RIDGELAND (AP) — Obesity rates are dropping among Mississippi elementary school students and leveling out overall — important milestones in keeping young people healthy, researchers said.

But obesity rates are steady or rising among black students. And, as finances continue to dwindle, schools’ efforts to reduce the problem are diminishing.

The state’s elementary school students made the biggest strides. The share of overweight and obese children in kindergarten through fifth grade fell from 43.6 percent in 2007 to 37.3 percent in 2011. That drop is too big to be explained by statistical variation in the survey, meaning it shows real improvement.

“We’ve begun to see some improvement,” said Therese Hanna, executive director for the Center for Mississippi Health Policy. “There’s a glimmer of hope.”

The findings were discussed Monday at a conference evaluating 2007’s Mississippi Healthy Students Act, a state law meant to promote nutrition, exercise and health education. The law is part of an effort by Mississippi leaders to fight the state’s expanding waistline, which translates into poor health and early death for many residents.

The share of all overweight and obese students also fell, from 43.9 percent in 2005 to 40.9 percent in 2011, but that change wasn’t large enough to rule out swings within the margin of error in the survey. Jerome Kolbo, a University of Southern Mississippi professor, said future surveys may produce conclusive evidence of overall drops.

He said one key will be what happens when younger students move on to middle school and high school.

Kolbo said there was a notable split between results for white and black girls. In 2005, 47.5 percent of black females were overweight or obese, climbing to 49.2 percent in 2011. For white female students, 39.9 percent were overweight or obese in 2005, falling to 32.3 percent in 2011.

“The disparity could widen as the cohort moves into middle and high school,” Kolbo said.

Kolbo said some research suggests black children may be more sedentary at home and that their parents may be more likely to serve fattening foods. There’s also some evidence that the problem may lie in poorer households. A separate survey by professors at Mississippi State University shows that parents in households with incomes of $20,000 are more than twice as likely to report that their children are obese than parents in households with income of $100,000 or more.

That parental survey shows that many parents don’t see their children as too heavy even when they are. While parents overall reported that 15 percent of children were overweight or obese, calculations done by researchers show that the share was actually 39 percent.

“What is the perception of the norm in this state?” asked Mississippi State’s Linda Southward. “It’s not where it needs to be in terms of a reality check.”

While parents say they’re trying to feed their children healthier food, specific questions about eating habits suggest they’re not making much progress.

Results have been better at schools, thanks in part to the law. More than 40 percent of schools visited by the University of Mississippi now offer no fried foods. Other results show that schools have increased time spent in physical education and health education.

But time spent in nutrition education has fallen, and progress toward installing expensive ovens that can replace fryers has stalled. Also dropping was training to promote healthy eating and the use of fresh fruits and vegetables.

Teresa Carithers of the University of Mississippi said that many school districts rely on commodity foods provided by the U.S. Department of Agriculture, and when fresh fruits and vegetables are unavailable through that program, they turn to canned or frozen foods to stay within their budget. And districts, especially those strapped for cash, may only pay for training that is required for employees.