learning process that the aims talk about and as such are
surely not 'what children need'!"

Personally reform was about offering children a better deal, period. A
better deal because what they were getting was not doing the job for the
world was changing and mathematical education was not keeping up. In the
UK a response was made to the Sputnik issue by looking at what young
children were doing. The Nuffield Foundation Mathematics Teaching
project of the early 1960s was created to produce a contemporary course
in mathematics for children between the ages of 5-13 that would produce
in them a "critical, logical, and creative turn of mind." It was
probably the beginning of MATHEMATICS for young children as before they
had only been offered arithmetic. It is interesting to note that the
parent's book from the project, said, amongst other things, "Whether we
like it or not, our children will be concerned in the future with more
abstract mathematics than their predecessors. The world of computers and
computer programs, of automatic production line processes, or of
operational research by managements, is a far cry from the world of the
nineteenth century clerk, mill-hand or small industrialist. Our most
important task must be to teach children to think mathematically for
themselves. From a gradual awareness of the patterns of ideas lying
behind their practical experiences, there must be built up a willingness
to accept the underlying mathematical ways of thinking which are proving
so vital in the development of modern technological society." That was
written in the mid 1960s and I wonder how it would sit today with those
anti-reform groups who appear to see the aim of school math as getting
their children into University. I am reminded of that Brian and Greg
Walker cartoon which shows a child asking father "Why do we have to do
Algebra?" and getting the reply "So you can help your children with
their homework"! And on the subject of entry into university I would
have to say that all my students in Florida had passed the test but few,
very few, very very few, knew mathematics. They were truly excellent at
passing tests though!

Let me go back in time and make a brief comment on what the UK has done.
In the late 1970s the (Labor) Prime Minister of the day, the Rt. Hon.
James Callaghan. MP, was concerned about the teaching of Mathematics in
schools and set up a panel to look at the problem. The terms of
reference for this committee were : ***To consider the teaching of
mathematics in primary and secondary schools in England and Wales, with
particular regard to the mathematics required in further and higher
education, employment and adult life generally, and to make
recommendations."*** The committee, chaired by Sir Wilfred (Bill)
Cockcroft, reported in January 1982, when Mrs. Thatcher (Conservative)
was the Prime Minister. Cockcroft looked at the 'past', looked at the
'present' and looked into the 'future' and then said in paragraph 800 of
the report: "We therefore believe major changes are essential."

(I was happy to receive a signed copy of the report from Sir Wilfred,
who wrote: "To John: With thanks for giving me the chance to see and
listen. Bill" Sir Wilfred could see 'reform' in action because it had
been happening in my development school for well over 20 years.)

The major change that was required was to teach for understanding rather
than by rote, which had been the style for years and years, and this was
addressed in paragraph 238 of 'The Cockcroft Report' -- "We have had
several submissions which have urged that more emphasis should be placed
on 'rote learning' The Oxford English Dictionary defines 'by rote' as
'in a mechanical manner, by routine; especially by the mere exercise of
memory without proper understanding of, or reflection upon, the matter
in question; ... ... we do not believe that it should ever be necessary
in the teaching of mathematics to commit things to memory without at the
same time seeking to develop a proper understanding of the mathematics
to which they relate. As our discussion of memory shows, such an
approach is unlikely to meet with long term success."

 

Mathematics needs long term success as children move through each stage
of the education system and into adult hood. How often do we hear that
the next stage in the learning process feels let down by the previous
stage. (And kindergarten has been known to blame the parents!!!) An
Inspectors job is strange but privileged. I must have visited over 500
classrooms and in everyone I was told the mathematics was perfect.
(Rather like the situation described in the Stigler and Hiebert book
*The Teaching Gap*, page 123/124)  The overall teaching style I saw was
'rote'. It was how teacher was taught by teachers who had been taught by
rote and it was the way 'she' taught. Principals were proud of the
outcome and could often produce test scores to prove their point. But
all too often the mathematics atrophied by the next stage. This was
perfectly illustrated in one city where the educational provision was in
4 stages: 5-8 yrs, 8-12 years, 12-16 years and 16-18 years. ALL the
subsequent stages found the entry levels were 'not what was expected'!
From within this system I even received complaints that bright
university students struggled to take their mathematics with them: -
"Indeed it is a common, and sometimes somewhat disconcerting, experience
to those embarking on degree courses in mathematics to find that their
understanding of topics which they have tackled with apparent success at
school is questioned and shown to be insufficient." (Mathematics Counts.
page 68 HMSO. London.)

 

But teaching for understanding is not easy for one has to know
mathematics and how children learn.

In their (US) paper *Reaching for Common Ground in K--12 Mathematics
Education* (Focus January  2006) Deborah Loewenberg Ball, Joan
Ferrini-Mundy, Jeremy Kilpatrick, R. James Milgram, Wilfried Schmid, and
Richard Schaar look for agreement in different sides on the Math Wars.
Although I am not sure who is on which side of the argument, I do
recognise that Joan Ferrini-Mundy has her name on the NCTM's *Principles
and Standards for School Mathematics 2000***^ ^** book and that Richard
Schaar is from Texas Instruments, who make calculators. In their joint
paper the authors assert, quite rightly, that "Mathematics requires
careful reasoning about precisely defined objects and concepts.", and
that students need to "understand the operations". "Precisely defined
objects and concepts" and "understand the operations", who could
disagree? But what does that mean and how does it manifest itself in the
classroom? As far as the key operation of multiplication is concerned
where do NCTM and Calculators stand? Sadly not together although they
claim to be! Let me explain: NCTM says on page 151 of *Principles and
Standards for School Mathematics* "It is important that students
understand what each number in a multiplication and division expression
represents. For example, in multiplication, unlike addition, the factors
in the problem can[^1]^1\]^ refer to different units. If students are
solving the problem 29x4 to find out how many legs are on 29 cats, 29 is
the number of cats (or number of groups) and 4 is the number of legs on
each cat (or the number of items in each group) and 116 is the total
number of legs on all the cats. Modeling multiplication problems with
pictures, diagrams, or concrete materials, students learn to be clear
about what each number in the problem represents."  I should add that no
pictures, diagrams, or concrete materials are used to make the point. In
fact the classroom picture used (page 142) is very much 'as it used to
be' where the results of mathematics are displayed and not the
mathematics itself, which would include the results! However, this is
NOT the definition that is found in American Dictionaries --
"Multiplication: the process of finding the number or quantity (product)
obtained by repeated additions of a specified number or quantity
(multiplicand) a specified number of times (multiplier); symbolized in
various ways (ex. 3x4=12 or 3.4=12, which means 3+3+3+3=12, to add the
number three together four times)." (Webster's 3rd Edition College
Dictionary) - nor in Japanese text books.

 

In the statistics section of *Principles and Standards for School
Mathematics* *2000* it says (page 49) "Recognizing that some numbers
represent the values of the data and others represent the frequency with
which those values occur is a big step." It is a huge step because if
one follows the NCTM definition of multiplication and take it forward
into a calculator one finds that 'it doesn't work' as the calculator
follows the definition of multiplication given in American Dictionaries.
Let me quote from my KAPPAN paper of February 2001 *(Dear Verity, Why
are all the dictionaries wrong?)* where I gave an example in which it
was necessary to find the mean height of 10 children, *"6 of whom were
120 cms. tall and 4 were 110 cms. Setting the calculator to the
statistics mode, we keyed the data in as (6x120) + (4x110). You know, '6
lots of 120' \[as per Standards 2000\], etc. Pressing x-bar, to get the
mean, we got 5.04 cms. Now nobody is that size. That's silly. So we then
keyed it in as (120x6) + (110x4), that is 120, 6 times etc., \[*as per
the dictionaries!\] *and got 116, which made sense."* How can this
possibly mean that the Common Ground authors agree?

 

I have heard it said that because the operation of multiplication is
commutative then 'it doesn't matter'. I note that neither the
dictionaries nor the NCTM guidelines say that for they are quite
specific. The Schodor Foundation website, a group that supports the NCTM
*Principles and Standards for School Mathematics* *2000*, actually
builds this confusion into what looks like a lesson on introducing
multiplication where the definition is given á la the dictionaries,
including its own, and then it is ignored as follows:-

 

> Student: So now that I understand addition and subtraction, are there
> any more operations?
>
>  
>
> Mentor: Yes there are. The next operation is called multiplication. We
> write multiplication problems in the form axb, or a times b. For
> example we will consider 5x3. What this means is that 5 is being added
> to itself 3 times (5+5+5), but a better way to think about it is that
> it means 5 groups of 3 units each. Therefore to solve 5x3 you would
> count the number of units in each group.
>
>  
>
> Student: I feel a little confused.
>
>  
>
> Mentor: Alright, we will use an example you can visualize. Picture 5
> separate plates, each with 3 quarters on them. How many quarters are
> there altogether?
>
>  
>
> Student: Well, if there are 3 quarters for each of the 5 plates, then
> there are 15 quarters altogether. So 5x3=15.
>
>  
>
> Mentor: Exactly. Now, what if we had 3 plates, each with 5 quarters?
>
>  
>
> Student: Then there would be 5 quarters for each of the 3 plates,
> meaning 15 quarters altogether. So 3x5=15. Does that mean that
> multiplication is commutative like addition? \[ Etc.\]

(<http://www.shodor.org/interactivate/discussions/intmult.html>)

 

 

It looks to me as if our 'Mentor', like many others, is confusing
'meaning' with 'operation'! Whilst the **[operation of
multiplication]{.underline}** is commutative, the **[meaning of
multiplication]{.underline}** is surely not. I wonder if those who take
this 'doesn't matter' stance  would say taking 3 pills a day for 21
days, 3x21, is the same as taking 21 pills a day for 3 days, 21x3 -- NOT
to be tried at home I should add.

 

This is not my idea of reform. This is not my idea of teaching. This is
not even my idea of mathematics. Is it really America's?

 

The definition of multiplication means that one cannot multiply 'things'
by 'things' yet traditional mathematics teaching has engraved "area \[of
a rectangle\] equals length times width" in the minds of generations of
students world wide. Is it any wonder that American researchers find
that students are confused - 'many elementary and middle-grades children
have difficulty with understanding perimeter and area. Often, these
children are using formulas such as P=2l+2w or A=lxw without
understanding how these formula relate to the attribute being measured
or the unit of measurement being used Kenney and Kouba (1997) and
Lindquist and Kouba (1989) -- or so it says in the NCTM Standards! I am
not convinced that student teachers who read their Math Methods text
which says "Now we are multiplying two lengths to get an area" and a
text book that says "rows x columns" is the way to go, are going to put
any minds at rest. As for myself, I daren't look at what advice was on
offer when it came to volume! In teaching about a=lxw we need children
to understand that 'l' and 'w' refer to different things. (See Math Wars
2 : It's the teaching, stupid. Marshall. KAPPAN January 2006)

 

I did though consider how the meaning of multiplication was applied to
fractions and was advised to consult a research based book edited by 'an
expert on rational numbers'. The chapter on multiplication is quite
clear that in 6x4, the 6 is the multiplicand and the 4 the multiplier,
fitting in with the American Dictionaries. However as the next chapter
discusses 2/3 x 4/5 I am told that the repeated addition nature of
multiplication cannot be taken forward when looking at the
multiplication of fractions. Surprisingly, no indication is given as to
just what multiplication experience children do take with them when
attempting such problems. It all looked very much 'yours is not to
reason why, just invert and multiply' (almost literally!) as a series of
bullet type instructions are given! Against this confusion how do we
expect children to 'read' statements such as 2/3 x 4/5 with feeling?
What images are created in the mind when children see such statements?
Where could it come from? What is the story? Is it really too much to
say that we have 'two thirds, four fifths of a time' -- a carry over
from previous teaching? The point being, like in our area problem, the
language of multiplication is taken along with them. After all,
understanding is about tackling new problems -- "There is general
agreement that understanding in mathematics implies an ability to
recognize and make use of a mathematical concept in a variety of
settings, including some which are not immediately familiar."
(Cockcroft, Sir Wilfred. Mathematics Counts. HMSO. London. (1982) page
68)

 

Many years ago I was asked for advice about introducing young children
to Geometry. The key here was 'young children', young children who were
at the concrete operational stage of their development. This recognition
of how children develop, so vital in the teaching of mathematics,
demanded that we start with 3-dimensional shapes. This seems to be at
odds with the reform of NCTM for a cursory glance at the illustrations
in *Principles and Standards for School Mathematics* *2000,* and in the
methods book I was given*,* indicates that in the K-2 Geometry section
2-dimensional shapes are the way to go. But is it? In the section of
*Principles and Standards for School Mathematics* *2000* entitled
Reasoning and Proof 3-dimensional shapes are given for children to
handle but there is an overwhelming desire to call them by their
2-dimensional names, at least I think that is so. After all, what is a
'thick circle'? A pattern is shown in figure 4.27 (page 123) that a
child has made and is proud to see the shapes as 2-dimensional. Where is
this going? My children see cylinders and rectangular prisms (cuboids),
etc., all over the place. The door and the cereal packet are the same
shape -- perhaps even being at odds with Pierre van Hiele (e.g."
Children might say, 'It is a rectangle because it looks like a box' !!!)

