When President Obama signed the Healthy, Hunger Free Kids Act earlier this month, he joked that if he hadn’t been able to get the bill passed he would have been “sleeping on the couch.” His wife, Michelle, laughed this off: “Let’s just say, it got done so we don’t have to go down that road,” she told the crowd at a D.C. elementary school for the signing.

The bill, which was a priority for the first lady, is designed to improve both access to and quality of school food, and it contains many provisions that will help in Michelle Obama’s campaign to end childhood obesity within a generation — and a few that may actually hurt it. The fight over how and what we feed our kids at school is a complex one; clear thinking about what we need is often hampered by persistent myths.

1. School meals are free for the children who really need them.

This is certainly the intent of the National School Lunch and Breakfast programs, which offer free and reduced-price meals to children, based on their families’ income, as well as full-price meals to any student. Currently, students are eligible for free meals if that income is below 130 percent of the federal poverty line — $23,803 for a family of three, for instance — and for reduced-price meals if it is somewhat higher — up to $33,874 for that family of three.

Unfortunately, these thresholds are unrealistically low, especially in areas with high living costs. The 2008 Household Food Security survey by the U.S. Department of Agriculture found that more than a fifth of households with the most severe form of food insecurity — in which children themselves sometimes went without meals — had incomes above the cutoff for reduced-price school meals.

Even some children whose family incomes are low enough to qualify for free school meals never actually get them. The process for establishing eligibility is cumbersome, expensive and prone to mistakes. In a recent USDA study, more than a third of children denied certification for free or reduced-price meals were found to have been denied in error. And even after getting approval, at some schools a child must wait each time as a cafeteria cashier checks eligibility.

Finally, there is a stigma attached to free meals, which deters some families from applying and discourages some students from eating the meals for which they qualify. Direct certification, a process in which state or local welfare agencies notify schools of eligible children, has been shown to reduce mistakes and bring more kids into the program.

The new law contains a modest expansion of that procedure. But the

only way to fully eliminate the errors, the administrative burden and the stigma, is to provide school meals the way we provide books, desks and chairs: free for all.

2. Most students who don’t take part in the National School Lunch Program eat a healthy lunch brought from home.

Even if eligibility for free lunch is problematic, students can always brown-bag it, right? That’s not what I’ve seen in school cafeterias across the country.

In the USDA’s most recent comprehensive study of school food, 62 percent of students chose the school lunch and about 10 percent of the students brought lunch from home on the day being surveyed.

What happened to everyone else? Some did not eat lunch (4 percent of elementary students and 8 percent of high school students). Others bought food from a la carte options in the cafeteria, left the campus to purchase food, or bought from vending machines or school stores.

What they were getting on their own was typically not as healthy as the school lunch that met the federal nutrition guidelines, known as the reimbursable meal. According to one recent nutrient assessment, high schoolers who participated in the lunch program consumed significantly greater amounts of vitamins A and B12, calcium, potassium and other nutrients than nonparticipants did.

Other studies have found that kids in the school lunch program drink more milk and eat fewer snack foods, sweets and sweetened beverages than others.

While certainly some households send carefully crafted healthy lunches, far too many children arrive at school with a brown bag containing a sweet drink and a bag of chips.

3. Kids won’t eat vegetables.

This belief is at the heart of many school menus — kids won’t eat anything green, so we shouldn’t waste time and money trying. A number of schools are systematically disproving this myth.

In Compton, Calif., Tracie Thomas introduced salad bars, which are now one of the most popular options for students. In New Orleans, chef April Neujean conducts tastings with her kindergartners — one for each letter of the alphabet — as they learn their ABCs (Apples, Bananas, Carrots, Daikon radishes).

I have seen students enthusiastically eating all sorts of healthy options, especially where they have first encountered the foods in a school garden or classroom cooking demonstration, helped to plant or harvest the vegetables or even met the farmer growing their greens.

Kids will eat vegetables, even in the cafeteria, though they are far less likely to do this if they can purchase salty snacks and sweets from a display near the cash register, a vending machine or a snack bar.

For example, a study in Texas found that students with access to a la carte foods ate only three-quarters as many fruits and vegetables as did those without such easy access to other snacks. A survey in Kentucky found that students who bought extra snacks to go with their lunch had greater fruit “plate waste” — or uneaten food — than did students who passed up such purchases.

4. Schools need to sell junk food to break even.

Most cafeterias have pizza, chips, french fries and cookies for sale alongside healthy meals that are federally reimbursable. The food service directors I have interviewed uniformly believed that they must sell such items in order to break even and that the a la carte sales were subsidizing the official, federally regulated school lunch. A new cost study, however, shows this to be yet another school food myth.

Junk food sales don’t even pay for themselves: On average, they bring in just 71 percent of the costs associated with offering them. Thus, school districts wind up diverting to a la carte sales substantial portions of the federal cash reimbursements intended to subsidize healthy meals.

The new legislation will help the cafeterias doing battle with vending machines. It gives the secretary of agriculture the authority to regulate all foods for sale in schools participating in the school lunch program.

5. Higher federal nutrition standards will ensure healthy eating.

Take a look at what happened last time Congress mandated higher nutrition standards for school food.

In the mid-1990s, Congress decided that school meals should comply with the Dietary Guidelines for Americans, which specified that no more than 30 percent of calories should come from fat.

In an effort to comply, many schools eliminated whole milk, but then found their meals falling below the calorie minimums set by the USDA. They couldn’t afford to add another fruit or vegetable, so many schools began offering sweetened, flavored milk, replacing the now-forbidden calories from fat with calories from high-fructose corn syrup.

The new standards, developed by the Institute of Medicine, call for a dramatic reduction in sodium to be phased in. This might work well if sodium were simultaneously reduced in the foods sold at corner stores and fast-food restaurants, but without such changes everywhere, it could actually lead to a drop in participation as school meals become more healthy.

Nutritional standards can do only so much to get kids to eat balanced meals. The basic federal meal guidelines used by a majority of schools require them to offer five components: meat or meat alternate, a grain product, fluid milk, and two servings of fruit and vegetables.

The school meal is counted as reimbursable if students pick at least three of those components. A grilled chicken breast, a green salad and a carton of low-fat milk constitute a reimbursable meal, but so do a hot dog roll (the grain), a serving of french fries (the vegetable) and a dish of canned peaches (the fruit).

We need to do much more with food and health education, and make sure that what we offer in the cafeteria reflects what we are teaching in the classroom. That kind of integration with the curriculum is far more feasible in a universal free program where eating school lunch becomes the norm.

The Healthy, Hunger Free Kids Act authorizes pilot programs in individual schools and districts to experiment with universal free-meal approaches. The National School Lunch and Breakfast programs will come up again in five years, the next scheduled Child Nutrition Reauthorization. Let’s start now to make universal free school meals the goal for that legislation.