----------------------------------------------------------------------------------
  **Date**               **Author**             **Subject**
  ---------------------- ---------------------- ------------------------------------
  January 9, 2007        Agar, Robin            [Delaware Program](#RobinAgar)

  December 29, 2006      Askey, Richard         [Suggestions](#RichardAskey3)

  December 23, 2006      Forman, Frank          [American Biology Teacher: Mary
                                                Theresa Ortiz: Numbers, Neurons &
                                                Tides, Oh My! Mathematics, the
                                                Forgotten Tool in
                                                Biology](#FrankForman3)

  December 23, 2006      Forman, Frank          [Frank H. Heppner, Karen R. Kouttab,
                                                William Croasdale: Inquiry: Does it
                                                Favor the Prepared Mind? (with reply
                                                and response)](#FrankForman2)

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

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

  December 16, 2006      Koepp, Caroline        [Comments](#CarolineKoepp)

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

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

  December 03, 2006      Forman, Frank          [Questions for the National
                                                Mathematics Advisory
                                                Panel](#FrankForman)

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

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

  November 16, 2006      Rotman, Jack           [Location suggestion for Meeting 7,
                                                8 or 9](#JackRotman)

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

  November 9, 2006       Palisano, Katherine    [Letter to school
                                                board](#KatherinePalisano)

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

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

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

  November 5, 2006       Shacter, John          [Re: PANEL COMPOSITION AND
                                                MISSION](#JohnShacter6)
  ----------------------------------------------------------------------------------

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#RobinAgar .anchor}Robin Agar
\[mailto:robinagar@hotmail.com\]\
**Sent:** Tuesday, January 09, 2007 11:51 AM\
**To:** National Math Panel\
**Subject:** Delaware Program

Hi.  I\'m sure that you have so much to do and so much information to
sort through that you really don\'t need to hear from the public. 
However, I wanted to tell you about a program that we have here in DE
that is a wonderful tool for educators to increase interest in Math,
Science and Technology subjects.

I am a coordinator for the What in the World? program, a career
awareness program.  We expose students in grades 3-12 to careers that
deal with math, technology, and science.  There are many programs
throughout the entire school year. The programs are only 2 hours long. 
Each presenter brings an object that probably wouldn\'t be recognized by
the students.  Then they explain what it is and how it helps them do
their jobs while stressing the importance of Math, Science or
Technology. The presenters speak for about 10 minutes to each group of
students.  The students rotate to other presenters in order to be
exposed to a wide base of careers.

This has such a wonderful effect on the students.  It\'s amazing to
see.  Too often students are only aware of a limited number of career
choices.  This program helps them not only see more options, but it
stresses the importance of Math from an early age on.  We illustrate how
necessary the subjects are for almost any career path. 

I think this should be implemented country wide.  I realize that it is a
small thing, but it truly makes a big difference.  I would love to tell
you more about the program, but I\'m afraid that I would be wasting your
time. 

Please contact me if you would like more info or if you have any
questions at all.  And please think about this being a suggestion to
other states as well.  We are all responsible for our children\'s
education.  This is a way that many people can help!

Sincerely,

Robin E. Agar

Delaware Business, Industry, Education Alliance

Program Coordinator

"What in the World?" Program

\-\-\-\--Original Message\-\-\-\--\
From: []{#RichardAskey3 .anchor}Richard Askey\
Sent: Friday, December 29, 2006 3:20 PM\
To: National Math Panel\
Subject: suggestions

Dear Tyrrell and others,

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

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

Teacher education and licencing: The National Research Council did

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

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

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

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

wrote that the questions seem reasonable but a content expert

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

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

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

involved. When testing experts look at exams they have a

completely different focus. They worry about whether the results

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

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

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

do this they have questions at this level overused in comparison

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

exam sets too low a level of knowledge which candidates and

people educating them and those hiring them expect. To put

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

questions will give a similar ranking to people taking it to

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

but students will have to have a much better knowledge of

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

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

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

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

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

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

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

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

years.

When the National Board for Professional Teaching Standards was

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

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

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

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

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

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

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

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

My question was asked almost 10 years ago.

The Presidential Award winning elementary school mathematics teacher

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

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

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

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

the primary emphasis was on innovation rather than what the content

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

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

would be appropriate.

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

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

expecting much from the preliminary report since there has not been

enough time to work on it.

Sincerely,

Dick

Richard Askey

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

From: []{#FrankForman3 .anchor}Premise Checker
\[mailto:checker@panix.com\]

Sent: Saturday, December 23, 2006 9:08 PM

To: National Math Panel

Subject: American Biology Teacher: Mary Theresa Ortiz: Numbers, Neurons

& Tides, Oh My! Mathematics, the Forgotten Tool in Biology

This is another article I found from The American Biology Teacher. Its

thesis is that math can and should be used widely in biology. All the
more

reason to offer excellent training in math at the secondary level.

\[I have a splendid little book by C.J. Pennycuick, Newton Rules Biology

(Oxford UP, 1992). It shows how a few simple physical and mathematical

principles can give useful insight into biological behavior. We
ordinarily

think of the math used in biology as involving evolution and the
probability

theory behind it, much more advanced math. This book could well prove
useful

for high school math teachers when presenting real-world applications.\]

Mary Theresa Ortiz: Numbers, Neurons & Tides, Oh My! Mathematics, the

Forgotten Tool in Biology

The American Biology Teacher

Volume 68, Issue 8 (October 2006), pp. 458-462

Mary Theresa Ortiz, Ph.D., is Professor, Department of Biological

Sciences, Kingsborough Community College, Brooklyn, NY 11235;

e-mail: MOrtiz@kbcc.cuny.edu. She teaches General Biology, Human

Anatomy & Physiology, Marine Science, and other courses.

Writing Across the Curriculum has been an important focus in higher

education for quite some time. Writing is important, and the

attention it is receiving is well deserved. However, just as

important is \"Math Across the Curriculum.\" It is amazing how many

students in the biological sciences cannot perform the simplest of

mathematical calculations. Some even have difficulty calculating

their grades. It has been this instructor\'s experience that

students will do just about anything to avoid \"doing math.\" Yet

mathematics is an important part of, not only the many fields in

biology, but our daily lives. So important, in fact, that the

November 14, 2002 issue of Nature featured a series of articles in

a special \"Insight\" section devoted to \"Computational Biology\"

(Surridge, 2002).

In several courses in the Department of Biological Sciences at

Kings borough Community College, a campus of The City University of

New York, I have applied mathematics to course curriculum topics to

provide students with a broad based learning experience. In this

paper mathematical applications used in Human Anatomy & Physiology,

General Biology, and Marine Biology courses are presented. These

approaches can be incorporated into class discussions as well as

extended to other class topics.

Mathematical Applications in Human Anatomy & Physiology

Students often ask, \"Where can you apply mathematics to Human

Anatomy & Physiology?\" The answer is, \"In many areas!\" Encouraging

students to develop an appreciation for the physiological

capacities of the human body can be challenging, but it is well

worth the effort. The examples presented below should hopefully

inspire the reader to delve into additional applications.

Kings borough Community College offers a three-semester sequence in

Human Anatomy & Physiology to students seeking careers in the

Allied Health Sciences.\^\* The first semester is a three-hour

combined lecture and laboratory course that meets twice per week.

This first course focuses on introductory anatomical and

physiological principles, the cell, tissues and the integument. Two

of the topics addressed in the course are measurement and

anatomical terminology. After these topics are introduced, each is

reinforced in a laboratory session incorporating mathematics.

Students are provided with a worksheet titled \"Your Body

Measurements\" (Appendix 1). The sheet contains a list of body parts

(in anatomical terms) for each student to complete in both English

and metric units using available instruments (such as tape

measures, rulers, and scales). In addition, students are asked to

make comparisons between the right and left sides of the body to

expose students to the variability within individuals. The exercise

is a valuable one because, by the time each student has worked

through it, he/she has performed extensive practical measurements

while strengthening his/her anatomical vocabulary.

Second semester topics in Human Anatomy & Physiology at Kings

borough Community College include the musculoskeletal, nervous,

endocrine, and digestive systems. The nervous system, with its

conduction of electrochemical impulses, provides the creative

instructor with many opportunities to include mathematical

applications. For example, nerve fibers can be classified according

to their speed of conduction, as follows:

Question: What is the longest it takes for a nerve impulse to

travel from the head of a six-foot man to his toes along Class A

fibers? Class B fibers? Class C fibers?

Solution: This problem adds a twist since the units provided are in

different measuring systems. First, one must convert conduction

speeds to English units or the height of the man into metric units.

Let\'s convert the man\'s height into metric units. A six-foot man is

1.8 meters tall. (How would you arrive at this figure?) For Class A

fibers with a conduction speed of 15.0 m/s, using the formula

T=D/R, where T = Time (s), D=Distance (m), and R=Rate (m/s), the

time required is:

Therefore, it takes 0.1 seconds for a nervous impulse to travel

from head to toe in a six-foot man along Class A fibers.

When students see how fast impulses are conducted, they begin to

appreciate the incredible efficiency of the human body. The same

method can be used to calculate this time for Class B and C fibers.

Also, a challenge problem asking how much faster or slower impulses

will travel on nerve fiber Class A than B can be posed. Students

can be challenged further while at the same time making the problem

more interesting. For example, on occasion students have been asked

to determine how long it would take a nervous impulse to travel to

the moon along Class A fibers. The instructor may supply the

distance to the Earth\'s moon (250,000.0 miles-be careful with

units!) or may opt to have students research this value. Still more

challenges may be given by asking what would happen to the speed of

conduction along any of these fibers if additional myelination were

present, or if temperatures were decreased. In all of these

problems students gain insight into the workings of the human

nervous system through mathematical applications.

In the last of the three semesters of Human Anatomy & Physiology,

topics discussed include the cardiovascular, respiratory,

excretory, immune, and reproductive systems. The cardiovascular

system, with its fluid dynamics and electromechanical properties,

lends itself to many mathematical applications. There are the

classic calculations employing the formula for cardiac output:

CO = SV × HR, where SV is Stroke Volume and HR is Heart Rate.

However, one can explore further. For example, the following

problem stimulates students to gain more of an appreciation for

size and numbers when considering the capacity of blood:

Given:

1\. The total blood volume of a typical human adult is

approximately 5.0 liters (L).

2\. There are about 5.0 million red blood cells (RBCs) in 1.0 uL of

blood.

3\. There are about 5.0 thousand white blood cells (WBCs) in 1.0 uL

of blood. (Saladin, 2001)

Find:

1\. The total number of RBCs in the body.

2\. The total number of WBCs in the body.

Solution: Knowing that there are 10\^6 uL in 1.0 L, and given \"a\"

and \"b\" above, we multiply as follows:

In other words there are 25,000,000,000,000.0 or 25 trillion RBCs

in the body! The solution to Problem 2 is similar:

That is, there are 25,000,000,000.0 or 25 billion WBCs in the body!

This can be taken a step further. Each erythrocyte (RBC) contains

about 280.0 million hemoglobin protein molecules. Students can

calculate the number of hemoglobin molecules in the body by

multiplying the solution in Problem 1 by 280.0 million. Did you get

7.0 × 10\^21 or 7,000,000,000,000,000,000,000.0?

The human excretory system also provides opportunities for

mathematical applications. Using the equation for glomerular

filtration rate, students can see just how much filtering of blood

the kidneys perform each day. Let\'s look at an example.

Glomerular filtration rate (GFR) is the amount of filtrate in mL

formed per minute by both kidneys combined (Saladin, 2001;

Guyton, 1976). The GFR is expressed as:

where NFP is the net filtration pressure (in mmHg) and K\[f\] is

the filtration coefficient (= 12.5 mL/min/mmHg). If the GRF is

200.0 L/day, the NFP can be easily calculated by rearranging the

equation for GFR, and by converting GFR from L/day to mL/min.

