c:\doc\web\97\09\saxon.txt
To: arthurhu@halcyon.com
From: "James Kilpatrick"
Subject: NCTM Standards and "Need" for reform
Date sent: Fri, 31 Oct 1997 16:56:29 -0600
Arthur, If you have not had a chance to read the articles the late John
Saxon wrote about the NCTM articles here they are. Saxon use to pay
thousands of dollars and run these in Education Week. A rue man that put
him money along with his beliefs out into the real world.
Jimmy
To: arthurhu@halcyon.com
From: "James Kilpatrick"
Subject: NCTM Standards and "Need" for reform
Date sent: Fri, 31 Oct 1997 16:56:29 -0600
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Education Week - October 11, 1995
When African-American students and Hispanic students make high scores
on a normed test such as the SAT or the ACT the scores prove to the
students, to the students' teachers, and to the students' prospective
employers that the students' understanding of mathematics equals that of
able white and Asian students and exceeds the understanding of most
students. The job of math educators is to find ways for blacks, Hispanics,
and all other students to make high scores.
The authors of the Assessment Standards for Mathematics, published by
the National Council of Teachers of Mathematics (NCTM) in May 1995, do not
seem to share this view. A careful reading of the Assessment Standards has
convinced me that the leaders of the NCTM want to raise the grades and the
self-esteem of minority students and other students by changing the way
tests are given and graded instead of ensuring that the students know what
they should know. The leaders of the NCTM do not seem to realize that the
approach they recommend will delay the day of reckoning until the students
graduate from high school and try to get into a college or try to find a
good job. Then the students will find that they are totally unprepared to
compete and will spend the rest of their lives thinking that the world is
unfair. I believe that this "feel good" approach to grading is wrong as it
will cause grievous long-term damage to many of the very students that the
NCTM wants to help.
The introduction of the Assessment Standards contains the passage,
"Too often, tests designed for other purposes have been used unintentionally
as filters that deny under- represented groups access to the further study
of mathematics. Today the mathematical development of each child in a
diverse multicultural society must be valued. Assessment procedures must no
longer be used to deny students the opportunities to learn important
mathematics."
The statement that tests given to measure what students have learned
deny students access to the further study of mathematics is ridiculous. If
students score poorly, it informs the teacher that there is a problem that
should be addressed and corrected. At first, I was puzzled by the phrase
under- represented groups; however, the words diverse multicultural society
gave me the clue needed to understand this new euphemism. My understanding
was further enhanced when I read further and found this statement:
"Assessments have too often ignored differences in students' experience,
physical condition, gender, and ethnic, cultural, and social backgrounds in
an effort to be fair. This practice has led to assessments that do not take
differences among students into account."
The document also says that new:
". . . assessment strategies and practices need to be developed that will
enable teachers and others to assess students' performance in a manner that
reflects the NCTM's reform VISION for school mathematics. For school
assessment practices to inform educators as they progress toward this
VISION, it is essential that we move away from the `rank order of
achievement' approach in assessment toward an approach that is
philosophically consistent with the NCTM's VISION of school mathematics and
classroom instruction."
We have printed the word "vision" in bold face because the authors of
the NCTM Standards seem enamored of this word. The word "vision" appears 56
times in the first two volumes of the Standards and appears 18 times in the
first six pages of the Assessment Standards for a total of 74 times.
I am pleased that the NCTM has "visions" but what we need are
measurable gains in students' achievement. We do not need "visions." We need
a way to teach mathematics that works and we need it now. The NCTM assumed
control of the philosophy of teaching mathematics some thirty years ago.
They were responsible for the "New Math" of the seventies, the Agenda for
the Eighties, the Standards for Curriculum (1989), Standards for Teaching
(1991), and now we have the Standards for Evaluation (1995). The NCTM did
not then, nor does it now, test and prove its recommendations to be
effective before they are forced on the nation. The "New Math" was not
tested and its failure was blamed on the teachers. The Agenda for the
Eighties was not tested and did not work, and now we have yet another
totally untested and unproven set of recommendations called the Standards.
The major book companies are in business to make money for their
stockholders. This is the American way and this is true for all of our
corporations. In fact, it is the emphasis on the bottom line that makes
America productive. So don't blame the book companies. They will do whatever
is required to stay in business. They cannot be blamed if their customers
demand and purchase inferior products. For thirty years these companies have
done their best to follow the recommendations of the NCTM. I do not know of
a single school that has used books that follow the NCTM's methods to
produce measurable gains. Schools of education at our universities are
parroting the recommendations of the NCTM, so public school administrators
are afraid to think for themselves. The public schools can cover their
fannies if they use books that follow the recommendations of the NCTM even
though this results in no gains for their students. You can't blame the
superintendents and the curriculum directors because few of them have ever
taken college calculus, chemistry or physics - subjects that are taught at
the college level in their high schools. I was in the book store at the
University of Oklahoma last week and saw used copies of the NCTM Standards
for sale. I assume that this fine university and other universities all over
the nation are following the party line and teaching the totally untested
Standards as gospel. What else can their departments of education teach and
be respectable?
The preface of the Assessment Standards states that the senior author
was Dr. Thomas Romberg, Professor of Education at the University of
Wisconsin, and that the recommendations of the Assessment Standards were
endorsed by the last six presidents of the NCTM. It lists the names of 41
distinguished educators who helped in its creation and further states that
the document was revised as a result of more than two thousand responses
from reviewers. How could all of these fine people be endorsing pedagogy
that has not been tested and proven to be effective?
