+-----------------------+-----------------------+-----------------------+
| **Date**              | **Author**            | **Subject**           |
+-----------------------+-----------------------+-----------------------+
| December 03, 2006     | Forman, Frank         | [Questions for the    |
|                       |                       | National Mathematics  |
|                       |                       | Advisory              |
|                       |                       | Panel](#FrankForman)  |
+-----------------------+-----------------------+-----------------------+
| November 8, 2006      | Schaar, Richard       | [Thank you and        |
|                       |                       | Com                   |
|                       |                       | ment](#RichardSchaar) |
+-----------------------+-----------------------+-----------------------+
| October 30, 2006      | Moschkovich, Judit N. | [Statement for        |
|                       |                       | National Math         |
|                       |                       | Pane                  |
|                       |                       | l](#JuditMoschkovich) |
+-----------------------+-----------------------+-----------------------+
| October 17, 2006      | Shacter, John         | [Re: Ideas for the    |
|                       |                       | National Math         |
|                       |                       | Panel](#JohnShacter2) |
+-----------------------+-----------------------+-----------------------+
| October 16, 2006      | Marshall, John        | [RE: Some views of US |
|                       |                       | math](#JohnMarshall)  |
+-----------------------+-----------------------+-----------------------+
| October 12, 2006      | Gill, Lisa Brady      | [NatMathPanel_T       |
|                       |                       | Icomments](#LisaGill) |
+-----------------------+-----------------------+-----------------------+
| October 09, 2006      | Wyrick, Emily         | [Concerned            |
|                       |                       | T                     |
|                       |                       | eacher](#EmilyWyrick) |
+-----------------------+-----------------------+-----------------------+
| October 06, 2006      | Wetherbee, Ted        | [NCTM Focal Points    |
|                       |                       | \>\> NMAP             |
|                       |                       | r                     |
|                       |                       | eview](#TedWetherbee) |
+-----------------------+-----------------------+-----------------------+
| September 20, 2006    | Boone, Delores        | [I Need Specific      |
|                       |                       | Information, Please,  |
|                       |                       | ASAP](#DeloresBoone)  |
+-----------------------+-----------------------+-----------------------+
| September 12, 2006    | Clements, WIC         | [Math                 |
|                       |                       | /Music](#WICClements) |
+-----------------------+-----------------------+-----------------------+
| September 04, 2006    | Marshall, John        | [Some Views of US     |
|                       |                       | Math](#JohnMarshall)  |
+-----------------------+-----------------------+-----------------------+
| September 01, 2006    | Bryant, Billy         | [Mathematical         |
|                       |                       | Achie                 |
|                       |                       | vement](#BillyBryant) |
+-----------------------+-----------------------+-----------------------+
| September 01, 2006    | Marain, Dave          | [Statement to the     |
|                       |                       | National Math         |
|                       |                       | Panel](#DaveMarain3)  |
+-----------------------+-----------------------+-----------------------+
| August 31, 2006       | Kalinowski, Melissa   | [RE: National Math    |
|                       |                       | Panel Meeting in      |
|                       |                       | Cambridge from        |
|                       |                       | 9/13-14               |
|                       |                       | ](#MelissaKalinowski) |
+-----------------------+-----------------------+-----------------------+
| August 30, 2006       | Rufino, Erwin         | [Letter of            |
|                       |                       | Co](#ErwinRufino)     |
|                       |                       |                       |
|                       |                       | [mments regarding     |
|                       |                       | upcoming 9/13/06 and  |
|                       |                       | 9                     |
|                       |                       | /14/06](#ErwinRufino) |
|                       |                       |                       |
|                       |                       | [meeting in           |
|                       |                       | Cambridge,            |
|                       |                       | MA](#ErwinRufino)     |
+-----------------------+-----------------------+-----------------------+
| August 29, 2006       | Mowers, Kathy         | [Re: Deadline for     |
|                       |                       | Math Panel            |
|                       |                       | Co                    |
|                       |                       | mments](#KathyMowers) |
+-----------------------+-----------------------+-----------------------+
| August 29, 2006       | Jaffe, Cheryl H.      | [Comments for         |
|                       |                       | National Mathematics  |
|                       |                       | Advisory              |
|                       |                       | Panel](#CherylJaffe)  |
+-----------------------+-----------------------+-----------------------+
| August 26, 2006       | Rusk, Richard W.      | [National Math        |
|                       |                       | Advisory              |
|                       |                       | Panel](#RichardRusk)  |
+-----------------------+-----------------------+-----------------------+
| August 23, 2006       | Elwell, Jim           | [Letter to            |
|                       |                       | NMAP](#JimElwell)     |
+-----------------------+-----------------------+-----------------------+
| August 18, 2006       | Pickar, Tony          | [Public               |
|                       |                       | Input](#TonyPickar)   |
+-----------------------+-----------------------+-----------------------+
| August 03, 2006       | Marain, Dave          | [Re: Questions to the |
|                       |                       | Panel](#DaveMarain4)  |
+-----------------------+-----------------------+-----------------------+
| July 28, 2006         | Shacter, John         | [Teaching Math with   |
|                       |                       | the \"KISS\" Approach |
|                       |                       | (                     |
|                       |                       | rev.)](#JohnShacter2) |
+-----------------------+-----------------------+-----------------------+
| July 13, 2006         | Shacter, John         | [Teaching Math with   |
|                       |                       | the \"KISS\"          |
|                       |                       | Ap                    |
|                       |                       | proach](#JohnShacter) |
+-----------------------+-----------------------+-----------------------+
| June 19, 2006         | Cantrell, Marsha H.   | [Comments for June    |
|                       |                       | 2                     |
|                       |                       | 9th](#MarshaCantrell) |
+-----------------------+-----------------------+-----------------------+
| June 18, 2006         | Becker, Jerry         | [For Your             |
|                       |                       | Inform                |
|                       |                       | ation](#JerryBecker2) |
+-----------------------+-----------------------+-----------------------+
| June 12, 2006         | Johnson, Doug         | [Math                 |
|                       |                       | Ed](#DougJohnson)     |
+-----------------------+-----------------------+-----------------------+
| May 25, 2006          | Raeth, John S.        | [Algebra              |
|                       |                       | Reform](#JohnRaeth)   |
+-----------------------+-----------------------+-----------------------+
| May 11, 2006          | Malkevitch, Joseph    | [Mathematics          |
|                       |                       | Educatio              |
|                       |                       | n](#JosephMalkevitch) |
+-----------------------+-----------------------+-----------------------+
| May 10, 2006          | Seidel, Celisa        | [math](#CelisaSeidel) |
+-----------------------+-----------------------+-----------------------+
| May 10, 2006          | Gray, Marta           | [Studies re:          |
|                       |                       | Math                  |
|                       |                       | ematics](#MartaGray4) |
+-----------------------+-----------------------+-----------------------+
| May 4, 2006           | Denney, Dawn          | [Math teacher\'s      |
|                       |                       | conc                  |
|                       |                       | ern\...](#DawnDenney) |
+-----------------------+-----------------------+-----------------------+

