There's not much in Lynne Cheney's diagnosis of what's wrong with public education that I'd take issue with. Who could dispute her contention that the teacher certification process delivers teachers who know too little of what they are expected to teach, that the standardized tests used to measure student achievement often encourage fragmented learning or that textbooks are often dumbed-down and boring?

What bothers me is not her diagnosis but her prescription: that all-purpose elixir called "choice." The problems identified by Cheney, who, as chairman of the National Endowment for the Humanities, is a sort of official kibitzer on the nation's intellectual life, are serious. Schools of education do spend too much time on teaching technique and too little on content; the Scholastic Aptitude Test (which came in for special criticism in Cheney's 52-page report) does lead some teachers to "teach to the test" and the briefest look at some of the texts used in the public schools leaves no doubt that publishers, in the name of "readability," have squeezed the blood out of what should be inherently interesting subjects.

But they are separable problems, subject to different solutions. On the subject of teacher preparation, for instance, Cheney plumps for alternative certification, which would allow schools to employ subject-matter experts as teachers -- whether they have taken courses in educational methods or not. But as Stanford's Lee Shulman has pointed out, neither subject mastery nor teaching technique, standing alone, makes for good teaching.

Good teachers know how to teach: how to present the same material in a dozen different ways, produce the effective analogies and demonstrations, relate the material to matters of current interest, supplement the textbooks with illustrations from other disciplines and in general bring life to their teaching. This requires pedagogic skill.

But as Shulman notes, it also requires a deep mastery of the subject matter. Merely to replace teaching experts with subject-matter experts is no solution at all. Combining the two would not only make sense for training teachers but also might reduce the reliance on test-guided instruction. Teachers who have mastered both subject matter and technique could give students the academic wherewithal to pass standardized tests without teaching to the test. They are likely to love their subjects and to pass that affection on to their students. Moreover, they are likely to choose livelier books than the dumbed-down texts too many school systems now use.

Much of what has gone wrong in teaching results from an overreliance on proxies for mastery. The questions on the SAT, for instance, are proxies for the subject matter they cover. A student who reads a lot is likely to do well on the vocabulary portion of the SAT. But too many teachers, under pressure for better SAT results, try to teach vocabulary directly -- with disappointing results.

Perhaps the most outlandish example of the proxy fallacy is E. D. Hirsch's "Cultural Literacy." Hirsch began with the credible notion that there is a body of specific information that well-educated people know, or at any rate, know about: "quadratic formula," "nolo contendere," "best-laid plans," "Nob Hill." Then in response to the implicit challenge, he tried to list these bits of information in his "Dictionary of Cultural Literacy."

The conclusion, whether Hirsch intended it or not, is that learning the list is a useful proxy for the knowledge base that familiarity with the words on the list implies. It is, of course, no such thing -- no more than reading book reviews is a viable substitute for reading books.

Interestingly, Cheney herself falls victim to the proxy fallacy in her nostrum for curing the ills of public education: choice. Educational choice, whether it refers to a voucher system in which parents are free to choose between private and public schools, or only to a choice among public schools, may be a worthwhile idea. But choice as a proxy for improved public education won't wash. Being free to choose your own doctor may be a good idea, but if the problem is that medical schools place too little emphasis on, say, nutrition, choice alone won't be enough to fix it.

To a large extent, the problem with schools is that the formalization of teaching credentials and the overemphasis (in teachers' colleges) on technique have given us teachers with too little mastery of their subjects.

The cure for that is not to expand the choice among poorly trained teachers but to overhaul the way we train teachers. Lee Shulman's idea may be a good place to start.