The Standards are not standards in any sense of the word. They are
totally non-specific and talk about giving students "mathematical power" -
whatever that is. Read these documents yourself. They are full of vignettes
and suggest pedagogy that might be effective. The Standards recommend that
the emphasis in mathematics education be switched from teaching fundamental
concepts to teaching the art of problem-solving. This is a horrible mistake!
Teaching the concepts and the skills necessary to apply the concepts to
solving problems must come first. We have had three generations of
non-productive nonsense from the NCTM. Enough is enough!!
The denizens of many state departments of education follow the lead of
the NCTM and write recipes for success from vantage points of failure. Texas
and California have led the way in this effort for over two decades and the
results have been catastrophic. Scores in California have hit rock bottom,
as have the scores in many Texas systems. In addition, Kentucky and South
Carolina have set the NCTM recommendations in concrete and I believe that
the math achievement in these states will go even lower. Oregon has also
copied the recommendations of the NCTM Standards to the dismay of many
teachers.
Hans Christian Anderson pointed out that only a child can, with
impunity, say that the Emperor is wearing no clothes. I am a septuagenarian
and not a child, but I can speak with impunity because I own my own company.
I cannot be fired or intimidated. The math scores of students in America
have been falling for decades as schools have slavishly tried to follow the
recommendations of the NCTM. Scores on college entrance exams have improved
a little recently, but this improvement came because the tests have been
renormed. Almost all of our major state universities have huge numbers of
students in remedial math classes. Many people are realizing that it's time
for the NCTM to put-up or shut-up. We need no more "visions."
America desperately needs a method of teaching mathematics successfully
in inner-city schools. We need a method that works in rural schools, in
small-town schools, and in suburban schools. We need something that works,
and has been proven to work in massive test programs, and we need it now. We
can no longer afford to implement untested pedagogy because it is
recommended by people who are supposed to be experts. The NCTM recommends
introducing calculators in elementary schools, having students write essays
about how they tackle word problems, using groups to solve "real-world"
problems, and giving group grades for those projects. They have not been
able to name one school that has used these methods to cause measurable
gains. I don't say they are wrong. I just say we have had enough of their
pie-in-the-sky "visions."
Saxon Publishers has used other methods to create a mathematics program
for grades K-12 that has produced huge gains at all grade levels and at all
ability levels. The books have been tested and found to be effective in
thousands of schools nationwide. Most of the high schools that have used the
Saxon math books have raised college board scores in math a minimum of 20
percent, have doubled the number of seniors enrolled in academic math
courses, have tripled calculus enrollment, and have reduced the enrollment
in "dum-dum" (remedial) math courses such as consumer math by over 50
percent.
These books have produced wonderful gains across the entire ability
spectrum. Hillary Clinton attended Maine East High School in suburban
Chicago in the tenth and eleventh grades. When Saxon Math was introduced at
Maine East they had three sections of calculus. Last year, they had ten
sections of calculus, and thirty-eight seniors completed three semesters of
calculus plus a semester of differential equations. College board scores
have risen 19 percent. At inner-city North Dallas High School, the passing
rate on the Texas math test rose from 10 percent passing to 91 percent
passing. In five years, the pre-algebra enrollment went from 160 to 320.
Algebra I enrollment increased from 75 to 270. Algebra II enrollment
increased from 20 to 170, and calculus enrollment from 5 to 16. In spite of
these increases, which were reported by Mike Wallace on "60 Minutes," the
superintendent threw the Saxon books out - probably because of objections of
people who believed in the NCTM. The numbers of math teachers quickly
dropped from twelve to eight because of decreases in math enrollment and the
number of classes of Algebra II dropped from eight to two. The school board
of the Dallas Independent School District watched this happen and did
nothing.
The school boards in other major school systems also turn to the NCTM
for guidance, forgetting that the NCTM's recommended methods have, to our
knowledge, produced no measurable gains in any inner-city school in America.
The NCTM seems to ignore this on-going inner-city tragedy. Saxon Math books
have been used with great success in many schools with heavy minority
enrollment. Over one hundred schools in Georgia, Alabama, and Mississippi
have proven that minority students can make great gains by using Saxon Math
books. In thirty years, the NCTM has come up with nothing that works, yet
they denigrate and deny at every opportunity the gains caused by the Saxon
Math books. Responsible organizations should lead, follow, or get out of the
way. The NCTM has proven that it is incapable of leading and yet refuses to
get out of the way. They haven't been successful in teaching and now they
want to use "feel good" grading. I am sick and tired of the ineptness of
these people.
Large school systems tend to have curriculum coordinators and math
coordinators who have what I call an "NCTM mentality." They ask if the
publisher uses the methods recommended by the NCTM and they don't seem to
care about results. Saxon Publishers uses the NCTM methods that work and
refuses to use the NCTM methods that do not work. Because we think for
ourselves and are critical of the NCTM, many school systems are afraid to
try our books because the administrators have become senior administrators
by playing the game and going along to get along. They will not risk their
fine jobs by trying programs that are not approved at the state and national
levels.
Saxon Math books produce measurable results at all grade levels and for
students of every ability level. The results are most immediately apparent
in elementary schools in grades K-5, which causes us to place emphasis on
the promotion of our elementary books. This year we offered to give a class
set of books for one class in each of the grades K, 1, 2, 3, 4, and 5 in one
thousand schools so that teachers can watch the wonderful things that happen
when Saxon Math books are used. Unfortunately, at this time we have only
five hundred takers. (At $3,500 per school, this amounted to $1,750,000 in
free books for pilots.) We plan to do the same thing in two thousand
elementary schools next year for a total of $7,000,000 in free books for
pilots. We also have pilot programs for middle school and high school math
books. Teachers and administrators have to see it happen to believe it is
possible.