\-\-\-\--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.

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

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

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

(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 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 www.nexus.edu.au/teachstud/gat/vandeur.htm,

but many or most of its files have been moved to

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.\]

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:

+++++++++

\-\-\-\--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

[]{#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

[Moschkovich Math
Panel.doc](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/moschkovich-math-panel.doc)

\-\-\-\--Original Message\-\-\-\--\
From:[]{#JohnShacter2 .anchor} 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.

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#JohnMarshall .anchor}John Marshall
\[mailto:jm0603@gmail.com\]\
**Sent:** Monday, October 16, 2006 6:09 AM\
**To:** National Math Panel\
**Subject:** RE: Some views of US math

Ida

 

I had hoped to make further comments for the National Math Panel to
consider but life seems so hectic at present that time doesn't allow.
However, I would like to offer the attached articles from KAPPAN written
on the MATHEMATICS WARS theme, which I hope will make a point.

 

If time permits in the not too distant future I will try a write
further.

 

Good Luck

 

John Marshall

Inspector of School, UK

Lecturer University of South Florida. USA

[Marshall Math Wars Taking
Sides.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/marshall.math-wars-taking-sides.pdf)

[Marshall Math Wars 2 It\'s the Teaching
stupid.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/marshall.math-wars-2-its-teaching-stupid.pdf)

[]{#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

[NatMathPanel_TIcomments.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/natmathpanel_t1comments.pdf)

\-\-\-\--Original Message\-\-\-\--\
From:[]{#EmilyWyrick .anchor} 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)

[Dear Janet
Gossell.doc](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/dear-janet-gossell.doc)

\-\-\-\--Original Message\-\-\-\--\
From: []{#TedWetherbee .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#DeloresBoone .anchor}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\-\-\-\--