First we convert the GFR into mL/min:

Next, we calculate the NFP:

By changing the values for GFR and NFP, an instructor can challenge

students to see what would happen in cases of hypertension, and

what effects this might have on the kidneys and the rest of the

body. Problems such as these may help students appreciate just how

incredible humans are as engineering marvels.

Mathematical Applications in General Biology

Mathematics can be integrated into lessons addressing even the most

basic of biological concepts. During lessons on cell structure,

students learn about the cell membrane\'s electrical potential, and

how the inside of a cell differs compared to the outside. This

trans-membrane potential can seem quite abstract to beginning

students of biology. Let us consider that the internal voltage of a

cell is 70.0 mV with respect to the extracellular space. Students

may grapple with this idea, especially when you consider that the

trans-membrane potential is established by the intracellular and

extracellular concentrations of primarily two positive ions

(potassium and sodium). After all, one might ask, how could two

positives produce a negative? If an analogy with money is used,

something abstract can be transformed into something real. To

explain a negative trans-membrane potential created by

concentrations of positive ions, try the following:

Select two students, and hypothetically give each a sum of

money. Perhaps give Student \"A\" \$30 and Student \"B\" \$100.

Further explain that, since each student has a sum of money,

neither is in debt, or in the \"red\" or in a \"negative position/\'

Yet, Student A has less money compared to Student B. In other

words, Student A sees herself/himself in a negative situation in

comparison to Student B. Once students grasp this idea, it is

easy to make the transition from dollars to ions. Sure, both

sides of the cell membrane are positive, but the inside is less

positive compared to the outside.

This analogy usually gets the idea across, and I have yet to

encounter a student who did not understand money! Depending on your

student audience, you could go further and begin to discuss more

complex mathematical applications involving the cell membrane, such

as the use of Markov models to predict trans-membrane protein

topologies (Russo, 2003).

In the General Biology course offered at Kingsborough Community

College, a series of laboratory experiences allows students to

explore terrestrial adaptations in organisms to physical

parameters, such as temperature and water availability. One of the

physical parameters studied is gravity and its effects on plants

and animals. During the course of the exercise, gravity and

gravitational forces are defined both in words and through

mathematical equations (Gemmell et. al, 1996). The acceleration due

to gravity on a planet\'s surface is given by the planet\'s mass and

radius. If:

\* m = the mass of a body

\* g\[p\] = the surface gravity on a planet (i.e. the gravitational

force)

Then: The force acting on the body, weight, is defined as

In addition, if:

M\[p\] the mass of a planet (where p = planet)

R\[P\] the radius of the planet

G the universal constant of gravitation = 6.7 × 10\^ -8 dyne cm/gm\^2

Then the gravitational force the planet exerts is gp, and is given

by:

For Earth, we can say:

Where \"E\" = Earth. Values of g\[p\] may be related to the Earth\'s

surface gravity by letting g\[E\] = 1.0 for Earth. Then Equation 3

above becomes:

Solving for G we get:

If we substitute the value for G in Equation 4 into Equation 2, we

get:

Therefore, if we know a planet\'s mass (M\[p\]) and size (radius =

R\[p\]), and the Earth\'s mass (M\[E\]) and size (radius = R\[E\]), then

we can calculate its surface gravity in terms of Earth\'s surface

gravity.

Once this foundation is established, thought-provoking questions

may be posed.

For example, the radius of the Earth is 6.38 × 10\^8 cm, and the

mass of the Earth is 5.98 × 10\^27gm. What is the acceleration due

to gravity on Earth? A simple substitution gives:

or, the familiar value of 980 cm/s\^2.

Probing further, the instructor could ask, \"How might this change

on a larger, or smaller planet? What effect would it have on the

organisms on such planets?\" These and other questions encourage

students to think about how increased or decreased gravitational

forces would affect the organisms living in such an environment, or

even in an aquatic environment. Would they be tall, short, large,

or small? Why? By bridging mathematics with biology in this way,

students are afforded an opportunity to explore the possibilities

of life on other worlds.

A common application of mathematics to general biology and genetics

worth mentioning is the Hardy-Weinberg Equilibrium. This algebraic

tool, useful for predicting traits in successful generations of

populations, has previously been discussed in the literature (Ortiz

et.al., 2000; Winterer, 2001). It makes use of algebra and

arithmetic to analyze population genetics problems, and challenges

students to apply mathematical skills to biology.

Mathematical Applications in Marine Biology

Marine biology is offered to biology majors and marine biology

students as part of their requirements in pursuit of an Associate

in Science degree. The course includes a broad range of topics in

marine biology, including marine environments (coastal, estuaries,

reefs, benthos, pelagic), marine organisms (bacteria, protistans,

fungi, plants, animals), and human interactions with marine

environments (pollution, mining, aquaculture). Part of the

laboratory work in this course includes water sampling and testing,

and collection and identification of marine organisms. The optimal

time of day for performing these activities is during low tide when

many organisms are more easily land accessible. In lecture,

students must do tide calculations so they can plan for ideal

intertidal conditions for conducting collections and

experimentation.

To help assess whether students have grasped the concept of tidal

changes, tide calculations are included in their examinations.

Sample questions may be as follows:

1\. If the tide is high at 11:00 AM, at what time will the next low

tide occur?

2\. If the tide is high today at 10:00 AM, and you would like to

collect and test water samples, at what times tomorrow will the

tide be low for optimal access?

In the New York metropolitan area, there are two high tides per

day, with high tide occurring approximately one hour later each

day (Sumich, 1996) Given this, and the information in the

previous quiz questions: the answer to Problem 1 would be about

5:00 PM that day, and the answers to Problem 2 would be about

4:00 AM and 5:00 PM. If students were planning to test water,

they may opt for the second high tide of the day

Another area in marine biology where calculations may be

incorporated is in water composition. For example:

If the salinity of a seawater sample was 3.2%, how would this value

be expressed in parts per thousand (ppt)?

A simple proportion will aid in finding the missing value, as

follows:

Cross-multiplying we get:

And, solving for N we get:

These calculations are simple, yet very practical for successfully

completing laboratory and fieldwork.

Discussion

Bioinformatics, the application of computer science, mathematics,

and statistics to manipulate biological data, is an emerging field

that includes data storage and retrieval, computational testing of

biological hypotheses, and brings together tools and methods to

analyze very large amounts of noisy data (Bloom, 2001; Heath &

Ramakrishnan, 2002; Onellette, 2003). Bioinformatics involves basic

molecular biology and biochemistry combined with training in

mathematics and computer engineering and science. The demand for

bioinformaticians has outpaced the supply as many colleges and

universities have not yet developed undergraduate and graduate

programs to meet this demand (Hughley & Karplus, 2003; Fischer,

2001). At the University of California at Santa Cruz, course

requirements for a degree in bioinformatics include biochemistry,

cell biology, inorganic and organic chemistry, and calculus (four

semesters), engineering and discrete mathematics, and statistics.

The curriculum integrates mathematics, biology, and engineering to

train students for success in this highly interdisciplinary field.

It is worth noting the importance mathematics plays in

bioinformatics. What better incentive could there be for

incorporating mathematical applications into biology courses than

to adequately prepare our students for careers in emerging

scientific fields such as bioinformatics, genomics, and proteomics?

The focus of a 2003 workshop sponsored by the National Institutes

of Health and the National Science Foundation was the establishment

of stronger links between mathematics and biology. The workshops

sought to integrate both fields by finding mathematical techniques

to solve biological problems. Several promising application areas

were presented:

\* forecasting the effects of global climate change

\* evaluating movements of agricultural pests

\* calculating marine reserves parameters needed to sustain fish

populations

\* calculating the spreading of alleles from genetically modified

organisms to natural ones

\* understanding the dynamics of infectious disease outbreaks.

Solving biological problems such as these will depend on advanced

mathematical techniques. How will the students of today solve the

biological problems of tomorrow if they have not been provided with

a basic biomathematical foundation on which to build (Hastings &

Palmer, 2003) ?

The importance of integrating mathematics with biology increases

over time. As the biology curriculum changes to keep pace with

technological advances, so must the ways the material is presented.

The examples provided here are meant to serve as a springboard from

which each reader may go forward and expand upon. By incorporating

these approaches to problem solving, critical thinking skills are

enhanced. The instructor can develop a pool of questions that,

along with reinforcement of mathematical applications to problem

solving, will improve scientific literacy. By promoting

mathematical understanding we enrich and improve understanding of

biological phenomena and, in general, the biological sciences.

Mathematics is a forgotten tool that we should use. A little

creativity can go a long way, and the pay-off will be a boon of

well-prepared biologists in the years to come.

Acknowledgments

I thank my students and colleagues for their input and comments

relating to this work, and my family and friends for their unending

support.

References

1\. Bloom M. 2001. Biology in silico: The bioinformatics

revolution. The American Biology Teacher. 63(6): 397-403.

2\. Fischer J. 2001. Managing the unmanageable. ASEE Prism. 11(4):

18-23.

3\. Gemmell D.J., Lanzetta P., Muzio J.N., Ortiz M.T., Pilchman P.,

Sarinsky G., Stavroulakis A.M., Taras L. 1996. General Biology

II Laboratory Manual, Revised Edition. New York: McGraw-Hill,

Inc.

4\. Guyton A.C. 1976. Textbook Of Medical Physiology, Fifth

Edition. Philadelphia: W.B. Saunders Company.

5\. Hastings A., Palmer M.A. 2003. A bright future for biologists

and mathematicians. Science. 299: 2003-2004.

6\. Heath L.S., Ramakrishnan N. 2002. The emerging landscape of

bioinformatics software systems. Computer. 35(7): 41-45.

7\. Hughley R., Karplus K. 2003. Bioinformatics: A new field in

engineering education. Journal of Engineering Education. 92(1):

101-104.

8\. Onellette J. 2003. Switching from physics to biology. The

Industrial Physicist. May-June: 20-23.

9\. Ortiz M.T., Taras L., Stavroulakis A.M. 2000. The

Hardy-Weinberg Equilibrium-some helpful suggestions. The

American Biology Teacher. 62(1): 20-22.

10\. Russo E. 2003. Transmembrane potential. The Scientist. 17(3): 34.

11\. Saladin K. S. 2001. Anatomy & Physiology: The Unity Of Form And

Function, Second Edition. Boston: McGraw Hill.

12\. Sumich J. L. 1996. An Introduction to the Biology of Marine

Life, Sixth Edition. Dubuque, IA: Wm. C. Brown Publishers.

13\. Surridge C. Senior Editor 2002. Nature insight computational

biology. Nature. 420: 205 ff.

14\. Winterer J. 2001. A lab exercise explaining Hardy-Weinberg

Equilibrium and evolution effectively. The American Biology

Teacher. 63(9): 678-687.

Appendix 1

\* The Human Anatomy & Physiology course at Kingsborough Community

College is now two semesters; the course content remains the same.

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

From: []{#FrankForman2 .anchor}Premise Checker
\[mailto:checker@panix.com\]

Sent: Saturday, December 23, 2006 8:39 PM

To: National Math Panel

Cc: Ginsburg, Alan; De Kanter, Adriana; Jensen, Sarah; Thomson, Kenneth

Subject: Frank H. Heppner, Karen R. Kouttab, William Croasdale: Inquiry:

Does it Favor the Prepared Mind? (with reply and response)

This does not deal explicitly with math education, but the arguments

about \"inquiry\" vs. traditional methods of instruction go over into

math education as well. It\'s good to have a discussion, rather than

just pronouncements of one point of view. So I pass it on to the Panel

for their consideration.

\[I found this grazing the web. First, there was an article linked by

Arts & Letters Daily, http://aldaily.com, a splendid service now run

by the Chronicle of Higher Education that I check regularly. The

linked article was about critical thinking and came from Skeptical

Inquirer. One of its references was to Johnson, Mathew, and Massimo

Pigliucci (2004), \"Is knowledge of science associated with higher

skepticism of pseudoscientific claims?\" The American Biology Teacher

66(8): 536-548. The answer is that the association is all too weak,

when it does exist. Finding that article led me to other articles in

The American Biology Teacher and what you see below. Serendipity

strikes!\]

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

Frank H. Heppner, Karen R. Kouttab, William Croasdale: Inquiry: Does

it Favor the Prepared Mind?