 

Looking at the Geometry issue of *Teaching Children Mathematics*
(January 1999) there is an article (Shape Up) where the authors are
critical of some misconceptions some children acquire. The advice
offered suggests readers should "1) Emphasize the properties and
characteristics of a concept, 2) Provide many examples and non examples
....., 3) Play close attention to language use, and 4) challenge
understanding and broaden generalities." The reader is then invited to
give students "a collection of geometric solids and thin attribute block
pieces ..." Evidently these thin attribute block pieces can be handled!
It is my view that journals should not publish such papers. I don't
think they do so to deliberately confuse teachers/children but rather
because the editorial staff genuinely believes that 'a circle has a
thickness'. (The editor once told me where I could buy some!)
Incidentally, the same magazine carries a paper that claims there is no
such thing as a plane shape with thickness (Education Hannah. It's a
what? : Cockcroft and Marshall)

 

In my travels I have spoken with many suppliers of educational materials
and this has been quite illuminating. It is clear that they have a
different, and in some way understandable perspective, to me. I see good
math products and bad math products. They see profitable products and
non profitable products. It seems that bad products sell. The bottom
line is that if 'the market' wants 'thick circles' etc.,  then they will
supply 'thick circles' etc., by the tonne for it pays the mortgage. (My
neighbor even has a book that encourages these misconceptions claiming,
amongst other things, that a carrot is a triangle, and her young
(preschool) grandson loves it!!!! When he gets to school he will get an
'A' I am told. When he gets to my class at college he will get 'F'.)
Only recently I had a conversation with a supplier who told me quite
bluntly that the 'in thing' is now 'probability' but his buyers are not
interested in concepts but rather knowing that the probability of
getting a '3' is 1/6 for the test. (I assume this is a 1-6 dice!!) As I
said earlier, it pays the mortgage.

 

I could go on. Quite naturally friends in both the USA and UK ask me
what education is like in the other country. I would have to say that I
haven't seen a good math lesson in the US neither has my wife finding
ourselves rather like the professor  in the Hiebert and Stigler book I
mentioned earlier -- "In US lessons, there are the students and there is
the teacher. I have trouble finding the mathematics; ..." Having visited
something like 50 students teaching 6 lessons (not all math) I asked her
how many lessons she would be pleased if our son had been in when he was
young. The answer was none. However, a recurring theme in my
conversations is the quality of those student teachers we met. There is
a small group of truly outstanding people wanting to teach and I say
this without wanting to add any 'grade inflation' to the word. Not all
we met are in this category, far from it. If things are going to get
better it is these people who will do it. They must be given their head.
Why America feels it so necessary to have such central control when all
it does is make sure everyone gets mediocrity is beyond me. When the
county (or State) says this is what must be done then they had better be
right. Setting schools free may, I say may, just allow some quality to
come through which can then be replicated.  Getting this workforce
excited about teaching mathematics, and retaining them, is going to need
a vast rethink across the board.

 

 

Teaching mathematics is a huge challenge and an enormous task. It has
been a lifetime work for many who would claim to only have scratched the
surface. Getting it right for our children is vital as Thomas Friedman
says in his book; The World is Flat, and Senator John Glenn, in his
report, Before it's Too Late. The bottom line as I see it is clearly
expressed by Keith Devlin in his book The Math Instinct. (Thunder's
Mouth Press. New York. 2005. ISBN 1-56025-672-9 Page 241) where he
writes: "The problem is that humans operate on meanings. In fact, the
human brain evolved as a meaning-seeking device. We see, and seek,
meaning anywhere and everywhere. A computer can be programmed to
obediently follow rules for manipulating symbols, with no understanding
of what those symbols mean, until we tell t to stop. But people do not
function in that way." I look forward to your conclusions.

 

John Marshall

Monday, September 04, 2006

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\-\-\-\--Original Message\-\-\-\--\
[]{#DennisBrownridge .anchor}**From:** Dennis Brownridge\
**Sent:** Saturday, September 02, 2006 12:10 AM\
**To:** National Math Panel\
**Subject:** Teaching of Measurement

 

August 31, 2006

 

**Comments to National Mathematics Advisory Panel**

NationalMathPanel@ed.gov

 

            As a teacher with 30 years experience, I'm convinced that
the greatest single weakness of our current mathematics curricula is our
failure to teach a coherent system of measuring units. Measurement is
the most widespread use of mathematics, but our textbooks don't explain
the most fundamental measurement concepts, such as coherence (units
defined with the same equations as the quantities they measure), base
vs. derived, precision vs. accuracy, manipulation of prefixes, and
engineering notation. These are essential skills that students need in
their science courses, the workplace, and everyday life.

            The only complete, coherent, and practical system of units
is the International System (SI), the simplified modern version of the
various metric systems. SI has become the world standard and was adopted
by Congress in 1988 as the preferred system for the United States. It is
a simple system that, in my experience, students can master very
quickly.

            But alas, measurement coverage in our current textbooks is
woefully inadequate and outdated, if not plain misinformed. Even
elementary quantities such as volume, mass, weight, and density are
confusing to our students because we measure them with such a
bewildering array of non-SI units.

          There are literally hundreds of non-SI units used in the
United States today, in one field or another. To be fluent in all of
them, a person would have to memorize countless definitions and
multi-digit factors. Clearly this is an impossible task. The schools
couldn't hope to teach more than a tiny fraction of those non-SI units a
student might encounter. And textbooks don't attempt to do so. They
don't define such common but irrational non-SI units as the acre (43 560
square feet) or fluid ounce (231/128 cubic inches). So students are
unable to do even everyday calculations in area and volume.  

          The only solution to this dilemma is to teach SI as the
primary system, as NCTM has recommended. Of course, we must also teach a
few non-SI units that are used worldwide and essential in everyday life,
such as the minute, hour, and angular degree. But the mistake made by
our current texts is to reduce the whole subject of measurement to
little more than a tedious exercise in converting units. Math courses
today generally teach a few token relationships, such as 12 inches per
foot, 3 feet per yard, and 16 ounces per pound. But this isn't nearly
enough information to do simple, real-world problems with non-SI units.
(If a rectangular aquarium measures 10 × 10 × 20 inches, how many
gallons does it hold?)  Moreover, by teaching a handful of relationships
and ignoring the rest we are giving students a false sense of
understanding. They don't realize that a pound of force is entirely
different from a pound of mass; that ounces of soft drink are volume
units unrelated to avoirdupois ounces; or that an ounce of gold or
silver is 1/14.583 pound, not 1/16 pound.

          The result of all this is that---unless they have learned SI
in their science classes---most students today are completely unequipped
to do realistic problems involving measurement. They are ignorant not
only of SI, but of non-SI units as well.

          Thank you for the opportunity to comment on this important
issue.

 

 

Dennis R. Brownridge, PhD

The Orme School of Arizona

[]{#BillyBryant .anchor}\-\-\-\--Original Message\-\-\-\--

From: Billy Bryant

Sent: Friday, September 01, 2006 9:28 PM

To: National Math Panel

Subject: Mathematical Achievement

Sirs:

 

The minds of the mathematical wizards are already made up, so my
comments will most likely fall upon deaf ears.  Such is the case in the
local schools.

 

A few decades ago Americans usually ranked about third internationally
in mathematics.  Today we rank about 25th.  There are several reasons
for the decline, but the major reason is the \"New Math\", I believe.

 

My wife and I both have reasonably good math backgrounds and are raising
a granddaughter.  She comes home with math homework that we both have
trouble helping her with.  The answers are simple: but the \"new math\"
solutions require a degree in math to figure out.

 

Statistics show that the new methods of teaching math do not work.  So
why keep beating a dead horse?  Go back to the old tried and proven
methods and bring American children back to the top in international
standing!  The only reason schools are still force-feeding the new
method is: nobody has the guts to stand up and say, \"It doesn\'t
work!\".

 

Thank you for your time!

 

Sincerely,

 

Billy F. Bryant

[]{#DaveMarain5 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Dave Marain

Sent: Friday, September 01, 2006 8:41 PM

To: National Math Panel

Subject: Statement to the National Math Panel

This email is being sent by the deadline date of 9-1-06. Pls confirm
receipt of this email.\
\
The teachers of the mathematics department of Ramapo H.S. wish to
express their strong sentiments embodied in the attached statement. We
know the Panel will read this and the hundreds (thousands?) of other
similar statements and hopefully will accept these as a mandate for
change in mathematics education in this country. It's not about reform
or preserving tradition. It's about what we feel is best for our most
precious national treasure, our children. Do not abandon another
generation. Listen to our teachers -- no one knows better what is needed
in our classrooms.\
\
Sincerely,\
Dave Marain\
Supervisor of Mathematics & Business

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[]{#MichelleAlves .anchor}\-\-\-\--Original Message\-\-\-\--

From: Michelle Alves

Sent: Friday, September 01, 2006 4:52 PM

To: National Math Panel

Subject: Re: pre-registration for Sept. math panel

Hi Jennifer,\
\
Here are Elon\'s comments.

Thank you,\
Michelle Alves

Chief Executive Officer

Digi-Block, Inc.

![](media/image18.wmf)

[]{#BertBeck .anchor}\-\-\-\--Original Message\-\-\-\--

From: Bert Beck

Sent: Friday, September 01, 2006 1:47 PM

To: National Math Panel

Subject: REVISED paper submitted for National Mathematics Advisory Panel

> Good morning Jennifer,
>
>  
>
> I apologize. A small change has been made in the text of the document
> submitted for the National Mathematics Advisory Panel. Please delete
> the previous submission and download the attached documents instead.
>
>  
>
> Please call or e-mail with any questions or concerns.
>
>  
>
> Thank you.
>
>  
>
> Bert Beck
>
> Office of the Superintendent
>
> Orange County Department of Education

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[]{#MelissaKalinowski .anchor}\-\-\-\--Original Message\-\-\-\--

From: Melissa Kalinowski

Sent: Thursday, August 31, 2006 7:56 PM

To: National Math Panel

Subject: RE: National Math Panel Meeting in Cambridge from 9/13-14

Hi Jennifer,

Please accept the submission of written comments for the National Math
Panel meeting. Best regards.

Melissa Kalinowski

Elementary Marketing Director

PLATO Learning

![](media/image22.wmf)

[]{#BenWeintraub .anchor}\-\-\-\--Original Message\-\-\-\--

From: Ben Weintraub

Sent: Wednesday, August 30, 2006 5:56 PM

To: National Math Panel

Subject: National Math Panel Testimony

My name is Ben Weintraub. I am the CEO of Merit Software. Merit Software
has been producing educational math software sold to schools since 1983.
I have been with the company since 1990.

When the No Child Left Behind Act was passed, we sought to conduct
scientific-based research on the efficacy of our products. Prior to
2001, Merit had received a lot of nice comments from teachers about our
products. Many teachers had told us they were sure that our software was
the reason that their students improved their math ability.

The software is known for providing context-sensitive tutorials for
students while tracking scores for teachers. The approach allows
students to apply skills as they learn them, breaks troublesome concepts
down into understandable parts, provides multiple forms of help when
needed, and enhances communication among students, teachers, parents,
and administrators.

We felt that Merit programs were a good candidate to be the subject of
research because all student work is done on the computer, time-on-task
can be measured, and students advance when they demonstrate readiness.

In 2002 we began a research partnership with faculty at the Marshall
University Graduate School of Education in West Virginia to evaluate
Merit as a curriculum supplement.

The initial research was conducted on the use of Merit reading and
writing programs at a rural middle school. The evaluation was a
longitudinal study and divided students into control and treatment
groups. The results showed that the lower quartile students made
long-term gains in reading/language arts, and other subjects that were
not covered by the software. Math was one of these subjects. A paper
about the research was published this summer in the Journal of Computer
Assisted Learning.

In 2005 another study was started using Merit math software at a urban
middle school. In this evaluation, the school used our software for
fractions, word problems, pre-algebra, and basic algebra. The results
showed that:

\- The standardized test scores of the Merit treatment group were higher
compared to those who did not use the software.

\- The treatment has an extremely large impact. An effect size of .844
was calculated for the treatment group\'s test scores. Following
established guidelines by Cohen, where .14 is considered to be a large
impact, .844 indicates a substantial increase in math scores from pre to
post test.

\- A p-value of .001 was determined for the math scores of the treatment
group. This is evidence that these results were not a fluke or a
statistical oddity.

\- Positive results transferred to other areas of academic achievement.
Gains were seen in test scores for science, social studies and
reading/language arts.

\- Socioeconomic variables, such as ethnicity and free-lunch
eligibility, were found to be a statistically insignificant factor in
overall test scores gains.

A detailed paper about this research, which has been submitted as
exhibit to my testimony, was published this summer in i-Manager\'s
Journal of Educational Technology.

In conclusion, today\'s curriculum supplements can be very powerful and
can have a dramatic effect on student performance. Clearly there are
ways to prepare our nation\'s students for algebra. The evidence shows
that using supplemental software in schools can work.

Not every math software product sold to schools does work, or can work.
However, the ones that will work provide personalized instruction; allow
students to apply skills as they learn them; and tap into students\' own
desire to improve their skills.

Please let me know if I can be of further assistance to the Panel.

Ben Weintraub

Merit Software

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[]{#KathyMowers .anchor}\-\-\-\--Original Message\-\-\-\--

From: Kathy Mowers

Sent: Tuesday, August 29, 2006 4:42 PM

To: National Math Panel

Subject: Re: deadline for Math Panel comments

Jennifer: I have attached two copies of the AMATYC letter in PDF format.
For inclusion in the Panelists\' meeting material, would you please use
the letter with the signature?

If a decision is made to post the letter on the web, I would prefer that
my signature not be posted, so I\'ve attached the same letter without my
signature (AMATYC letter to NMAP no signature.pdf).

Please let me know if there are any technical problems with the files.

