Summer is the season when children play outdoors tirelessly until nightfall, burning up all the energy they had stockpiled throughout the school year, right?

Reality check: According to a new national study of younger elementary school students, the risk of gaining excessive weight is far greater during the summer than when they are in school.

A nationally representative sample of 18,170 kindergartners was weighed in the early fall and again in the late spring from 2010 through 2013, when the children were finishing second grade. The prevalence of children who were overweight increased to 28.7 percent from 23.3 percent. The prevalence of those who measured as obese grew to 11.5 percent from 8.9 percent. Most strikingly, according to the study published on Wednesday in the journal Obesity, all of the increases were during the summer breaks. No increase in the prevalence of being overweight or obese was seen during the school year.

“It’s dispiriting how little progress we can see as a result of all these school-based fitness and nutrition programs,” said Paul von Hippel, the lead author and an associate professor of public affairs at the University of Texas at Austin. He was referring to initiatives such as soda bans, recalibrated school cafeteria food and more attention to physical education and nutrition curriculums.