The American Biology Teacher

Volume 68, Issue 7 (September 2006), pp. 390-392

\[reply and response included.\]

A. Department of Biological Sciences, University of Rhode Island,

Kingston, RI 02881, B. North Kingston High School, North Kingston,

RI 02852, C. Department of Education, University of Rhode Island,

Kingston, RI 02881, E-mail: birdman@uriedu

\"Inquiry,\" a loosely-defined constellation of constructivist

teaching methods, has in recent years become the best-practice

science teaching method of choice for providing students with the

means to develop higher order thinking skills while simultaneously

acquiring scientific concepts (Haury, 1993). Inquiry is typically

contrasted with \"direct instruction,\" exemplified by the

traditional college lecture. The National Science Foundation offers

strong support for inquiry-based education: from 2000-2003, 279

funded projects in the Division of Undergraduate Education had the

word \"inquiry\" in their title or abstract. Inquiry instruction is

the benchmark for science teaching in the National Science

Education Standards (National Research Council, 1996). Inquiry has

strong advocates (Handelsman, et al., 2004) who argue that the jury

has essentially returned a favorable verdict on inquiry\'s

superiority to \"traditional, passive methods,\" and that inquiry

needs to become standard practice in college science teaching.

However, little attention has been paid to the role of intellectual

development in students\' capacity to learn profitably in an inquiry

environment. The practical difficulties of inquiry instruction,

especially in elementary and secondary school science, have been

pointed out (Costenson & Lawson, 1986), and we believe that many of

the research studies supporting the effectiveness of inquiry,

especially early ones, do not meet contemporary standards of rigor.

Recently, a contrarian view has been presented that suggests that

at least in some circumstances, direct instruction may be more

effective than inquiry learning in science instruction (Klahr &

Nigam, 2004). We suggest that before American science education

accepts inquiry without further question as a universal teaching

method, it be subject to the same kind of examination that should

perhaps have been given to \"New Math,\" programmed instruction, and

the first generation of \"multi-media.\"

A number of research articles published between 1975-2004 featured

qualitative descriptions or discussions of inquiry practices

(Leonard, 1983; Windschitl & Buttemer, 2000). A few articles

provided quantitative evidence generally in favor of inquiry

(McKinnon & Renner, 1971; Schneider & Renner, 1980), but others

reported no appreciable or significant differences in academic

achievement among the groups compared (Cavallo, 1994; Lunsford &

Herzog, 1997). There is the possibility that some of the success

reported for inquiry methods might have been due to expectancy

phenomena, such as the \"Hawthorne Effect\" (Mayo, 1933), where the

attention paid to the subjects in a performance experiment may

produce the favorable effect noted.

If the academic abilities and skills of the students were not

established through any pretest before the comparison study was

begun, then actual measurements remain as cross-sectional

comparisons only and may reflect improvements students would have

acquired as they matured during the course. Some studies were brief

one-time, one-semester investigations involving small groups of

students (Lock, 1992; Graybill, 1975), sometimes in as few as one

or two classrooms (Tamir & Jungwirth, 1975; Germann, 1989). Does

inquiry-oriented teaching provide students with long-term benefits?

We do not know; the initial research did not follow the progress of

these students into other high school or college courses to

determine if any skills acquired during inquiry instruction

persisted or were used in other subjects.

Inquiry instruction is not new to education theorists or

instructors; in one form or another inquiry learning has been a

focus of pedagogical interest and practice since the turn of the

20th century when Dewey (1944) first emphasized learning through

hands-on practice. Dewey wanted students to become more involved in

their own learning and felt they would pursue multiple areas of

study organized around a central theme if the question the students

chose to solve was of interest to them.

Dewey felt that \"the engaged learner\" would acquire both knowledge

and skills by becoming more involved in his or her own education.

The hypotheses Dewey proposed intrigued many who wanted to move

away from the very basic practice and memorization methods used in

most schools at that time. Various reform movements of the 20th

century would later alternate between an emphasis on skill versus

content.

After the publication of A Nation at Risk, (United States

Department of Education, 1983) another reform movement began that

again emphasized inquiry-centered instruction in the classroom.

Curriculum once more was modified, this time to incorporate more

\"hands-on\" manipulative experiences for students both in the

laboratory setting and in the general classroom (Moreno, 1999). The

term \"inquiry\" began to be used to describe several instructional

methods that could be described as \"student-centered.\" Inquiry

instruction started to require more involvement or active learning

on the part of students and less focus on the teacher\'s direction

and presentation of material.

As additional instructors began to modify instruction to

incorporate inquiry methods, concerns appeared as both students and

teachers attempted to shift their focus from scientific concepts to

scientific process. Teachers reported that inquiry instruction

required additional time and materials to develop, and took

additional time and effort from students (Moss, 1997).

Intellectual Development & Inquiry Return to TOC

Piaget (1964) developed a scheme of intellectual development in

children wherein higher order thinking develops in a series of

demarcated stages. Piaget\'s scheme essentially stopped at

mid-adolescence. Perry (1999) in the 50s and 60s extended Piaget\'s

concept of a staged intellectual development through the college

years into adulthood. In both schemes, an individual at a

particular stage has a characteristic epistemology, and that

epistemology affects how the student views the nature of knowledge,

its acquisition, and the roles of teacher and student. Both schemes

posit that if knowledge is presented to a student in a way that is

not consonant with his/her current epistemology, a variety of

unproductive reactions can result, from confusion to rebellion.

Many of the adverse reactions to inquiry sometimes reported in

inquiry studies are consonant with students at a stage of

intellectual development where they cannot yet recognize that

knowledge is tentative, and that the role of the teacher is as a

guide, rather than transmitter of received wisdom. A student at an

early developmental stage (which might include many students in

high school or earlier, and possibly many college freshmen) might

well react to inquiry teaching with feelings of insecurity and seek

additional guidance/direction from teachers, which in inquiry

teaching might not be forthcoming. Lawson and Johnson\'s (2002)

finding that neo-Piagetian developmental level predicted success in

both inquiry and expository teaching methods in biology suggests

that consideration of developmental level may be important in

evaluating the results of tests on the effectiveness of inquiry.

If the purpose of science education is only to prepare students to

become future scientists, and it is assumed that these students are

in a state of intellectual development appropriate to the method,

inquiry is probably the ideal teaching method. It is an approach

that likely would have had the most appeal to science teachers when

they were themselves students. If, however, science education\'s

goals include an increase in science literacy among the general

public, and creating a favorable impression of science among that

group, universal adoption of inquiry to teach students who are not

yet ready to receive its benefits may well have a paradoxical

effect, and produce results opposite to those intended.

Before consigning \"conventional\" direct-instruction science

teaching to the dustbin, we ask if the real problem with the

lecture as a teaching technique is a boring lecturer rather than

lecturing itself, or the problem with a \"cook-book\" lab is the

recipes in the book.

References Return to TOC

1\. Cavallo A.M.L. 1994. Do females learn about biological topics

by rote more than males? The American Biology Teacher.

56:348-352.

2\. Costenson K., Lawson A.E. 1986. Why isn\'t inquiry used in more

classrooms? The American Biology Teacher. 48:150-158.

3\. Dewey J. 1944. Democracy and Education: An Introduction to the

Philosophy of Education. New York, NY: The Free Press, Division

of Simon and Schuster Inc.

4\. Germann P.J. 1989. Directed-inquiry approach to learning

science process skills: Treatment effects and

aptitude-treatment interactions. Journal of Research in Science

Teaching. 26:237-250.

5\. Graybill L. 1975. Sex differences in problem solving ability.

Journal of Research in Science Teaching. 12:341-346.

6\. Handelsman J., Ebert-May D., Beichner R., Bruns P., Chang A.,

DeHaan R., Gentile J., Lauffer S., Stewart J., Tilghman S.M.,

Wood W.B. 2004. Scientific teaching. Science. 304:521-522.

7\. Haury D.L. 1993. Teaching Science through Inquiry. Available

online at:

http://www.eric.ed.gov/ERICWebPortal/Home.portal?\_nfpb=true&rERICExtSearch_SearchValue_0=Haury+Inquiry&rERICExtSearch_SearchType_0=kw&r_pageLabel=RecordDetails&robjectId=0900000b801b4a85&raccno=ED359048.

8\. Klahr D., Nigam M. 2004. The equivalence of learning paths in

early science instruction: Effects of direct instruction and

discovery learning. Psychological Science. 15:661-667.

9\. Lawson A.E., Johnson M.A. 2002. The validity of Kolb learning

styles and Neo-Piagetian developmental levels in college

biology. Studies in Higher Education. 27:79-90.

10\. Leonard W.H. 1983. An experimental study of a BSCS-style

laboratory approach for university general biology. Journal of

Research in Science Teaching. 20:807-813.

11\. Lock R. 1992. Gender and practical skill performance. Journal

of Research in Science Teaching. 29:227-241.

12\. Lunsford B.E., Herzog M.J.R. 1997. Active learning in anatomy

and physiology: Student reactions and outcomes in a

nontraditional Anatomy and Physiology course. The American

Biology Teacher. 59:80-84.

13\. Mayo E. 1933. Human Problems of an Industrial Civilization. New

York, NY: Macmillan.

14\. McKinnon J.W., Renner J.W. 1971. Are colleges concerned with

intellectual development? American Institute of Physics.

39:1047-1052.

15\. Moreno N. P. 1999. K-12 Science education reform: A primer for

scientists. BioScience. 49:569-576.

16\. Moss R. 1997. A discovery laboratory for studying gene

regulation. The American Biology Teacher. 59:522-526.

17\. National Research Council. 1996. National Science Education

Standards. Washington, DC: National Academy Press.

18\. Perry W.G. 1999. Forms of Ethical and Intellectual Development

in the College Years: A Scheme. San Francisco, CA: Jossey-Bass.

19\. Piaget J. 1964. Part 1: Cognitive development in children:

Development and learning. Journal of Research in Science

Teaching. 2:176-186.

20\. Schneider L.S., Renner J.W. 1980. Concrete and formal teaching.

Journal of Research in Science Teaching. 17:503-518.

21\. Tamir P., Jungwirth E. 1975. Students\' growth as a result of

studying BSCS biology for several years. Journal of Research in

Science Teaching. 12:263-279.

22\. Windschitl M., Buttemer H. 2000. What should the inquiry

experience be for the learner? The American Biology Teacher.

62:346-350.

23\. United States Department of Education, National Commission on

Excellence in Education. 1983. A Nation at Riske. Washington,

DC\.

++++++++++++++++=

Rodger W. Bybee: How Inquiry Could Contribute to the Prepared Mind

The American Biology Teacher

Volume 68, Issue 8 (October 2006), pp. 454-457

BSCS, Colorado Springs, CO 80918

The editorial \"Inquiry: Does It Favor the Prepared Mind?\" (Heppner,

Kouttab & Croasdale; September, 2006) argued that inquiry teaching

strategies are ineffective because students are not developmentally

prepared for such educational approaches. The authors suggest that

the research base for inquiry is inadequate and they propose that

direct instruction is the viable alternative. They make the latter

recommendation based on the research of David Klahr and Milena

Nigam (2004). On balance, I found the editorial disconcerting. My

concern is not based on the weakly supported criticism of inquiry

as much as the authors\' failure to construct more than they

criticize. What does favor the prepared mind? Can the authors make

the case that direct instruction favors the prepared mind?

In this brief essay, I will present an alternative by proposing

inquiry-oriented strategies that could contribute to the prepared

mind. I begin with a definition.

Inquiry as presented in science education has several different and

quite distinctive meanings. Beginning with a definition that I

developed using a common dictionary form will help set the

parameters for further discussion.