Many of my friends have urged me to temper my speech and not be so
critical of the NCTM. They remind me that one can catch more flies with
honey than with vinegar. I reply that I am not trying to catch flies. I am
trying to improve math education in America, a task that is very difficult
when the NCTM refuses to test its recommendations and prove that they are
effective, when it is hostile to any other approach, and when so many math
and curriculum directors do not realize they are trying to implement
"visions" by using methods that are suspect because they have not been
tested and proven to be effective. The NCTM refuses, for example, to
consider the fact that the over-use of calculators in elementary schools is
increasing the number of middle school students who are bereft of
fundamental skills. The NCTM also refuses to realize that all they have done
for thirty years is to produce "fads for the decade." They are so insistent
that their untested fads be implemented that others are not encouraged to
find a way that really works. Thus, book companies are afraid to innovate.
To be dogmatic is one thing, but to be so wrong that it prevents others from
trying to end the disaster is totally inexcusable.
-John Saxon
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Last Modified: Tuesday, 10-Dec-96 11:17:37 CST
261
To: arthurhu@halcyon.com
From: "James Kilpatrick"
Subject: NCTM Standards and "Need" for reform
Date sent: Fri, 31 Oct 1997 16:56:29 -0600
[The NCTM Math Standards are A Very Bad Joke]
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Education Week - February 1996
I recently read with dismay a newspaper article in which Jack Price,
the president of the National Council of Teachers of Mathematics (NCTM),
announced that he has appointed a commission on the "Future of the
Standards" to be chaired by past President Mary Lindquist. The Standards are
the highly touted Standards for School Mathematics whose recommendations
have produced no measurable gains in any school system in America since they
were published in 1989. Many schools are trying to follow these unworkable
recommendations and refuse to consider that they are unworkable. As a
result, the disaster in math education will continue unabated.
If we look at this document carefully, we can see that the so-called
Standards are not standards at all, but constitute a very bad joke. I cannot
understand how an organization with a track record of abject failure can
believe it is in the best interest of America for them to continue to make
wild guesses in an attempt to rectify the disaster their predecessors'
guesses have caused. I would like to review the past history of the NCTM and
ask the reader if it is most probable that the leaders of this organization
have had no idea of what they have been doing for over thirty years and have
no idea of what they are doing now. It is time to think the unthinkable --
that the leaders of this organization are totally inept and that we should
demand concrete proof of the efficacy of future recommendations before we
even consider implementing them.
The NCTM has been producing "fads for the decade" for a full generation
and none of these fads has worked. First came the new math of the sixties
and seventies, which asked schools to switch emphasis from fundamentals to
the study of the properties of real numbers and to other off-the-wall
concepts such as the over-emphasis on the study of number systems whose base
is not ten. Instead of telling the students that numbers could be added in
any order and could be multiplied in any order, students were told of the
commutative properties of real numbers under the operations of addition and
multiplication. To make things abundantly clear, they were told that A + B =
B + A, and that AB = BA for any real numbers A and B. Of course, the use of
big words with small meanings led to great confusion about a topic that was
very simple. Students were taught to write the numbers twenty-one and
fifty-five in base-two numerals as 10101 and 110111. The leaders of the NCTM
seemed to believe that if students could demonstrate their understanding of
base-two numbers, it would enhance their understanding of base-ten numerals.
The Russians had just launched Sputnik and there was a mad dash to "catch up
with the Russians." The cold war was at its peak. So, the decision to
implement the new math without testing it beforehand was somehow reasonable
because we could not take a chance of being left behind in technology. The
NCTM used its regional and state organizations to force the "new math" into
schools all over the nation. The teachers objected to being forced to switch
their emphasis away from fundamentals, but teachers wanted to do what was
right, so they went along. Anyone who objected was considered unpatriotic.
Parents were bewildered and some students cried a lot. But, the teachers
still sneaked in the topics and concepts they knew were important, so the
scores of students did not decline precipitously at the outset.
By 1978 or so, the leaders of the NCTM realized that things were not
going well, so they threw together another set of recommendations that were
totally untested and titled them The Agenda for the Eighties. The cold war
was still going strong and we could again stomach the failure to test before
implementation. By the end of the eighties, many of the older teachers had
retired and the new teachers were the product of the new math era. The
decline in the mathematic abilities of American students became more
apparent. The NCTM responded by calling together a new set of experts and in
1989 published the Standards for School Mathematics. These people who had
been unsuccessful in teaching American students the math necessary for the
twentieth century believed they knew exactly what mathematics would be
necessary for the twenty-first century. Their "vision" was clear. They
agreed that paper-and-pencil algorithms were inherently bad and therefore
unnecessary, and that practice was really drill in disguise. They hated the
word drill with a passion. They saw "clearly" that much more emphasis should
be put on the use of calculators. They believed that we should avail
ourselves of everything that technology has to offer. They believed that we
should introduce calculators in elementary schools and let the individual
students decide whether a computation required just an estimate, or could be
completed with paper and pencil, or whether a calculator should be used.
They have pushed the use of calculators in elementary schools with reckless
abandon. As a result, our middle and high schools have an overabundance of
students who do not know basic math facts and who cannot estimate well
enough to know whether a calculator's answer is even in the ballpark.
This result is most apparent in schools with heavy minority enrollment.
The leaders of the NCTM refuse to face up to what they have done. Instead,
they believe that minorities can be brought up to speed if we water down the
tests we use. I quote from the Assessment Standards of the NCTM:
Too often, tests designed for other purposes have been used unintentionally
as filters that deny underrepresented groups access to the further study of
mathematics. Today the mathematical development of each child in a diverse
multicultural society must be valued. Assessment procedures must no longer
be used to deny students the opportunities to learn important mathematics.
