Mathews is the author of "Escalante," a book about the calculus teacher who was featured in the movie "Stand and Deliver."
No one suspected that a mathematics textbook series could ever become underground literature. But in many schools around the nation, often unknown to principals and superintendents, teachers are covertly dispensing the cranky, drill-laden wisdom of John Saxon, a maverick publisher the American educational establishment would prefer to see sent to the corner with a very large dunce cap.
Saxon, a former air force officer, has no education degree and earned a solid D the first time he took calculus. But while failing miserably to attain respectability in the highest circles of education research, Saxon has sold 2.3 million books. His success, and the acidic reaction to it, has exposed a deep split in the American educational-reform movement between classroom teachers and reformers. It also highlights a national failure to examine how well the $4 billion American textbook industry actually performs in the neediest schools.
Saxon began peddling his first textbook 12 years ago after scrounging $80,000 from savings, his mother's will and a second mortgage on his house. Encouraged by publicity in conservative publications like the National Review, he wrote several more math books in the dining room of his Norman, Okla., home. He eventually created a series of texts taking students from finger-counting through calculus. "In a lot of schools we doubled the math scores," said Saxon, 69. "I was so proud I literally waited for the phone to ring and letters to come in from educators all over the country. Instead of that, I was attacked."
To state education departments and textbook advisory committees, Saxon is the worst of the old school. (In education land, those are fighting words.) Much of the debate has turned on whether Saxon has proven that his methods work. Mary Lindquist, president of the National Council of Teachers of Mathematics (NCTM), cites studies in Pittsburgh and Broken Arrow, Okla., showing little or no improvement in Saxon students. "He tends to train students in a fairly well-defined traditional collection of problems," said James Fey, University of Maryland professor of mathematics and curriculum instruction, "and our belief is that kids need a more flexible ability to apply their mathematics to novel problems." In response, Saxon cites several districts around the nation which have embraced his methods and shown improved test scores. And, he wonders, why must he prove his case while mainstream textbook companies sell their wares with little hard evidence of their efficacy?
Saxon's biggest score came a decade ago in Dallas. The city school board, inspired by rave reviews from teachers who had tested Saxon's pre-algebra book, bought $600,000 worth of texts. They also bought a large dose of the author. In well-creased slacks and blue blazer, Saxon leapt atop a cafeteria table at a Dallas teachers' meeting to evangelize the crowd. He immediately alienated half his listeners. "He was saying how we didn't know what we were doing and he was going to show us how," said Charles Hodge, a mathematics teacher at North Dallas High.
Saxon was preaching from experience. After he retired from the air force, became a junior-college-algebra teacher in Oklahoma. There he discovered that students would absorb concepts more easily if they nibbled at them daily for several weeks, rather than devouring them in two days and moving on. Applying those principles, he expects teachers using his methods to give short 10-minute lectures each day, followed by classwork and homework that focus more on previous lessons than on what was presented that period. "The way you learn to walk is, you take a step and then you take another and another and before long you run," said Tom Taylor, a North Dallas High School teacher who likes the Saxon books. "You don't sit there and philosophize about how to walk."
In Dallas, Saxon had particular problems appealing to teachers of advanced math courses. They preferred to continue lecturing and resisted turning their classes into drill sessions. But in lower grades, the method paid quick dividends. Dallas mathematics director Mary Lester recalls that math-achievement levels in the middle schools "almost doubled." The big winners, according to Hodge and a few other teachers who stuck with the program, were students from poorer, less-educated families. Not only were they learning more, but they developed a taste for continuing in math classes. "I used to hate math," said Nelly Fernandez, a 1990 graduate of North Dallas High, but with Saxon, "it felt easy ... The repetition really helps sink it in as opposed to other books that introduce one concept and then jump to another."
Similar stories are heard in Saxon classrooms throughout the country. "The test scores really went over the top," said superintendent Mike Walters, who introduced the Saxon series in rural Petal, Miss. "What really was surprising was the extent that our kids started electing to take higher math courses." The senior-class members at Window Rock High on the Navajo Indian Reservation in Arizona were so pleased with their improved test scores that they made Saxon their graduation speaker. Despite such tributes, only 12 states have any Saxon book on their recommended list, and most have limited their approval to a few titles.
Saxon demands frequent practice so students will solve his problems correctly. The new thinking, however, suggests that the right answer isn't as important as the method students use to reach their answer. The National Council of Teachers of Mathematics encourages students to do complex exercises in groups and worry more about how to approach a difficult issue than whether they've misplaced a decimal point. Saxon is as irritating as a tax auditor to reformers who ask math teachers to break old habits and mark tests as though they were English papers, focusing as much on the clarity of the steps toward a solution as on the correctness of the answer.
Like every math-text author, Saxon relies heavily on word problems. But he thinks students learn better by doing them rather than talking about how to do them. His emphasis on drill is similar in some respects to the Kumon system, popular in afterschool math centers in Japan. Of course there are reformers there, too: having consistently produced students who outscore their Western counterparts, Japanese officials now worry that their methods yield only skillful mathematicians who are not sufficiently creative.
To Frank Wang, a 28-year-old MIT mathematician who is Saxon's executive vice president, the current fascination with what educators call "critical thinking" borders in some cases on the simple-minded. Wang's favorite example is an exercise in problem solving in the new Scott, Foresman junior-high text called "Transition Mathematics." It reads: "Monty tried one way to do the problem. When that did not work, he tried the same way again." The student is asked what Monty should have done. The answer in the teachers' guide: "He should have tried another way."
Cathy Feldman, coauthor of "Transition Mathematics" said the Monty question was just to check whether students had read the chapter. She said that the book, hailed by many educators, is full of challenging assignments "to create flexible and independent students." But state schoolboard members, such as Will
Davis in Texas, freely admit that they've bought the books without much field testing, particularly in some poorer school districts which may need special help. Textbooks simply are not treated the same as pharmaceuticals.
Dallas textbook committees have done their best to follow the national trend. They replaced Saxon with the Scott, Foresman mathematics series, only to see it rejected by many teachers who think it too wordy and oblique. "They haven't even taken the Scott, Foresman out of the book room," said one Dallas teacher who asked not to be identified. Why the anonymity? Because in the name of education he's engaging in some civil disobedience-and copyright infringement. "I just take my old Saxon book down to the Xerox, and we do it one day at a time." So it has come to this: Pssst, Kid, want to buy a used math problem?
School boards don't just purchase texts, they buy entire systems of instruction. Any mathematics course uses word problems and homework, but there are key differences.
1. Teachers lecture in class for only 10 minutes, leaving rest of time for exercises.
2. Much of the class work reviews previous lessons, trying to reinforce skills before they are forgotten.
3. Books have few frills, no pictures and short explanations.
1. Teacher is in charge of class, may decide to apportion time for lectures or exercises in any way she wishes.
2. Emphasis is on learning concepts while acquiring math skills.
3. Books are colorful, graphic-laden; feature long explanations.