Chapter 14: attacks and counterattacks
“I don’t just get up in the morning;
I self-levitate because I’m so excited over this book.”
John, 1982 newspaper interview
John’s quote in September 1982 was clearly the opposite of his critics’ loathing of both his book and of him personally. No matter; the words of war that grew through the years were generally invigorating to John. He thought it great fun to take on competitors at any time, including the math educators, but he did sometimes get exasperated with them and would dismiss some of them as evil and vicious—“especially when their attacks on me are ‘ad hominem.’”1
The behind-the-scenes attacks actually started immediately after he published the results in Mathematics Teacher of his test in the 20-school Oklahoma study. Harry Tunic, the NCTM president wrote a letter to Albert Shanker, head of the American Federation of Teachers, and wanted to know what connection there was between the Oklahoma federation and John.2 Mr. Tunic said it was obvious that John was wrong. Mr. Shanker responded they had followed John’s test carefully and explained the process that was used. John said that Mr. Shanker told Mr. Tunic, “We completely endorse what he has done and we believe he is making a contribution to math education in America.” Mr. Shanker suggested that Mr. Tunic contact John personally. That contact never happened. John said he was taken aback by this early effort of the NCTM president to undermine his work. It did help him, though, understand the battle that was to come.
While inexperienced teachers in the field too often mimic the words and thoughts of those with supervisory power over them without much investigation on their own, the leadership of various organizations such as NCTM provided teachers a solid core of resistance to anyone they considered not “on their side.” These were people with power and money and political connections from the national level through all the state capitols. John had shown he was a maverick doing his own thing. It would definitely become a match-up of David and Goliath proportions, as described in numerous news articles. Their own more cunning use of words were couched in academic tones to make John’s more direct words, which left nothing to anyone’s imagination, look simple and thus simple-minded in delivery and meaning.
Every now and then, a real burst of ridicule was shown by one of his critics. A high school teacher in Minneapolis said, “There’s no application to anything in real life. Students wind up more like trained monkeys.”3 That comment—of Saxon students being like “trained monkeys”—became a sneering refrain among numerous teachers who towed the line of NCTM thinking.
The resistance of teachers to changing their methods had been bemoaned for 20 years by NCTM, who claimed that was the real reason their program hadn’t succeeded. Teachers’ attitudes could work against John, as well. The math department chair in Park Ridge, Illinois, said the teachers had tried John’s books and dropped the program after a year because they didn’t like his approach. It was not because the students failed with the program, however. “The teachers didn’t like it. It’s a completely different approach. It’s not about the teacher teaching in front of the classroom,” said the department chairman.4 The oddity of this reasoning by teachers, when the whole function of their new position under NCTM guidelines was to be nothing more than a “facilitator” in a room run by children who determine how and when they will learn, was hard to reconcile by Saxon supporters.
A few days after NCTM released its Curriculum Standards in 1989, a news story ran on March 22 under the headline, “EDUCATION: Math Teachers Push for Reasoning over Rote.” The New York Times, reported, “Society now requires mathematical knowledge far beyond the ‘shopkeeper arithmetic skills’ traditionally taught in schools.” These were words right out of NCTM promotional materials. Those who believed in teaching the “traditional”—or internationally-based algorithms and principles—along with improving teaching techniques in order to increase interest among students were caught off guard by the NCTM promotional blitz begun that year. It was left to John and his sales representatives to try and counter this new public relations campaign of NCTM.
The reporter also quoted NCTM officials who emphasized the report “offered guidelines, not rigid recommendations for school officials and others to follow in revising curriculum.” Members of the council stressed that they were not proposing a “national mathematics curriculum,” or trying to impose a “highly theoretical straitjacket” on teachers and students, he wrote. The council, he noted, had 75,000 members. That number alone would give heavy weight to the NCTM program. The analogy of David and Goliath came to mind, once again, among Saxon supporters.
Shirley M. Frye, president of NCTM, helped start the early spin in that New York Times article by saying, “Students are not computing machines. They are thinking machines.” The growth of technology was the basis for their new document she said because it had “transformed the aspect of mathematics.” The NCTM Standards were simply recommending a departure from tradition by promoting the use of calculators and computers to determine the best answers to questions involving the concepts of “place value, multiplication, and number sense,” along with more cooperative activities in class. This, said the council leader, better reflected the way problems are solved at work in the community.
John Dossey, the previous NCTM president, claimed that many of the report’s recommendations were drawn from the way math was already being taught around the country, particularly in elementary education. He said the council’s efforts stood in contrast to the much-criticized new-math initiative in the 1960’s because that one was put into practice “from the top down.” This, he insisted, would not follow that path.
John was also quoted in that 1989 story as calling the council’s goals “most admirable,” but, he also said, “They haven’t proven that these methods will work. Paper and pencil work.”
In a 1995 interview involving John and Richard Long, director of governmental affairs for NCTM, Mr. Long insisted that while they had put out their recommendations based on input from 20,000 individuals, “People can pull out what they like or don’t like and build their curriculum.” He then said to John, “If we don’t have this kind of discussion today, how are we going to progress?” When that discussion turned to the decreasing test scores, Mr. Long said, “Actually, we’re seeing scores going up.” He then changed the subject by saying to the show’s host, “We like the Standards debate because it gives us a common basis for discussion.” A caller to the talk show asked why parents should trust NCTM. Mr. Long responded, “We’re not asking for your trust. We’re asking for skepticism. Use what you like and don’t use what you don’t like.” Later on he said that any school that uses just one program is “doing it wrong. “Our program isn’t talking about a textbook. It is talking about a wide range of options.”5
Yet, the power of NCTM’s “guidelines” that have been codified into state laws and mandated into teaching programs was defying Mr. Long’s comments.