I am intrigued by the euphemism "underrepresented groups." I assume
that this appellation means African-Americans, Native-Americans, and
Hispanics. The idea that we cannot teach these students the same mathematics
that Asian and Caucasian students learn is outrageous. The job of the NCTM
is to find a way to do it. We do not need to change the tests. All Americans
must compete in the same job market and applicants are selected for jobs
based on their ability to produce, not on their racial background. If
students score poorly on norm-based math tests, this tells the teachers that
more time should be devoted to their math education. The idea that testing
denies students the opportunity to learn important mathematics is repulsive.
The introduction of the Standards says that we need (1) mathematically
literate workers, (2) lifelong learning, (3) opportunity for all, and (4) an
informed electorate. The explanation of (3) opportunity for all, is
interesting.
3. Opportunity for all. The social injustices of past schooling practices
can no longer be tolerated. Current statistics indicate that those who study
advanced mathematics are most often white males. Women and most minorities
study less mathematics and are seriously underrepresented in careers using
science and technology. Creating a just society in which women and various
ethnic groups enjoy equal opportunities and equitable treatment is no longer
an issue. Mathematics has become a critical filter for employment and full
participation in our society. We cannot afford to have the majority of our
population mathematically illiterate: Equity has become an economic
necessity.
What a wonderful job of breast-beating. You can't say that on the
surface the authors of this document do not seem to care. The Standards have
produced no gains in the number of women who take higher-level math courses
or in the number of minorities who do so. Such gains will never accrue
because the fundamental philosophy of the Standards is not valid. If gains
were possible, the NCTM would have been able to find a teensy-weensy gain
somewhere and would have shouted the results to the world. Instead, what
they recommend will cause the gap between the knowledge of the gifted and
the less gifted to become greater and will cause our society to become more
polarized. The people who wrote the Standards are good people and have
worked hard on this document. They really, really care and want to help.
They are almost all professors of education who have been long removed from
the public school classroom. They say right up-front that there is no data
to buttress their claims. They say that they want to create a vision of what
is possible. In fact, they use the word vision twenty-four times in the
first volume of the Standards. Their description of their vision is the
total content of the Standards, and is nebulous at best.
The authors say that the Standards are necessary to "protect schools
from shoddy products." Publishers want to sell books and if following the
recommendations of the Standards is the way to sell books, they will try to
follow these recommendations. The administrators in our schools are afraid
to think for themselves as most of them are "not gifted" in mathematics, and
so they go along with the gag. The result is a deluge of shoddy products
from which teachers cannot teach and from which students cannot learn. The
professors of education who caused these shoddy products to be produced will
be horrified at my pointing out that they are the cause. They demand that
schools use the constructivist approach so that students can discover the
mathematics they need to know. They justify this blind leap with the
following statement:
Our premise is that what a student learns depends to a great degree on how
he or she has learned it.
This is totally false. What a student knows depends on what a student
knows. The discovery method is not a sure-fire method. Many students have to
practice the use of a concept every day for a very, very, long time before
the concept and the skills necessary to apply the concept can be
internalized. We cannot base American mathematics education on a premise.
We are no longer in a cold war and we cannot accept the recommendations for
the constructivist approach without proof that it works in some school
somewhere. Saxon Publishers has proven that an improved version of direct
instruction works for students at every ability level. The idea that
students should be encouraged to invent the mathematics they need is not
valid. Students need to be led, albeit gently.
If we look at the Standards we see that this document articulates five
general goals for students: (1) that they learn to value mathematics, (2)
that they become confident in their ability to do mathematics, (3) that they
become mathematical problem solvers, (4) that they learn to communicate
mathematically, and (5) that they learn to reason mathematically. As
Lawrence Welk would say, "Wonnerful, wonnerful, won-nerful." But how are
publishers to write books that allow students to meet these goals? How are
teachers to conduct their classes to meet these goals? Specifically, what
does a teacher do to teach students to value mathematics, to become problem
solvers, to communicate, and to reason mathematically? The Standards do not
address these questions, and asking these questions without recommended
methods that have been tested and proven is certainly not a solution.
The Standards consist of a listing of words that are supposed to represent
everything good and nothing bad. The first four are (1) problem-solving, (2)
communication, (3) reasoning, and (4) connections. Let us look at the first
standard. Using mathematics to problem-solve is the art of applying the
concepts of mathematics in new and unusual situations. Thus, our first task
is to teach students the fundamental concepts and the skills necessary to
apply those concepts. Right? No, wrong! What the authors of the Standards
want is to teach the art of problem solving first and let the students pick
up the necessary concepts and skills as they tackle real-world problems.
Teachers are encouraged to place students in groups and direct them in the
art of group problem solving. The authors of the Standards do not realize
that mathematics is an individual sport. Each student must hit the ball
himself or herself. When students are placed in groups and asked to perform,
they will. They find a way for the smartest student to solve the problem and
to make it look like a group solution.
The disaster in math education is a direct result of poor leadership
from the top. It is one thing to make statements such as I have made, and it
is another thing to prove it. My associates and I have written math books
that have caused great gains at all grade levels and for students at all
ability levels. Almost every high school that has used our books has been
able to double the number of seniors who take academic math courses, to
triple calculus enrollment, and to raise college board scores from 20
percent in schools whose scores are average to over 40 percent in schools
whose scores are low. Best of all, these schools have been able to reduce,
by over 50 percent, the number of students taking "dum-dum," slow-track
courses such as basic math and consumer math.