Thanks,

Kathy Mowers

AMATYC President

Professor

Owensboro Community and Technical College

![](media/image25.wmf) ![](media/image26.wmf)

[]{#CherylJaffe .anchor}\-\-\-\--Original Message\-\-\-\--

From: Cheryl H. Jaffe

Sent: Tuesday, August 29, 2006 12:49 PM

To: National Math Panel

Subject: Comments for National Mathematics Advisory Panel

Dear Panel,

I have many issues that warrent discussion, two of which

are closely related to your focus (as I perceive it). One

is a data point on the issue of teacher salary and

quality. The other is an approach of teaching children

from a young age the tools which which to make solving

math

problems easier, indeed possible.

Regarding teacher salaries:

I lost my job after 9 years as a research engineer. I was

able to get a teaching license by taking a test\* and a

night class, and student teaching while receiving

severence pay. After the severence pay ran out, I was on

unemployment for a few months until I got a job as a high

school math teacher. My NET teacher salary was about the

same as I received on unemployment, only as a teacher I

had to pay for daycare out of that amount. Financially I

was better off on unemployment.

I had a good start as a math teacher because of my

approach of trying to make math easy for the kids, and

keeping math connected to the world. I had a lot to learn

about pedagogy, and a FANTASTIC set of colleagues to learn

it from (at Marlborough High School in Marlborough, MA).

Had I stayed in the field, I\'d have become a great

teacher. But an offer came along that I couldn\'t refuse -

by returning to engineering, I more than doubled my gross

salary, and things like pension are added OVER my salary

as a benefit, rather than being taken from my salary.

Not all great teachers are great mathemeticians, and not

all great mathematicians are great teachers. But there are

many who could and probably would be both if they could

support a family - I work with them in a field that pays a

living wage.

Regarding math tools:

During my brief but memorable experience teaching, I

noticed an overwhelming trend among students to work math

problems in manner that made them much more difficult

than they needed to be. For example, the approach to a

problem which asked for the circumference of a circle with

diameter 21 using the 22/7 approximation for pi, was to

multiply 21 and 22, and long divide that product by 7 (or

worse, long divide 22 by 7, and then multiply by 21!).

Not a single student simplified the problem by factoring

21 and

using the multiplicative identity to cancel the 7\'s, and

almost all of them made mistakes. I consider this the

mathematical equivalent to using your fingers to nail

shingles onto the roof. Most of these kids could recite

the properties of real numbers, just like I could pick a

hammer out of the tool box, but they didn\'t know how to

USE them. If I ever get enough time away from my job, I

would like to develop a curriculum for middle school

students (or younger!) which will teach them not to

memorize and regurgitate the properties of numbers, but to

USE them to make math easy. It should be taught with

basic arithmetic,

and retaught with algebra. I was teaching this with a 9th

grade remedial math class when one of my students told her

classmate to \"shut up - I\'m learning!\".

Although it is not as directly related to your focus, I

hope that the council will give some thought to one other

issue: how to prevent losing young gifted math learners to

boredom and underachievement. The law that allows schools

to discriminate on the basis of age makes it nearly

impossible for young gifted mathematicians to access

challenging material more than one or two hours per week,

and that\'s only in grades and schools that have good

identification procedures and programs for gifted kids.

It\'s not nearly enough.

Thank you for your time.

Sincerely,

Cheryl H. Jaffe

Systems Engineer

Northrop Grumman Corporation/Electronic Systems Division

[]{#JosephDeBartolo .anchor}\-\-\-\--Original Message\-\-\-\--

From: Joseph J. DeBartolo

Sent: Sunday, August 27, 2006 1:17 PM

To: National Math Panel

Subject: Comments to the National Math Advisory Panel Meeting

I have been a Connecticut Licensed Professional Engineer for over 45
years.  There is no question in the engineering community that designing
in metric is easier, faster, less prone to error, and cost effective. 
No doubt this is one of the reasons that the world, outside the U.S.,
now operates in the metric system.

 

Each year more American companies are taking advantage of the worldwide
market that is available for products that are designed in metric.  This
in turn increases the need to employees who are not only familiar with
metric units, but also have the ability to work in that system. 
Teaching these metric skills is essential to prepare our children for
those employment opportunities.

 

Respectfully,

 

Joseph J. DeBartolo, P.E.

[]{#RichardRusk .anchor}\-\-\-\--Original Message\-\-\-\--

From: Richard W. Rusk

Sent: Saturday, August 26, 2006 2:23 AM

To: National Math Panel

Subject: National Math Advisory Panel

I congratulate you on being selected to serve on the National Math
Advisory

Panel (NMAP). You have the very challenging task of improving math

education in the U. S. "in order to keep America competitive, support

America talent and creativity, encourage innovation throughout the
American

economy...." This panel will focus on improving math education to meet
21st

needs - a daunting task to say the least. Two facets of the challenge
are

to realize that the rest of the developed world uses the metric system
of

units as the only system of measurement throughout its economy and that
our

country doesn't rule the roost anymore. China and India are emerging

big-time and England is expecting to change highway signage to metric

before it welcomes visitors for the upcoming Olympics. The European
Union

is expecting to require that all goods coming into it be labeled in
metric

units only in a few years. While this idea is being negotiated with the
U.

S. the handwriting is on the wall. Are the Asian countries next?

Having encountered the resistance to increasing the emphasis on teaching

the metric system in the public schools in my home district I have some

sense of the problem. Whether for the better or worse our county has an

elected school board. Therefore, school administrators are very
sensitive

to public opinion. One must remember that our nation is a republic in

which we elect our president, senators, etc. to do the necessary
research

to act wisely on the issues at hand.

Having said that, I believe that it is a waste of time to teach the

antiquated inch/pound system in our schools unless it would be included
in

a single period lesson in a history of technology course. The time saved

could be used on understanding more advanced concepts. A change of such

magnitude will certainly cause problems. Students emerging from high

school without a background in the inch/pound system will certainly have

enough ingenuity to buy T bone steak by the pound until the supermarkets

catch up. Also some of the long time in-service faculty may need
workshops

to be brought up to speed on metric units. These temporary
inconveniences

will pale in contrast to the dividends accrued by taking this giant step

forward.

In summary, our nation will face many severe challenges as it moves
through

the 21st century. It is vitally important that it has the tools to move

forward. One of the important tools is complete metrication.

[]{#PierreAbbat .anchor}\-\-\-\--Original Message\-\-\-\--

From: Pierre Abbat

Sent: Friday, August 25, 2006 10:54 AM

To: National Math Panel

Subject: National Math Panel comments

To retain and increase American competitiveness, it is important to
teach the

metric system as the only system of measurement. Scientists and
engineers

have been using metric for over a century. When American children enter

physics class not knowing their own height in meters or their mass in

kilograms, they are at a disadvantage compared to children who have been

using these units all their lives.

The Internet has brought people all over the world together. I talk
daily with

people in Europe and Asia about hair care, food, and health. Using
different

units causes confusion when we talk to each other.

The metric system is based on 10. The customary system has a mixture of

different bases. In metric you have no unround internal conversion
factors

such as between gallons and acre-feet or between dry pints and liquid
pints.

All internal conversion factors are powers of 10.

Besides base 10, we should also teach base 2 (or 16) and base 60. Base 2
is

used with computers, and base 60 is used with time (we can\'t avoid it,
as a

second is 1/86400 day) and angles. These don\'t need to be taught as

intensively as base 10; no one I know of multiplies in base 60.

Pierre Abbat

[]{#GaryCarver .anchor}\-\-\-\--Original Message\-\-\-\--

From: Gary P. Carver

Sent: Friday, August 25, 2006 10:04 AM

To: National Math Panel

Subject: comments to NMAP

Comments to the National Mathematics Advisory Panel, U.S. Department of

Education:

To meet its purpose, the National Mathematics Advisory Panel must find

that teaching only the metric system of units in American schools should

begin immediately.

Everyday, people see and use both metric and customary units almost

interchangeably everywhere, except perhaps on highways and in gasoline

stations. As more and more metric products entered our economy, people

easily switched to, for example, buying soft drinks in liters and
aspirin

in milligrams. People adapted to using computers and the metric

terminology associated with them. People who work in many industries,

particularly technical industries such as medicine, engineering, and

science but also basic industries such as automotives, electrical, and

food packaging, use metric units at work and conventional units on their

drive home.

Students don't need to spend time in mathematics classes to learn both

systems and to learn the useless conversions among units. It is not only

a waste of time; it also is an activity that misleads students into

thinking that converting among units is an end in itself. In fact, units

are merely the means of measuring quantities. Measurement, including its

attributes such as precision, accuracy and uncertainty, and the way it
is

used to describe our perceptions of reality are the important concepts.

Despite the persistence of U.S. customary units in our society, the

National Mathematics Advisory Panel would fail if it missed the

opportunity to declare the metric system of units the only system of
units

to be taught in our schools. Students need to learn the concept of

measurement---and they can learn it best using metric units.

In summary, I have two recommendations:

1\. I urge the Panel to look beyond the unproductive teaching of our old

system and reject any classroom conversion of its units to the metric

units used in the global community.

2\. I propose that the Panel elevate the concept of measurement and
lower

the mechanical manipulation of measurement units in mathematics
education.

Sincerely,

Gary P. Carver

Former Director

U.S. Department of Commerce Metric Program

\-\-\-\--Original Message\-\-\-\--

[]{#JimElwell .anchor}From: Jim Elwell

Sent: Wednesday, August 23, 2006 3:12 PM

To: National Math Panel

Subject: letter to NMAP

Please see attached PDF letter.

Thank you.

Jim Elwell

[www.qsicorp.com](http://www.qsicorp.com/)

![](media/image27.wmf)

[]{#WilliamBrenner .anchor}\-\-\-\--Original Message\-\-\-\--

From: William Brenner

Sent: Tuesday, August 22, 2006 10:48 PM

To: National Math Panel

Subject: Teaching the Metric System

I am writing to urge the National Mathematics Advisory Panel to include

metric education among its priorities.

Thomas Jefferson introduced the metric system to this country about 200

years ago but was unsuccessful in getting it adopted, primarily because

Congress was unsure it had the constitutional authority to do so.

Jefferson did convince Congress to adopt a decimal-based money system,

however, saving us the horrors of 200 years of the highly unwieldy

shillings, pence, bobs, and pounds from which the British only recently

have been able to free themselves.

Today metric measures are used by 95.4 percent of the world\'s

population - - 5.7 billion people - - for everything they do. Even in

this country, people buy cola in liters, aspirin in milligrams, and

light bulbs in watts (electrical measures, and everything in science,

have always been metric-based). Our largest trading partners, Canada and

Mexico, are metric countries. Major U.S. industries, such as auto,

machine tool, electronics, soft drink, liquor, pharmaceutical, and

health care, are primarily or completely metricated.

The metric system is decimal-based, easy to use, and coherent; the

inch-pound system is not. The final step in fully aligning our
country\'s

measurements with the rest of the world is to teach the metric system as

the primary means of measurement in our nation\'s schools.

William Brenner, Vice President

National Institute of Building Sciences

Washington, D.C.

[]{#MaryGerke .anchor}\-\-\-\--Original Message\-\-\-\--

From: Mary Gerke

Sent: Monday, August 21, 2006 3:05 PM

To: National Math Panel

Subject: Metric Education

I am writing to urge you to recognize the importance

of the language of science; namely, the expanded

metric system known as SI.

As a science teacher, I am yearly embarrassed to tell

my students that the United States is the ONLY country

still using an antiquated and incoherent measurement

system. These students find the SI vocabulary simple

to learn and easy to use. Why SI is not a subject of

maximum priority for the National Math Advisory Panel

is NOT understood.

Why must our students be burdened with TWO measurement

systems and yet be expected to surpass students from

other countires not so burdened?

[]{#WilliamHooper .anchor}\-\-\-\--Original Message\-\-\-\--

From: William Hooper

Sent: Sunday, August 20, 2006 8:33 PM

To: National Math Panel

Subject: Comments to Nat'l Math Advisory Panel meeting

I should like to submit the following comments and recommendations to

the National Mathematics Advisory Panel meeting on 2006 September 13

and 14.

===================================

If we wish to keep America competitive in a world where everyone else

uses metric measures for everyday trade and commerce, it is vital

that we have a major effort to educate our children to use the

International Metric system (SI). For our children to succeed in this

world, where 95% of the population uses metric, our children must be

able to use the metric system with ease and familiarity. Familiarity

with metric is especially important for high tech jobs that are so

critical to American competitiveness.

Teaching an occasional unit on the metric system won\'t do. Just

learning \"about\" the metric system won\'t do either. Our students need

to learn to USE the metric system with facility. What is needed is a

major emphasis on using and teaching metric consistently throughout

the mathematics curriculum.

The best and surest way to do this is to stop teaching (and stop

USING) the Old English system at all levels of mathematics. Indeed,

mathematics teachers need to solicit the aid of their colleagues in

other disciplines to assist this effort by using metric in their

teaching as well, from 2 cm margins on reports in English to 100 m

dashes on the athletic track.

Teaching metric rather than Old English measurements has additional

advantages. It saves time and money because it is easier to teach.

When used in everyday business it saves more time and money because

it is easier to use and reduces errors. Since metric is used

virtually everywhere else in the world, teaching it will facilitate

travel and tourism, both making it easier for our people who travel

to metric countries as well as making it easier for us to accommodate

visitors from metric countries who come here.