From: []{#WICClements .anchor}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

\-\-\-\--Original Message\-\-\-\--\
**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? \[ Etc.\]

(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

[Math Wars Taking
Sides.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/math-wars-taking-sides.pdf)

[Math Wars 2 It\'s the Teaching
,stupid.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/math-wars-2-it's-the-teaching-stupid.pdf)

http://www.ed.gov/about/bdscomm/list/mathpanel/documents/

\-\-\-\--Original Message\-\-\-\--

From: []{#BillyBryant .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#DaveMarain3 .anchor}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

[Nat_Math_Panel_Statm_9-1.doc](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/nat-math-panel-statm-9-1.doc)

\-\-\-\--Original Message\-\-\-\--

From: []{#MelissaKalinowski .anchor}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

[Kalinowski.Melissa.doc](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/kalinowski-melissa.doc)

\-\-\-\--Original Message\-\-\-\--

From: []{#ErwinRufino .anchor}Erwin Rufino
\[mailto:erwin_rufino@dot.ca.gov\]

Sent: Wednesday, August 30, 2006 1:39 PM

To: National Math Panel

Subject: Letter of Comments regarding upcoming 9/13/06 and 9/14/06

meeting in Cambridge, MA

Dear Math Panel:

I have been made aware of the President\'s mandate to establish this
Panel

to increase the competitiveness of American students in mathematics and

science. In conjunction with the meeting to be held in Cambridge, MA, I

am hereby transmitting to you my letter of comments which I strongly

believe should be addressed in the agenda for this meeting.
Unfortunately

I will be unable to be present at this event.

I greatly appreciate your receptiveness on this matter.

(See attached file: NMAP.pdf)

Sincerely,

Erwin B. Rufino, P.E.

Transportation Engineer

State of California

Department of Transportation

[NMAP.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/nmap.pdf)

\-\-\-\--Original Message\-\-\-\--

From: []{#KathyMowers .anchor}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

[AMATYC letter to NMAP w
signature.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/amatyc-letter-to-nmap-w-signature.pdf)

[AMATYC letter to NMAP no
signature.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/amatyc-letter-to-nmap-no-signature.pdf)

\-\-\-\--Original Message\-\-\-\--

From: []{#CherylJaffe .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#RichardRusk .anchor}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.

\-\-\-\--Original Message\-\-\-\--

From: []{#JimElwell .anchor}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

[Elwell letter to
NMAP.pdf](http://www.ed.gov/about/bdscomm/list/mathpanel/documents/elwell-letter-to-nmap.pdf)

\-\-\-\--Original Message\-\-\-\--

From: []{#TonyPickar .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#DaveMarain4 .anchor}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

\-\-\--Original Message\-\-\-\--\
From: John Shacter \[mailto:jsplg@comcast.net\]\
Sent: Friday, July 28, 2006 10:48 AM\
To: Graban, Jennifer\
Subject: Teaching Math with the \"KISS\" Approach (rev.)

Hi Jennifer - Thanks v. m. for your kind message.\
\
Below is a slightly extended version of my letter. The additions are in
the fourth to last, large paragraph.\
\
I cannot do a lot of traveling for a five-minute presentation. However,
I will send you additional, rather brief e-mails, and I would like to
submit to more extensive questions by and discussion with the panelists.
I like to believe, that they will not be wasting their time with me, and
that it is unlikely that any other advisor will have the same set of
practical math-user ideas for them.\
\
Thanks again for your interest. \-- You have been very kind \--\
\
John

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--\
\
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, pointing out that this is like a detective
game. If you only have one \"clue\" or equation, but two \"unknowns\", A
and B, then there are an infinite number of valid combinations of A and
B, until and unless you get a second \"clue\". If I have a bit more
time, I also show them how the infinite number of valid combinations can
be represented by a line in the x/y plot or graph, and that there is an
even \"larger\" number of infinite combinations which are not valid
combinations\... 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,
until well into middle school \-- like 7th or 8th grade.\
\
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

\-\-\-\--Original Message\-\-\-\--

From: []{#JohnShacter .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#MarshaCantrell .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#JerryBecker2 .anchor}Jerry Becker \[mailto:jbecker@siu.edu\]

Sent: Sunday, June 18, 2006 1:56 PM

To: National Math Panel

Subject: FOR YOUR INFORMATION

FOR YOUR INFORMATION \... FROM THE MATH-TEACH LISTSERVE. THE RESPONSE

TO WILSON IS BY MICHAEL GOLDENBERG, A PARTICIPANT ON THAT LISTSERVE.

