Washington ? “Call Ray Simon,” says Secretary of Education Rod Paige to a visitor, who does. Simon, Arkansas’ chief school officer, confirms that in the last five years the new high school teachers graduated by his state’s colleges included 1,193 physical education teachers. And one physics teacher.

That, says Paige, is just one indicator of the cultural problems that make education in grades K through 12 resistant to change. It is particularly difficult to improve using federal leverage. Paige, the first black secretary of education, and the first to rise to that office from an urban school system — he was Houston’s school superintendent — says his strongest weapon for reform is: shame.

He means the power to embarrass states if their results on the National Assessment of Educational Progress (NAEP) — the “nation’s report card” administered and designed since 1983 by Education Department officials and the Educational Testing Service (ETS) — reveal that they are not progressing. This shaming power, although of uncertain effect, is, unfortunately, the principal lever created by the No Child Left Behind Act enacted in 2001.

Meaningful school choice — competition not just between public schools, but also between public and private schools — is probably the only strong means of enforcing accountability. It turns parents into consumers — comparison shoppers for schools. Although the choice provisions of the 2001 law are trivial, Paige has another hope.

Jan. 31 was the deadline for the states to file their accountability plans for achieving and measuring year-by-year progress by underperforming schools and students. Starting in 2005, states must administer their own standardized tests annually to all students in grades 3 through 8. The results will provide school-by-school results which can then be measured against NAEP to check the rigor of state tests and standards.

Each school’s and district’s results will be published, allowing school shopping by parents moving within a community or to a new community. And a school’s unsatisfactory results will turn attentive parents into indignant consumers. Even if a state produces only a minimally rigorous accountability plan, NAEP test results will reveal the shortcomings of that state’s educational product, measured against performances nationwide.

Paige’s hopefulness must be tempered by a fact and a danger. The fact is that the shaming power, such as it is, depends on attentive parents. But an ETS survey last year revealed an attentiveness deficit: only 12 percent of adults — and only 36 percent of educators — even know that No Child Left Behind is law. The danger is that governors, at the behest of their accountability-averse public education establishments, may try to foment an anti-testing backlash.

Educational shortcomings do not reflect government parsimony. The percentage increases in spending for the U.S. departments of defense, health and human services, and education, 1996-2003, have been 48, 96 and 132, respectively. Total spending per pupil, adjusted for inflation, is two and a half times what is was in 1965. But NAEP reading scores are essentially unchanged. This refutes the durable delusion that schools’ cognitive outputs vary directly with financial inputs.

Actually, we have known for 37 years that, as the 1966 Coleman Report stated, “Schools are remarkably similar in the effect they have on the achievement of their pupils when the socioeconomic background of the students is taken into account.” Meaning the quality of a school will mirror the quality of the pupils’ families.

Which is why in 1991, an ETS official estimated that about 90 percent of the performance differences among schools can be explained by five variables: number of days pupils are absent, number of hours pupils spend watching television, number of pages pupils read for homework, quantity and quality of reading matter in pupils’ homes and — much the most important variable — the number of parents in the home.

America’s school year is about 180 days, the shortest in the industrial world. And Paige tartly notes that days when substitute teachers teach often amount to days subtracted from the school year. Asked how long a school should be in session, Paige brusquely answers: “It depends on what is going on in it.”

That depends decisively on the 9/91 factor: Between their births and their 19th birthdays, children spend 9 percent of their time in school and 91 percent elsewhere. And the inner city “elsewhere” often is homes without two parents.

Paige is asked if, given the cultural impediments to improvement, trying to move education with a lever as slender as No Child Left Behind is heavy lifting. His laughing response — “Heavy lifting was putting a Reagan sign in front of your house in my district” — is not really an answer, or a denial.