There are those who would argue that we still need to teach Old

English measurements because students will encounter them, since

those old mesurements are still in wide use in the US (although

nowhere else). I disagree! Instead, I maintain that the students know

enough of it already. Those in the upper grades who will soon be in

the job market have already had at least 12 years of schooling in the

Old English system. They don\'t need any more. Those in the earlier

grades who have 12 years of schooling yet ahead of them, will find

that by the time they finish those 12 years, the metric system will

be even more prevalent than it is now and it will be more necessary

to know metric than to know the Old English measures.

I ask the Panel, please, not to relegate the metric system to a long

\"list of topics to be taught\"; instead, please make metric education

one of the main pillars of mathematics education. There are few

specific recommendations that could go further to fostering greater

knowledge of and improved performance in mathematics among American

students. That should be our goal and teaching metric will help us

get there.

Sincerely,

(Dr.) William Hooper, BS, MS, EdD

Professor of Physics and Astronomy (ret.)

The University of Virginia\'s College at Wise

[]{#TonyPickar .anchor}\-\-\-\--Original Message\-\-\-\--

From: Tony Pickar

Sent: Friday, August 18, 2006 2:44 PM

To: National Math Panel

Subject: public input

> Hello,
>
> I am a K-12 mathematics curriculum coordinator for DCEverest Schools
> in Wausau, Wisconsin.  I am just concerned that your recommendations
> for math education follow the vision set forth by NCTM in their
> Standards documents, PSSM Principles and Standards for School
> Mathematics, and other documents.  I have spent many hours instilling
> NCTM\'s vision and philosophy in educators around the state, and I
> truly believe that NCTM\'s vision for mathematics for all is the only
> way that we will prepare students for living in the 21st century.  I
> fully support the methods suggested by NCTM (cooperative learning,
> technology, and manipulatives) along with the NSF curriculua of
> (Elementary: Everyday Math, Math Trailblazers, Investigations   Middle
> School: Connected Math, MathScape, Maths in Context   and High
> School:  Core-plus, Math Connections, and IMP.) as useful tools to
> make mathematics instruction more meaningful for our students.  Thank
> you very much for your time and feel free to contact me at the address
> below.
>
>  
>
> Sincerely,
>
> Tony Pickar\
> Math Curriculum Coordinator\
> D. C. Everest School District

[]{#ArthurHu .anchor}\-\-\-\--Original Message\-\-\-\--

From: Arthur Hu

Sent: Thursday, August 03, 2006 10:51 PM

To: National Math Panel

Subject: Parent for real math

I am a parent from Kirkland/Bothell WA, and I am appalled at the NSF
funded textbooks my teachers were forced to use by the district. The
homework took much more time, and taught much less. They took an entire
booklet to cover median and average, yet did not teach the simple
formula average = sum of items divided by number of items. The whole
movement seems devoted to making students work harder to learn less. If
the US is to maintain technical leadership, it cannot abandon the
teaching of mathematics as it has been taught for generations since the
invention algebra. The new methods refute, rather than teach classic
time tested methods of computation and mathematics.

 

Arthur Hu

Parent of 3 boys grades 5 through 9

[]{#DaveMarain4 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Dave Marain

Sent: Thursday, August 03, 2006 3:39 PM

To: National Math Panel

Subject: Re: Questions to the Panel

HI Ida!\
Thank you for your quick response. I'm still in shock that you're taking
the time to reply! You're my only reason to still have some faith in
this panel.\
\
I did read the executive order and there were enough references to
secondary math (up to calculus) that I still see a real need for a
current secondary teacher on the panel.\
\
There is also a section devoted to culling opinions from others not on
the panel, including parents, other experts, etc. I will certainly try
to voice my opinion in person and attend the next meeting but that
remains unlikely.\
\
You need to understand the source of my frustration and cynicism
regarding bureaucratic processes. It's been almost 20 years since NCTM
came out with their first set of Curriculum recommendations. Math ed
professors have written new books, districts have made several new
textbook adoptions and students' arithmetic and algebra skills continue
to steadily erode. There's more than anecdotal evidence here. The
educators I work with every day, savvy students and parents echo these
sentiments ad nauseam. Still, new curriculum committees, researchers and
textbook companies continue to ignore the obvious that Liping Ma has
been calling for -- a 'profound understanding of fundamental
mathematics' is essential. Perhaps her presence will turn things around,
but who knows. And there's more\... Higher-order problem-solving in
which students from other nations successfully engage require one to
apply their knowledge, just like on our SATs and math contests. The
problem is that our students DO NOT HAVE THE KNOWLEDGE TO APPLY! We have
a generation of clever problem-solvers who are tech-savvy, who know how
to work-around many issues, but YOU CANNOT WORK-AROUND THE ESSENTIAL
SKILLS OF ARITHMETIC AND ALGEBRA. You can't fake the Laws of Exponents!
You can't consistently achieve accurate solutions to problems by
pressing the 'Solve' key on a graphing calculator. Parents know this,
educators know this yet educational 'experts' IGNORE THIS!\
\
Yes, there are some members of the panel who seem to share some of my
concerns. However, it takes bold courageous individuals to make a sea
change happen and that is what I believe is needed here. From my
contacts with many other educators and parents, my views are not so
extreme and are not isolated.\
\
Understand that I will continue to endeavor to be heard by this
committee. However, I really don't believe my lone voice will amount to
much. I do believe a blog that gets the attention of education
journalists can reach thousands. I know you will wish me all the best
with this! I know Tyrrell will send me another boilerplate response. I
know that real change will only occur if one can be heard. Thank you for
caring\...\
\
\
Sincerely,\
Dave Marain\
Supervisor of Mathematics & Business

[]{#DaveMarain3 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Dave Marain

Sent: Wednesday, August 02, 2006 6:05 AM

To: National Math Panel

Subject: Re: Questions to the Panel

Dear Ida,\
I continue to be optimistic that the Panel will come to appreciate the
need for more input from educators and the populace at large before
attempting to reach consensus. The College Board recently made a
decision to revise their timeline for their new AP Audit process. This
resulted from seeking direct input (via email) from professional
educators who provided cogent arguments for delaying the original
deadline for submission. My point is that they elicited and listened to
a broad spectrum of views. This sends the message that they truly care
about producing the best possible product. Although you make strong
arguments for not setting up an electronic forum, they do not dispel for
me the unfortunate message that this Panel does not truly care about the
broad opinions of a large cross-section of math educators.\
\
Yes, that is my opinion Ida. However, I am deeply concerned about the
makeup of the Panel and what I've read so far coming from the Panel.
First there is no direct representation from current secondary
mathematics. How is it possible that an elementary and secondary
educator were not selected for the group? That is unconscionable.
Further, the Panel seems to be more concerned with research requirements
for a doctoral dissertation than substance. That's not what our children
need. There are significant problems in math education in this country.
This Panel should first define these problems and then make specific
recommendations for their solution based on Best Practices and informed
by current research. That's not what I see happening but of course I
only have a very limited view of the proceedings.\
\
I am writing this to you personally because you are the only one
associated with the Panel who has taken the time to respond personally
and not with an insensitive form letter as I received from another
individual. I believe you value my comments. I am hoping that my
statement to the Panel regarding the need for National Standards and the
AP model was truly acknowledged and will be given serious
consideration.\
\
Sincerely,\
Dave Marain

[]{#LorelleYoung .anchor}\-\-\-\--Original Message\-\-\-\--

From: Lorelle Young

Sent: Wednesday, July 19, 2006 1:54 PM

To: National Math Panel

Subject: Teach only the metric system

Ladies and Gentlemen.

 

Thank you for inviting letters from interested parties.  My letter is
attached.

 

Sincerely,

 

Lorelle Young, President

U.S. Metric Association, Inc.

![](media/image28.wmf)

[]{#JohnShacter .anchor}\-\-\-\--Original Message\-\-\-\--

From: John Shacter

Sent: Thursday, July 13, 2006 11:12 PM

To: National Math Panel

Subject: Teaching Math with the "KISS" Approach

Please pass this on to the Math Advisory Panel. I\'ll be glad to
elaborate, including visits, if requested.\
\
By the way, the acronym KISS refers to: \"Keep It Simple, Stupid.\"\
\
I am a semi-retired engineer, management-and-technology consultant, and
educator. You can find more background information in the Who\'s Who
volumes on Science and Engineering, and on Finance and Business. I have
thus been a user of math, for many decades, rather than a mathematician.
I am a bit concerned, that the Math Advisory Panel will come up with a
more complex approach than needed.\
\
For example, the panel which doesn\'t seem to include a single engineer,
technologist, or business \"types,\" could actually place barriers
against the KISS approach and **make students hate math even more than
they already do today**, if it were to set overly ambitious objectives
of trying to teach the complexities or rote-vocabulary of math in an
attempt to convert the maximum number of public-school students into
future mathematicians.\
\
I am also a frequently invited local and regional substitute teacher and
prefer the teaching of math in any public-school grade, but especially
grades 3-12. As a user of math, I firmly believe in the \"KISS\"
approach of teaching any subject, especially math. The students seem to
like my style and ask for me to be re-invited. Some of the teachers have
asked me to teach or tutor their own children.\
\
(By the way, this is not very relevant, but I received my early
education in Vienna, Austria. There are some differences in the way math
is being taught in different countries or regions, and our own students
seem to fall behind, the more years they spend in our classrooms.
However, our parents and students seem to score highest in
\"self-esteem.\")\
\
Generally, students (and some teachers) claim that they \"hate\" math.
However, all of them just \"love\" money, and I am shameless enough to
take full advantage of that combination. So when I see the students\'
eyes fog over, I just switch for awhile and teach them about \"budget\"
or \"profit\" concepts, differences between savings and investments, or
why \"money management\" doesn\'t just consist of knowing how to sign a
credit card!\
\
Students need to understand how to reason qualitatively and
quantitatively (with math), and how to express any aspect of this
reasoning clearly and effectively, orally and in writing.\
\
Moreover, for illustrative purposes \-- most students in third grade
need to know instantly what 7 times 8 is. Memorizing the
multiplication-division table for math is just as important and basic to
more advanced math-learning, as memorizing the alphabet is for learning
English vocabulary. Thus, they need to know, eyeball-to-eyeball, (no
pen, paper or calculator) what 56 divided by 7 or 8 is, and what
5**[7]{.underline}** divided by 7 or 8 is, with and without the use of
\"remainders\".\
\
In third or (latest) fourth grade, they also need to know how to handle
decimals, fractions and percents, and how to proceed to translate
quickly and smoothly from one system to either one of the other two.
They also need to know, again eyeball-to-eyeball, what 3 divided by 1/3
is (and the answer is [NOT]{.underline} 1!), or how to multiply or
divide integers and decimals by 10, 100, 1000, etc.\
\
(Unfortunately, the way some of our colleges educate our teachers, some
of them may not be able to supply all of the above simple, elementary
arithmetical answers. Moreover, many of today\'s enormous-size text
books may tend to cause more delayed hernias rather than simple
understandings.)\
\
Finally, still illustrative of my teaching in the third or fourth grade,
I introduce my students teasingly to simple algebra, and when I tell
them that they had just been introduced, I finally use the word
\"algebra\" which adults seem to be so proud of. I start with the use of
a question mark \-- like: 2 + ? = 5. What is the question mark? (Most of
them know immediately.)\
\
Then I claim that I hate question marks \-- will they allow me to ask
instead: 2 + A = 5. Now what is \"A\"? (Most of them think that is a
silly question, since the answer is still the same.) And then I may ask
them about 2 + A + B = 5, etc. etc. They seem to delight in all of this
teasing and go home bragging to their parents that this crazy substitute
teacher taught them \"algebra\" which they weren\'t supposed to be ready
for any of that until middle school.\
\
I am going to send you a simple, short memo telling the reader all
he/she needs to know to operate with \"fractions\". The way we teach
them, many students seem to think that \"fractions\" are rather
difficult or complex.\
\
You have many other advisors. So I may offer a bit of pleasant
competition. Let\'s select, say, 45 fourth or fifth graders. Give your
favorite expert 15 students by random selection, and give me 30. Then
let\'s see who can add greater gains to his group in a defined area of
math \-- say solving problems with integers, decimals, fractions and
percents, and being able to translate any one of them to the others. We
can  then analyze the effectiveness of competing approaches in conveying
math and hopefully making students like it, as well.\
=============\
\
**Would any of this type of practical experience be of any value to the
math advisory panel? If so, I shall be glad to elaborate or assist the
panel, including visits, as well as I can. I have many other ideas on
how to make major, not marginal improvements in curricula and teaching.
However, I also believe that many of our gaps in quantitative reasoning
and other subjects can be traced to an inadequate understanding of basic
math.\
**\
Cordially, John\
John Shacter

[]{#DonJordon .anchor}\-\-\-\--Original Message\-\-\-\--

From: Don Jordan

Sent: Monday, July 10, 2006 5:16 PM

To: National Math Panel

Subject: Teaching Metric in the US

To Members of the National Metric Panel.

From: Dr. Don M. Jordan, professor Univ of South Carolina

Six months to two years of elementary arithmetic could be eliminated
with the adoption of SI-Metric.

I have attached documents in support of my belief that the US
Educational Systems suffers because of the lack of a strong plan to
teach metric to students K -12. The Child receives the old US English
System at home. The Student must receive metric education in grades k-12
at the schools with very little time spent on the old US English system.

\*\*\*\*

Did you know that..?

? Metric minimizes the likelihood of error.

? Metric does not have the numerous conversion factors of other systems.

? Metric has one unit for a quantity.

? Metric is legal, logical and preferred.