The constant reference to John’s books as “traditional” was designed to put him in a defensive posture, another standard move by ideologists who have their own program to promote. It wasn’t until years later that the description of Saxon Mathematics as “traditional” was recognized as a misnomer in several ways. The traditional of anything generally refers to how things have been done for a period of time and, therefore, because those actions have become embedded in an environment due to consistent use, they are considered to be a standardized—or structured—approach. The “progressive” of anything is supposed to reflect a new way of acting (or a reforming of old ways) and because it is a “new way,” it, by its nature, is considered a less formal approach and a more exciting program.
John’s program design did ask students to follow a consistent structure, or routine, each day with their lessons. Among the many understandings he had about students’ learning, one was this: When students can focus on a consistent presentation and they don’t have to figure out what is being asked in a different way while they are learning a concept, they can learn it more efficiently, which usually means more effectively. This, he said, is what gave students true “self-esteem.”
Mr. Long, however, in that 1995 interview, said that learning and self esteem aren’t like the “the chicken or egg” question. “Students have to have a sense of who they are and be active learners.” 6 In essence, to him, self-esteem and success came simultaneously in the same package.
Critics also considered John’s black and white books, without any color and graphics, as dull and dry. He chose not to spend money to “color up” mathematics and used the space and money to explain how to work the problems, he said.
To show how the welcomed skepticism was not universally accepted among NCTM leaders, except maybe Mr. Long, and how their irritation could be carried to childish extremes, John blamed “pompous math educators who condemn my methods” for rescinding an invitation to give a paper at a Texas math conference in 1986.7 “I was informed that my name had been removed from the list of acceptable speakers by a special vote of the executive committee.” That committee, he said, was composed of the mathematics director of the Texas Education Agency, the president of the state math supervisors’ association, and three professors of math education from the University of Texas-Austin.
The leaders of the 1990 NCTM Southeastern Regional Conference, held in Chattanooga, Tennessee, also refused to arrange a room for John to speak.8 He then rented a room at a nearby hotel and 140 math teachers showed up. More than 300 teachers stopped by his booth and 103 signed up for information. His supporters said the ease with which mathematics education leaders were willing to cut off opportunities for teachers to hear divergent views made their claims of promoting “diversity” suspect.
The most consistent wrestling with John and his program would come from NCTM spokespeople whose comments would be parroted by university or school district staffs who supported the group’s ideology. Admittedly, he had helped set up this confrontational relationship with his steaming advertisements in Mathematics Teacher magazine and other articles in national publications. As he had said, he thought if he could make them mad, they would start trying to prove their product was better than his. Only then, said John, could schools really compare his product with those of others and decide what was best for their students.
In at least two situations, opportunities were offered to John’s critics for response and they were accepted. One was after he had submitted an article in 1982 to Curriculum Review, a quarterly magazine, which had then asked for a commentary from Daniel Yates, a co-editor of the NCTM’s Mathematics Teacher magazine. His response would run in the same issue with John’s article.9 John had written about the disastrous results of American mathematics education, after which he gave a capsulized history of the results of his study in the 20 Oklahoma schools. After that he listed various fundamental skills of algebra that all students should study and said that students should be able to pass a comprehensive test at the end of the year which would be judged against a standard and not against their peers. He talked about the importance of review but said this could not be the “spiral” approach. He said such spiral reviews were “spastic.” He then explained his incremental approach by saying, “Many youngsters arrive at an understanding of seemingly simple abstractions quite slowly and this late understanding occurs in students at every ability level.”
Mr. Yates opened with an attempt to show his own special knowledge and thus superior standing in mathematics education: “…Although it would be nice to agree that the author has indeed found the royal road to learning algebra, unfortunately that assessment must be considered premature. The fact is that despite the author’s rhetoric and media hype, we are still looking for the research evidence to support the glowing findings of this study… One is reminded of another recent controversial development in mathematics. The Chisanbop Method of counting and computation received a media blitz and attracted many followers with a team of talented kids and a stream of marketing hype. Yet when the facts emerged, it became clear that Chisanbop was no cure-all for computational ills.” Then, the following words were boxed by the magazine to highlight them: “Despite the intriguing possibilities of such panaceas, we would do well to remember the caveat: “Things that seem too good to be true, usually are.”
Mr. Yates spent the rest of his rebuttal article disagreeing that “inadequate textbooks and faulty pedagogy” were the root of the problem. Instead, he listed the need for homogeneous grouping of math students (actually opposed by NCTM Standards); getting parents not to push unprepared students into college tracks; and decreasing pressure on Algebra I teachers to complete the coursework so students are ready for Algebra II. (Yet he disliked Algebra I being spread over two years.) He also saw the need to provide adequate teacher training for teachers weak in math skills; to improve the poor employment conditions; and to eliminate the increasing number of uncertified or unendorsed teachers in high school math classes.
He argued against John’s resistance to “spiral” reviews because John’s view was different from the meaning “adopted by most math educators.” Mr. Yates maintained the spiral review approached the previous topic from a “different viewpoint and/or with a greater degree of sophistication.” This, he said, provided learners with a better perspective and enhanced understanding. Finally, he said, “…the literature has demonstrated without any doubt that the spiral approach is an important and effective instructional tool in…teaching math.” (Yet there is no reference to where that literature can be found.)
Mr. Yates wrote, “Having studied Saxon’s article to see how his philosophy and approach differ from the standard textbook, I must confess that his distinctions [from the two year program for Algebra I] elude me…Are increments really much different from units, except that they are simply smaller segments of information delivered at a slower pace? And does this slower pace…eliminate large portions of context?”
