Word: saxonism
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They are often expected to memorize a good deal of difficult abstract theory about the basic properties of real numbers such as "associative," "distributive" and "commutative." The last term means simply that three and four always make seven in whatever order they happen to be added. Saxon, by contrast, uses diagrams and examples to make the same point clear and only afterward says...
...exchange the order of the numbers in an addition problem without changing the answer to the problem." According to Gerry Murphy, head of the math department at Hackley School in Tarrytown, N.Y., Saxon also tries to confront two fundamental weaknesses that afflict most Algebra I texts: the lack of a sense of continuity and connection among topics, and student failure to remember the material already covered. Saxon presents the material in small linked units, without the traditional division into chapters. Saxon treats the problem of retention by the obvious and old-fashioned device of a large number of daily cumulative...
...report card on Saxon includes some low grades. Some teachers who have examined the book are put off by the absence of traditional chapters. Others find the book "mechanistic" and too repetitive, and think it might be boring to use in class. Bruce Vogeli, professor of mathematics at Columbia University's Teachers College, sees Saxon's innovations as insignificant and ineffectual: "One can't teach algebra only as a skill. Drill and practice are only part of the problem." He likens drilling to the lowest common denominator of algebra. Mathematical literacy, assert Saxon's critics...
Criticism of Saxon tends to divide along the same lines as the debate about the future of American mathematics teaching. There are those who advocate a return to basics through practice and drill, and those who insist that practice without abstract theory is ultimately limiting. Both sides are in a sense right. Yet Saxon's main point contradicts neither. He simply affirms that Algebra I is not the place for obscure theory, which can be introduced later, when students know how to use algebra well enough to profit from it. "Algebra is the basic language of all mathematics beyond...
...root of the word algebra is the Arabic al-jabr, which means "bringing together." Saxon's synthesis of traditional practice and drill with the fundamentals of modern algebraic theory taught clearly may provide an alternative to the present dismal state of mathematics teaching. Alfred North Whitehead, the English mathematician and philosopher, once noted that "the study of mathematics is apt to commence in disappointment." If John Saxon is right, the study of algebra may not end so. -By Richard Stengel. Reported by Jeanne-Marie North/New York