? Six months to two years of elementary arithmetic could be eliminated
with the adoption of SI-Metric.

? IBM during metric conversion reduced fastener part numbers from 38,000
to 4,000.

? One bottling industry reduced its container sizes from 53 to 7.

? You would weigh 82 kilograms instead of 180 pounds.

? Public Law 103-227 of March 31, 1994, asserts that mathematics and
science education, including the metric system of measurement, will be
strengthened throughout the system, especially in the early grades.

? All major science and education organizations have encouraged the
United States to fully adopt the metric system as the language of
measurement.

? The National Association of Academies of Science and the United States
Metric Association are writing the National Metric Education Guidelines.

METRIC FACTS

English is the international language of business.

Metric is the international language of measurement.

? The Metric System - How to teach young people what they need to know!

1\. Teach using only the Metric System.

2\. Use rulers and measuring tools that have only metric scale units.

3\. Teach measurement and physical quantities using materials and
examples that students can see and touch.

4\. Select, estimate, compare and use appropriate units to measure:

length (meter/centimeter); mass (kilogram/gram); volume;
(liter/milliliter); temperature (degree Celsius)

5\. Teach by actively involving the students in measuring activities.

6\. Universities and Colleges that educate elementary school teachers
should teach the system and how to use it.

7\. The change to the metric system is for all people and all
disciplines (not just science, engineering and math).

What US Needs:

A Certified Metric Specialist in each of the 1,646 Schools in the United
States.

See www.cosm.sc.edu/jordan under Metric for more information

If you want to know how to become a Certified Metric Specialist, write
or email

Dr. Don M. Jordan / Center for Science Education / College of Arts &
Science / Sumwalt Rm. 323 / USC Columbia, SC / 29208 jordan@gwm.sc.edu /
803.777.7007

Metric Week in South Carolina is sponsored by the

South Carolina Academy of Science, Founded in 1924 &

The Center for Science Education at USC

\*\*\*\*\*

See attached for more information:

We need to establish the National Metric Teaching Guidelines and have
every teacher in K-8 trained in metric measurement. Until this is done,
the US will continue to have teachers in the class room that do not feel
comfortable or knowledge about the metic system. The teacher needs to
become a believer!

thanks for taking the time to read my comments.

don jordan

Dr. Don M. Jordan

College of Arts & Sciences

Center for Science Education

![](media/image29.wmf)![](media/image30.wmf)![](media/image31.wmf)

[]{#RandallGroth .anchor}\-\-\-\--Original Message\-\-\-\--

From: Randall Groth

Sent: Friday, July 07, 2006 9:58 PM

To: National Math Panel

Subject: Evidence Standards

Dear Panel Members,

I recently read the evidence standards Dr. Benbow suggested for

determining the types of studies that will be considered in the panel\'s

final report (posted at http://mathpanelwatch.blogspot.com/). At one

point, Dr. Benbow commented, \"We will not limit ourselves to data from

just one type of methodological design.\" However, the evidence
standards

she proposed are applicable only to quantitative studies.

If the intent truly is NOT to limit the final report \"to data from just

one type of methodological design,\" I urge the panel to consider the

following references if they have not done so already:

\(1\) Lester, F.K. (1996). Criteria to evaluate research. Journal for

Research in Mathematics Education, 27, 130-132.

In this article, Lester describes a set of criteria for evaluating

research that cuts across various paradigms and methodological designs.

\(2\) Simon, M.A. (2004). Raising issues of quality in mathematics

education research. Journal for Research in Mathematics Education, 35,

157-163.

Simon begins by recognizing the fact that a number of new and adapted

methodologies have recently been used in the field of mathematics

education research. He argues that this should be considered a sign of

the field\'s vitality. He then reflects on issues of quality in

qualitative research.

\(3\) Lesh, R., & Clarke, D. (2000). Formulating operational definitions

of desired outcomes of instruction in mathematics and science education.

In A.E. Kelly & R.A. Lesh (Eds.), Handbook of research design in

mathematics and science education (pp. 113-149). Mahwah, NJ: Erlbaum.

Lesh and Clarke offer a critique of elements of the traditional

quantitative paradigm for research. They go on to provide a convincing

argument that traditional quantitative studies are not the only kind of

\"scientific\" study. They offer multi-tiered teaching experiment

methodology as an example of a scientific research paradigm.

Thank you for reading this input. Good luck in your deliberations.

Randall E. Groth, Ph.D.

Assistant Professor of Mathematics Education

Salisbury University

[]{#TonyHusemann .anchor}\-\-\-\--Original Message\-\-\-\--

From: Tony Husemann

Sent: Thursday, July 06, 2006 9:12 AM

To: National Math Panel

Subject: Re: National Math Panel's Focus

Dear Math Panel Members,

Having just completed the teaching of a \"Special\" Math Methods course

at Florida Atlantic University, I asked my students a question which

appears in an article in EdWeek concerning your panel\'s work. To wit,

beginning perhaps in 1927 when NCTM published a report on how to solve

problems with math education, America has had one such report or study

after another done. In almost 80 years since that early NCTM study,

researchers continue to say \"there isn\'t much research\" on how to
solve

America\'s math education problems. How is it, with over 75 years of

research into the matter, there still \"isn\'t much research\" on how to

teach math to minorities?

Perhaps, there is an approach problem. Students in my course noted the

absence of any but one actual classroom math teacher on your panel. I

noted for them that a previous, highly acclaimed panel, the Glenn

Commission, had also had only one math teacher on it. Perhaps, research

could be conducted by sampling mathematics teachers in America\'s public

and private schools and asking them \"how do you teach math with

success?\" Comparisons between schools and teachers and their techniques

might reveal weaknesses or comparative strengths in teaching techniques

between schools with different racial and SES make-ups that could

potentially point to better methods in the weaker schools. Sample the

teachers! Instead of asking other \"expert\" who have either never been
in

a public school classroom, or were 20 years ago and have not been back

since!

Secondly, the class noted with me a disparity in how tests are

designed. For example, it is a well known educational paradigm to test

not only what you taught, but the way it was taught. Many of the lower

performing math students benefit greatly from the use of manipulatives

in their math learning. But, nothing like manipulatives is ever

incorporated into the State or National exams they must take to

demonstrate math ability. Perhaps the \"standardized\" tests could be

re-standardized to test the way math is actually taught to those pupils

who have \"traditionally\" done poorly on the present set of exams.

Lastly, there is the issue of culture. My special methods math classes

were made up of teachers who came from low income schools on a grant to

improve their teaching. They all testify to the truth of the most recent

PDK-Gallup Pol on American\'s Opinions of our schools. That is, the

troubles with schools actually originate outside of the schools

themselves. There are powerful anti-educational forces at work in the

communities around schools, but parents still expect the schools to fix

those problems. Perhaps, as Coleman noted in 1966, and Vera and Hayes

documented further in 1978, minorities perceive that social barriers,

not educational ones, prevent their success in our society. That topic

has also had lots of study, but little done to change the outcomes for

lower SES families.

In fact, an examination of the latest NAEP reports shows a clear,

almost startling trend in math scores. Overall, a bit more than 505 of

the Nation\'s students are at the \"basic to proficient\" quartile. But,

switch the view to see how males do vs females, and a disparity appears.

Continue across the top to compare blacks, Hispanics, and then \"free

lunch\" to no-free-lunch students and an amazing picture immediately

emerges. If you are poor, or black, or Hispanic, our math educational

program fails you. Surprised? You, no doubt will say \"Of course not,

that\'s why the Panel was convened.\" Really? After almost 80 years of

reports with titles like \"A nation at risk\" or \"The gathering storm\"
or

\"Before it\'s too late\" the distinguished Presidential Panel to
improve

mathematics instruction isn\'t even surprised we STILL can\'t get it

right? Maybe, that\'s our real problem. We actually do not expect to

accomplish anything, and so, once more, we won\'t!

I would love to be involved in some real research into how to improve

math education fro minorities in this country, before it really is \"too

late.\" My contact information is below, and besides, perhaps you would

consider this-try surveying the 2.3 million member NEA teachers for a

change. \"What\'s wrong with our public school system of education?\"
might

be a good start-up question to ask them.

Anthony J (Tony) Husemann

CCA Science Team Leader

[]{#FrankLester .anchor}\-\-\-\--Original Message\-\-\-\--

From: Frank Lester

Sent: Tuesday, July 04, 2006 12:28 PM

To: National Math Panel

Subject: Letters to Drs. Faulkner and Benbow

Dear Drs. Faulkner and Benbow,

I am contacting the two of you in your roles as chair and vice-chair of
the National Mathematics Advisory Panel to inform you of a resource that
may be of value to the Panel in it deliberations.? Specifically, I am
editing a revision of the *Handbook of Research on Mathematics Teaching
and Learning* that was originally published in 1992 by Macmillan.? The
1992 handbook has been the most widely cited reference on research in
mathematics education in the world and the second edition is likely to
be just as valuable to the research community.

The new edition, titled *Second Handbook of Research on Mathematics
Teaching and Learning*, will be published in the Spring of 2007 by
Information Age Publishing Co. and distributed by the National Council
of Teachers of Mathematics.? Members of the advisory board for the new
handbook include:

Douglas Grouws, University of Missouri

James Hiebert, University of Delaware

Carolyn Kieran, University of Quebec at Montreal

Judith Sowder, San Diego State University

Lee Stiff, North Carolina State University

In order to give you a sense of the scope of the handbook, I am
attaching a copy of the table of contents (note: the final two chapters
are under development and do not yet have titles), which includes a list
of authors and their affiliations.? Should you wish to gain access to
any of the chapters, please contact me and I will endeavor to have PDF
versions sent to you. (I should add that the volume is large, more than
4 500 manuscript pages, with the average length of a chapter being about
150 pages.)

I look forward to your reply.

Sincerely yours,

Frank Lester

![](media/image32.wmf)

[]{#MarkHenschel .anchor}\-\-\-\--Original Message\-\-\-\--

From: Mark Henschel

Sent: Monday, July 03, 2006 1:47 PM

To: National Math Panel

Subject: The need to teach SI in the early grades

Dear Sir/Madam:

On the issue of teaching math in American schools, I just want to

reinforce what numerous other people have probably already mentioned to

you, and that is the need to teach SI metric units in all math classes

at all grade levels.

The thing I have noticed about science education is that often the only

time students are exposed to the use of SI units is in high school

science classes. Math teachers tend to concentrate on teaching

inch-pound units, so students do not become proficient in the use of

both systems.

The Metric System can be looked upon as a foreign language. Students

must be exposed early and often to a foreign language to become

proficient. Thus, teachers in elementary school classrooms, fourth,

fifth, and sixth grades especially, should concentrate on teaching

students to understand and use SI units.

Then, when students do take science classes in high school, students

will be able to concentrate on the science, and not on learning the

Metric System.

I would hope that all elementary school teachers learn to use and teach

SI units. Certainly, they should not be afraid to teach the metric

system. If they are comfortable with the use of SI, this attitude will

carry over to students, and the students will also be able to use the

Metric System as they work their way through high school, college, and

into adult life.

Mark Henschel

[]{#MichelleBergey .anchor}\-\-\-\--Original Message\-\-\-\--

From: Michelle Bergey

Sent: Monday, July 03, 2006 1:36 PM

To: National Math Panel

Subject: best practices for math instruction

Sirs and Madams:

I am an elementary teacher in a Title I school in

California. I have struggled for years trying to

research the best practices for teaching math. I am a

big fan of Liping Ma, and have tried many ways to

approach math differently than the way I was taught.

It takes years of work and practice on the part of the

teacher, However, there is one strategy that I have

employed that is research-based, easy to implement,

and immediately effective in raising student

achievement: Distributed Practice.

One of the problems with math instruction that

interferes with student mastery is rooted firmly in

the very way the math textbooks are set up to begin

with. Textbook publishers have set up their books in a

very compartmentalized, linear fashion - with very

little opportunity for distributed practice at all. In

the textbook that I am currently using, which is very

similar to all of the other \"approved\" texts available

\- the chapters (and lessons) all cover separate

distinct skills, test the skills after 5 or so short

lessons, and then move on to another skill.

Any student in the US knows how this works - you are

taught something in October, forget about it over the

winter break, cram for finals (or state tests), and

then promptly forget it. But research shows that

mastery of any skill takes 20+ separate practice

sessions (see Marzano et al). Imagine yourself, as an

intelligent, educated, motivated person - being

introduced to sin, cosin, and tangent in one day,

reviewing it the next day, being tested on it on

Friday, and then really never doing much with it until

the \'Unit Review\'. This is the equivalent to what is

happening in many of our math classrooms each week.

There is never the opportunity for true mastery of

mathematical skills. Teachers can provide this

opportunity by dividing up homework assignments over

time, or by creating weekly homework problems that

reach back and review previously taught concepts.

However, textbook publishers, at the very least, could

provide a \'Distributed Practice\' workbook for students

that continually loops back to practice skills that

were taught yesterday, last week, last month, even

last year.

All students can benefit from this strategy, not

just minority and socioeconomically disadvantaged

students. The wonderful thing about using distributed

practice sessions as a strategy to boost achievement

is that not only does it work extremely well - it

doesn\'t cost anything! It just means that you make

sure students get repeated opportunities to master

skills - not just introduce, test, and move on. There

is an outstanding example of a study done with Air

Force Academy calculus students where the only

difference in instruction was how the homework

problems were assigned. Control classes did homework

problems in mass. The treatment group did the

assignments in a distributed fashion. It is a very

interesting study and can be found at

http://www.coedu.usf.edu/fjer/1997/1997_Revak.htm

I am sure that your panel is looking at many ways to

improve mathematics instruction across the nation.