At Sparta High School in Sparta, Illinois, ACT scores jumped from 15.90
to 21.55 between 1987 and 1989, and have averaged 21.43 since that time, a
gain of 34.7 percent. In four years, the average ACT scores at Maine East
High School in Park Ridge, Illinois, went from 18.9 to 22.9, a gain of 21
percent, and the calculus enrollment went from three sections to nine
sections. The ACT scores at Blackfoot High School in Blackfoot, Idaho, went
from 13.1 in 1987 to 20.6 in 1993, a gain of 57 percent. Revere High School
in Ovid, Colorado, reports that of seniors who completed Saxon's Advanced
Math book in 1992, all are still in college, and from the class of 1993, all
but one are still in college. Math teacher Kathleen Killifer says that their
ACT scores are up but that she is more proud of the number of math students
who are successful in college. Superintendent Harold Barnett in
Cartersville, Georgia, reports that his eighth graders' ranking on the state
test of basic skills went from 47th in 1988 to 53rd in 1989 (Pre-Saxon). The
scores jumped to 9th in 1990, 12th in 1991, and have been 1st in the state
for the last four years. Agatha Kent is curriculum director for the Screven
County Schools in Sylvania, Georgia. She reports that the second year Saxon
math was used the enrollment in Algebra I went from 84 to 173, a gain of 106
percent. This is a 3,000-student system, 45 percent white, located halfway
between Augusta and Savannah. We have had success like this in hundreds of
schools and have compiled a booklet of about 135 reports similar to those
above. If you drop us a line or give us a call, we will be happy to send you
a copy.
We have overwhelming proof that a turnaround in math education is
possible by switching from touchy-feely books to books that use a much
improved method of direct instruction. The direct instruction methods in the
past have had great flaws. Direct instruction will work well when used
properly. The NCTM's basic philosophy for thirty years has been terribly
flawed. We have followed the lead of "experts" who have been unable to
produce even small gains in any school anywhere. Can you imagine the
national celebration the NCTM would be having if they produced even one of
the gains that I report in this article? There have been no measurable gains
in any school in America for over thirty years as a result of using the
NCTM's recommendations, yet this organization has announced plans to put out
another set of wild guesses!!! American parents want out. They want charter
schools and vouchers. The number of students being home-schooled has
increased dramatically, and school systems are throwing up their hands and
moving to site-based management because anything the teachers come up with
will be better than what we have now.
Saxon Publishers has developed books that work wonderfully well. This
year our promotions will emphasize our elementary math program which
produces measurable results almost immediately. We will attempt to give away
one class set of books for grades K, 1, 2, 3, 4, and 5 to three thousand
elementary schools for use in the 1996-97 school year. We will inservice the
teachers at no charge and use our money to prove to these schools that a
quick turnaround in math achievement is possible. I say that we will attempt
to do this because people with what I call an "NCTM mentality" are doing
everything they can to keep the schools from finding a better way if it is
not recommended by the NCTM. What are they afraid of? They are afraid I will
prove them wrong. What would you say if you were a 50- or 60- year-old
"expert" in math education and someone threatened to prove that your
philosophy had caused the disaster in math education in America? I like to
think that I would not object because American students deserve the best.
But I am not an "expert" in math education. I am a retired Air Force test
pilot who has two degrees in engineering. What does John Saxon know?
Now we will find out. I have lured these people out of the forest and
into the long grass, and then out of the long grass into the short grass.
There is no longer any place to hide. So the battle will continue this year
on a playing field that is not yet level. But, it gets more and more level
every year. Direct instruction will produce results and touchy-feely math
will not. The next few years will produce the evidence. Saxon Publishers
will attempt to give away $10,000,000 in free math books in pilots each year
for the next three years. The schools that are brave enough to let me prove
my contentions will lead the way. I encourage these schools to accept free
pilot books from other publishers who want to compete.
If schools are willing to test the books, they can prove to themselves which
method is the best.
--John H. Saxon, Jr.
Founder
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Last Modified: Tuesday, 10-Dec-96 11:02:37 CST
888
To: arthurhu@halcyon.com
From: "James Kilpatrick"
Subject: NCTM Standards and "Need" for reform
Date sent: Fri, 31 Oct 1997 16:56:29 -0600
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Education Week - November 1995
I believe that the present disaster in mathematics education in America
will be dramatically exacerbated in the next decade because of recent
actions of the NCTM (National Council of Teachers of Mathematics). These
actions are capricious at best and approach total irresponsibility at worst.
This organization has decided, arbitrarily and unilaterally, to replace
preparation for calculus, physics, chemistry, and engineering with a
watered-down mathematics curriculum that will emphasize the teaching of
probability and statistics and will encourage the replacement of the
development of paper-and-pencil skills in the lower grades with drills on
calculators and computers. This drastic shift in emphasis will leave
American students bereft of the detailed knowledge of the parts that permit
the whole to be comprehended. The NCTM has also decided to veer away from
norm-based testing, possibly because they do not believe that members of
"underrepresented groups" are capable of scoring well. This switch will deny
individual African-American students and Hispanic students the opportunity
to make high scores on normed-tests that prove they are just as capable as
Asian students or white students.
America is on the road to becoming a follower in technology and science
rather than a leader. Our captains of industry tell us that they are at a
disadvantage in worldwide competition because our labor pool is
mathematically incompetent. This incompetence has been documented by tests
which show that 82 percent of our 17 year olds do not know what the word
"area" means and also by international test results wherein American
students score near the bottom of the students in the nations tested. The
engineering and physics departments of American universities are overrun
with foreign-born students and teachers because most American university
students do not know the mathematics necessary to be successful in
engineering and physics.