In.quir.y (In\' kwir\' e) n., pl. ies. 1. An outcome of science

teaching that is characterized by knowledge and understanding of

the processes and methods of science. 2. Outcomes of science

teaching that refer to specific skills and abilities integral to

the processes and methods of science. 3. The instructional

strategies used to achieve students\' knowledge and understanding

of science concepts,principles, and facts and/or the outcomes

described in the aforementioned definitions 1 and 2.

This short statement differentiates between inquiry as teaching

strategies and inquiry as outcomes of science teaching. The

National Science Education Standards (NRC, 1996), for example,

includes inquiry as both content outcomes and teaching strategies.

My discussion here centers on instructional approaches that science

teachers may use to achieve students\' knowledge of science

concepts, an understanding of inquiry, and develop abilities

associated with inquiry. This is how inquiry could contribute to

the prepared mind.

Historically, there always have been individuals and groups

advocating different strategies for teaching science. On one end of

a continuum is direct instruction. Lecture serves as the example of

this teaching method. At the other end of this continuum is full,

unguided inquiry. The extreme position in this view is that

students must discover scientific knowledge themselves without any

guidance from the teacher. In reality, most science teaching is

probably somewhere in the middle of the continuum. Effective

science teaching embodies a variety of strategies and methods. One

difficulty, however, is that terms such as \"direct instruction\" and

\"inquiry learning\" often are argued from either/or positions. This

was the case in the Heppner et al. editorial when the authors

caution against science educators accepting inquiry, without

further question, as a universal teaching method.

Research headed by David Klahr has stimulated review and discussion

of the relative importance of direct instruction and inquiry

learning (Klahr has used the term \"discovery learning\") as

instructional approaches to science teaching (Chen & Klahr, 1999;

Klahr, Chen & Toth, 2001; Klahr & Li, 2005; Klahr & Nigam, 2004).

In a 1999 study, Chen and Klahr investigated an important aspect of

scientific reasoning. They asked the question: What is the

effectiveness of different instructional strategies in children\'s

acquisition of the domain-general strategy, Control of Variables

Strategy (CVS). They had children ages 7-to 10-years-old design and

evaluate experiments after direct instruction about CVS and without

direct instruction, i.e., inquiry learning in the extreme, unguided

form. They reported that with direct instruction children did learn

and could transfer the basic strategy for designing unconfounded

experiments, that is, they could apply CVS (Chen & Klahr, 1999).

Before continuing this discussion of Klahr\'s research I will

introduce a report on the use of the laboratory in high school

science. I later return to Klahr\'s research.

Recently the National Research Council published America\'s Lab

Report: Investigations in High School Science (NRC, 2006). The NRC

proposed the phrase \"integrated instructional units\" to describe

the design of instructional units that carefully combine laboratory

experiences with other types of teaching strategies, including

lectures, reading, and discussion. Research indicates that

integrated instructional units increase students\' mastery of

subject matter compared with other modes of instruction, and, very

importantly, these units aid the development of more sophisticated

aspects of scientific reasoning, increase students\' interest in

science, and somewhat improve students\' understanding of the nature

of science when this goal is explicitly targeted (NCR, 2006, p.

100). All of these are valued goals of science education. Upon

reading this, I immediately made several connections. First,

integrated instructional units had the design features of the SCIS

learning cycle and the BSCS 5E Instructional Model Second,

integrated instructional units were neither exclusively \"direct

instruction\" but may include direct instruction, nor were they

unguided inquiry, but they could include activities and strategies

embodying the essential features of guided inquiry (NRC, 2000).

Third, both the NRC report and David Klahr\'s research claimed

support for their respective strategies as being effective for the

development of some aspects of scientific reasoning, which is a

critical outcome of inquiry-based instruction.

The research methodology used by Klahr and his colleagues actually

paralleled that of an instructional model or an integrated

instructional unit. Although evident in the articles, Klahr and

colleagues concluded that direct instruction was the critical

strategy. The following quotes are from the methodological section

in one of the key articles cited in the direct instruction versus

inquiry learning debate (Chen & Klahr, 1999). The entire

methodology could well be described as an integrated instructional

unit that centers on students learning the key concepts of Control

of Variables Strategy.

The present study consisted of two parts. Part I included

hands-on design of experiments. Children were asked to set up

experimental apparatus so as to test the possible effects of

different variables. The hands-on study was further divided into

four phases. In Phase I, children were presented with materials

in a source domain in which they performed an initial

exploration followed by (for some groups) training. Then they

were assessed in the same domain in Phase 2. In Phases 3 and 4,

children were presented with problems in two additional domains

(Transfer-1 and Transfer-2). Part II was a paper-and-pencil

posttest given two months after Part I. The posttest examined

children\'s ability to transfer the strategy to remote

situations.Chen & Klahr, 1999, p. 4

Dave Klahr and his colleagues present a very well-designed study

that, in my view, most likely used an integrated instructional

approach that closely resembles the BSCS 5E Instructional Model.

With an engagement based on the orientation and hands-on in

introduction to materials, the researchers had the students

continue with an exploration, proceed to an explanation and

demonstration of CVS, and then had the students apply or elaborate

CVS to new situations for which they used the terms assessment and

Transfer-1 and -2.

One could reasonably argue that the research methods employed by

Klahr and his colleagues used instructional sequences that

integrated different strategies but then isolated one strategy,

direct instruction, as the key factor in learning. Others have

generalized these results to claim that direct instruction is the

best way to teach the processes and methods of science and, in the

extreme, all of science. (Adelson, 2004; Cavanagh, 2004; Begley,

2004a, b). Such extreme generalizations based on the methodology

and data of the Klahr studies, in my view, extend beyond the

reasonable limits of the studies. However, the research does

provide insights that may help answer questions about effective

instructional strategies that could be identified as

inquiry-oriented.

How does inquiry-based instruction contribute to the prepared mind?

This, it seems to me, is a reasonable and appropriate question.

Answering the question may advance our understanding of the form

and function of inquiry in science education. Based on recent

reports from the National Research Council (NRC, 1999, 2005, 2006),

I argue that using an integrated instructional sequence that

incorporates varied teaching methods holds the key to a reasonable

and appropriate inquiry-oriented approach that contributes to a

prepared mind.

The design of integrated instructional units requires the careful

selection of activities on the basis of research-based ideas likely

to enhance learning. Laboratory and other experiences are

explicitly linked. As I mentioned earlier, the learning cycle or

the BSCS 5E Instructional Model both meet the design criteria for

integrated instructional units. The strategies used in such units

may include direct instruction, discrepant events, laboratories,

discussions, demonstrations, readings, debates, virtual field

trips, and other activities and methods common to curriculum and

instruction in science.

Table 1 presents linkages among the research of Klahr, the BSCS 5E

Instructional Model, and the essential features of inquiry as

described in the National Research Council report Inquiry and the

National Science Education Standards (NRC, 2000).

Table 1.

Linking Research, Instruction & Inquiry

In conclusion, I have tried to bring some clarity to the term

inquiry as it applies to school science programs and the

preparation of young minds. First, teaching science as inquiry

includes understanding scientific inquiry and developing the

cognitive abilities associated with the processes and methods of

science. Second, inquiry can refer to an integrated and linked

instructional sequence designed with the intention of helping

students learn science concepts, as well as understanding inquiry

and developing cognitive abilities aligned with inquiry. It is past

time to move beyond the old either/or arguments of inquiry vs.

direct instruction. Science teachers have always used multiple

strategies, so we need not make a decision about the one best

strategy for teaching science. There isn\'t one, there are many

strategies that can be applied to achieve different outcomes.

Science teachers should try to sequence them in coherent and

focused ways. This is how inquiry can contribute to the prepared

mind.

References

1\. Adelson R. 2004. Instruction versus exploration in science

learning: Recent psychological research calls \"discovery

learning\" into question. Monitor. On Psychology. 35(6): 34.

2\. Begley S. 2004a, 10 December. The best ways to make

schoolchildren learn? We just don\'t know. Wall Street Journal.

pp B1.

3\. Begley S. 2004b, 17 December. To improve education, we need

clinical trials to show what works. Wall Street Journal. pp B1.

4\. Cavanagh S. 2004. NCLB could alter science teaching. Education

Week. 24(11): 1 12-13.

5\. Chen Z., Klahr D. 1999. All other things being equal:

Acquisition and transfer of the control of variables strategy.

Child Development. 70(5): 1098-1120.

6\. Klahr D., Chen Z., Toth E. 2001. Cognitive development and

science education: Ships that pass in the night on beacons of

mutual illumination? In Klahr D., Carver S. Cognition and

Instruction: 25 Years of Progress. Mohwak, NJ: Erlbaum.

7\. Klahr D., Nigam M. 2004. The equivalence of learning paths in

early science instruction: Effects of direct instruction and

discovery learning. Psychological Science. 15(10): 661-667.

8\. Klahr D., Li J. June 2005. Cognitive research and elementary

science instruction: From laboratory, to the classroom, and

back. Journal of Science Education and Technology. Vol. 14(No.

2):

9\. National Research Council 1996. National Science Education

Standards. Washington, DC: The National Academy Press.

10\. National Research Council 2000. Inquiry and the National

Science Education Standards: A Guide for Teaching and Learning.

Washington, DC: The National Academy Press.

11\. National Research Council 2006. America\'s Lab Report:

Investigations in High School Science. Washington, DC: The

National Academy Press.

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

Frank Heppner, Karen Kouttab, William Croasdale: Response

The American Biology Teacher

Volume 68, Issue 8 (October 2006), pp. 457-457

Our intent in this editorial was to provoke discussion on four

points: 1. \"Inquiry\" is the dominant paradigm for the science

education establishment today, but this one-size-fits-all approach

may not produce beneficial results in all situations. 2. \"Inquiry\"

has been so broadly defined that it is difficult to predict its

usefulness in a given case because different research-based studies

may have been testing different phenomena. 3. Where studies have

shown less-than-stellar results for inquiry, developmental factors

may have been a determining factor; intellectual development has

been understudied in the applicability of inquiry. A study on

effectiveness of teaching methods for college juniors may not have

great utility in predicting its value for 4th graders and

vice-versa. 4. In enthusiasm for inquiry as the most effective

approach to teaching science both to prospective scientists and the

general student population, there has been general disregard for

the outstanding success of traditional methods in producing the

large generation of very capable and imaginative scientists who

grew up in the \'50s through the \'70s, most of whom learned their

science from didactic sages-on-a-stage, some inspiring, most not.

In his very thoroughly prepared response, Bybee does a better job

than we did of documenting the wide variety of ideas that have

appeared under the blanket term \"inquiry.\" However, by including so

many approaches under the heading inquiry, the word becomes almost

synonymous with \"education,\" and any argument over the superiority

of inquiry versus direct instruction or vice versa becomes moot.

For example, he proposes that the following quality be included as

part of the definition of inquiry, \"\... inquiry includes

understanding scientific inquiry and developing the cognitive

abilities associated with the processes and methods of science.\" A

good conventional science lecturer using Socratic teaching methods

can accomplish this, too.

We did not argue, as Bybee suggests, that inquiry strategies are

ineffective because students are not developmentally prepared. To

the contrary, we proposed that in studies where inquiry showed no

clear edge over conventional teaching, these results may have been

due to developmental factors, rather than a problem with inquiry

itself. Further, we did not suggest that direct instruction is the

viable alternative to inquiry. Rather, we posited that good direct

instruction may be more effective than mediocre inquiry activities

in a given population.

We are not inquiry opponents, and we do not believe our piece

suggests this. In our collective 80 years of teaching high school

and college science, we have regularly used (and still use) inquiry

activities. However, we have discovered that inquiry does not

produce positive results for all students all the time, and the

teaching approach has to be tailored to the characteristics of the

intended audience. One of our goals in offering this editorial was

to suggest that in some circumstances, a good, well-prepared (and

perhaps even inspiring) lecturer can be just as effective (or more

so) as a pre-packaged inquiry activity in helping students

understand the process of science, and to force all science teaching
into the inquiry mold may well be counterproductive in specific cases.