There are certainly many things that can be done, but

if teachers in the US were told that starting tomorrow

they could try to implement a \'distributed practice\'

strategy in their classroom - you would see an

immediate result - not something that would take ten

years to show any movement in student achievement.

Good luck on your mission! It is a worthy one!

Michelle Bergey

teacher

Twentynine Palms Elementary

California

[]{#PaulTrusten .anchor}\-\-\-\--Original Message\-\-\-\--

From: Paul Trusten, R.Ph.

Sent: Wednesday, June 28, 2006 11:36 AM

To: National Math Panel

Subject: metric system should be sole measurement system taught in U.S.

To the members of the National Math Panel,

 

With U.S. students now demonstrating declines in their scientific
abilities,  and our nation itself facing formidable intellectual
competition from the rest of the world, it is time for our country to
take a necessary step forward, and adopt the International System of
Units (SI), the modern metric system, as our primary system of
measurement. To do that, we must teach the SI as the *sole* system of
measurement in our schools.

 

To many Americans, such a call for change seems to reek of political
correctness, or to represent yet another act of bureaucratic meddling in
their lives . These are misconceptions. On the contrary, metrication  is
a long-overdue, practical change for the nation.  Nor is it intended to
be a short-term, patchwork action for change. It is a change for all
Americans, and in all future times.  In granting powers to Congress, The
U.S. Constitution ranks measurement as important as money;  the powers
to set both are enumerated in the same article.

 

For many years in U.S. popular culture, measurement has been perceived
as a nationalistic, and even a poetic, activity.  And, it used to
be convenient for Americans to teach a traditional system of measurement
units when our country was isolated and primarily agrarian.  *But, it is
now time for U.S. educators to demonstrate  to their students that
 measurement is a part of science*.  The measurement language of science
is the SI, which is the legally preferred system of measurement for
trade and commerce in the U.S.  (*Metric Conversion Act of 1975*, Pub.
L. 94-168, enacted December 23, 1975, as amended by the *Omnibus Trade
and Competitiveness Act of 1988* \[Pub. L. 100-418, August 23, 1988\]).

 

We no longer have the agrarian luxury of using pounds and miles
officially.  We can no longer hide behind the delaying effects of
telegraph, telephone, and teletype. This is the global, digital age.
 The age of the kilogram and the kilometer are upon us.

 

Our old units of measurement will remain secure in song, story, and
tradition.  But, In trade, commerce,  and academia, measurement can no
longer be perceived a jingoistic tool or a vent for poetic license.  It
is what you as a panel are using this week to assess U.S. mathematics
education, what U.S. industry uses to understand its problems and
processes, what American highway designers and architects use to solve
crucial problems of structural integrity and safety, what our science
workers use to conduct science, and what the U.S. consumer uses to
easily reckon a fair deal.  In all of these activities, Americans need
to have the same measurement advantage that the citizens of most other
countries have had for centuries: a true standard of measurement based
on decimal numeration.

 

Not only will metric-only education equip U.S. students for global
competition, it will also relieve them of the useless burden of learning
an obsolete measurement system and  performing the exercises in
fractions that accompany it. So, in that sense, a change to teaching the
SI as the sole measurement system will represent a synergistic advance
in U.S. mathematics instruction. It will free up the process as well as
the knowledge.

 

Take a look at the bottled water being served at your panel discussion
this week. It is likely that the water is bottled in half-liters. The
overwrap on many bottled water products sold in the U.S. now features
the prominent statement (the part that \"screams\" at you)  that the
bottles are in half-liter sizes, even though federal law requires U.S.
customary volume also to be stated on the labeling.  U.S. students are
participants in this increasingly metric society, and they must be able
to master it comfortably.  In your deliberations this week, please work
to establish the teaching of the SI as the sole system of measurement in
U.S. schools. We need to get ready now!

 

\"SI\"ncerely,

 

 

Paul Trusten, R.Ph.

Public Relations Director

U.S. Metric Association, Inc.

[]{#MarshaCantrell .anchor}\-\-\-\--Original Message\-\-\-\--

From: Marsha H. Cantrell

Sent: Monday, June 19, 2006 1:14 PM

To: National Math Panel

Subject: comments for June 29th

I will not be able to attend the National Math Panel meeting on June

29th but would like to submit my comments.

I have e-mailed several panel members about my concerns but also, I

stay in touch frequently with many other key math professors

interested in change.

1\. To those members of the panel which represent the colleges of

education and psychology: Math should be taught by those individuals

with a degree in math or science.

Degrees in elementary education and secondary education are very

poor substitutes, and furthermore, in most cases, they are terribly

inadequate.

2\. Middle School education degrees should be banned or dissolved

immediately.

3\. Teachers of math and/or science must take core courses within the

math or science departments. Courses \"designed\" for math teachers

are in inadequate.

4\. Math and science departments within the state universities must

take the lead on teaching math teachers. A guideline for teaching a

certain grade level should be as follows: An elementary math teacher

should be able to teach Algebra I. An Algebra I should be competent

in Geometry and Alg. II. A high school teacher should understand

college algebra, discreet mathematics, stats. and use calculus, and

have had a course in logic. I would even suggest that elementary and

middle school teachers have upper level calculus and geometry

courses.

5\. In elementary schools, develop math specialists. A math teacher

should teach math in grades 3-6.

6\. Calculators must not be used in grades 1-9.

7\. Textbooks should have content, not pretty pictures. Challenging

problems (which have been removed) should be part of the daily

routine.

8\. Teach the math algorithms and refer to them daily. Speak in math

terms: \"dividing is also multiplying by the reciprocal,\" not
\"flipping the

fraction. What is an inverse? What is a reciprocal?, etc.

9\. Lastly, get the NCTM on board. They are hopelessly stuck in the

70\'s. Phrases such as \"math can be fun,\" and \"discovering math,\"

and cute educational catch phrases will not replace good teaching nor

solve this most urgent problem.

10\. Public school students coming into our program are generally 2

years behind. Algebra I students can not solve or factor, and

precalculus students spend time coloring conics shapes instead of

\"completing the square\" and sketching the foci, vertices, and center.

A foundational course (trigonometry), for the most part, is ignored,

leaving polar forms and rotational conics almost impossible to teach.

Sincerely,

Marsha H. Cantrell

Math Department Chair

Westminster Schools of Augusta, GA

[]{#DaveMarain2 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Dave Marain

Sent: Thursday, June 15, 2006 5:51 PM

To: National Math Panel

Subject: Re: Questions to the Panel

Dear Ida,

Thanks for the quick reply.

I'm a bit confused. Setting up a message board or forum generally
involves minimum expense and time. It would enable panel members, and
anyone who is invited to join, the opportunity to view ALL messages
posted and reply to all. It's more global than email. My recommendation
for a live chat is based on its effective use by Education Week on a
regular basis. Usually 2-3 experts are available for a period of time to
reply to emails sent in real time by people all over the country. The
panelists reply to selected emails. Fascinating stuff\...\
\
Again, I do not expect to receive any special consideration here. I only
expect that my requests be given equal consideration to others. Perhaps
I have a bit more passion and resolve than some and, I guess you can
tell that I don't easily give up! Of course, you could stop my emails
instantly by recommending to Secretary Spellings that she appoint a new
panel member (only half-kidding).

Sincerely,\
Dave Marain

[]{#ForrestHobbs .anchor}\-\-\-\--Original Message\-\-\-\--

From: Forrest Hobbs

Sent: Thursday, June 15, 2006 3:58 PM

To: National Math Panel

Subject: Math curriculum review

I would like to send information about the Math-U-See curriculum for

the panels review. Our website is www.mathusee.com. We have been

involved in the home school/private tutorial world and have grown into

the recommended curriculum for most all learning challenged students.

We are designed very differently than a standard school book with

multiple strands of mathematics concurrently. We use manipulative

based methods up through Algebra 1 as well. I am hoping to introduce

the panel to what we have to offer children from Kindergarten through

pre-Calculus/Trigonometry. Thanks for your attention.

Sincerely, Forrest Hobbs; Regional Representative of Math-U-See, Inc.

[]{#DaveMarain1 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Dave Marain

Sent: Wednesday, June 14, 2006 9:43

To: National Math Panel

Subject: Questions to the Panel

Dear Tyrrell,

The following is a brief statement and below it a question I am posing
to the National Mathematics Panel for the public sessions in Chapel
Hill, NC, on June 28th and 29th. I sincerely hope this will be conveyed
to every member of the panel and replied to.\
\
After teaching AP  and University calculus for the past 33 years, I have
worked with and met hundreds of AP teachers. Rarely have I ever heard
from anyone that the AP syllabus was restrictive. Never do I hear that
it's unfair that all students need to be exposed to a common body of
clearly delineated concepts, procedures, algorithms and problem-solving
experiences outlined in the Acorn book we all receive from the College
Board. I'm not told in what sequence I should teach the topics. The
syllabus does not prescribe a particular pedagogical or assessment
style. In fact, there is considerable freedom in these areas and many
effective models are presented as examples. But by the time I finish the
course I know that the calculus my students have been exposed to is
comparable to the calculus taught in every AP classroom in every
district in every state. There are many variables of course that
determine how well they have learned but not WHAT they have learned if I
covered at least what was recommended. This is true equity that empowers
all of our students regardless of their socioeconomic background.\
\
In this educator's opinion, it is essential that we require all students
to develop reasonable proficiency with the major ideas of algebra,
geometry, etc. For too long it has been argued that there is no general
agreement of what these ideas are among mathematicians and math
education specialists. This view is clearly not shared by nations that
outperform us in mathematics. Showing recent progress on NAEP is of
little comfort to me. Showing significant progress in the next
international study like TIMSS would tell a far different story however.
Professor Schmidt called for a more coherent curriculum. He and I have
communicated recently and we both strongly share the view that this
nation needs to develop a more standardized mathematics curriculum that
transcends state borders and avoids unnecessary efforts and
duplication.\
\
Therefore, I would like to hear the responses of at least 5 panel
members to the following question:\
\
What consideration would you personally give to developing syllabi for
courses below calculus that are patterned after the Advanced Placement
Calculus model? That is, developing a suggested syllabus of topics,
themes, concepts, algorithms for precalculus through prealgebra and
beyond?\
\
Dear Panel Members, a radical approach to changing math education was
adopted rapidly nearly 50 years when Sputnik was launched. Who on this
panel is willing to boldly suggest the radical changes needed to restore
our preeminence in mathematics in this century? Actually, I don't really
care about being the best. I'd settle for competitiveness!\
\
Sincerely,\
Dave Marain\
Supervisor of Mathematics & Business

[]{#DougJohnson .anchor}\-\-\-\--Original Message\-\-\-\--

From: Doug Johnson

Sent: Monday, June 12, 2006 5:14 PM

To: National Math Panel

Subject: math ed

National Mathematics Panel Members:

 

I am pleased to see the government form the National Math Panel to
support and improve the delivery of math instruction in our nation.  I
have taught math, science, and English for twenty-six years in the state
of Washington.  My assignments have included levels from second grade to
college.  Most of my work has been at the high school level.  I have
been the chairman of the math department at Ellensburg High School with
an assignment of algebra through AP Calculus for eight years now.

 

I was a little disappointed to see the K-12 teachers underrepresented on
the panel.  There are thousands of us out here getting it done day by
day, many with outstanding programs, working hard, challenging kids, and
changing their lives and futures.  Hopefully, a balance more toward the
teachers "in the trenches" will be promoted.

 

My main concern, however, has more to do with curriculum than with panel
personnel.  For approximately two decades, the National Council of
Teachers of Mathematics has "led the charge" on the math reform effort. 
Their efforts have led to some positive change in the math education
world, specifically emphasis on problem solving and concept
development.  These gains, however, have come in my opinion at a
debilitating cost to students.  Excessive attention to these skills has
resulted in math programs (often labeled as "integrated") that present
material in a seemingly random order that does not make sequential sense
to the students.  Students are not immersed in any particular topic
sufficiently, and mastery is not achieved.  But that's not the main
shortcoming of most of these programs.  This major shortcoming is the
lack of drill and practice.  Most students need to work repeatedly on
problems on one concept before they "get it."  Without mastery on each
topic, math becomes a confusing hodge-podge of material, and the kids
drop out of mathematics, psychologically or literally.  In Ellensburg,
we get students from other schools with integrated programs.  They need
considerable remediation, lots of drill and practice, and extra
attention to get up to speed. When I teach at the local university, it
is common to get students from integrated programs with major skills
shortcomings.  It is now a conversation among some college math and
science departments about the lack of basic high school math skills in
freshmen.

 

 

Here in Washington, we are subject to the Washington Assessment of
Student Learning, or "WASL" test.  It is given in the sophomore year,
and passage is a graduation requirement.  The math test is based mostly
on NCTM type standards, and has little emphasis on algebraic skills. 
Here in Ellensburg, we view this as a mistake.  We refuse to adopt
integrated texts. Instead, we use a more traditional text and supplement
it with WASL-type work twice a week throughout the year.  A few weeks
before the test, we place special emphasis on WASL work, to the
exclusion of all else.  The system is working, and this spring we scored
approximately twenty percent above the state average on the test.  We
think this supports our contention that traditional programs, taught
well, lead to success.  And we don't have to compromise the futures of
those Ellensburg kids who want to go to study math, science, engineering
and other math-related fields. These students need basic algebraic and
other math skills. We believe integrated math programs often cripple
potential mathematicians and scientists.  In our experience,
well-structured traditional programs, supplemented by "reform math"
practice, lead to success on both.

