John H. Saxon Jr. was teaching an algebra I class at Oscar Rose Junior College in Oklahoma City when he first realized that when it comes to algebra, once is not enough.

One day, he says, he gave the “most magnificent lecture.” He finished in 20 minutes, and, reluctant to release his students 40 minutes early, planned to have them do problems on the blackboard for 20 more minutes. He gave the same problem on the board that he’d just finished explaining in his lecture.

“They all wrote it on the board. And they all stood there looking at the board. Not one of them understood. With my 20-minute, beautiful stand-up lecture, nobody got a thing.”

He explained it again, and yet again, and assigned the same problem as homework. Then he went down to his office and, he says, thought to himself, “John, something just happened there, and a smart man would be able to figure out what.”

The conclusion he arrived at--that one learns to work out mathematics problems by working them out over and over--became the basis for a method and text for teaching algebra that have, so far, produced large gains in achievement for many students and a flurry of rejection slips from publishers.

The latest report came last week: The test scores of a group of first-year algebra “Saxon students” were, on the average, 37 percent higher than those of second-year-algebra students whose teachers used other commercial texts.

The test results were monitored and certified correct by the Oklahoma Federation of Teachers (oft), which has agreed to verify the accuracy of the tests, although it remains a neutral party.

The scores are the latest of several such comparisons, all of which have shown that students taught with the method, which stresses repetition and a different organization of material, consistently outscore others, sometimes by enormous margins.

Saxon Students Outscore Others

The initial comparative tests, carried out on 1,365 Oklahoma students taking algebra I, showed the Saxon students outscoring their counterparts by as much as 141 percent on tests of basic skills. For example, on a 15-question test about positive and negative numbers, the test group scored109 percent higher than the control group.

The marked difference in achievement occurred, according to Mr. Saxon, a former test pilot and career Air Force officer who teaches mathematics at the Oklahoma City junior college, because the Saxon students had been taught with a method that runs counter to the those used most commonly to teach algebra.

Rather than moving from discrete topic to topic, and seldom mentioning the preceding ones after beginning the next, the Sax-on method provides a continuous review of integrated topics. “Repetitive homework” is one key factor, Mr. Saxon says; another is a different ordering of the material.

And because the material is repeated, he argues, the method gives students the means to master a subject that has been the source of a great deal of frustration for many students.

Mostly by way of a sort of educational grapevine, the method has aroused interest--sometimes cautious--among educators and has been the subject of several national articles. Prentice-Hall has published two junior-college texts by Mr. Saxon.

But, due to lack of interest from textbook publishers, Mr. Saxon has published the high-school text, Algebra I: An Incremental Development, himself, under the imprint of his own publishing company, Grassdale Publishers Inc. He relies mostly on word-of-mouth for advertising. Even so, he says, he has sold 9,000 “examination” copies, and the book was used in about 50 school districts last year, most in Oklahoma and California. New Mexico and Tennessee, both states that provide districts with a wide range of choices on their state-adoption textbook list, have added the book

In the field of textbook publishing, which is dominated by large publishing companies and influenced to a degree by state-adoption textbook lists, Mr. Saxon stands out.

The beginning of what has subsequently become his mission occurred several years ago; since then, he has become intensely preoccupied with the process of convincing educators to adopt his method, and he believes that significant change will occur in students’ mathematics achievement if they do.

He is, he says, something of a fanatic. “There are very few people of limited ability who are afforded the opportunity to make a major contribution. I have been afforded that opportunity, and it’s overpowering.” He adds, “Ask any fanatic--he’ll tell you how right he is. Why should I be different from any other fanatic?”

The rationale behind the method is simple, just common sense, Mr. Saxon acknowledges. “Kids cannot learn through a single exposure, and in particular they can’t learn abstractions in a single exposure.” Nevertheless, he says, most algebra texts pay insufficient attention to this.

And because the material recurs, he says, students also get a sense of continuity and become more confident that they can master it.

“Most math books,” he says, “are like the Book of Revelation--horror stories and surprises from beginning to end. Students see my book as the 23rd Psalm--it’s a nice safe place to go.”

The experience of his students was matched by his own early encounters with higher mathematics. “Math was always difficult for me. It almost kept me from doing the things I wanted to do. All of the things I did were made possible by the math.”

He argues now that many students do not pursue science and mathematics careers because they are entirely put off by algebra. “This is the reason they won’t take chemistry. They’ve cut and run. They can’t handle the percentages and they can’t handle simple ratios.”

The method is effective, Mr. Saxon says, even with students of modest ability who often do poorly in algebra. These students, he argues, are victims of a system that favors high-ability students.

“All our math education is set up almost with malice aforethought to restrict knowledge to the brilliant few,” he says. “The others can also understand abstractions. It just takes more exposure.”

Most of the reaction to the text has been favorable, although some educators argue that students will grow bored with the constant repetition.

Larry S. Gregory, mathematics specialist for the state department of education in Tennessee, points out that the data that show the dramatic gains are based on “fairly limited objectives.” He also notes that Mr. Saxon wrote the tests.

The claim that the method is novel also troubles some educators; most texts do include some review. “It’s a matter of degree,” Mr. Gregory says. Although not sufficiently familiar with the text to know whether Mr. Saxon makes good his promise to include all concepts in all lessons, Mr. Gregory says that if he does, that would be “more than is done in a typical book.”

Mr. Saxon argues that the method is not so much new as ignored, not tried and found wanting but found difficult and left untried. “One of the things that has bothered me the most is that what I’m doing is so obvious; how can be it be so overlooked?” he says.

Highly Successful Method

Teachers who have used the method, however, report that it is a highly successful way of teaching algebra. Mickey Yarberry, an Oklahoma City junior-high mathematics teacher who taught with the Saxon text for two years, says that although the method takes some getting used to, the results are worth it. “In a way, it is more confusing at first because you’re teaching 15 different things,” she says. But everyone becomes accustomed to it, they make rapid progress.

She says that she began using the text, at the request of Mr. Saxon, with some doubt. She taught one algebra class using the Saxon book, and another using a different text.

She was convinced, she says, that the teacher, not the text, was the vital factor in students’ success. “I went in as a real skeptic,” she says.ought that I could outteach his book.”

But midway through the year, she says, it became apparent that the Saxon students were doing better. Now, she says, she isn’t sure she would want to teach out of another book. Other teachers in Oklahoma have also reported that they like the book, according to Lee Graham, president of the Oklahoma Federation of Teachers. Mr. Graham, who is not a mathematics teacher, says he has heard no unfavorable comments about the book, and that several teachers at the school where he works like it very much.

In New Mexico, which recently added the book to the state-adoption list, state education officials have not field-tested it and hence have no hard data on its effectiveness. But comments from teachers and other mathematics educators have been favorable, according to William A. Trujillo, secondary mathematics specialist for the state department of education.

“Around the state, I’ve gotten a positive response,” Mr. Trujillo says. In general, he says, those who reviewed the book said that the approach seemed to be one that would benefit the student.

“The cover of the book says ‘incremental learning,”’ he says. “That, in effect, is what it is.” He says that the book does differ from some standard algebra texts currently in use in that it offers more of a balance between skill development and concept development. Some texts, he says, stress one at the expense of the other. “What I see Saxon as trying to do is get a blend of the two. It’s a different approach to learning not just algebra, but math.”

Marketing the book, several officials point out, may be a problem, since the book has no sequel and is not part of a series. Schools may be deterred from using it because there is no text with which to follow it. Mr. Saxon, however, is working on that.