To correct this situation, we need a no-frills national mathematics
program that concentrates on pre-calculus fundamentals. We have to get our
best students (30 percent) through advanced placement calculus in high
school and get the next ability group (40 percent) prepared for calculus as
college freshman. The rest of the students should master the fundamentals of
mathematics that are required to be productive members of our labor pool,
enabling us to compete with Europe and Asia. It can be done.
Jaime Escalante, whose exploits were documented in the film Stand and
Deliver, had 150 students in advanced placement calculus at Garfield High
School in 1988-89. This school is in the heavily-Hispanic East Los Angeles
area. If all of our schools had the same percentage of students in calculus,
there would be no crisis in American scientific education.
Rather than implement a program to prepare students for engineering and
the hard sciences, as well as for advanced mathematics, the mathematics
education "experts" of the NCTM have come up with a document called
Standards for School Mathematics. When I read the document, I found
absolutely no mention of preparing students for chemistry, nor any mention
of preparing students for physics or engineering. The document even
denigrates the idea of preparing students for calculus. The document
discusses the mathematics needed for business, economics, linguistics,
biology, medicine, and sociology, and says,
"However, the fundamental mathematical ideas needed in these areas are not
necessarily those studied in the traditional algebra-geometry-pre
calculus-calculus sequence, a sequence designed with engineering and
physical science applications in mind."
Who decided on this violent shift in emphasis in the mathematics
education of American students? What could they have been thinking? Do they
not realize we must maintain our leadership in the hard sciences and in
technology if we are to maintain our standard of living? My trip through
engineering school was total trauma because I had so much difficulty with
the fundamentals of math necessary to survive and the math teachers were
trying. Now, we don't even want to try! What math do linguistic students and
sociology students need that justifies watering down preparation for the
hard sciences?
Our country is at risk and the NCTM is now insisting on a radical,
totally untested shift in the mathematics curriculum that veers away from
preparing students for calculus and the hard sciences. The Standards details
how this watering-down process is to be carried out. Students will devote
less attention to memorizing subtraction facts and will have less
paper-and-pencil practice with fractions and less paper-and-pencil practice
with long division. Books will de-emphasize the teaching of radical
expressions, conic sections, paper-and-pencil solutions of trigonometric
equations, and the solutions of the old-fashioned fundamental word problems
that have been used historically to teach the concepts and skills necessary
to solve all problems.
Most of us are afraid of people who know mathematics because each of us
feels that our knowledge of mathematics is inadequate. Thus we fear that
someone who does know mathematics can somehow peer into our souls and detect
this gross inadequacy of which we are so ashamed.
This is the reason that no one (that I know of), with the exception of
the mathematician Morris Kline, had the gumption to question the arrant
nonsense emphasized in the "new math" books, nonsense that knowledgeable
authorities have refrained from speaking out against even to the present
day. Many of our prominent "experts" in math education today were "gofers"
for the originators of the "new math" and have built their careers espousing
the "new math" philosophy. To admit that the "new math" was a horrendous
error would cast aspersions on their careers as "experts" in math education.
The NCTM has backed the "new math" philosophy for 30 years, and to suggest
that the "new math" was a terrible blunder would be a stain on the
escutcheon of this organization.
In the late 1970s, it became apparent to some of the insiders that all
was not well in math education. Calculators and computers for classroom use
had been recommended since 1972. The use of these instruments had not been
shown to be effective at that time, but a drowning man will grasp at any
straw. The NCTM felt that leadership was necessary, so they threw together a
document called The Agenda for the Eighties in which it was recommended
again that calculators and computers be used in classrooms and that the
emphasis in math classes be shifted to problem-solving of "real-world"
problems.
The efficacy of the use of calculators in elementary schools still had
not been proved, and many people questioned the wisdom of introducing
calculators before students had become proficient with paper-and-pencil
exercises. In 1984, a meta-analysis of all the tests on the use of
calculators in elementary schools was compiled. One of the tests in this
analysis showed that calculators were damaging to the calculating ability of
average fourth-graders. This one significant negative finding would cause a
prudent man to proceed with caution. But the NCTM ignored this finding and
recommended that calculators be made available in every elementary grade and
that "students be allowed to decide when it was better to estimate, to use
paper and pencil, or to use a calculator." They even used the meta-analysis
to justify this recommendation and said that the findings for the use of
calculators outweighed the findings against the use of the calculators. So
they again heavily recommended calculators for use in elementary schools.
Can you imagine what would happen to the Federal Drug Administration if it
approved a drug that tests showed was damaging only to average
ten-year-olds?
Had the NCTM said that this finding was enough to require further tests
and had it conducted large-scale tests for several years in inner-city
schools, rural schools, and suburban schools with no negative findings, but
with very positive findings, a foundation for a tentative approval of
calculators in elementary schools might have been established. But they did
not do this and yet they have been successful in forcing calculators into
almost every elementary school in America. As a result, middle schools all
over the country report that many of their students are bereft of
fundamental skills. This fact alone convinces me that this organization is
almost totally out of control.
Jack Nicklaus is an expert golfer because he has won more major golf
tournaments than any other man. Pete Sampras and Steffi Graf are members of
the pantheon of kings and queens of tennis because of their successes. Only
in American mathematics education do people with a track record of abject
failure arrogate the title of "expert." We have implemented their
recommendations for years and years without requiring proof of efficacy
first. I say that the time has come to question the "math experts,"
especially since they have asked the country to join them in another
untested and questionable shift in pedagogy that I believe will cause great
harm to America and should be called the "new new math."