 

Thank you,

Doug Johnson

[]{#KirkAvent .anchor}\-\-\-\--Original Message\-\-\-\--

From: Kirk Avent

Sent: Sunday, June 11, 2006 6:54 PM

To: National Math Panel

Subject: High school math

Dear Committee:

 

My son recently graduated from Phillips Exeter Academy. His math courses
were extraordinary. No textbooks, just problems. Principles of
mathematics emerged as students worked problems, rather than the usual
teacher-based approach where the principles are presented by the teacher
then reinforced by problems worked by the student.

 

"Oh, sure", you say. "Fine for an elite school like Exeter but
impossible in an inner city school".  Wrong! The math department has a
program for urban schools called the Exeter Mathematics Institute.
Please check it out at:
<http://math.exeter.edu/dept/development/EMI.html>.

 

 

I suggest you contact the math department chairman at Phillips Exeter
Academy: Joyce Kemp, <jkemp@exeter.edu>.

 

Kirk Avent

[]{#DianeHirakawa .anchor}

\-\-\-\--Original Message\-\-\-\--

From: Diane Hirakawa

Sent: Friday, June 09, 2006 7:22 PM

To: National Math Panel

Subject: Suggestions for Elem. Math

Good Morning,

My passion is math in the elementary schools.

 

I recently retired with 23 years of teaching experience in southern
California.  Presently, I work with children and their parents in my
home on a smaller scale.  For these weekly tutoring session, I use many
of the same ideas which provided highly successful math students in my
grades 1-6 classrooms.

 

In  June, 2006, issue of \"The Achiever\" magazine I read that you have
established a national advisory panel on math.  I am hoping that you
will consider my highly successful, 23 years of experience and the
insight I am about to share with you.

 

Please feel free to contact me if you would like more in-depth
descriptions of my brief summaries listed in this email.

 

1)  TIME:  Teaches must allocate additional minutes  for math
instruction and exploration in the elementary school classrooms,
throughout all grade levels.

 

2)  SMALL GROUPS:  Teachers must review and check math concepts in small
groups rotated after their whole-group instruction.  The children not
with the teacher can be exploring already taught concepts with
manipulative tools either at their seats or with a volunteer, until it
is time for their math group with the teacher.

 

3\) MANIPULATIVE TOOLS:  Classrooms must have the tools for the children
to manipulative to make sense of the algorithms.  Paper and pencil
algorithms should not be taught at the beginning of the new learning,
but after the manipulative tools has been used.  Many of the expensive
tools can be made with 60 lb. weight paper.

 

4)  ERROR CORRECTIONS:  Every single missed test question must be
corrected one on one with the teacher or with a trained, competent
volunteer.  This is essential for each individual student.

 

5)  CONNECTIONS:  The teacher and the parents must make connections to
the children\'s lives outside of the classroom using the math
standards.  Each student must see how the math can be used in his/her
life.  (Example: For the concept of \"square area\", a standard in all
grade levels, some students might consider the size of a soccer field,
others the size of a tennis court, swimming pool, or playground
hopscotch square.)  It must make sense to them.

 

If each teacher in America would follow these 5 guidelines, as I have
for 23 years, we would be doing a great favor to the children learning
math in our school systems.  They would leave the elementary schools
prepared for junior high algebra and higher level math in the high
schools. 

 

By the way, my younger son is a high school math teacher and my older
son is a research scientist.  Specific teachers and myself helped them
through the maze of math.

 

Thank you for your time

[]{#MattMcCauley .anchor}\-\-\-\--Original Message\-\-\-\--

From: Matt McCauley

Sent: Tuesday, June 06, 2006 1:59 PM

To: National Math Panel

Subject: Constructivist vs. Traditional

We have reviewed the Project 2061 study as well as other literature.  As
a middle school math materials review team we are preparing to recommend
Connected Math Project 2 as our core middle school math text.  We have a
group of parents who are unhappy about this.  These parents seem to be
parents of higher achieving students.  Can you suggest any research data
that we can use to show the effects of CMP2 with high achieving
students?  Do you know of any data that shows a comparison of student
data between traditional math and a constructivist approach?

 

Matt McCauley

Executive Director of K-12 Teaching and Learning

Olympia School District

[]{#PamelaGood .anchor}\-\-\-\--Original Message\-\-\-\--

From: Pamela Good

Sent: Tuesday, June 06, 2006 10:30 AM

To: National Math Panel

Subject: Math Skills commentary

Hello,

 

My name is Pamela Good.  I am a pharmacist, and I am very interested in
the work of the National Math Panel.  My 17-year-old daughter will be a
high school senior this fall, and she will be taking AP Calculus.  So
far, she has been an A student in math, except for a B in one semester
of Geometry.  Our journey to get her there has not been easy.  She is an
honor student at a Wichita, Kansas public high school with an enrollment
of about 1800 students.

 

One thing I would like to encourage the panel to do is to contact the
Sylvan Learning Center.  They have broken down every math skill into
it\'s tiniest part.  When they initially assess a student\'s math
skills, they know which tiny skills are in place, and which ones are
missing and need to be taught.  They get results by teaching these very
small skills, repeating them, making sure there is retention of these
skills, and then building on them.  Without our tutoring experience
there in earlier years, I\'m sure my daughter would not be where she is
today in her math education.  They have alot of experience in tutoring
for deficient math skills, and I feel that they have alot of valuable
insight on why students are not learning math in school.

 

Another thing that I feel is really important is to look at how much
support outside the classroom it takes to get students to learn math. 
My daughter has gone in before school and stayed after school frequently
to get additional help from her teachers.  She has also had a
highly-educated math parent at home who was willing to help her when she
had trouble learning new concepts, which was quite often.  One hour a
day in a math class is not sufficient to teach new skills to most
students.  It takes alot of demonstration and repetition to get the
skill mastered.  At Sylvan, they teach based on \"mastery\" of a
concept, and then they repeat the skill and retest the skill at
intervals until there is \"retention\", which is key.  It\'s too bad we
can\'t translate that into our school classrooms.

 

One other problem that we have had is that the math teachers of higher
level classes tend to teach at a higher level, assuming that only the
brightest of the bright will be in those classes anyway.  My daughter is
bright, but she needs alot of repetition to master new skills.  Teachers
need to teach math, especially in high school, at an appropriate level
so that these students can learn.  They also need to slow down when they
are teaching.  You can\'t teach at breakneck speed and assume that they
will \"get it the first time.\"  They need to allow time for the new
information to soak in.

 

I hope these comments are helpful.

Thanks very much for listening,

Sincerely,

Pamela Good

[]{#BobHarbort .anchor}\-\-\-\--Original Message\-\-\-\--

From: Bob Harbort

Sent: Monday, May 29, 2006 11:50 AM

To: National Math Panel

Subject: Comment from a college teacher

There is an aspect of American math education that I feel is not being
addressed adequately, and I am writing to bring it to your attention. I
base the following remarks on twenty-three years of college teaching,
several years of analyzing my institution\'s student retention data and
associated student records, interviews with hundreds of students, and a
number of discussions with middle and high school teachers in Georgia.\
\
While we are certainly not doing all we could do to prepare students
mathematically in middle school and high school, the push to get started
earlier and earlier has an unintended consequence that threatens
whatever small successes might be there: In Georgia public school
systems, students who are capable in math but are not among the very
brightest almost always finish their high school education with a year
(and sometimes two) of *no* math classes.\
\
At my institution, we give all entering students who do not transfer in
Calculus I a mathematics assessment test that is normed to our student
population and its performance. What we are seeing is that students who
may have been proficient at college algebra in tenth grade retain some
of the conceptual framework as college freshmen, but they have lost much
of the mechanical proficiency in math that comes with repeated practice.
They lost it because they haven\'t had a math class in the previous year
or two, and so have gotten out of practice as surely as a tennis player
would after a year or two of not practicing.\
\
This lack of mechanical proficiency in mathematical subjects is
frustrating for affected college students, and it hurts their academic
performance in college. They are resentful of having to \"retake\"
material they\'ve already studied, they come to hate math, and they
generally shy away from majoring in disciplines that have a foundation
in mathematics, *even if they came to college to major in a STEM
discipline in the first place.*\
 

Consideration of the need for a \"training discipline\" in mathematics
foundations is sadly lacking in *overall* middle and high school
curriculum planning. People may be doing the right things in terms of
individual classes, but setting curricula up so that students are not
continually challenged to stay proficient in their math skills is very
shortsighted.

Bob Harbort, Ph.D.

[]{#PatNaughtin .anchor}\-\-\-\--Original Message\-\-\-\--

From: Pat Naughtin

Sent: Friday, May 26, 2006 4:33 AM

To: National Math Panel

Subject: Pat Naughtin submission to National math panel

National Math Panel\
Department of Education\
USA\
NationalMathPanel@ed.gov\
\
Ladies and Gentlemen,\
\
I am writing in response to Executive Order 13398 and your inquiry into
shortfalls in mathematics education in the USA. Specifically, I am
responding to Section 1 of the Executive Order 13398: National
Mathematics Advisory Panel that reads:\
\
*To help keep America competitive, support American talent and
creativity, encourage innovation throughout the American economy, and
help State, local, territorial, and tribal governments give the
Nation\'s children and youth the education they need to succeed, it
shall be the policy of the United States to foster greater knowledge of
and improved performance in mathematics among American students.\
*\
I am aware that not being a citizen of the USA --- I live in Geelong,
Australia --- could be seen as an impediment but I consider that I am a
suitable respondent under:\
\
*(iii) experts on matters relating to the policy set forth in section 1\
\
 (v) such other individuals as the Panel deems appropriate or as the
Secretary may direct\
*\
or simply as a faraway foreign friend of the USA.\
\
I am aware that the USA faces significant issues in the area of
mathematics:

-   Almost half of American 17-year-olds do not have the basic
    understanding of math needed to qualify for a production
    associate\'s job at a modern auto plant.

-   On the most recent PISA test, American 15-year-olds performed below
    the international average in mathematics literacy and
    problem-solving.

-   Only seven percent of fourth-and eighth-graders achieved the
    advanced level on the 2003 TIMSS test.

-   Students from low-income families who acquire strong math skills by
    the eighth-grade are 10 times more likely to finish college than
    peers of the same socio-economic background who do not.

-   USA students are currently performing below their international
    peers on math and science assessments.