From this description, it could be deduced that Mr. Yates had not looked at an actual copy of John’s book. This was to become a common mistake among his critics. They determined opinions based on “what they had heard from others” or from what they read in media articles or even in John’s advertisements. But they never looked inside the books in question.
Then using a bizarre single example to prove a broad generality about the effects of the standard curriculum on gifted students, whom John felt were being severely damaged by schools’ poor mathematics education, Mr. Yates wrote, “The inadequate textbooks and faulty pedagogy still managed to produce a team of eight high school students that placed first in the 22nd International Mathematical Olympiad in July 1981, defeating teams from 27 nations.”
Further offering a total conjecture, Mr. Yates said, “And there is no shortage of young college students choosing engineering, computer science, business, and other areas that require strong pre-college prep in math.” It must be remembered that only one year later, the 1983 federal document called A Nation At Risk was published decrying the disaster being witnessed in mathematics and science education among America’s students.
Ignoring the total absence of respected education research methodologies and results that started with the “new math” of the 1960’s, Mr. Yates declared, “The most serious obstacle to becoming a believer in Saxon’s philosophy is the absence of critical information relating to his experiment. Mathematics education researchers maintain that in order to make valid inferences about experimental research, it is essential for the experimenter to submit the details of that research to professional scrutiny. Until other mathematicians have the opportunity to evaluate the research and to clarify questions regarding research procedures, one is not in a position to make valid inferences about the effectiveness of the experimental treatment…”
An example of the belittling that John was to be subjected to by members of the elite mathematics establishment came with the following comments from Mr. Yates: “What we have witnessed then, is either the making of an important new development in the teaching of high school algebra or, more likely, a sincere and well-meaning effort by someone who is probably a dedicated teacher but who may be unsophisticated in the methods of educational research. Unfortunately, at this point we have insufficient information to determine which is the case.”
With this being written in a quarterly journal, John was not able to respond to Mr. Yates until December of that year.10 In a letter to the editor, he wrote, “…As I read his article again, it was suddenly apparent that all of his questions could have been answered by looking at my book and by reviewing the tests and test data that had been offered free of charge. Over 10,000 people bought individual copies of the book, and over 500 wrote for copies of the tests and test results. But Mr. Yates had not. Although the names of the 20 schools where the test was conducted were listed, he had not bothered to contact the administrators or the teachers in any of these schools. My name and address were given and he had not called me. I would have been happy to answer any questions he had.
“…I would have told him that Dr. Tom Payzant, superintendent of Oklahoma City Public Schools, conducted a major test in six Oklahoma City high schools during 1981-82. I was not allowed to participate in these tests in any way…at the end of the year, students who used my book scored 50.8 percent higher than the control group that used the standard textbook…I could have told Mr. Yates that over 500 school systems in the U.S. are conducting tests of my book this year.
“I do not fault Mr. Yates for questioning any claims I have made. But I consider that writing a critical article without making any attempt to ascertain the facts is both unprofessional and reprehensible. I will soon have two new algebra books in print, which will also be fully tested. If Mr. Yates cares to comment on the results, I would welcome his participation—if he does his research first.”
In the second situation, Dr. Zalman Usiskin, another NCTM supporter and a professor at the University of Chicago, wrote a review of John’s Algebra I book.11 In effect, Dr. Usiskin, who is not a mathematician but a mathematics educator, ripped John’s book to pieces.
John said, “It was devastating. He said the book was dry and sterile. And it didn’t mention ‘careers’! Can you imagine the Indian kids on the reservations, when they study math, won’t know they could become a physicist? These people are idiots. He said my book has ‘symbol pushing’ for no reason. He ridiculed the fundamental skills in algebra that are needed in higher math. Then he recommended the book not be purchased.”12
In an amazing admission that should have caused his review not to be published at all, Dr. Usiskin confessed he had not seen the book personally. That meant he was making a blind judgment on the book’s contents. That, in turn, meant his “education research” had to be suspect.
John did not hesitate to write a responding letter to the editor of the magazine, which was published in the February 1983 issue: “I was dismayed when I read Zalman Usiskin’s review of my algebra book…I experienced feelings that must have been very similar to those of an accused heretic who had been hauled before the priests of the Inquisition. The tone of the review was condescending, as if the writer had a direct line to the real truth that was somehow unavailable to ordinary mortals. It seems Usiskin is using the book review to put me in my place. His review is interspersed with petty, irrelevant observations—that I am president of my own book company, that I use the words “breakthrough in algebra” to describe my book—and even ends with a suggestion that the book not be purchased. He did not bother to check with any of the teachers who have taught from my book to see if my claims are exaggerated.”
Because Usiskin had criticized John’s idea that standard textbooks’ focus too much on “real world problems,” John responded, “Students…generally have other things on their minds at age 15. People who insist on forcing real-world problems on these chameleons before they are ready are responsible, in part, for the mass exodus from math and science that we observe and regret. We must make students adept at solving equations before we ask them to use equations to work word problems—and then we must teach concepts and let applications wait for a while if necessary. If word problems about fairies and giants intrigue 15-year-olds, and if these problems teach concepts and do not turn students against mathematics, then these problems are relevant as well as most necessary. Word problems are a part of math and should be worked every night, not relegated to a chapter where they are treated as a thing apart.”
Dr. Usiskin was given the chance to respond with a message directly following John’s letter in the magazine. In what came to be a joke with John—that of mathematics educators listing their alphabet organizations and publications as a reason for their beliefs being accepted without question—the education professor wrote the following:
“Compared to recommendations in reports emanating from NCTM, NCSM, CBMS, and MAA in recent years, Saxon’s solution represents a perpetuation of the status quo if not a step backward in exacerbating an already poor situation. For example, Saxon wants us to ‘let applications wait for a while,’ thus bringing back a major blunder of the new mathematics texts of the sixties. My own views toward first year algebra (listed as two publications in the NCTM 1979 Yearbook) are also quite different from the portrayal given in his letter. Most publishers are as sensitive as Saxon to criticism, correcting errors and even making major changes in later editions. We can hope that Saxon will do the same.”