The major thrust of this program will be an attempt to teach students
the art of solving "real-world problems" without first teaching the concepts
and skills. The idea is to let skill development and concept understanding
evolve from the use of the concepts and skills in the solutions of
real-world problems. The initial concept understanding is supposed to result
from the explanation of the teacher (which seldom occurs), and then the
emphasis is to be on applications of the concept. Of course, the "experts"
believe that there is no need to prove that this approach is feasible before
it is forced on the students of America. They have talked almost every
responsible organization in American education into endorsing the Standards.
They list the endorsement of forty organizations, including the National
Association of Secondary School Principals, the National Society of
Professional Engineers, and the American Association of Physics Teachers.
Even the astronaut Sally Ride has endorsed the Standards. Who could be
against standards for American mathematics education? I assume that these
people endorsed the program without fully realizing what they were
endorsing. Certainly everyone is in favor of doing something about the sad
state of math and science education in America, and, as do our "experts,"
they grasp at any straw.
The Standards are replete with nonsense such as the following:
Our premise is that what a student learns depends to a great degree on how
he or she has learned it. For example, one could expect to see students
recording measurements of real objects, collecting information and
describing their properties using statistics, and exploring the properties
of a function by examining its graph. This vision sees students studying
much of the same mathematics currently taught but with quite a different
emphasis; it also sees some mathematics being taught that in the past has
received little emphasis in schools.
This premise and vision gibberish is followed by statements that
students should learn to value mathematics, become mathematically confident,
become mathematical problem-solvers, learn to communicate mathematically,
and learn to reason mathematically. If one reads the entire Standards
document carefully, it is really difficult to decide whether it was written
behind the looking glass by the Red Queen or if it was written by a physical
education instructor, as Jaime Escalante has contended.
We need to get as many students as we can through calculus in high
school. We need students who are competent in the use of fractions,
decimals, mixed numbers, percent, and ratios. We need students who know
trigonometry and analytic geometry. We need a work force that allows
Americans to compete successfully in a technological world. We do not need
guidelines that recommend leaving students ill-prepared for chemistry and
physics, and that ridicule preparation for calculus.
This violent shift in emphasis recommended by the NCTM stems from the
failure of the experts to find a way to teach the concepts and skills first.
The first draft of the Standards stated that because we have been unable to
teach the concepts and skills first and then teach the applications, we must
have been trying to do it the wrong way. Thus we should try to do it the
other way: we should try to teach the concepts and skills through the study
of real-world problems. The fallacy of this reasoning is self-evident.
I was aghast at this wild surmise and was chagrined that one of the
authors of the Standards deleted this statement before the final version was
printed. This statement was a dead giveaway to the pie-in-the-sky, fuzzy
thinking that lay behind the whole document. America has depended on our
"experts" in mathematics education for 30 years and they have let us down.
Now they propose that we accept a set of nebulous recommendations that are
totally unproven. The book companies are working feverishly to publish books
that try to meet the guidelines, and the result will be an acceleration of
the disaster in mathematics and science education. It will take at least ten
years for the full extent of the coming disaster to become apparent. College
math enrollment will decline, and the number of American students in physics
and engineering will decline even further.
The mathematical knowledge required for success in chemistry, physics,
and engineering has not changed. High school students avoid chemistry, not
because they fear studying electron orbitals, but because they lack the
concepts and skills necessary to work problems that involve chemical
combinations by weight and other problems that require mastery of the
concepts of percent and ratio. Students avoid physics because they have not
yet mastered the basic manipulatory skills of algebra and the basic concepts
of trigonometry.
The Standards document stresses that there must be a shift in
mathematics education away from practicing problems categorized by type,
such as coin problems, age problems, digit problems, work problems, and
trains-leaving-Detroit-at-midnight problems. There is absolutely no way that
this shift in emphasis can be justified. These problems have been developed
by teachers over the years to teach the thought processes and skills that
are necessary to solve other problems that are new and strange. The document
also says that "type" problems should be replaced with "non-standard
problems" and with "open-ended problems" and "extended problem-solving
projects." The idea of non-standard problems is ludicrous. Don't the authors
of the Standards realize that all of the problems in the first course in
algebra are non-standard to students who have never studied algebra before?
Throwing out a tried-and-true method and replacing it with an untested one
is totally irresponsible.
The real damage these people do is caused by the fact that they focus
on methods rather than on results. They actively disparage any positive
results from programs that do not use their methods. Saxon Publishers has
produced a K-12 math series that has, in almost every system that has used
the 9-12 program, doubled academic math enrollment, tripled calculus
enrollment, raised college board scores from 19 percent in schools whose
scores were already high to over 50 percent in schools whose scores were
low. The use of Saxon math books has resulted in large increases in the
number of minority students and women who take upper division math courses
and large decreases in the number of students who take dum-dum math courses
such as consumer math. Because I use methods the NCTM considers to be
impure, many people who have what I call an NCTM mentality refuse to
investigate my claims and refuse to consider that these results could accrue
from the use of Saxon Math. I received a letter on NCTM stationery from Jack
Price dated August 11, 1994, in which he insinuated that I am a liar and a
character assassin for making these claims. This man is the president of the
NCTM and he is not doing his job. He has not even investigated my claims!!
I would be happy to furnish to anyone who writes me a copy of this
correspondence, and I'll include a report from 92 schools in 38 states that
buttresses my claims. I will also be happy to send you a list of schools in
your state whose students have experienced huge gains in math achievement as
a result of the use of the Saxon Math books, and a list of teachers from
these schools who are willing to have you call them so they can tell you how
thrilled they are about their successes with Saxon.