And I agree with Secretary Spellings when she says that there is a
\'*need for today\'s high school graduates to have solid math skills ---
whether they are proceeding to college or going straight into the
workforce*\'.\
\
**I am writing because I believe that almost all of these issues and
problems will evaporate once you have adequate metrication policies and
practices in place. I am writing to encourage you to support the use of
direct metrication in USA schools.\
**\
I recommend that your committee considers how best to encourage the use
of the metric system in schools, to discourage the use of old pre-metric
measures and, critically, to avoid conversions between measuring methods
altogether.\
\
Let me refer back to the beginning of the 20th century when Alexander
Graham Bell (1847/1922) said:\
\
*All the difficulties in the metric system are in translating from one
system to the other, but the moment you use the metric system alone
there is no difficulty.\
*\
That in a nutshell is a major problem of the current mathematical
education system. You have just spent 100 years trying to translate.
\'*from one system to the other\'* with little success. I suggest that
you abandon this approach.\
\
Speaking of Alexander Graham Bell, I would like to recall an address
that Dr. Bell gave to a House committee in support of a bill to switch
to the metric system. This was exactly 100 years ago, in 1906.
Fortunately, his speech, \'Our Heterogeneous System of Weights and
Measures\' was recorded in the March, 1906 issue of The National
Geographic Magazine, and can be found at:
<http://lamar.colostate.edu/~hillger/laws/bell-1906-03.html>\
\
There is also further, more recent, evidence that this approach does not
work.\
\
Richard P Phelps in his paper, \'The Case for U.S. Metric Conversion
Now\' in Education Week (1992 December 9) estimated that each child in
the USA currently spends around a year of their life at school learning
how to convert from old measures to other old measures, or how to
convert from metric units back to old pre-metric measures.\
\
In this article, Richard P. Phelps states:\
\
*It (USA education system) teaches two systems of measurement in the
schools and, the confusion from learning two systems aside, there is a
cost to the time spent in teaching two systems. A full year of
mathematics instruction is lost to the duplication of effort.\
*You can view Phelp\'s article at:
<http://www.edweek.org/ew/articles/1992/12/09/14phelps.h12.html> .\
\
When students from the USA are compared with students from other nations
it is no wonder that they compare unfavourably given this (conversion)
handicap.\
\
Lorelle Young, President of the United States Metric Association
(founded in 1916) estimates that about 60 % of industry in the USA is
now metric. As children who are currently in school leave for the world
of work, they will mostly work in industries that are already
predominately metric. As their schools have not prepared them to be in
the workforce they will have to learn the mathematics they need \'on the
job\'.\
\
Personally, I disagree with Lorelle Young; I think that her estimate is
too low. I travelled extensively in the USA from March to May last year
and I found factory after factory internally using metric units for all
their work and then, as I put it in an article in the USMA newsletter
Metric Today, \'Dumbed it down at the door\' of their factory so that
others would not know that they preferred metric units internally. From
an educator\'s point of view you need to investigate how much of this
\'hidden metric\' will be relevant to your students. Surely one of your
goals is to prepare student for work in industry in the USA.\
\
Somewhat facetiously, I wrote about my experiences in the USA in an
article entitled, \'Don\'t use metric!\' that you can download as a pdf
file from <http://www.metricationmatters.com/articles.> You might find
this amusing but I wrote it with serious intent -- to highlight the fact
that the USA is now all metric.\
\
**There is now no activity in the USA that is not wholly based on the
metric system.\
**\
Sure many deny this, but while:\
·    all medicine is totally metric,\
·    all food values are totally metric,\
·    every car, truck, and tractor is totally metric, and\
·    every yard that a football team achieves is defined legally as
exactly 914.4 millimetres\
they don\'t have much room to manoeuvre.\
\
In his 1906 address to the House committee, Alexander Graham Bell said,\
\
*Few people have any adequate conception of the amount of unnecessary
labor involved in the use of our present weights and measures.\
*\
I believe that the cost of this \'*unnecessary labor\'* is still with
us. But I have seen few serious attempts to put a figure on this cost.
My own researches have only found three attempts to answer this
question. They are from Jos. V. Collins in 1915, Richard P. Phelps in
1992 (cited above), and some thoughts of my own in 2006.\
\
In 1915, Collins in \'A metrical tragedy\' estimated the cost of
non-metrication at that time as \'a total annual loss of \$315 000
000\'. You can find a full transcript of Jos. V Collins\' article at:
<http://www.worldwideschool.org/library/books/socl/education/AMetricalTragedy/Chap1.html>\
\
Richard P Phelps estimated that, *\'there is a cost to the time spent in
teaching two systems. A full year of mathematics instruction is lost to
the duplication of effort\'.* My estimate of the cost of this wasted
effort in the schools of the USA is about 85 billion dollars per year
based on the idea that 10 % of the education budgets of the USA is
wasted effort.*\
*\
My own estimates of non-metrication costs in the USA are based on a
Confederation of British Industry (CBI) survey of its members about
metrication in 1980 --- after 15 years of British metrication. They
found that:\
\
*\... the extra cost of continuing to work in dual systems of measuring
was around £5 000 million every year (in the UK).\
*\
For companies on which the survey was based, the increased production
cost for each company who used dual measures averaged at 9% of the
company's gross profit, and 14% of its net profit when compared to a
fully metric CBI company.\
\
If this percentage (9 %) is applied to the USA economy as a whole and we
make a bold, but not wild, assumption that it costs about 9 % of gross
turnover to use dual measurements (metric and U.S. Customary) then based
on a 2005 estimated Gross Domestic Product for the USA of \$12.735
trillion dollars it costs the USA about 1.15 trillion dollars per year
to use dual measures instead of metric units.\
\
My estimate sounded so outrageous that I was moved to compare it with
Jos. V Collins\' and Richard P Phelp\'s estimates of costs to the USA
economy. In 1915, Collins wrote \'Total annual loss of \$315 000 000\'
could be attributed per year to non-metrication in the USA. If you allow
for inflation between 1915 and 2005, Collin\'s figure for annual losses
becomes \$6 100 000 000 per year. If Richard P Phelp\'s estimate of 10 %
wasted costs in education were applied to the whole economy, the loss
would be about \$1.27 trillion per year. To paraphrase the USA Senator
Everett McKinley Dirksen (1896/1969):

**a trillion this year, and a trillion next year, pretty soon adds up to
real money.**

I wish the National Mathematics Advisory Panel every success with their
deliberations, and I sincerely hope that you will achieve the goals as
laid out in your charter. However, I don\'t think that you can achieve
them unless you boldly confront the issues related to the international
metric system. Please don\'t sweep it under the carpet yet again --- I
even doubt that your great nation can afford to do so.\
\
Yours faithfully,\
\
Pat Naughtin\
2006-05-26

[]{#JohnRaeth .anchor}\-\-\-\--Original Message\-\-\-\--

From: John S. Raeth

Sent: Thursday, May 25, 2006 4:31 AM

To: National Math Panel

Subject: Algebra Reform

Mr. Faulkner,

 

    This note is in response to the article in AAAS\'s U.S. Math
Education, \"Well-Balanced Panel to Tackle Algebra Reform\" in the 19
May 2006 edition of *Science* on page 982.

 

    It is refreshing to hear that an intelligent debate is ongoing in
reference to math education.

 

    As a high school math educator, it is significant that I agree with
the points of view of what might be referred to as both sides of the
discussion.  It is significant because both points of view, algebra
reform and \'more rigorous instruction on basic skills\', are very
important.

 

    It is an unfortunate fact that students entering high school do not
have the arithmetic skills they need to perform satisfactorily in my
algebra classes.  In fact, I have monitored this closely as have many of
my colleagues.  This is one area that I have counseled my students on
during the course of the year.  It is fairly easy to note after
observing verbal responses and written results that the students are
picking up the algebra concepts but are struggling with advancement
because they cannot perform at the basic level in arithmetic.

 

    This is one result of the lack of rigor in elementary and middle
school arithmetic education techniques.  By the time these students
arrive in the high school setting, they have \'learned\' two bad
habits:  they have not learned to do the basic arithmetic and they have
not learned the disciplines they need with higher concepts.  This is
true whether or not they will be moving on to science, engineering, or
other subject area where mathematics will play an integral role.

 

    Algebra reform is also very important.  It is critical that algebra
be taught in a way that will be more relative to modern lives and
circumstances.  In other words, more realistic.  As I am sure you are
aware, one of the first and loudest questions heard is:  \'How or why
are we ever going to use this.\'  Therefore, it is a challenge to
encourage and motivate learners, especially from the beginning of the
curriculum.  That needs to start early. 

 

    We cannot wait until High School.

 

    So, instead of being adversaries, rigorous arithmetic and rigorous
algebra education need to be partners instead of critics.

 

    Another area of concern is the distinct lack of practical and
applicable professional and commercial secondary level math education
materials.  For example, I just attended a conference that was supposed
to be designed for secondary level mathematics educators.  It was led by
a well-known and experienced math educator, a doctor with many years of
experience in education \-- elementary education.  One of his first
comments was that his experience was in elementary and special education
and that we would need to adapt what we experience to our secondary
education classes.  This is typical of what we face in High School.

 

    Finally, I encourage your panel to foster this forum in a public
manner \-- encourage input and suggestions from all that experience out
there.  It will be successful and meaningful.

 

    Thank you for your significant and much needed contributions.

 

John S. Raeth

Harlem High School, Georgia

[]{#LauraJones .anchor}\-\-\-\--Original Message\-\-\-\--

From: Laura R. Jones

Sent: Tuesday, May 23, 2006 8:11 AM

To: National Math Panel

Subject: math club for girls

I wanted to let you know about a local resource that has been working to
encourage girls in math and science for 12 years---the GEMS club. Here
is the web site, and I would be happy to share my experiences and
research with the panel.

[www.gemsclub.org](http://www.gemsclub.org/).

 

 

**Laura Reasoner Jones**

Project Manager, K12nects II

Cluster III School-Based Technology Specialist

Fairfax County Public Schools

[]{#MartaGray1 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Marta Gray

Sent: Sunday, May 21, 2006 7:49 AM

To: National Math Panel

Subject: RE: Curriculum Directors

Since you are listening\...\...\...\...\...

The Fordham Foundation report, \"State of the State Math Standards
2005\", was written by mathematicians that evaluated the state standards
of 49 states. Most states standards were graded a C, D, or F. Many
states rely on teachers and math educators to write these standards. If
every state was required to subject their standards to a panel of
mathematicians for review, with the stipulation that standards must
receive a grade of B or better, we could improve the standards greatly.
This would filter down to classrooms, as curriculums and teacher
training would be consistent with high standards. Having a low target to
begin with guarantees poor student performance.

Another issue that has a tremendous impact on the classroom is the
constant and steady stream of interruptions ranging from announcements,
to phone calls, to impromptu assemblies. Some of these interruptions
cannot be helped such as fire drills, evacuation drills, and the like,
but the cumulative effect is staggering. I am not exaggerating when I
tell you that it is not uncommon to have 6 interruptions in an hour and
I have heard this from many other teachers as well. This has a negative
effect on student concentration and takes the teacher away from students
that require his/her attention. I have read that top achieving nations
have gone as far as requiring \"quiet zones\" in the surrounding areas
of schools. Learning takes immense concentration. I don\'t know if the
panel can address this issue but it\'s toll on productivity is huge.

This may sound extremely negative but it is the \"truth from the
trenches\". Adolesence is an emotioal time and many students go through
a period of rebellion against authority and the establishment. Kids are
quite sophisticated these days and understand that middle school grades
do not \"count\" toward high school graduation. Parents with skills
adequately counter this issue and keep their children on track through
this tumultuous time. Unfortunately, many parents are ineffective in
dealing with this situation. Their children make little or no effort
during these years. It is tragic when these kids grow up enough to
decide that they want to do well in school but are so far behind at that
point, the odds are almost insurmountable that they will overcome lost
skills in their quest for a high school dimploma. This is a problem many
teachers face with students in \"at-risk\" schools. We try to motivate
kids but this job would be much easier if grades counted toward
graduation starting in 6th grade instead of 9th. It is amazing that many
of the kids most resistant to trying in school during adolesence, tend
to be \"stars\" if we are able to get them back on track before too much
ground is lost.

Thank you for your consideration of these ideas. I realize that solving
these issues may be beyond the reach of this panel but I thought you
should be aware of issues that many teachers see on a daily basis.

Respectfully,

Marta Gray

[]{#MartaGray2 .anchor}\-\-\-\--Original Message\-\-\-\--

From: Marta Gray

Sent: Thursday, May 18, 2006 5:01 PM

To: National Math Panel

Subject: Curriculum Directors

Dear Esteemed Panel Members,

As you consider the best interests of students in the U.S., please
remember that many speak English as their second language. These
students can succeed in math as long as their parents are able to
support them at home. It has been my experience that textbooks with lots
of examples/visuals help parents to remember the concept being taught,
which enables them to assist their son/daughter in their native
language. Many of the math programs on the market are so wordy that the
math gets lost and students that might otherwise perform well, suffer.

Thank you for your time.

Marta Gray

McLoughlin Middle School

Vancouver, Washington

[]{#JoanCotter .anchor}\-\-\-\--Original Message\-\-\-\--

From: Joan Cotter

Sent: Wednesday, May 17, 2006 8:40 PM

To: National Math Panel

Subject: First grade mathematics research

National Math Panel:

I have done research with children in the first grade employing some
techniques?used in Asia. The results were outstanding; the attached
article published by the NCTM (National Council of Teachers of
Mathematics) details the results. It shows a great disparity between the
way children are traditionally taught in the U.S. and what they could be
doing.

Some examples follow:

1\. The children could determine quantities up to 100 visually without
counting, by grouping in 5s as well as 10s.

2\. Children can learn addition and subtraction visually
[without]{.underline} counting. Five-month-old babies can add and
subtract up to three. Japanese children are discouraged from counting
when they start school. This approach is also much easier for children
with learning problems. (In the U.S. we traditionally spend a year
teaching children how to count and spend two years telling them not to.)

3\. It has been known for decades that flash cards and timed tests are a
poor way to teach the facts. The children in the experimental group used
visual strategies combined with games for practice. The AL abacus
enabled them to see and practice the strategies.

4\. Place value is the single most important topic in arithmetic.
Average American students don\'t understand it until the end of fourth
grade. The experimental children used the ?math way? of number naming;
they understood place value in first grade as do Asian students.

5\. The children learned to add four-digit numbers with carrying on the
AL abacus. A few days later they had figured out how to do the standard
paper and pencil algorithm.

6\. The children could mentally add two-digit numbers (with carrying).

7\. By using part/part/whole circle sets, the children easily solved
problems, including those with missing addends.

My background includes a degree in electrical engineering, a Montessori
teacher for children ages 3-6, tutor for children with learning
problems, mathematics teacher for grades 6-8, a?doctorate in mathematics
education and early childhood, and the author of the K-Gr 4 *RightStart
Mathematics* program. Currently I am writing middle school mathematics
curricula.?

I am very interested in improving mathematics in the U.S. What we do in
the early years has a profound influence in later years. Please read the
attachment.

Joan Cotter, Ph.D.

![](media/image33.wmf)

[]{#SusanSocha .anchor}\-\-\-\--Original Message\-\-\-\--

From: Susan C. Socha

Sent: Sunday, May 14, 2006 4:16 PM

To: National Math Panel

Subject: Special education teachers and mathematics

Hello

I am a teacher in Fairfax County Public schools, and I don\'t see
anything about special education being addressed on the list.

n every high school, the special education department is always the
largest. The special education teachers, more often than not, have never
been regular classroom teachers. They\'ve never been responsible for
teaching 120+ students a day. They are usually people who have a
bachelor\'s degree in any subject, and then go get a masters in special
ed.

The real problem comes in the mathematics classroom. We are assigned
special education teachers to team with. These special education
teachers have no content knowledge, and often don\'t even want to be in
math. The new program that gets special education teachers to be
\"highly qualified\" requires them to do 40 hours of some sort of math
class. Believe me, they need more than 40 hours. Why not let the math
teachers attend 40 hours of class to become highly qualified in special
education? We have the weakest teachers (special education) working with
the weakest students. Please, take this into consideration.

Special education teachers should be like a doctor who decides to become
a surgeon. A teacher should spend at least 5 years in a regular
classroom, then go and get qualified for special ed. At that point, they
would be a specialist and paid more, and they WOULD be highly qualified.

Thanks for your time

Susan Socha

[^1]: ^\[^