An interesting note about Dr. Usiskin was that he ultimately became the director of the University of Chicago School Mathematics Project (UCSMP), a program founded in 1983 to emphasize reading in mathematics, problem-solving, everyday applications, and the use of calculators, computers, and other technologies.13 They publish Everyday Math, which was created with $5.4 million in grants from the National Science Foundation during the 1990’s and was one of the 10 “exemplary math programs” listed by the U.S. Department of Education. In a letter on NCTM stationery, the council leadership agreed with these textbook designations by the USDOE, which, in effect, gave endorsement to Everyday Math.14 Yet they claim fervently that NCTM never endorses any product.
Letters to the editors began appearing regarding this exchange between John and Dr. Usiskin. One example was from a professor at Northwest Missouri State University who wrote, “…it is clear from Saxon’s response to Usiskin’s review that he has some fundamental misconceptions about the organization of the math curriculum…A reason for the unbelievable exodus of students from the high school math program is that verbal problems have not been appropriately developed in previous grades, and we continue to push meaningless symbolism on students without developing a rational for it.”15
After one of John’s articles ran in The Washington Post in late 1983, a professor of mathematics at the U. S. Naval Academy, J.C. Abbott, had blistering comments in a letter to the editor.16 “I am afraid that Mr. Saxon’s lack of advanced training in mathematics has stunted his professional growth. He doesn’t seem to understand the difference between an arithmetician and a mathematician. One of the reasons I became a mathematician was to find ways to avoid the drudgery of arithmetic; and we’ve done pretty well at that in the computer age.
“Mr. Saxon may well see America as a ‘mathematical wasteland,’ but I fear that he has not kept abreast of the vast explosion of new mathematical knowledge during the last 42 years, involved as he is in teaching the facts of the likes of sine 30 degrees and percentages.
“I am just as happy I do not have to teach with his textbook and can devote more time to the more difficult task of conveying new and abstract ideas. I hope and confidently expect that my students will be well prepared for the scientific advances of the future, even if they fail to recite sine 30 degrees.”
The professor had opened his letter to the editor by commenting that John was a West Point graduate, but Dr. Abbott obviously didn’t know, or acknowledge, that John possessed three engineering degrees and had taught for five years at the U.S. Air Force Academy. The arrogance of such individuals was always a source of amazement, and often of amusement, among those who supported John and his books.
Openly expressing such amazement, a woman wrote the following response to Dr. Abbott’s letter in a letter of her own to the editor at the Post. 17 Penelope Brindley of Alexandria, Virginia, wrote, “Two things are clear from J.C. Abbott’s letter Nov. 9. He apparently has never taught anything but college-level math to anyone but the cream of the crop, the type of student sent to a school such as the Naval Academy. I wonder if he’s looked seriously at Mr. Saxon’s books.
“There is considerable difference between teaching the best math students in a college setting and teaching Algebra 1 to mediocre students in the trenches of high school. Naturally, Mr. Abbott does not see any need for constant review of previously taught concepts. He teaches some of the brightest and most motivated students in the country—students who have undergone a very rigorous selection procedure and whose strength is likely to be math and science. They do not need constant review.
“The typical high school math teacher, alas, has a completely different kind of student in class. She must teach elementary algebra to all levels of students, many of whom have a great deal of difficulty with the basic concepts. These students will never become mathematicians, not even to ‘avoid the drudgery of arithmetic.’ Yet, they need to learn some college math for a variety of reasons: to meet college requirements, to support their work in science, to be taught how to reason logically.
“Last year, for the first time in 10 years of teaching high school math, I used a Saxon textbook. My Algebra 1 class at Woodbridge Senior High School, full of kids who will never be more than fair math students, outscored every other Algebra 1 class at exam time, including classes of ‘accelerated’ algebra students. They did not accomplish this by boring drills; instead they were gently led to review the material with a wide variety of interesting problems. And they are proud of their math ability, some for the first time.
“As for Mr. Saxon’s credentials (his lack of training in advanced mathematics): even Mr. Abbott would have to admit that being a mathematician and being able to explain math concepts are, at times, mutually exclusive. Mr. Saxon’s texts are wonderful. It is obvious to me he knows his stuff, and has mastered the ‘difficult task of conveying new and abstract ideas.’ I never had an easier time teaching Algebra 1. Mr. Abbott missed the point entirely. Mr. Saxon’s books are designed so that all students can learn math, not just Naval Academy midshipmen.
The news media loved the “Saxon story.” It was full of conflict and emotion and a fight that many parents had begun joining. Following the journalistic principle of “showing both sides,” however, they always sought out individuals who had negative comments to John’s appearances or writings. There was Dr. L. Ray Carry, a professor at the University of Texas-Austin, who said, “My negative reaction to Saxon is to his promotional strategy rather than his textbook itself. There has not been what I personally consider an evaluation of Saxon’s book in schools using standardized tests or careful scrutiny of experts in the field.” He thought John’s book would add to the problem of students not being able to do problem-solving because, “It’s mainly drill.” The reporter did not say whether he asked if Dr. Carry had reviewed John’s actual textbooks.
