Mary Budiac, who teaches third grade in Wisconsin, mentions the time one student’s father called up her cell phone. His daughter had an unusually poor score on a test — some little, twice-weekly low-stakes test, but he was fretting.

Needlessly, it turns out: The girl just filled in the wrong set of circles. Next quiz, she wouldn’t. Crisis averted, but Ms. Budiac says that’s the kind of attention to academics she sees out of her students’ parents.

Ninety-nine percent of whom are low-income. Ninety-eight percent are native speakers of Spanish, and nearly all live in the crime-plagued neighborhoods of Milwaukee’s south side around Ms. Budiac’s school, St. Anthony’s, which their children attend on vouchers from Milwaukee’s school choice program. Ms. Budiac said she didn’t see this kind of parental engagement when she taught in a prosperous small town. At St. Anthony’s, she sees half her students’ parents daily.

Ms. Budiac isn’t the only one. The school is a standing refutation of some of the most persistent myths about school choice. Perhaps the most patronizing is that poor parents are disengaged and won’t choose a rigorous education when offered it.

What tipped off the father on the phone was a test. St. Anthony’s does a lot of those, so it can see whether or not children are mastering the material and whether they’re ready to push ahead. The idea, says the president of the school, Terry Brown, is to keep children, whatever their age, working on material tough enough that they’ll get about 85% of the answers right — not too hard, not too easy.

It’s key to the approach the school instituted four years ago. An ordinary parochial school that didn’t think it was doing enough, St. Anthony’s switched to the sometimes-scorned direct instruction method. Now, lessons and classroom techniques are tightly coordinated, the teachers get huge amounts of ongoing coaching, and the children’s scores on state tests are showing dramatic improvements. The fifth-graders read “A Midsummer Night’s Dream.” The elementary school has gone from having one child to 18 of them in high school-level algebra.

“We have the same parents that other schools do,” principal of St. Anthony’s, Ramon Cruz, says, other than that nearly all are poor enough to qualify for the school choice program.

Mr. Cruz, who ran direct instruction programs as a Milwaukee Public Schools principal, says it’s different with school choice: “In choice, we can say this is what it is, this is what we demand.” Public schools can pursue rigor, but it’s much easier because St. Anthony’s doesn’t have to negotiate each change with bureaucracy and a union. “In a Catholic school, it’s easier,” he says.

St. Anthony’s can tell those parents it will keep their children two hours more a day, that they’ll be graded on how many books they read from the 30,000-book school library and the book’s challenge level.

“We have local control, so we can put in place what we feel is best for the students,” the school’s curriculum specialist, Mary Schmidt, says. “We can follow it and modify it as the data informs us.”

The school is free as well to embrace other strategies that, in public schools, get tangled in politics. On language, for instance, St. Anthony’s offers English immersion. The support staff speaks Spanish for parents’ benefit, but from the first day, all the instruction is in English. Four-year-old kindergartners who started in September speaking only Spanish are learning English vocabulary; they’ll be starting to read, in English, by January, says Mr. Brown. You can’t get English immersion at Milwaukee public schools, which use slower bilingual methods. Nationwide, few school issues are so fraught with politics as how to teach English to immigrant children. Yet, Mr. Cruz says, parents drive it at St. Anthony’s. They bring children from public schools, he says, and specifically tell him they prefer St. Anthony’s approach — “They want the kids to learn the English language.”

Meanwhile, the school is unabashedly Catholic. Weekly Mass, more rigorous religion classes, the image of the Virgin of Guadalupe in each room — these things pass on a core element of families’ cultural identity, their Catholicism, even as the history and literature curriculum and the language immersion are traditionally American. The school can do these things because the parents are there by choice. It can afford to do them because, though the voucher costs taxpayers less than the state aid alone per child at the Milwaukee Public Schools, it is triple the typical parochial school funding. This is what the customers want. St. Anthony’s enrollment has doubled in four years. At just over 1,000 students, it’s easily the largest school in the choice program. A recent report, widely touted, contended that school choice has been ineffective in Milwaukee because poor parents choose badly. There were problems with the paper: It excluded private school choice, covering only the eeniemeenie-minie-moe inside the public system. The researchers didn’t use any surveys of Milwaukee parents, just extrapolating national data.

Whereas looking at the facts in the classrooms at St. Anthony’s gives you a different conclusion: Here are children getting a better education, a more rigorous one, and parents are flocking to it. Here, the notion that poor parents don’t know what’s best for their children crashes into a countervailing fact — that no one cares so much about a child’s education as his parents, even if they’re poor.