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

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

[]{#JoanCotter2 .anchor}

\-\-\-\--Original Message\-\-\-\--\
From: Joan Cotter\
Sent: Monday, December 18, 2006 10:14 PM\
To: National Math Panel\
Subject: Comments to NMP

Dear Jennifer:

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

·       Focus Area: Learning processes

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

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

Group in Fives and Tens.

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

Avoid Counting for Adding and Subtracting.

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

Name Numbers Explicitly.

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

Teach the Thousands in First Grade.

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

Use Correct Vocabulary.

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

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

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

Who\'s Teaching the Math?

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

Joan A. Cotter, Ph.D.

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#CarolineKoepp .anchor}gentlemill@aol.com
\[mailto:gentlemill@aol.com\]\
**Sent:** Saturday, December 16, 2006 12:59 PM\
**To:** National Math Panel\
**Subject:** comments

Dr. Larry R. Faulkner,

 

I am a parent of two students.  One is a graduate and one is still a
student of District 196, comprising the Rosemount-Apple Valley- Eagan
area in Minnesota.

 

I am an engineer and fully realize the importance of mathematics and
sciences courses and comprehension.  I hope that your panel can find
ways which can convey to the rest of our nation the importance these
academic subjects have to our well-being as individuals and as a nation.

 

The most troubling issue in the education system is the lack of
competency of a teacher in subject matter.  Once we achieve that,
excellence will be easier to reach.  There is one instructor who is not
only competent in his subject material, but has achieved the level of
instruction excellence.

 

The purpose of my communication with you is to inform you of a specific
mathematics teacher at Apple Valley High School.  He is Barry Gimpel. 
Mr. Gimpel is as perfect a math instructor as is humanly possible.  He
really cares about the subject he teaches and he cares that his students
not only do well in his classes, but that they truly understand the
subject material.  He is organized.  Every day he has his materials
ready:  overheads, lecture, class participation, assignments.  And he
has each day structured so he does not waste class time.  He has each of
his lectures recorded on video so that if a student is absent, the child
can borrow the video and not miss anything!  He maintains order in his
classroom; the students respect him.  And part of the reason why he
gains that respect is because of his sense of humor; it\'s just right. 
He willingly offers his out-of-class time for students struggling.  He
believes that feedback should be as immediate as possible:  most test
scores are posted on the school\'s \"parent portal\" website the same
day, and if he needs more time, never later than the next day.  He even
emails scores to the parents who provide email addresses.  He realizes
the importance of the involvement of the family.

 

The man is amazing.  I couldn\'t have hoped for a better math instructor
for my children.  Unfortunately, there aren\'t enough teachers like him
and my children have not been \"lucky\" enough to have the same caliber
of instruction for all of their math classes.  It would be wonderful for
all children, parents, and the nation if your panel could raise the bar.

 

Thank-you for your consideration,

Caroline Koepp, P.E.

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

Subject: Metric Education in the Classroom

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

hear Chemistry teachers talk about how much time they waste teaching

metric because it is not taught in the early years.

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

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

K-8. and

That Colleges of Education at our Universities should have somewhere in

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

all teachers should be tested on metric measurement.

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

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

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

language of measurement.

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

something about it. I hope you will.

Thanks for taking the time to read my statement.

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

Center for Science Education

![](media/image1.wmf)

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

Dear Jennifer and Tyrrell,

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

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

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

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

be inadequate for the job which needs to be done.

Sincerely,

Dick

Richard Askey

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

Frank Forman here:

Questions for the National Mathematics Advisory Panel

2006 December 3

Dear National Math Panel and Tyrrell Flawn,

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

and as a MS-Word attachment which is formatted.

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

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

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

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

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

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

prevented that. So here they are.

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

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

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

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

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

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

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

and advised me about how to do so.

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

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

ideas or clarifications, I shall provide them.

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

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

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

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

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

of usefulness.

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

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

verbose.

QUESTIONS FOR THE NATIONAL MATHEMATICS ADVISORY PANEL

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

articulate its aims and methods.

1\. The Usefulness of Mathematics

2\. The Crisis in Mathematics Education

3\. Truth to be Told to a Benevolent Despot

4\. The Structure of Educational Governance

5\. Treatment of the Gifted

6\. The Panel as a Sham

7\. Taboo Issues

Appendix 1: Charter of the National Mathematics Advisory Panel

Appendix 2: I Samuel 17

The Duchess\'s Epilogue

QUESTION 1. THE USEFULNESS OF MATHEMATICS (three articles)

ARTICLE 1. WHETHER MATHEMATICS IS USEFUL?

It would seem that mathematics is widely used.

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

who will become active scientists and engineers. Engineers use mostly

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

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

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

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

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

technical discussions about regulations if the lawyers knew basic set

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

set formulas rather than long-winded phrases.

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

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

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

politicians, preachers, and lawyers is horrendous. Deirdre McCloskey

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

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

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

Art of Cross-Examination.

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

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

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

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

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

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

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

bogus reasoning. Learning mathematics is essential to this goal.

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

It would seem that we know generally enough about the general

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

business of instilling the habits of exact reasoning that characterize

mathematics.

Objection 1. Attempts of specify more exactly just what mathematical

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

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

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

the high points, are circular and not helpful.

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

What is thinking mathematically?

\* making meaningful connections with prior mathematical experiences

and knowledge including strategies and procedures

\* creating logical pathways to solutions

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

done to proceed with an investigation

\* explaining mathematical ideas and workings.

What is reasoning mathematically?

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

use in a situation

\* developing logical pathways to solutions

\* reflecting on decisions and making appropriate changes to thinking

\* making sense of the mathematics encountered

\* engaging in mathematical conversations.

What is working mathematically?

\* sharing mathematical ideas

\* challenging and defending mathematical thinking and reasoning

\* solving problems

\* using technologies appropriately to support mathematical working

\* representing mathematical problems and solutions in different ways.

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

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

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

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

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

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

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

biological and social scientists cannot. Far transfer is about Latin

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

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

mathematics, specifically, to other fields.

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

mathematical thinking and the transfer of that thinking to other

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

dwell upon this issue of transfer.

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

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

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

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

Mathematical Thinking,\" Journal for Research in Mathematics

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

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

Furthermore, informal characterizations of how mathematicians think

can also be illuminating.

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

up in dark rooms for research reasons.

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

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

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

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

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

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

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

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

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

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

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

And this:

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

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

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

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

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

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

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

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

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

engineer just does it, kludging along; the physicist calculates

carefully and produces a carefully cooked egg; and the mathematician

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

previous problem.\"

These and many more from

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

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

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

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

think like a mathematician.

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

issue. Shifting students from useless to useful math courses will

accomplish far more than all manner of improving teaching methods for

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

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

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

ARTICLE 3. WHETHER GEOMETRY IS AT ALL USEFUL?

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

to all in evaluating arguments of all sorts.

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

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

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

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

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

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

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

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

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

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

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

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

enough for scientists and engineers simply to know various formulae,

like the Pythagorean theorem, which can be taught quickly using

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

which comes at the expense of studying probability and statistics.

Knowing how to spot bogus statistical arguments is helpful to

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

geometry.

On the contrary, teachers should continue to acquaint students with

rigorous reasoning, though not necessarily through geometry. The Panel

should ask how this acquaintance might be accomplished more

effectively and efficiently. A balance should be struck between the

conservative principle of retaining the wisdom of the past (which

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

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

cumulation of centuries of imbecilities.\"

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

mathematics. Recall the ghosts of departed quantities, abolished by

Bolzano and Cauchy (see

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

nineteenth century and reinstated rigorously by Abraham Robinson in

the 1960s.

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

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

teacher yourself, your students will discover that these opinions fall

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

judges come to opposite conclusions or issue concurring opinions? We

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

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

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

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

it).

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

comes at too high an opportunity cost of teaching probability and

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

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

more proven way to acquaint students with the method of rigorous

deductive thinking. Trigonometry has largely been eliminated as being

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

experience with the deductive method is too important to forego.

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

consists of is understood much too poorly.)

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

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

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

education problem in the country is licked!)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

articles.)

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

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

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

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

ARTICLE 2. WHETHER ANYTHING NEEDS TO BE DONE?

It would seem that the failure of schools to adequately educate

students is an urgent matter.

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

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

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

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

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

math majors at a college.

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

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

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

studying mathematics after high school. The Panel needs to clarify

just what failures need to be addressed and how.

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

work

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

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

that the public wants to protect children from their irresponsibility.

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

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

recognition of this, voters regularly elect politicians to cope with

this suboptimality by mandating forced savings for adults and

compulsory education for children.

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

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

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

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

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

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

share of political contributions from the National Trial Lawyers

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

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

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

hypothetical withdrawal of Federal funds after 2013/14.

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

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

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

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

learned everything their parents wanted them to. Certainly by the

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

mandate instruction:

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

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

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

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

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

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

learning how to learn, early on.

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

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

mathematics they come to realize they need at any time.

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

Objection 2. Businesses will not provide training, since trained

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

provided.

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

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

brain is more supple at earlier ages.

Objection 4. Workers have short planning horizons set in the

Environment of Evolutionary Adaptation (EEA), generally the Lower

Paleolithic.

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

adult education and the extent to which mathematics education should

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

to learn.\"

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

articles in the Journal for Research in Mathematics Education that I

spotted go into the matter.

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

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

bill for training.

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

not all that it is cracked up to be.

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

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

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

how big this molehill is.

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

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

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

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

depending on how they are counted

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

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

more than draw straight lines on logarithmic paper.

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

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

so much more needed as computerization of basic work through the

ability to make sophisticated new products as product cycles continue

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

will lag so far behind the trends toward computerization and global

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

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

common sense of the matter.\"

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

between requiring certain courses for all and making others available.

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

required in schools already. Furthermore, courses are indeed available

for those who want to further their mathematical learning.

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

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

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

DESPOT WHAT TO DO?

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

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

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

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

simply have different desires about what public goods they want

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

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

for too many things they don\'t want.

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

learn in mathematics that there is really no difference between the

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

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

Panel.

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

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

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

transcendental source of (absolute) morality vs. the contextualist

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

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

one takes an extreme position on these matters.

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

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

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

there are four principle philosophies of education:

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

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

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

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

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

for moral education, specifically so named. Conservatives generally

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

to mathematics, however.

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

education should be organized around specific subjects and around the

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

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

who strive to draw up curriculum standards.

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

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

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

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

liberals.

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

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

to liberals, even if they characteristically are concerned with

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

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

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

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

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

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

ultimate in free-market choice.

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

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

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

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

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

panel today without insisting that trigonometry be mandated or even

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

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

consensus will lag behind reality.

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

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

closer approximation to this reality.

Objection 2. Cultural literacy does not require much knowledge of

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

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

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

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

Dictionary of Cultural Literacy, third edition, 2002)

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

mathematical literacy can be achieved in popular culture as well as

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

be taught. General familiarity with statistics would benefit the

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

arguments. This is hardly an arbitrary claim.

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

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

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

functions, and geometric shapes (see geometry) and their

relationships. Some branches of mathematics are characterized by use

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

arithmetic, algebra, geometry, and calculus.\"

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

remember the quadratic equation! I have asked countless folks to

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

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

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

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

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

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

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

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

society, equations are absent in popular culture.

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

Universities of Paris and Oxford and was unknown to mathematicians of

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

graphs representing continuous change, but since this concept did not

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

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

the world that it seems like first nature.)

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

QUESTION 4. THE STRUCTURE OF EDUCATIONAL GOVERNANCE

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

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

longer getting all the Federal monies they would have if educational

progress is not adequate constitutes the right mix between central and

local control.

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

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

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

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

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

teachers from the educrats!

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

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

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

all Panelists are strongly urged to read.)

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

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

should be taken to allow experimentation and not punish trying out

promising practices that eventually fail. A superior form of

educational governance would view failures positively, as being

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

through Failure shows this for engineering, but it is applicable

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

network among educators as it is in achieving immediate results on

standardized tests. The plain reality is that humans communicate

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

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

empirical studies no matter how good.\^

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

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

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

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

socio-biology, whose respective paradigms of utility and fitness

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

case of Ford Motor Company using statistical analysis to defend itself

in the Pinto liability case, as deliberately including a dangerous

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

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

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

awarded huge damages to the injured.)