Uri Triesman, another University of Texas-Austin professor, admitted, “There’s a lot of emotion around him, a lot of demonizing.” He said it was time to find a middle ground between the two warring factions. “Saxon has some real wisdom about structure and review. But the goal should be setting high standards for all children. It’s time for neutral people to sit down and look at the strengths of both approaches.”18
At his former University of Georgia, John received both hostile and supportive comments from professors about his mathematics program.19 Larry Hatfield, head of the mathematics education department, said John showed math as a grim chore of “getting the right answer.” It was like taking a dose of castor oil, detested by children and, when forced upon them swallowed with as little thought about the matter as possible, the professor said. “If you went across this country, you would find virtually everyone would criticize John Saxon’s books.”
But this time the reporter went to some classrooms where students were using a pilot Saxon Algebra II book on the university campus. Desperate to help them, the math department had turned to Saxon, wrote the reporter. “They don’t sit through lectures, nor get to use computers, like all other UGA algebra students. They are given an hour of drills a day and help-upon-demand from mathematics professor John Hollingsworth.” He said, “The students are progressing—ploddingly in some cases, nimbly in others.” The reporter wrote, “Hollingsworth is pleased. The students are ecstatic. These are students who never liked math. Now many come early to class (of dozens in the program) and, once there, work confidently.”
Hatfield snorted, “All it shows is that kids like not having to think. They like scoring high on tests…It gives students a false sense of confidence…It would be better to focus on charts and graphs and probabilities and statistics—everyday math that students are likely to need at the store or on the job.” This comment would confirm John’s assessment of the purpose of the 1989 NCTM Standards—which was not to help prepare students to enroll in higher mathematics and science coursework but to help them, primarily, live what the NCTMer’s considered “everyday lives.”
The reporter continued, “Critics now concede that students using Saxon will score high on tests like the ITBS and the SAT. But do rising test scores prove the worth of a textbook, or merely signal rote prep for what some educators believe is meaningless tests?”
“The tests need to be changed,” explained another University of Georgia mathematics education professor, Bill McKillip (who wrote his own math book). “Some of the skills they measure—solving a quadratic equation or dividing a 5-digit number by a 3-digit number—are of no social utility.” Once again, this kind of comment showed the focus was on teaching mathematics as a “social skill” and not one that would allow students to go beyond general math, if the students ever chose to do so, in studying fields that required algebra or more advanced mathematical knowledge and skills.
Dr. Hatfield added, “You can’t tell me that a high ITBS score signifies competence or understanding. All it signifies is that on that day, the child got four out of five right. When we take those high-scoring kids and probe beyond the surface, they haven’t a twit of an idea how mathematics works.” He predicted, “Saxon’s methods will fall from favor and soon be forgotten, particularly once Saxon, a marketing whiz, is no longer around to hype them. But if Saxon’s methods were to take hold,” says Hatfield, “We are doomed as a culture.”
In another room, UGA Professor C. Henry Edwards said only 22 percent of his students could correctly figure how much carpet would be needed for a dorm room that was 9 x12 feet. “You have to wonder how these students have good high school averages and still are not able to give answers for questions like these?” He said while there are broader societal influences (besides schools), he could see the move toward using Saxon’s methods growing in future years.
Major NCTM player Marilyn Burns, author of numerous books and widely acclaimed speaker and consultant, does not condone repetition, mastery, and speed activities valued by the Korean-originated Kumon Mathematics, she said, or the Saxon methods.20 She said that only in math “do we separate skills into such a vacuum. We don’t expect to dribble the ball without learning how to play basketball.” In a surprisingly honest assessment, she admitted, “Teachers for the most part do not become teachers because of a love of math. So our challenge is to make teachers feel differently about math so they won’t pass a fear of the subject down to their students.”
This admission supported critics of NCTM as they pushed for mathematics teaching to become more literature-based, largely because elementary teachers were generally more comfortable in that subject area. The NCTM belief that girls and children of color preferred literary approaches to all learning, including mathematics, was confirmed in a 1993 report 21 of a “widespread grassroots movement for elementary teachers to use passages from quality children’s literature to teach estimation, graphing, number patterns, and exponential growth”22 This was spurred in equal measure by the “whole language” philosophy to teach reading, according to the newspaper reporter.
Further, “A very important added benefit, researchers said, is that elementary teachers—who frequently have weak math backgrounds and consequently tend to slight math in their teaching—are more willing to experiment when math is presented in a familiar context.” Rosamond Welchman-Tischler, coordinator of the early childhood division of the college of education at Brooklyn College, who wrote the NCTM’s guide to using literature to teach math, said, “An awful lot of teachers are math-phobic. Teachers would not go to a ‘math workshop’ but they would come to one on ‘children’s literature.’”
The California director of mathematics education agreed his state’s heavy emphasis on “meaningful contexts” would seem to support the use of children’s literature. Dr. Tischer cautioned, however, that it was vital for teachers to strike a balance between mathematics and meaning when dealing with powerful literary themes.
The reporter then wrote, “Skeptical observers note there is little or no research that proves the efficacy of the approach over traditional methods.”
That reporter also quoted John as “a critic of ‘inquiry based’ approach to mathematics teaching.” He said, “Any technique that fails to emphasize rote learning is merely window dressing for untested experimentation. What we need is something that works, not more good ideas that have not been tested.”
Following a discussion about the challenge of changing the public perception of mathematics as being a cold, mechanical subject, Professor Robert Davis of Rutgers University said during a television interview, “We want math to look more like poetry, not just words.”23 Being a lover of great poetry, John likely would have helped Dr. Davis visit some quotes among mathematicians and their discipline’s connection with poetic thinking: 24
“The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal.” ~William James
“It is impossible to be a mathematician without being a poet in the soul.”~Sophia Kovalevskaya
“Pure mathematics is, in its way, the poetry of logical ideas.”~Albert Einstein
What seems to be a common thread in quotes such as these is that a poetic richness can be seen in the beauty of mathematics, not that mathematics has to be made less powerful by submerging it into poetic format. Even John, who memorized great poetry and could write it from memory, as he did with Robert Frost’s The Road Less Traveled two months before he died, understood how a poet’s soul could support a math teacher’s heart.
