Bruce Fuller is a professor of education and public policy at the University of California at Berkeley and the author of “Standardized Childhood.”

Stakes were low but passions ran high as fervid 4-year-olds shouted the names of farm animals in Spanish and then in English. “Vaca, cow! Pollo, chicken!” Acing the translation, they snapped colorful tokens onto matching pictures as I watched a feisty round of bilingual bingo at a California preschool last month.

Meanwhile, enthused political leaders are gambling sizably more, suddenly promising free and universal preschool for all families. In his State of the Union address, President Obama renewed his pitch to boost annual pre-kindergarten spending by $7.5 billion. New York Mayor Bill de Blasio is pushing to outbid Gov. Andrew M. Cuomo’s go-slow plan to extend preschool to all young children. Democratic leaders in California unveiled a blueprint to subsidize pre-K for all children, even aiding those from wealthy families.

But an unbounded entitlement would not reduce children’s early gaps in learning. It could even exacerbate disparities. The issue is how, not whether, to invest more in preschool, mindfully preventing learning disparities before they emerge. Poor youngsters enter kindergarten already four to six months behind their middle-class peers in oral language and preliteracy skills.

Nor is the issue whether the nation can afford to lift poor children: Americans spend more than $53 billion each year on their pets, far more than family and government outlays for child care and preschool.

But as the pre-K bandwagon gains steam, it’s careering into hazardous territory. Policymakers must take stock of evidence that has emerged over the past decade and get beyond the hyperbolic mythology stirred by well-meaning preschool advocates.

Myth 1: All young children benefit from preschool. The pre-K lobby hopes to extend formal schooling a year or two below kindergarten as an entitlement for all families, no matter how rich or poor. But youngsters from middle-class and well-off homes benefit little from preschool, according to four independent teams of scholars, each tracking large national samples of children over the past decade.

Yet these scholarly groups consistently find distinct and lasting gains for poor children, as I discovered in tracking of 14,162 youngsters nationwide with Stanford University economist Susanna Loeb. The minuscule gains experienced by middle-class children largely fade out by fifth grade, according to a second longitudinal study overseen by the National Institute of Child Health and Human Development. Still, gains for poor children persist with greater strength when they attend high-quality preschools and then enter comparatively robust elementary schools.

Politicians such as de Blasio ignore these consistent findings when arguing, as he did last year, that subsidized pre-K should be “for everyone, doesn’t matter if you’re wealthy, doesn’t matter if you’re poor, doesn’t matter what color you are.” But empirically, a child’s home environment sharply conditions the efficacy of preschool.

Myth 2: A full day in preschool yields stronger gains than half-day programs. Young children attending quality half-day programs display the same learning gains as those attending full-day programs, according to a 2010 review by Child Trends, a respected Bethesda-based think tank.

The one crucial exception is for black children from low-income families. They display steeper growth in language and cognitive reasoning skills after attending full-day programs, detailed in a forthcoming University of California at Berkeley study on which I worked. Our team also found that preschool packs a stronger punch when children from poorer families attend for two years rather than just one.

Myth 3: Unionized teachers, not those in community centers, lift young children. Labor leaders see potential growth in new teaching posts and union members. But this would require granting school districts a monopoly over pre-K, wrestling control from the array of nonprofits, churches and grass-roots agencies that have long run preschools. A 2005 study found that more than three-fifths of all 4-year-olds attend community-rooted programs, not public schools, in many states from Massachusetts to California.

Preschools hosted by school districts are no more effective, on average, because nonprofits serve children under identical state safety and quality standards. Handing the robust pre-K sector over to school districts also would reinforce vast disparities in per-pupil spending and encourage strong urban teachers to migrate to suburban districts that pay higher salaries. A handful of states, including Oklahoma, instead allocate more for 4-year-olds and children from poor families, a progressive incentive for local preschools to attract disadvantaged youngsters.

Public schools will continue to reinforce inequality and harden achievement gaps until gross disparities in children’s early development are narrowed. But we must avoid squandering scarce dollars on full-day programs for children who gain little from preschool — essentially to buy the political support of their well-off parents. The rekindled push to expand preschool is welcome. But unless public dollars are focused on high-quality programs for poor families — while bolstering the neighborhood organizations that serve them — good intentions will turn into dashed hopes.