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

control from teachers, schools, districts, and counties and

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

standards, any previous drift toward increasing critical thinking in

the school curriculum, has been halted.

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

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

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

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

foster lateral thinking is to let teaching innovations bubble up from

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

Progress in some instances.

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

structure of educational governance, along with thinking about what

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

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

dwell upon and about which to make representations to the

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

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

irresponsibility ) or optimum = minimum (which would stifle

innovation). Indeed, establishing a learning network about successful

and unsuccessful innovations could well lead to better (though not

immediately measurable) improvements in math education than any

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

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

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

accountability. There being no real prospect of privatizing education,

the No Child Left Behind Act strengthens accountability, and

strengthens it beyond what the States are capable of.

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

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

ensure that the basics still be learned and that Adequate Yearly

Progress continue to be made.

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

when it is reauthorized, to allow different standards varying by

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

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

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

mastery of basic skills.

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

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

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

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

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

be given to flexibility within counties, districts, and individual

schools, but within the overall framework of making Adequate Yearly

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

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

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

QUESTION 5. TREATMENT OF THE GIFTED (two articles)

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

GIFTED?

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

design curricular practices that work mostly for the gifted and pass

over the heads of normal kids.

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

problem.

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

axiomatic approach has largely been abandoned, for introducing

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

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

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

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

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

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

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

criticism as being inappropriately advanced conceptually for most

students.

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

differential effects on different students of various programs, search

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

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

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

viz.:

For vnto euery one that hath shall be giuen,

and he shall haue abundance:

but from him that that not

shal be taken away

euen that which he hath.

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

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

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

transcendental and absolute source for morality that dominates on one

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

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

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

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

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

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

Factors, clusters determined through factor analysis, the others being

conscientiousness, agreeableness, extroversion, and neuroticism).

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

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

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

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

students rather than drilling them on formulae, whereby they construct

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

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

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

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

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

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

issue of the Zentralblatt für Didaktik der Mathematik/International

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

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

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

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

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

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

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

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

that is several diverse ways of approaching problems and, moreover

begin to do so at the earliest ages.

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

but many or most of its files have been moved to

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

there.

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

drop out. They do not achieve their potential.

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

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

increasingly rely on the special contribution of their gifted in an

increasingly competitive world.

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

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

Gifted Education and the Disruption of Community should not be

slighted.

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

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

counseling able students or developing their social skills through

activities such as leadership training and small-group interaction

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

creativity, many programs forego substantial academic content and,

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

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

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

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

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

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

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

educators frequently dissuade students from attempting intellectually

challenging programs by exaggerating the emotional and social risks of

strategies like acceleration and early college attendance (Daurio,

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

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

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

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

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

ARTICLE 1. WHETHER THE PANEL IS A SHAM?

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

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

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

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

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

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

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

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

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

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

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

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

regardless of the facts of the situation and therefore should be

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

points of views.

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

wars up front and relate them to various philosophies of mathematics

education.

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

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

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

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

continue to strive.

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

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

competition in irrelevant tests of irrelevant courses has become an

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

\"competitive,\" itself a dubious notion.

Objection 1. Good preparation in mathematics is increasingly important

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

applying science and using engineering skills.

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

will be more and more needed in the future economy.

Objection 3. Being better prepared in mathematics will enable American

workers to do better in international economic competition.

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

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

having indicators is indispensable. Those who rail against them are

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

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

number of workers will be engaged in jobs that actually utilize

mathematics beyond arithmetic, wee know from biology that animals

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

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

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

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

exterminating the losing side. An appendix contains the original

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

Reply to Objection 2. Since the relationship between mathematics

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

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

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

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

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

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

the Olympic games that they cheated. They thought it tremendously

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

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

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

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

ends.

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

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

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

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

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

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

QUESTION 7: TABOO ISSUES

This page intentionally blank.

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

APPENDIX 1: CHARTER OF THE NATIONAL MATHEMATICS ADVISORY PANEL

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

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

charter.\]

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

Authority

The National Mathematics Advisory Panel (Panel) is established within

the Department of Education under Executive Order 13398 by the

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

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

U.S.C. App.).

Background

In order to keep America competitive, support American talent and

creativity, encourage innovation throughout the American economy, and

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

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

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

of and improved performance in mathematics among American students.

Purpose and Functions

The Panel shall advise the President and the Secretary of Education

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

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

mathematics instruction, consistent with policy set forth in section 1

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

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

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

February 28, 2008.

The Panel shall obtain information and advice as appropriate in the

course of its work from:

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

directed by the head of the agency concerned;

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

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

4\. Parents and teachers; and

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

Secretary may direct.

Structure

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

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

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

Secretary may specify at the time of appointment; and

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

Federal agencies, designated by the Secretary after consultation with

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

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

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

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

members will provide personal and independent advice based on their

own individual expertise and experience.

Meetings

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

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

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

as appropriate, deal with particular subject matters, and establish

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

exclusively of members of the Panel.

The Secretary or her designee shall name the Designated Federal

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

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

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

meetings of the Panel.

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

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

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

Meetings are conducted and records of the proceedings kept as required

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

constitute a quorum but a lesser number may hold hearings.

Estimated Annual Cost

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

States shall serve without compensation and may receive travel

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

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

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

Funds will be provided by the Department of Education to administer

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

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

approximately \$1,000,000.

Report

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

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

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

contain recommendations, based on the best available scientific

evidence, on the following:

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

competence in algebra and readiness for higher levels of mathematics;

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

promoting mathematical competence;

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

backgrounds learn mathematics;

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

for improving mathematics learning;

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

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

mathematics;

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

instruction in mathematics that combine the different elements of

learning processes, curricula, instruction, teacher training and

support, and standards, assessments, and accountability;

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

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

basic mathematics, geometry, algebra, and calculus and other

mathematical disciplines;

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

deems appropriate; and

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

Secretary may require.

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

of Executive Order 13398, to submit such additional reports relating

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

Termination

Unless extended by the President, this Advisory Panel shall terminate

April 18, 2008.

This charter expires April 18, 2008.

Approved:

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

Date Secretary

Filing date:

+++++++++

\-\-\-\--Original Message\-\-\-\--\
[]{#RonAndLindaJohnston .anchor}From: Ron and Linda Johnston\
Sent: Wednesday, November 22, 2006 2:00 PM\
To: National Math Panel\
Subject: The Role of English Instruction in Mathematics\
\
\
Dear Panel Members,\
\
Please accept my paper on what I believe to be the missing link in\
mathematics education. The two page paper is being submitted as an\
attachment in PDF format. Thank you for this.opportunity to bring so\
important a matter to your attention. .\
\
Sincerely, Ron Johnston

![](media/image2.wmf)

[]{#JohnStallcup .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Stallcup\
Sent: Friday, November 17, 2006 6:42 PM\
To: National Math Panel\
Subject: National Math Panel Meeting_Public Comment

**Public Comment to** *"The National Math Advisory Panel"*

**Palo Alto, California November 5,6 2006**

**Presented by: John Stallcup**

**Co-Founder APREMAT/USA**

Mr. Chairman and panel members welcome to California, I thank you and
the Panel for this opportunity to speak today. I am the initiator and
Co-Founder of APREMAT/USA. APREMAT is the most effective Spanish
language early elementary math program in existence and is in use today
by over two million first, second, and third grade students in a number
of Latin American countries. APREMAT/USA as a program of the Heritage of
America Foundation will be providing the APREMAT program free to the two
million Spanish speaking first, second, and third grade students in the
US who by and large are failing to become proficient in mathematics.

I want to point to four areas of opportunity that need the Panel's
attention:

[First:]{.underline} There is a lack of focus, attention, energy or
concerted effort, on effective early elementary math education in
general and specifically for English language learners. Not only is
there no one person or entity in charge of early elementary math
education at the federal, or state level but no major grant making
authority either public or private funds early elementary math programs
that reach large numbers of students even though efforts to improve
reading are well funded across the board at all levels and by
corporations including Toyota and State Farm.

The lack of effective early elementary math instruction creates the
pervasive lack of computational skills in the middle grades and is a
primary cause of future problems learning algebra and higher math. You
cannot reasonably expect the average student to be able to master
Algebra without having learned their computational skills to the level
of automaticity.

There is a National Institute for Literacy, a National Science
Foundation, a Reading First initiative, support from all levels of
government and non profits for reading programs large and small. Not
only is there no National Institute for Mathematics, or a National
Mathematics Foundation, there isn't even a Mathematics **Second**
Initiative. There are no governmental organizations or initiatives
(present company excluded) focused exclusively on mathematics education
let alone elementary mathematics.

Symbols and hero's matter a great deal. Laura Bush and many other
celebrities champion reading. Who will champion mathematics? Without
focus you get failure. Without funding you flounder. Without attention
there is no energy.

If Mathematics education is ***"Mission Critical"*** you sure can't tell
by where the attention, energy and resources are going.

[Second:]{.underline} Math is a world language and a fungible skill set.
There are a number of proven well researched early elementary math
instructional programs being effectively employed to teach literally
millions of less academically fortunate students around the world that
could be effectively employed here with little funding or iteration and
are not. I would be surprised if anyone in the room had ever heard of
APREMAT before today and that is emblematic of a key problem in our
attempt at improving math education in the US. Cost effective, easy to
implement early elementary math instructional practice and programs have
been developed, researched and fielded around the world, and all but
completely ignored in the US to our continuing detriment.

There is near universal employment of the Abacus in parts of China to
enable their five year old students to acquire number sense, and compute
large columns of figures easily. Chinese students are getting a two year
head start over our best math students because they employ a simple,
easy to use, inexpensive, tool. In practice a near system wide
***"advanced placement"*** program. Chinese educators understand the
positive impact of the manipulative aspects of the abacus on brain
function for learning more complex subjects. All we need to get started
is a set of well produced Utube training pod casts, a few million
dollars for a supply of Abacus and the will to use them.

Many countries in Latin America use the APREMAT program. First initiated
in 1998 by a Honduran foundation APREMAT is already effectively used by
over two million first, second, and third grade students to learn
mathematics because it works. Unlike the US, if you don't pass the math
exam for your grade level in Latin America you do not advance to the
next grade.

If you think we have problems finding qualified math teachers willing to
work in harsh environments, imagine the problems educators have in the
jungles of Latin America (no roads, no windows, dirt floors, no college
degrees, no money, etc). Yet the second poorest country in Latin
America, Honduras created an effective easy to use, consistently
administered, inexpensive, research based, instructional practice for
teaching math on the radio in Spanish.

Two thirds of the three and a half million Hispanic k-3 students in the
US speak Spanish at home and are by a large margin not *"proficient"* in
math by any definition. Hispanic students taking the California high
school exit exam fail to pass the math portion more often than the
reading portion. The word's "destination disaster" come to mind.

[Third:]{.underline} We can choose to use the internet to empower math
education or not. But we cannot claim there is not an effective,
inexpensive way to do so. The greatest potential opportunity to advance
the level of mathematics instruction occurred a few weeks ago when
Google bought Utube. The internet is already an effective, albeit
disorganized "force multiplier" for education. The future of math
education may in large part be determined by how well educators,
organize and integrate online distance learning with the classroom.

Imagine if someone had bothered to video tape a years worth of Jaime
Escalante teaching calculus. India and Singapore are collaborating on
[www.heymath.com](http://www.heymath.com/) a math instruction website
for high school students. A great deal of math instructional content is
already available online, whether The Math Forum at Drexel University or
MIT's Open University. The opportunity is ***"here and now"*** to
organize both existing and new content into easy to use, effective math
education ***"toolsets"*** for students and teachers. The content is not
well organized or easy to navigate but I suspect the Googleplex down the
road could fix that in very little time.