As time went on, an even more strident tone of comments was voiced by NCTMers in news stories. There was an official with NCTM in 1986 at a conference in Connecticut who said, “I wouldn’t debate him…I don’t think he knows much mathematics. He sells books by confrontation.”
In the same news story, NCTM President John Dossey refused to talk about Saxon, saying John had threatened a lawsuit against NCTM, which John denied.25 John did tell the reporter he knew why they were unwilling to talk with him. “I’m a pariah,” he said.
In 1988, another news story said that critics were reluctant to go on record against John, fearing reprisals from him. “They believe Saxon tries to intimidate them, using advertisements in various newspapers and magazines.”26
Reprisals might have been their word for it, but to John it was about correcting faulty thinking. He called them out on ideas that opposed the purposes of mathematical thinking—such as striving to reach a definitive answer to a question. “Being able to reason is more important than being able to get the right answer,” announced Shirley Frye of California’s NCTM in 1989.27 She said that by using manipulatives and unconventional ways, students would learn to switch to “different systems” and “getting the right answer is not the only objective.” John responded, “This comes after an American scientist shows we are behind other countries.” Then he added, “The real test will come ahead when these fourth graders are in the workforce.”
A true story about reprisals centered on Thaddeus Lott, an African American principal in Houston, Texas, who experienced both active and passive hostilities, only it was because he opposed the general NCTM holistic approach to teaching. Mr. Lott had insisted that his high-risk school population with its 96-percent African American students be taught with “direct instruction” methods. That included phonics, the opposite of the “whole language” fad, and Saxon Math. Test results had proved the wisdom of his decisions.
In 1986, however, a zealous proponent of whole language took over the district and
ordered that phonics was to be banished from the schools.28 Mr. Lott refused to follow the orders and was the only principal to stand his ground. His story, printed in newspapers across the country, told of how a “war of attrition” had been waged against him. “His supplies were cut and business people like George Scott of the watchdog Tax Research Association came to Lott’s aid.” Then a central administrator staged a raid on the school intended to show that one of the teachers had cheated to pump up test scores.
“The ugly insinuation was that only through such subterfuge could an overwhelmingly black school outscore ‘white’ schools.” When the probe proved to be bogus and was exposed on national television during the Thanksgiving holidays in 1991, “a red-faced superintendent apologized.” When Supt. Rod Paige became the new Houston leader, he promoted Mr. Lott to manage a cluster of four charter schools.
John did resent the accusation that his “noisy battle” with math educators was part of his effort to sell more books. Considering how much money John offered to give away to get districts to try his books, there could be no comparison with competitors who would not match his offers. The other mantra chanted by his critics suggested his books focused strictly on the kind of skills that appeared in achievement tests. He countered, “By the end of a first year algebra course, my students tackle sophisticated equations and they can do it ‘whomp, whomp, bang,’ and come up with the right answer!”
A frequent complaint that had to be overcome by teachers using Saxon for the first time was the fact they could not skip sections and “come back to them.” That complaint became, “It’s his way or nothing.” The point was that John had carefully and systematically designed the separate lessons to build on each other. That’s what made his design so different from the “hunks” or chapters that teachers could skip over or ignore in the standard books. Some teachers were also quoted as saying the Saxon book was so repetitive that it would bore advanced students to tears.29
For example, a University of Minnesota professor said, “Saxon’s program appears to produce excellent results statistically, but it does nothing for the potentially gifted student.”30 Those students, he said, didn’t need “hundreds of routine exercises” and that “six examples would suffice.” He concluded, “Given the anti-elitist bias of our time, I fear these students will be sacrificed to the goal of statistical mass achievement.” Yet, it was the NCTM and progressives’ program that “elitist advanced mathematics” classes should be abandoned in favor of totally heterogeneous grouping.
Another teacher rebuffed the idea that honor students would complain about repetition. “They do it in athletics, band, and any performing group,” she said.31 “Success comes through knowledge and execution. I know [the Saxon] students in Algebra 2 are not having as much trouble as they did in the past. To me, that says something.”
Still, there was continual fussing that John’s book missed the point by focusing on rote learning and drill without ever showing students the mathematical abstractions that lay behind a problem’s solution. The critics contended that teaching math the Saxon way was like teaching students to read by requiring them to memorize their Weekly Readers.
John chastised them by responding, “People are always saying to me, ‘John, doesn’t the constant repetition bore the kids?’ I say, ‘Yes, just like winning every basketball game bores them.’ Kids like to do what they do well. Even smart kids benefit from practice.”
More often than not, however, John would simply say about such critics, “They’re full of hooey.”
That might have been a good description of an interviewer in 1989 with Paul Burke, a representative of NCTM.32 The television reporter, who quickly showed his disdain for the suggestion that more students needed to study higher mathematics, asked Mr. Burke, “Why do you need calculus to write up an order? In the service economy, why do we need trig to sell hamburgers?” Mr. Burke answered, “You don’t. You use percent, logic, statistics, and those should be required. Then, algebra would be offered if a student wanted it.” In reference to reports of low math scores, Mr. Burke added, “It’s not about fixing the misery of kids. It’s partly aimed at competitiveness. Those kids interested in science are more interested in mathematics in high school anyway.” In other words, interest in mathematics for the study of sciences is a natural one, not a created one, which was totally the opposite of what NCTM claimed they believed.