On Jun 17, 2006, at 11:00 AM, W. Stephen Wilson wrote:

\>From the for-what-it\'s-worth department, if you can figure out how

\>to be effective at teaching 2+2=5 the WWC will put it up on their

\>web site if you can document it well. They are not

\>concerned about content although in the case of 2+2=5 they might

\>notice. They don\'t, however, notice that mathematicians view what

\>they do put up as the same as 2+2=5, but they can\'t tell and don\'t

\>ask.

Really? Please cite some examples of the above, if you wouldn\'t mind.

\>Some things don\'t require research. If a program does not include

\>the math necessary to move on to higher math then you do not need a

\>study to show that kids don\'t learn the content that isn\'t there.

I believe that\'s called circular reasoning. You presume to know

precisely what math kids need to know to move on to \"higher math.\"

You presume to know without telling us what comprises this apparently

fixed, well-defined, and universally agreed-upon body of knowledge

known as \"higher math.\" You presume to know just how high, again

without telling us, everyone should go in this undefined \"higher

math.\" And you presume that we should build K12 curricula precisely

on the goal of getting students to study that \"higher math.\"

The holes in the above would fill the Albert Hall. So please, Steve,

fill some of them in. And let us know exactly how you\'ve been able to

answer a question that no one else has been able to in a satisfactory

manner for the past 100 years or so: what, exactly, is THE math

content that all kids MUST know (or else, I guess, all hell will

break loose), and when must they know it. And how do you know this is

best for everyone, and that there are no alternative plans that might

serve many, many students far better than your own?

Given your influence on the panel now meeting, I would assume you can

dash of a complete and articulate answer to these questions with no

trouble. Or didn\'t any of them impact your decision-making in helping

to pack the panel as you did?

\>Before studies are done they should be reviewed for content and then

\>the issue should be which one teaches best.

\>Steve

Jerry P. Becker

Dept. of Curriculum & Instruction

Southern Illinois University

E-mail: jbecker@siu.edu

\-\-\-\--Original Message\-\-\-\--

From: []{#DougJohnson .anchor}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

\-\-\-\--Original Message\-\-\-\--

From: []{#JohnRaeth .anchor}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

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#JosephMalkevitch .anchor}Joseph Malkevitch
\[mailto:joeyc@cunyvm.cuny.edu\]\
**Sent:** Thursday, May 11, 2006 10:20 PM\
**To:** National Math Panel\
**Cc:** joseph malkevitch\
**Subject:** Mathematics Education

Dear Advisory Panel,

I have read President Bush\'s Executive Order which charges the National
Advisory Mathematics Panel. I am concerned  that the way the charges to
this Panel are framed, there is a high risk that a system which has been
doing a good job and has been improving will be changed in a way that
damages mathematics education in the United States.

In optimizing the teaching of mathematics in the United States we need
to balance the need to train large enough numbers of STEM workers
without producing the large number of math-phobic Americans which has
been a consequence of America\'s approach to mathematics education in
the past. Producing large numbers of math-phobic Americans produces a
cycle where many children do not take the interest in STEM subjects that
they might because of parental attitudes. Although America has brought
forth such remarkable mathematicians as Michael Friedman, Stephen Smale,
and William Thurston (to mention but a few), we have also for
generations produced otherwise well educated Americans who openly
acknowledge a lack of understanding of the purpose and value of
mathematics. This, despite the fact that on a daily basis these
individuals take advantage of cell phones, computers, DVD\'s, and
medical imaging techniques which would not exist without mathematics
developed in the 20th century.  

Currently, America is the envy of many countries (both in the Far East
and Europe) in having developed highly creative practitioners of
mathematics. Some statements in the Executive Order suggest to me a bias
which will not give enough attention to new tools that are increasingly
becoming part of K-12 curriculum (e.g. probability, statistics, graph
theory, use of computers and calculators) and points of view about the
reason to study mathematics (to get insight into questions about
optimization, fairness, information, risk, etc.) in favor of unwarranted
attention to mechanical skills in arithmetic and algebra. There are
hints in the charge to the advisory panel that instead of optimizing
mathematical content and conceptualization, the emphasis will be on
regimentation of the way mathematics is delivered to the students.
Instead of emphasizing traditional basic skills, we should be teaching
mathematical modeling tools that make it possible to use mathematical
ideas in a flexible way when faced with new situations. Let us not undo
the progress being made by having innovative Liberal Arts mathematics
courses in college that are helping educate future parents and Americans
with a broader vision of what mathematics is truly about and how
applications of mathematics pervade modern life. We need to broaden the
reforms set in motion by the NCTM\'s Standards so that America can meet
its needs for STEM discipline students while developing a general public
who are knowledgeable about mathematics and its nature.