[Fourth:]{.underline} Mathematics needs a new narrative. Mathematics as
a brand needs to be repositioned. When you listen to the majority of
Americans, discuss mathematics you get the distinct impression that
something in our bottled water or our Starbucks coffee has given us a
mass case of math phobic ***"dyscalculia*"**. This includes many
educators. In America we are ashamed when we are illiterate but it is ok
to be innumerate. The far too common and universally acceptable refrain
*"I am just no good at math"* implies a cultural belief in ability over
effort. This debilitating belief combined with the general acceptability
of being innumerate are two of the biggest impediments to increasing the
level of math achievement in the US.

In order to change the narrative two things must occur.

Parents must understand ***"How high is up".*** The ***"fraud of
proficiency"*** that now exists due to NCLB, must be exposed publicly to
enable parents to understand what mathematics problems their child needs
to be able to solve. This could be accomplished in part by providing an
online quiz based on the NAEP math questions with the national version
of ***"proficiency"*** as the yardstick. You could encourage daily
newspapers to publish the NAEP and TIMSS questions as well.

The Gross Rating Points (GRPs) of mathematics in the media (electronic &
print) need to be significantly increased. The number of hours available
of high quality, excellent, relevant, "Sticky" television programming
that either directly (Discovery Channel) or indirectly (CSI) teaches
science and history are in the thousands. The number of hours of
mathematics programming is to low to mention. Ask Madison Avenue and
Hollywood for help. I suspect no more proficient group of mathematics
professionals has ever been assembled. Expectations for this panel are
high. Educators across the country are hoping your work will result in
actionable concrete recommendations that work for all students no matter
their income, origin, or genotype. Although the Federal budget only
provides about 8% of education funding, you will set the mathematics
education agenda for at least the coming decade. The ability to
identify, clarify and help initiate fundamental positive changes in
mathematics education is in your hands.

I hope you create a clarifying focus on all levels of mathematics that
isn't there at the state or federal levels. I hope you encourage more
foundation support for early math education. I hope you will benchmark
and borrow proven effective mathematics instructional programs from
other nations. I believe if you leverage the internet today thru public
private collaborations you will accelerate the process of improvement
and last but not least please begin the process of changing the present
negative, exclusive debilitating, narrative to the positive, empowering,
inclusive, story that is mathematics. Thank you and good luck.

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#JackRotman .anchor}Jack Rotman \[mailto:rotmanj@lcc.edu\]\
**Sent:** Thursday, November 16, 2006 8:59 AM\
**To:** National Math Panel\
**Subject:** Location suggestion for Meeting 7, 8 or 9

In selecting sites for the June to October meetings next year, you might
want to consider the Lansing (MI) area.

 

Among the reasons for this region being valuable for the panel: 
Michigan State University is very active in K-12 education and the NCTM
in particular; several school districts in the area are responsive to
calls for reform and have experience with those processes; and Lansing
Community College has a long history of being professionally involved
with mathematics education at all levels..  I think you will find the
expert input from this area very helpful, and might provide insights
that are complementary to those from the other areas to have a meeting.

 

Thank you for your consideration of this idea.

 

*Jack Rotman*

*Professor, Department of Mathematical Skills*

*Lansing Community College*

\-\-\-\--Original Message\-\-\-\--\
[]{#HarteWillis .anchor}**From:** Harte Willis\
**Sent:** Tuesday, November 14, 2006 2:29 PM\
**To:** National Math Panel\
**Subject:** math book

Dear National Math Panel,

Greetings from Iowa!  After seeing the piece in today's Times about math
teaching, I wanted to bring your attention to a Russian middle school
math book I translated and adapted several years ago.  The response to
the textbook has been, as they say, overwhelming, and reviews uniformly
positive.  You may see the book at
[http://www.perpendicularpress.com](http://www.perpendicularpress.com/)

Thanks,

Will Harte,

George Washington High School,

 

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#KatherinePalisano .anchor}wpalisaw
\[mailto:wpalisaw@netzero.net\]\
**Sent:** Thursday, November 09, 2006 10:20 AM\
**To:** Clark, Holly\
**Subject:** November 4, 2006

I am sending you the following letters that may be of interest.

![](media/image1.wmf)

[]{#GaviKohlberg .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Gavi Kohlberg\
Sent: Thursday, November 09, 2006 11:36 PM\
To: National Math Panel\
Subject: Comment from Palo Alto

**Public comment for meeting of National Mathematics Advisory Panel**

**November 6, 2006**

**Gavi Kohlberg**

**Stanford School of Medicine**

**Former CEO of Digi-Block**

I strongly urge the National Mathematics Advisory Panel to examine
scientific evidence related to **innovative** teaching and learning
methods and tools. While evaluating long-practiced teaching techniques
is clearly valuable and necessary, evaluating innovations in math
education is of utmost importance. Innovations should have tremendous
importance to us in math education, just as they have tremendous
importance to us in fields such as medicine. Innovations let us do
things that we couldn't do before, or let us do things better than
before. For example, the advent of imaging technology allows us to see
within the human body without opening it up. Perhaps an advance in math
education could allow us to teach place value so well we would not have
to teach it over again each time we introduce a new procedure!

Just to make clear the potential benefits of innovation. Note that
identifying an advance that can teach a segment of mathematics 20%
"better" would lead to huge benefits if it were identified and applied
to a significant portion of our students. I strongly believe that such
innovations currently exist and are underutilized.

To ground this public comment in reality, I'd like to briefly give an
example of an innovation that I believe is underutilized that could have
a tremendous effect on our ability to teach students the foundations of
mathematics.

The Digi-Block teaching method, invented by my father, mathematician
Elon Kohlberg, and honed by many dedicated individuals and teachers over
the last several years has the potential of increasing students'
understanding of number sense dramatically (both in terms of depth of
understanding as well as in efficiency of learning).

The great advance of Digi-Block is its merging of theoretical
mathematical ideas (like the elegance and complexity of base-10) with
educational realities (for example, that young children benefit from
tactile experiences) to build an effective framework for children to
learn and explore mathematics. This framework gives young children the
ability to do such things as proof their answers to problems, or even
proof the algorithms themselves.

Yesterday Mr. Williams deplored the recommendation to take away time
from geometry teaching, noting that it was the lone course that
emphasized proofs in the K-12 curriculum. Here is an innovation that
allows proof to be an integral part of elementary school math.

So far there has been very positive feedback from teachers who have
successfully implemented Digi-Block. In addition there is currently a
research study over a year underway with students with significant
cognitive disabilities in Phoenix, Arizona led by Dr. MaryLou Cheal at
Arizona State University. The preliminary results of this study show
tremendous improvement in number sense in a cohort that is believed to
have extremely limited mathematical potential. Hopefully, similar
improvement will be shown through a study in a broader cohort in the
near future.

In my opinion, one of the weaknesses of math education, particularly at
the foundation, the elementary school level, is that very few of the
individuals involved, from teachers to policy makers, have a strong
background in both elementary school education and higher level
mathematics. This severely hurts our ability to identify and evaluate
innovations, like Digi-Block, that make important advances that must be
appreciated both mathematically and educationally. Yet this is a
potential strength of this panel, where as a whole, these abilities are
present. So I respectfully urge you to make sure that important
innovations are recognized and, if effective, recommended to be
incorporated into mainstream mathematics education now and in the
future.

Thank you.

[]{#RichardSchaar .anchor}\-\-\-\--Original Message\-\-\-\--\
From: Richard Schaar\
Sent: Wednesday, November 08, 2006 12:44 PM\
To: National Math Panel\
Subject: Thank you and comment

Tyrrell and Jennifer, I wanted to thank you for the opportunity to speak
to the National Math Panel.  I hope that I was able to answer
the members\' questions.  If they seek more information, most of my
points were from the document submitted by Texas Instruments to
the Panel.  The history of TI and Instructional Calculators and TI\'s
experience in elementary school is not so if the Panel has further
questions in that area, please contact me.  If there is a question on TI
written materials, you can contact any of us. 

 

In addition, I would like to thank you for letting us attend the day\'s
sessions, which we did.  There was a great deal of very helpful
information presented during the day.  It caused me to reflect on my
experience with National work in math and science education so I would
like to make a personal comment on the topic of a National Curriculum. 
Texas Instruments has supported many National efforts to solve our K-16
math education problems, the Glenn Commission, Susan Sclafani\'s Summit,
and now this Panel.  We also were deeply involved in the business
communities efforts in getting No Child Left Behind through the
Congress. 

 

At each step, we were told that a National Curriculum was politically
impossible.  I have even been told by some that we do not want a
National Curriculum because we cannot get it right. 

 

Frankly, I look to this Panel to get it right.  However, once it does,
with all decisions about books, curriculum, and standards made
locally, the Panel\'s recommendations maybe impossible to apply.. 
Each recommendation will have to be modified for the local district, and
who knows what will happen after the modification to the efficacy of the
intervention. 

 

We see it on a small scale with the successful Richardson program.  It
cannot be applied in the same way in the District next door because they
use different materials in a different way even though the state test is
still the metric.  I think that the Panel needs to take this issue into
consideration as it deliberates and consider it for inclusion in its
recommendations.

 

Once again, thank you and if you need any more information from us,
please feel free to contact us anytime.  You are doing critically
important work.

 

Regards,

Richard

[]{#JohnShacter4 .anchor}\-\-\-\--Original Message\-\-\-\--\
From: John Shacter\
Sent: Sunday, November 05, 2006 1:28 AM\
To: National Math Panel\
Subject: How to Make MAJOR (not just Marginal) Educational Improvements

Dear Members of National Math Panel -\
\
I wonder whether you shouldn\'t make your math-teaching recommendations
in the context of the following, somewhat broader challenge.\
\
After all \-- how can we decide what and how to teach **anything
(including math)**, except in the context of an accepted mission and of
specific performance criteria.\
\
I have sent you several more specific memos on the teaching of math,
money management, savings and stock investments, etc.,\
and I shall be glad to try to answer your questions or expressions of
interest.\
\
Best wishes - John Shacter\
\
=========================

HOW TO MAKE MAJOR (not just MARGINAL) EDUCATIONAL IMPROVEMENTS

Drafted by John Shacter, 11-04-06, for public consideration and,
hopefully, action.\
\-\-\-\-\-\-\-\-\-\-\-\-\-\--\
I shall begin by listing five rather basic assumptions for the reader\'s
consideration and approval.  \
\
To start: \-- Organizations without declared and accepted missions are
condemned to flounder and misallocate their always limited, precious
resources.\
There must be some reason for having ANY educational system.\
In order to develop and implement an acceptable reform package, it is
thus essential that we first agree on the basic mission for
\"education.\"\
\
**1. I PROPOSE THE FOLLOWING OVERALL MISSION FOR \"EDUCATION\":**

TO FACILITATE AND PROVIDE THE MEANS FOR STUDENTS (YOUNGSTERS AND ADULTS)
TO ENJOY QUALITY LIVES AND CAREERS IN TODAY\'S AND TOMORROW\'S
\"SHRINKING\" AND EVERMORE DEMANDING AND COMPETITIVE \"OUTSIDE\" WORLD.

(We shall elaborate on that mission statement, below. I don\'t claim any
originality for this draft-statement. However, there has been
demonstrably a surprising amount of confusion or outright bypassing by
the experts on this essential, basic point.)\
\
\-\-\-\-\-\-\--

2\. FROM NOW ON, WE SHOULD ALL AGREE THAT THE REAL COMPETITION IS NO
LONGER AMONG OUR DOMESTIC SCHOOLS, SYSTEMS OR STATES. IT IS BETWEEN OUR
NATION AND A DIVERSE AND RAPIDLY DEVELOPING GROUP OF LEADING NATIONS,
SUCH AS CHINA, INDIA, AND \-- YES \-- FINLAND.

\-\-\-\-\-\-\--

3\. AS PART OF EDUCATION, \"SCHOOLING\" IS A \"SERVICE\" \-- AND AS ANY
SERVICE \-- WHEN WE REVIEW ITS PERFORMANCE, OR HOW IT COULD BE IMPROVED,
WE SHOULD ALWAYS ASK THE INTENDED CUSTOMERS OF THE SERVICE, ALONG WITH
THE PROVIDERS OF THE SERVICE.

