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 [Image] ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- [Image] ---------------------------------------------------------------------------- [Image][Image] [Image] 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 11:17:37 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] ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- [Image] ---------------------------------------------------------------------------- [Image][Image] [Image] 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 11:02:37 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 [Image] ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- [Image] ---------------------------------------------------------------------------- [Image][Image] [Image] 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?] ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- [Image] ---------------------------------------------------------------------------- [Image][Image] [Image] 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