Eventually, Saxon explains how it is that a former Air Force officer became a crusading publisher of math textbooks.  When he retired from the military in 1970, Saxon had, among other things, spent five years as a test pilot, flown 55 combat missions in Korea, and taught electrical engineering at the U.S. Air Force Academy.  Saxon enjoyed teaching, so he accepted a position as an algebra instructor at Oscar Rose Junior College (now Rose State College) in Midwest City, Okla.  But at the end of his first semester, only 10 percent of the students had passed the final exam.

Saxon decided to change his entire approach to teaching mathematics.  Instead of introducing one new concept a day, the way traditional math books do, he resolved to spend just a few minutes at the beginning of each class on new material; students would use the remainder of the period working on material they had already learned.  “I finally figured out,” he says, “that you learn to work problems by working them repetitively, over a long period of time.”  This concept remains the heart of the Saxon approach to math. …

20 Oklahoma teachers agreed to test Saxon’s book side-by-side with another algebra textbook.  Participating in the study were 1,360 9th graders, 841 of whom used the regular textbook and 519 of whom used Saxon’s.  At the end of the study, the students were tested, and the results—certified by the Oklahoma Federation of Teachers—showed that the Saxon students outscored the others by more than two to one.

Armed with his test data, Saxon began seeking publicity [the author can’t conceive that Saxon wants to help teachers and students; no, he just wants fame for himself…].  He wrote a letter to conservative author and publisher William F. Buckley Jr., who was so impressed that he managed to secure a $6,500 grant to help Saxon defray his expenses.  Buckley also encouraged Saxon to write an article about his math method for The National Review; Saxon wrote two of them, and they struck a chord with the Review’s conservative readers.  Buckley championed Saxon in his syndicated column, writing: “He will probably figure as prominently in the history of mathematical pedagogy as Hyman Rickover in the history of the development of nuclear submarines.” …

Probably the most controversial aspect of Saxon’s approach to math is its use of what he calls “gentle repetition.”  New topics are introduced in bits and pieces, and old concepts are constantly reviewed.  “Instead of having 20 problems illustrating a new concept,” he says, “we have 24 or 25 review problems and only four to six problems of the new kind.  Certainly, four to six problems of the new kind are not enough for the students to ‘get it’ right away, but, since topics are never dropped in the Saxon books and are practiced in every subsequent problem set, by the end of the year, the students do ‘get it.’”

Critics of Saxon’s approach maintain that “gentle repetition” is nothing more than another term for “drill and practice” or “rote learning.”  Hogwash, says Saxon.  The naysayers, he says, “don’t realize that there is a difference between practice, which is thoughtful, considered repetition, and drill, which is blind, mindless repetition.”  Saxon scoffs at the NCTM’s [The National Council of Teachers of Mathematics] Curriculum and Evaluation Standards for School Mathematics and Professional Standards for Teaching Mathematics….

“I know of no data that supports the idea that the art of problem solving can be taught,” Saxon responds.  “If we are not well-grounded in facts, our abilities to think and reason are hampered.”  Frank Wang, who calls the “mindless repetition” charge against Saxon’s books “an oversimplification,” says: “One of the big buzzwords now in the education world is ‘problem solving.’  Well, we say you become a good problem solver by solving problems.”

NCTM President Mary Lindquist accuses Saxon…  “There’s no great revelation in what he’s doing.”  She believes his books are “too prescriptive.”  Saxon’s program, she adds, “certainly doesn’t go along with what research is telling us about how students learn.” …

For [Saxon], the bottom line is that his math books get results.  Schools that have used his books, he claims, show that it is possible “within three years” to: increase the number of students enrolled in academic mathematics by 50 percent to 100 percent; increase college board scores in mathematics by 20 percent to 50 percent; double enrollment in both calculus and physics classes; increase enrollment in chemistry by 20 percent to 50 percent; and decrease the number of students in nonacademic math courses by more than 50 percent.  To prove his point, he has a list of schools that use his books and the results they have achieved.

Window Rock High School, located on the vast Navajo Indian Reservation in northern Arizona, began using Saxon’s math books in 1985.  At the time, the school’s average score on the math section of the ACT was 11.6 (out of a possible 36 points).  By 1990, the average score had jumped to 18.2, and John Saxon had become a hero to the school’s 890 students.  The senior class went so far as to invite Saxon to speak at its graduation ceremony, an offer the publisher gladly accepted.  When he arrived, the students lined up to get his autograph, treating him more like a movie star than a publisher of textbooks.

If Saxon’s books are so good, why is it that they have been rejected by nearly half of the 22 states that adopt textbooks at the state level? …

An evaluator for the state of Virginia, for example, cited the following reasons for turning down one of Saxon’s algebra books: “The text does not adhere to the NCTM Standards…”

“Students will … use calculators and computer software confidently and appropriately to perform mathematical tasks.”

“Teacher performance will shift from authoritarian models based on ‘transmission of knowledge’ and ‘drill and practice’ to student-centered methods featuring ‘stimulation of learning’ and ‘active exploration.’  Teachers will help students learn how to verbalize their mathematical ideas; explore mathematical questions…; and understand that some mathematical questions have more than one right answer.”

Clearly, Saxon and the NCTM differ in several key areas.  In Saxon’s program, students don’t use calculators until they take Algebra I; the NCTM recommends the use of “appropriate calculators” as early as kindergarten.  Saxon likes to think of his program as “teacher proof” because of its heavy emphasis on textbooks.  The NCTM doesn’t believe that textbooks should drive instruction…

Since the learning process is long and slow, students often have difficulty understanding and retaining explanations that are clear to the teacher doing the explaining.  Comprehension of abstractions occurs over a period of time and cannot be forced, even by brilliant explanations.  This means that presentations by teachers who use this book should be abbreviated as much as possible because students learn by doing and learn much less when the teacher is talking.  The presentation that is brief and succinct is the most effective.  The new topic presented in each lesson will appear in the problem sets for the rest of the book, and the students will comprehend the concept in due time [by doing them over and over].  Most of the class period should be devoted to the homework problems, which concentrate on review…

This method of teaching is much more effective than giving in-depth explanations that are marginally comprehended and quickly forgotten.  To some teachers, a quick explanation followed by a work session where help is available is not as rewarding personally as is doing an outstanding job of “teaching”.  But we must remind ourselves that our job is to see that the students learn.  We have no other purpose.  Since the students learn by doing the problems themselves, the teacher’s job is to find some way to ensure that every student completes all the problems in every problem set.