AND IN THE CASE OF \"SCHOOLING,\" SOME OF THE MOST IMPORTANT CUSTOMERS
HAVE GIVEN US THEIR ANSWERS. FOR EXAMPLE, QUALITY EMPLOYERS,
PROFESSIONALS AND LEADERS OF QUALITY UNIVERSITIES HAVE BEEN TELLING US
THAT TOO MANY OF OUR

GRADUATES NEED \"REMEDIAL\" EDUCATION BEFORE THEY CAN BE FURTHER TRAINED
OR EDUCATED.

(We educators don\'t like the term \"remedial.\" We prefer the term
\"developmental\" education.)\
\
\-\-\-\-\-\-\--

4\. BECAUSE OF WHAT THEY READ OR HEAR IN THE MEDIA, MOST OF THE PUBLIC
IS FAIRLY SATISFIED WITH THEIR OWN LOCAL SCHOOLS, ALTHOUGH THEY MAY
EXPRESS SOMEWHAT VAGUELY CRITICAL VIEWS OF THE NATIONWIDE STATUS OR
PERFORMANCE OF \"EDUCATION\" AS A WHOLE.

THEREFORE, ANYONE WHO IS FAMILIAR WITH THESE CONDITIONS SHOULD AGREE
THAT MAJOR IMPROVEMENTS IN OUR SCHOOLING WILL CONTINUE TO BE VIRTUALLY
IMPOSSIBLE TO ACHIEVE, UNLESS A COALITION OF PROFESSIONAL GROUPS, ET AL.
IS FORMED AND WAYS ARE FOUND TO LAUNCH AN EFFECTIVE PUBLIC INFORMATION
AND MOBILIZATION INITIATIVE.  \
\
A BASIC MESSAGE AND SET OF RECOMMENDATIONS WILL THUS ALSO HAVE TO BE
DEVELOPED AND AGREED UPON. MOST OF THE SPECIFICS WILL OF COURSE HAVE TO
BE ADDRESSING VARIOUS APECTS OF ENRICHED AND UPDATED CURRICULUM AND
TEACHING APPROACHES.

\-\-\-\-\-\--

5\. FINALLY, IT IS ESSENTIAL THAT THE MESSAGE AND THE WHOLE REFORM
PROGRAM BE CONSTRUCTIVE AND FUTURE-ORIENTED, NOT CRITICAL AND
PAST-ORIENTED. WE SHOULD NOT BLAME TEACHERS FOR ANYTHING, BUT INDICATE
HOW THEY CAN BE FURTHER DEVELOPED. AFTER ALL, TEACHERS AS WELL AS
STUDENTS HAVE BEEN AMONG THE VICTIMS OF OUR INSTITUTIONAL INADEQUACIES.

\-\-\-\-\-\-\--\
\
Please allow me to elaborate on these points.\
\
\
It has become obvious that \-- for the sake of our quality lives and
careers, if not survival \-- we shall have to prepare most of our
public-school (and college) students more fully for quality jobs,
careers, and any meaningful and enjoyable participation in the ever
wider open and competitive \"flat outside world.\"\
\
So far, we have been losing ground to old and new foreign competition.
For example, whereas the Chinese and Indians turn out hundreds of
thousands of engineers per year, the U.S. is preparing only about
70,000, and a substantial portion of them are either foreign-born or the
children of foreign born parents. (However, we are by far the world\'s
undisputed number-one producer of LAWYERS per capita!)\
\
We must also meet this challenge to our school systems, communities, and
homes if we wish to prevent serious slippages in our economic, political
and security positions, as well as in our share of the world\'s quality
jobs. And we need to provide effective \"catch-up\" and \"enrichment\"
programs for interested adults, as well.\
\
However, this time \-- before we \"invent\" another round of educational
planning and improving \-- let\'s all commit to the following
proposition:\
\
IT SHOULD BE THE CORE MISSION OF OUR PUBLIC SCHOOLS TO PROVIDE THE
FULLEST POSSIBLE PREPARATION OF OUR GRADUATES FOR THE \"OUTSIDE
WORLD.\"\
\
Other interests can be added. However, they should not be allowed to
compete with this core mission.\
\
With 13 years of mandated schooling, not counting any pre-K programs, we
should be able to include the following three target areas as key parts
of the \"outside world\":\
\
A. QUALITY EMPLOYMENT AND CAREER\
B. QUALITY HIGHER EDUCATION OR ADVANCED CAREER TRAINING, AND\
C. QUALITY PARTICIPATION IN FAMILY, COMMUNITY AND SOCIETY.\
\
Once we can assume agreement on the above, let us reconfirm and resolve
that the public-school curricula of all states should include the
following basic and \"spice-up\" categories of knowledge and skills. I
have not attempted to tie each of the following items to just one of the
above three mission targets. Rather, I feel that many of the following
items would meet the requirements of more than one of the above mission
targets:\
\
1. EFFECTIVE COMMUNICATIONS \--\
INCLUDING EFFECTIVE LISTENING AND READING, WITH UNDERSTANDING AND
CRITICAL EVALUATION, FOLLOWED BY CLEAR AND EFFECTIVE SPEAKING AND
WRITING.\
\
Without effective communication, there can be hardly any expression or
payoff for any level of education. We currently list some \-- not all
\-- of these topics under titles like reading, vocabulary, spelling,
language arts, and writing. All too frequently, any or all of these
topics are inadequately presented, appreciated, and practiced. A very
simple spot interviewing process \-- say of customers in a mall \--
could quickly establish the existing gaps among the youngsters and
adults of any community.\
\
(I have in fact developed a list of rather simple questions which could
be applied in this kind of sampling process on this topic and any the
following ones. For example, one or a couple of the earliest questions
should test for effective LISTENING. Obviously, students should be
evaluated for levels of understanding and reasoning, and for clarity and
effectiveness of expression \-- not for the particular views they
express. Some teacher development will undoubtedly be required.)\
\
2. EFFECTIVE QUANTITATIVE OPERATIONS AND REASONING (MATH), including
\"numbers sense\", and including sound choices involving the development
and selection of preferred alternatives for a future with uncertainties
or \"probabilities,\" as well as with facts and data. (See also the next
topic.)\
\
In today\'s rapidly advancing and highly competitive world, this second
category of teaching and learning is almost as essential as the first
area.\
\
3. MONEY MANAGEMENT, including understanding budgeting, determining
profit or loss, assets and liabilities, savings versus stock
investments, etc.\
\
Properly presented, this and the following categories can be also
regarded as highly interesting and challenging \"spice-up\" areas. They
can be combined or interspersed with any current curriculum.\
\
4. INNOVATION, including scientific, technical/engineering, business,
societal/government, and artistic innovations, and successful project or
business startup requirements.\
\
5. PERSONAL SUCCESS REQUIREMENTS, including reliability, punctuality,
consideration for laws and morals, consideration for members of the
family, work-teams, neighborhood, society at large \-- and a willingness
to insist on the adoption of these personal qualities on the part of all
responsible individuals and groups.\
(This item to be applied at once, including a spirit of collaboration
and proper behavior in our schools, buses, etc.)\
\
6. AWARENESS OF THE BASIC ELEMENTS OF OUR COMMUNITY, STATE, NATION AND
WORLD, including key constitutional, political, societal, economic and
cultural factors, and current events, issues, and choices.\
\
7. AWARENESS OF MAJOR, PAST WORLD-WIDE AND U.S. DEVELOPMENTS from
ancient to current times.\
\
8. REPEATED REVISITATIONS OF CHALLENGING CAREER CONSIDERATIONS AND
PLANNING, starting in the elementary grades, with clusters of careers,
interesting and well informed outside volunteers, self-evaluation, etc.\
\
This outline of the proposed next round of educational planning and
improving will be continued in the form of additional memoranda.\
It is not intended to formulate an entirely new curriculum to take the
place of the current state or local curricula, BUT IS INTENDED TO
\"SPICE UP\" THE RATHER BORING AND SEEMINGLY PIECEMEAL OR OVERLY COMPLEX
APPROACHES THAT WE ARE TAKING IN SO MANY OF OUR TEXTBOOKS AND
CLASSROOMS, TODAY!\
AND IT IS ALSO INTENDED TO RELATE THE CURRICULUM AND TEACHING TO THE
REAL, OUTSIDE WORLD.\
\
More complete success will also depend upon the existence of ADULT
LEARNING PROGRAMS, of early PRE-K PROGRAMS, and of enriching AFTERNOON
AND SATURDAY PROGRAMS (like boys and girls clubs), particularly for
children who are in need of community subsidies and support.\
\
Obviously, current and future teachers will have to be introduced to
some new topics and approaches which would greatly broaden their
preparation in today\'s teachers colleges. Until these colleges enrich
their own staff and curriculum, this further development could be
arranged in combination with experienced, perhaps retired, local
volunteer-professionals or military retirees in communications, in the
sciences, in engineering, in enterprise and innovation planning and
management, etc. At least hundreds of age-appropriate, introductory
videos are also available. They should be prescreened and accessible to
every teacher at every public school. (If youngsters know anything, they
know how to watch television, and teachers can push the \"pause\" button
for discussion purposes. Most teachers or supervisors would want to
preview the videos before introducing them to the class. A considerable
fraction of the materials may be almost as \"new\" to the teachers as to
the students.)\
\
The professional volunteers could also assist the teaching process by
participating in teachers workshops as well as in regular classrooms.
Current certification requirements need to be broadened for this
purpose.\
\
The whole program is intended to be implemented in a positive and
constructive \-- not critical \-- school and community environment.
Let\'s make our teaching and learning as exciting, challenging,
profitable and enjoyable, as possible. One of the aims should be to make
our teachers and students look forward to their next day of \"work.\"\
\
©2006 John Shacter; semi-retired engineer, management-and-technology
consultant, and still very active volunteer-teacher and educational
consultant.\
Additional background information can be found in the Who\'s Who volumes
of Science and Engineering, and of Finance and Business.\
(By the way, John received his early primary and secondary education in
Vienna, Austria.)

 

\-\-\-\--Original Message\-\-\-\--\
**From:** []{#JohnShacter6 .anchor}John Shacter
\[mailto:jsplg@comcast.net\]\
**Sent:** Sunday, November 05, 2006 1:16 AM\
**To:** National Math Panel; Graban, Jennifer\
**Cc:** Graban, Jennifer\
**Subject:** Re: PANEL COMPOSITION AND MISSION

To: National Math Panel \-- per staff.\
\
Dear Staff Members \-- Ms.Graban and Clark \-- Thanks a million for your
responses and distributions!\
\
Regarding my previous point on the somewhat narrow composition of the
panel \--\
\
Most folks would agree that a former school principal serving on the
panel is hardly a substitute for having no \"PROFESSIONAL USERS OF
MATH,\" such as engineers or commercial-enterprise managers or financial
experts on the panel. **Everyone would probably agree that the current
discussions and probable future recommendations will be greatly
influenced by the composition of the panel.** Some of the  visitors at
open meetings have already expressed similar sentiments.\
\
**I am going to follow your suggestion and will submit a memo on \"HOW
TO MAKE MAJOR (NOT JUST MARGINAL) IMPROVEMENTS IN EDUCATION\" by
separate e-mail, to follow.** That memo is not limited to \"math\",
although math is of course included \-- and it happens to be my favorite
subject to teach to students of all ages and grades, including some
homeschoolers and adults (including college graduates.)\
\
**Frankly, I also don\'t see how the MATH panel can come up with the
most effective recommendations \-- except in the context of such an
OVERALL EDUCATIONAL CHALLENGE, as represented in my forthcoming memo.**
I would be interested whether any panel members will agree with me.\
\
I would of course welcome and shall try to respond to any questions or
expressions of interest by panel members.\
\
Cordially, John\
John Shacter