One of the most interesting confrontations occurred between John and Jack Price, the president of NCTM. It was immortalized in an exchange of letters between them in 1994.33 On Aug. 8, John asked Mr. Price for specific reasons for refusing to run his ads for issues in September, October, November, and December 1994. Mr. Price responded by asking John to “open your books for an independent audit to show how many books you have actually sold, how many you have given away, what districts use your books, and what districts have given up after a short trial. He also wanted John to give the actual numbers of the “tripling” of the calculus students. “Is that 1 to 3 or 100 to 300 and where?” He ended that paragraph by saying the Standards were research based.
But then Mr. Price stepped in it. In the next paragraph, he used a military analogy for their disagreements. “You blame career mathematics education for our poor showing internationally in math tests. When you were in the military, it seems to me that some small countries in Asia outsmarted us militarily. Was that your fault as a career military officer?” He then accused John of being an exemplar of Eric Hoffer’s “true believers” –those who feel they have the only right answer and who will go to any lengths to discredit anyone who dares to provide an alternative.
After this punch to John about a military failure in Viet Nam, Mr. Price actually suggested a truce. He told John to produce the facts without the divisive rhetoric and, “We’ll print your ads. Stop making outlandish statements, do some valid research, and join a community of mathematics scholars. Quit standing outside and taking potshots. Our circle is large enough to encompass reasonable dissent.” He closed his letter by saying the Standards are statements about “what we value, but they don’t prescribe how to meet them.” He told John he shouldn’t tear down the Standards and then use those Standards to sell his product.
On Aug. 18, John thanked him for his letter that had been divided into a “NCTM response” and “one from you.” He asked Mr. Price to clarify some of his sentences:
1) “Your ads are replete with innuendo, fabrications and what a less-responsible person might call outright lies.” John asked, “Please give me examples of this—be specific.”
2) He asked, “What do you mean by ‘character assassination’ and ‘name calling? I do not know of any instance in which I have said things that are untrue.”
3) Next, “You state that the standards are ‘research based.’ I have found that educators are prone to use the phrase “research shows that…” to prove anything they desire to prove. What research? Be specific please.”
And then the hammer dropped. “As for your reference to my military career and our failure in southeast Asia I remind you that our Constitution makes the President the commander of our military and makes the military subservient to our elected civilian government. The Presidents were Kennedy, Johnson, and Nixon. The senate passed the Gulf of Tonkin resolution. I was ordered both to Korea and to Viet Nam where I flew over 300 hours of combat to defend you and yours and me and mine. I did what I was told. Our leaders did make the mistakes and our leaders did cause the disaster. I am surprised that you contend that it was the military. We have not had military coups in America and never will have because the American military does what it is told.”
He continued, “My physics book was presented at two physics teachers’ conventions and I was well received. The editor of the Physics Teacher and the president of the association personally greeted me and wished me well. I was shocked because I anticipated different treatment. I investigated to find the reason and found it. Physics education is controlled by men and women who hold doctors’ degrees in physics. I realize now that I am not a threat to professors who hold doctors’ degrees in disciplines such as mathematics, physics, and chemistry.”
Closing, John said he would appreciate answers to his questions. He also said, “I do disagree with some things that the NCTM is doing and believe I should have the right to speak my piece.”
After waiting two months for a reply, John sent a two-page letter to all members of the NCTM Board on Oct. 26.34 He reminded them he had sent a copy of his first letter to Jack Price, dated Aug. 11. He told them that in Mr. Price’s response to that letter, he had called John a liar “in print, on NCTM stationary.” Because none of the board members responded to his first letter, he was forced to assume that Mr. Price spoke for them all.
He said, “You should be sufficiently mature to accept a challenge from someone who does not have a degree in education. To say that your response to my assertions has been puerile would be kind…History is replete with examples of governing bodies refusing to accept or even consider valid criticism.” John reminded them about kings in the ancient world who would kill the bearer of bad news and how the fairy tale of the emperor has no clothes made him believe, “You are not cut from a different cloth.”
In his fourth paragraph, John pointed out that his involvement had always been with mathematicians who said, “Prove it.” He was dismayed that the response of mathematics educators was, “Who are you?” He admitted his answer to that question was not convincing since he was a junior college teacher in Oklahoma and a retired Air Force officer whose degrees were in engineering.
Page two of his letter continued, “I had seen the new math fail and had watched as the ‘Agenda for the Eighties’ was born and died a merciful death. When the draft of the Standards was printed, I asked [NCTM president] John Dossey who had written it. He told me that it was written by Glenda Lapin, Christian Hirsch and Paul Trafton, all professors of education. In Jack Price’s letter to me he makes the claim that the Standards are research based…I have noted that the claim that something is research based is a standard statement from professors of education….The speaker often fails to mention that America has published more ‘research in education’ and has the lowest math scores of any industrialized nation. Jack also hit the nail on the head when he said that the Standards are a statement of what you value but that is the extent of the responsibility of NCTM. Pontius Pilate could not have stated it more clearly.”
John told the board they had turned math education over to book companies whose bottom line was their only interest. He pointed out the color- and picture-filled books that are “spastic” have names of NCTM notables listed as authors. He directed them to look at the title page of the Scott Foresman elementary math series, Exploring Mathematics. (He had included a copy of that page.) He said 24 “distinguished members of the NCTM are listed as authors including Mary Lindquist.” He quipped, “We are asked to believe that these 24 people wrote the book. I write math books for a living and I know that this is impossible. A book can be written by a senior author and at most two helpers.” He concluded that this list of 24 authors, who are curriculum directors, professors of education, and a past president of the NCTM, is an example of how book companies “use the NCTM to sell their inferior products.”
He then stated their behavior was reprehensible because they refused to find a better way to teach math and test their way in all 50 states. “By asking the math teachers of America to adopt your new list of fads without testing, you will cause the gap between the advantaged and disadvantaged to widen because inner city schools are so bad that they will do anything that you say so they can protect their rear ends.” He added that the members of textbook adoption committees have what he calls a “NCTM mentality.” He said, “They are good people and try to follow your lead. They do not think for themselves and refuse to look for proof. They want to follow the Standards but really don’t know how.”