Sincerely,

Joseph Malkevitch

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

> \-\-\-\--Original Message\-\-\-\--
>
> Date: Tue, 9 May 2006 22:37:26 -0700 (PDT)\
> From: []{#CelisaSeidel .anchor}Celisa Seidel
> \<celisaseidel@yahoo.com\>\
> Subject: math\
> To: personnel@renton.wednet.edu
>
> My daughter is a first grade student at Talbot Hill elementary in
> Renton,Washington.
>
> I feel like my daughter is not being taught math, at the appropriate
> level.  My boyfriend\'s son is a first grade student at Newport
> Heights in the Bellevue School District (Bellevue, Washington) and he
> is well beyond simple addition and subtraction.  My daughter, in
> fact, comes home with little math homework at all\...I feel this is a
> huge failure of the school\...
>
> I have compared the WASL scores between the two school districts and
> the two schools, aforementioned..and the difference is noticeable, to
> say the least\... 
>
> I went to Eastgate Elementary (in Bellevue, WA) for the first grade,
> we were working on timed multiplication tables and division in first
> grade\...My daughter is having difficulty with 13-9\...
>
> The teacher has not mentioned that she is below the standard in math,
> which is very frightening indeed\...
>
> I am not sure what changes need to be implemented, but something needs
> to be done\...This lack of education will definately affect the rest
> of her life negatively\...as she is forced to \'catch up\' so she will
> be at same level as the Bellevue School District students she will
> attend with, next year\...

\-\-\-\--Original Message\-\-\-\--

From: []{#MartaGray4 .anchor}Marta Gray \[mailto:Marta.Gray@vansd.org\]

Sent: Wednesday, May 10, 2006 2:18 PM

To: National Math Panel

Subject: Studies re: Mathematics

Dear Esteemed Panel Members,

I hope these studies are helpful to you in your search to identify the
best ways to teach students mathematics. As a middle school math
teacher, I am deeply concerned about the lack of skills and
understanding that students enter the eighth grade with. It is shocking
how few students have mastered even basic math facts.

I will continue to send you articles. I genuinely appreciate your
efforts. Real reform is desperately needed and I\'m afraid the NCTM
reforms have not been effective for many children. School districts are
pressured to teach to the state standards, which downplay the learning
of facts and algorithms.

As you will see in the following article \"The State of State Math
Standards 2005\", there is much room for improvement.

www.edexcellence.net/foundation/publication/publication.cfm?id=338

I have also included several other articles which have been extremely
informative, as follows:

http://darkwing.uoregon.edu/\~adiep/ft/becker.htm

www.nychold.com/myths-050504.html

www.nychold.com/talk-greenleaf-051002.pdf

Thanks for your time and for listening.

Sincerely,

Marta Gray

Middle School Math Teacher

McLoughlin Middle School

Vancouver, Washington

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#DawnDenney .anchor}Dawn Denney
\[mailto:ddenney@cabarrus.k12.nc.us\]\
**Sent:** Thursday, May 04, 2006 8:23 AM\
**To:** Bradshaw, Jim\
**Subject:** Math teacher\'s concern\...

As a high school National Board Certified teacher, I hope one thing that
comes out of all of this is that students get back to the basics in the
elementary schools.  It is amazing (sad) to see students at the high
school level struggle with Algebra because they can\'t work with
integers or fractions, much less whole numbers, without a calculator. 
Here in North Carolina, students are taught basic math facts with a
calculator starting in third grade.  The state calls calculators \"the
great equalizer.\"  I agree; we are bringing all of our students down
to the same low level of competency.

 

I have worked with the Japanese Kumon program of Math and Reading.  It
is awesome to see children of a young age succeed with their learning of
basic math facts and then continue, with confidence, to excel in
Pre-Algebra and beyond.

 

No one would ever think of using a computer program that allows a
computer to read for our kids.  Why then do we find it acceptable for
math?

 

Sincerely,

(Angela) Dawn Denney

Conord, NC

[^1]: ^\[^