-John Saxon
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Quick Search:
Customer Service/Sales: 1-800-284-7019, Local: (405) 329-7019
Fax: (405) 360-4205, Math Help Line: (405) 573-6451
If you have any questions please send e-mail to webmaster@saxonpub.com
Copyright © 1997 by Saxon Publishers, Inc.
Last Modified: Tuesday, 10-Dec-96 11:02:39 CST
538
To: arthurhu@halcyon.com
From: "James Kilpatrick"
Subject: NCTM Standards and "Need" for reform
Date sent: Fri, 31 Oct 1997 16:56:29 -0600
[What's Wrong with My Money?]
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San Francisco - June 1996
I am sick and tired of listening to the public schools whining about
not having enough money. The reason for the low scores in reading and math
is that the administrators are not doing their jobs. Many have doctor's
degrees in education, are paid handsome -- no very, very handsome --
salaries, and yet they are not producing.
It is time to throw down the gauntlet, so let us begin with the
administrators in the San Francisco Public Schools. Saxon Publishers wrote
the San Francisco superintendent and his curriculum coordinator about a year
and a half ago and offered to provide one class set of Saxon math books at
each grade K, 1, 2, 3, 4, and 5 to all of San Francisco's elementary schools
that have an enrollment of more than 250 students. The value of the books
was about $3,500 per school, and for all sixty-four elementary schools, this
came to approximately $224,000. The in-service for the teachers at a central
location was to be provided at no charge. This was to allow the San
Francisco schools to demonstrate in their own classrooms, using their own
teachers, that dramatic gains in student achievement in mathematics could
occur almost at once. And guess what? Neither the superintendent nor his
curriculum director did us the courtesy of a reply. They simply placed our
letter in the circular file. They were not interested in using my money to
see if the Saxon math books could improve the low math scores of San
Francisco students.
Now we are making our offer to the citizens and taxpayers of San
Francisco and we are throwing in an additional offer of one class set of our
wonderful phonics program at grades K, 1, and 2. The phonics books have a
value of $1,500 per school, so for the sixty-four schools, the latest offer
now comes to a total of $320,000.
The teachers must be volunteers and agree to teach each class in the
manner we recommend. If, at the end of the year, the San Francisco teachers
are not impressed with the results, they can burn the books and I am out a
very large sum of money.
We made the same offer to the Houston, Texas, administrators a year
ago, and they also put our offer in the circular file. We began cold-calling
principals and got seventy-one to accept. The results were amazing.
Two Houston principals played a hunch and purchased additional Saxon
math books for all of their classes. Their hunches paid off with spectacular
results. At Field Elementary School, Principal Mary Nikirk reported that the
percentage of third graders who passed the math portion of the Texas
Assessment of Academic Skills (TAAS) in the spring of 1995 was 45 percent.
This year, 94 percent passed. The fourth grade passing rate increased from
27 percent to 96 percent, and for the fifth grade it increased from 53
percent to 67 percent.
At Stevenson Elementary School, Principal Mary Cherbonnier reported the
passing rate for fourth grade students increased from 69 percent to 93
percent. The fifth grade rate increased from 61 percent to 85 percent.
Most of the elementary schools that accepted our offer for a free pilot
did not use Saxon books in all their classes. At Burrus Elementary, last
year only 34 percent of the fifth grade students passed the TAAS math
test.This year, 100 percent of the Saxon students passed. The Saxon students
helped pull the pass rate for the whole school up to 90 percent.
Last year at Rhoads Elementary, only 72 percent of the third grade
passed. This year, 97 percent of the Saxon students passed. This pulled the
whole school up to the 93 percent pass level. The fifth grade had a 44
percent pass rate last year. This year, the 100 percent pass rate of the
Saxon students pulled the pass rate of the whole school up to 75 percent.
These gains resulted from using Saxon math for only one year. Think of
what the pass rate will be after Houston elementary students get to use
Saxon math for all five years! The Texas Education Agency will have to
increase the difficulty of the TAAS test to get any type of curve at all.
Otherwise, almost all students will pass the TAAS test at every level. These
test results represent a total victory for "direct instruction" over the
"constructivist method," which has been advocated by the National Council of
Teachers of Mathematics (NCTM) for the last twenty years or so. The
constructivist method is "touchy-feely" math in which the students are
required to discover the math they are to learn, are to work in groups, and
have calculators available at all times.
Many administrators in large public school systems are walking examples
of the "Peter Principle." They refuse to think for themselves and cover
their fannies by supporting the latest fads introduced at the national level
by the NCTM and the International Reading Association -- the organizations
that have brought us the "new-new math" and whole language.
We will need a reply to our offer from the San Francisco Public Schools
by July 10, 1996. This may seem to be a short time, but I believe that a
year and a half from our initial offer should suffice. If the citizens of
San Francisco encourage the schools to accept my offer and tell them there
is nothing wrong with my money, I think we might have a chance.
We also sell a wonderful homeschool math program for parents who are
not satisfied with what their children are learning in the public schools.
The homeschool phonics program will be available within the next two or
three years.
--John H. Saxon, Jr.
Founder
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Quick Search:
Customer Service/Sales: 1-800-284-7019, Local: (405) 329-7019
Fax: (405) 360-4205, Math Help Line: (405) 573-6451
If you have any questions please send e-mail to webmaster@saxonpub.com
Copyright © 1997 by Saxon Publishers, Inc.
Last Modified: Tuesday, 10-Dec-96 11:02:45 CST
357