John asked for the chance for them all to discuss their differences in the Mathematics Teacher. Then, he said, “I pay $1,000 for each of my ads. You can have people disagree with me print their opinions at no charge. The NCTM should not be afraid of an open discussion by people who have opinions not shared by other educators. The Mathematics Teacher is the place to discuss our differences, not letters to school board members and legislators.”
This firestorm continued through January 1995. Even Professor Wayne Bishop, a mathematician at California State University-Los Angeles, wrote a letter to the editor complaining about the magazine’s refusal to print John’s advertisements.35 He said, “Although most of us are aware of the controversy surrounding Saxon’s books and his personality, this outrageous act must be rescinded at once.” Dr. Bishop said that while “no thinking person would accept everything that Saxon says as gospel, it is fact that an appreciable number of mathematics programs around the country have turned around dramatically after implementing his program.” He added that he keeps looking for data that supports “new reform” implementations. “If such schools exist, that information must be publicized so that progress-minded people can make informed choices.”
John responded directly under Dr. Bishop’s letter saying that it had been five years since the Standards were published and he was also waiting for some measurable gains that could be attributed to the precepts of those Standards.
Jack Price response was under John’s letter saying his ads were rejected because they contained inflammatory statements which was prohibited by all publishers. He added that he did have a discussion with Dr. Bishop but did not agree to support a “head-to-head comparison of Saxon’s programs with those more reflective of the Standards because that situation would be like comparing apples and oranges and using a scale to grade apples.”
It was during this interchange that Mr. Price incorrectly stated that the NCTM had never taken a stand on the worth of any mathematics program.36 (They had openly supported the “10 Exemplary Programs” listed by the U.S. Department of Education.) Mr. Price agreed, however, to find data about student performance in new programs where those data exist and provide dictations for a research base for the Standards. That information was never delivered.
The kicker for all of this wrangling with the NCTM magazine, supposedly supported by the fact that all publishers refused to run inflammatory remarks in their ads, was that John’s ad was published without editing by Teacher Magazine and Education Week in October 37 and another ad was printed in Education Week in November 1995.38
John’s trait had long been established of not forgetting unsettled differences, as reflected during his long skirmish with the Norman, Oklahoma, School District. He came back to the Jack Price letter exchange a year later in a double-spread advertisement in December 1996 in Education Week. With his typical blaring headline, John wrote about
“Arrogance Run Amok.”39 The ad started out by reprinting part of Mr. Price’s letter to John in 1994. Then John wrote, in large font inserted in the ad, “Let me tell you how it is, Jack. True leaders get out in front and find a better way and say, ‘Follow me.’”
He wrote, “You use the word ‘vision’ 74 times in the three volumes of the Standards—the first being about curriculum, the second volume about teaching, and the third volume about assessment. I am glad the leaders of NCTM have visions and are willing to state what they value, but American schools need more than that. We need leadership. We do not need someone to point the way and then step back.”
John said, “The use of this [referring to ‘constructivist, reform, or discovery’] method has been forced on publishers by the NCTM and has caused a national uproar. Taxpayers are demanding charter schools so their children can learn enough to survive in our technological society. They know their children can think and discover. That is why parenting is so difficult.”
Large font is again used as John finishes the full-page advertisement with “Followers of the NCTM at the state and local levels are truly frightening. They behave like religious zealots who know their first duty is to stone the heretic... Because of the dull-eyed resistance to large-scale testing of their theories by the leaders of the NCTM, schools are going to be forced to run their own tests.”
Again returning to a reference during the Jack Price letter exchange, John published an advertisement in Education Week in early 1996 that asked, “Do you believe the [24] authors listed in Scott, Foresman’ Exploring Mathematics really were the authors? A past president of NCTM and other authors wouldn’t put their names on a book if they hadn’t helped write it, would they? What did the 24 authors get for their work?” He then listed their names in the advertisement.40
Looking back to 1985, before NCTM even published their landmark Curriculum Standards document in 1989, John had argued the track record of the NCTM had been so bad that “they should make no further recommendations of any kind that have not been voted on by all members.”41 He said their promotion of calculator use, for example, showed that “Decisions of this magnitude should be made by a voting of all the members and not until after the recommended changes have been tested for a long period of time and proved to be superior.” Further, “I do not see how we can straighten out the mess we are in if a select few insist on implementing major changes without extensive testing and if the members of the inner circle establish censorship boards to prevent opposing views from being presented and to protect themselves from justifiable criticism.”
Writing these words in an advertisement for Curriculum Review magazine, John said, “I am chagrined that this piece has to appear in magazines other than the Mathematics Teacher. But the establishment educators don’t want the boat rocked. They don’t want to talk about it and don’t want anyone else to talk about it.”42
In retrospect, regarding the critics’ attacks on him, John admitted he could have done some things differently but then he talked himself out of that idea. “One of the things I could have done is go and meet them all. This may have been better. I think I made a mistake—not in the long run because we enjoy laughing at mistakes we made long ago. Maybe if I had gone out and shuffled my feet and been nice to them, asking for their approval, and said I wouldn’t make my claims so brash and upfront and ‘I’ll give you credit for what I have done—fix it up so you can save face so you claim you thought of it, and what I have done is not that big a deal.’ But these people made my skin crawl. They have literally destroyed math education.”43
Continuing his blunt observations, he said, “I didn’t ask people what they wanted in math. I wrote what kids needed. The fundamental fact is most math education people can’t think, or they would be mathematicians.”44
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