Four years ago, Lucy Dathan moved to New Canaan, Conn., where she enrolled her three children in public elementary school. They met new classmates. Their teachers were attentive. But something was amiss: Recess was limited to a 20-minute break after lunch, or about half the time as at their previous school, in California.

Ms. Dathan said a shift in her children’s mood was palpable. They found it difficult to focus on homework. They were restless and sometimes cranky after school, which she attributed to pent-up energy. With so little time for schoolyard play, she worried they were losing the ability to navigate personal relationships. “It was hard for them to adjust to only one recess,” she said in an interview.

So Ms. Dathan, who was elected to the Connecticut legislature in November, agreed to support a state bill that would require schools to provide at least 50 minutes of daily undirected play for students enrolled in preschool through fifth grade. “I haven’t had one person ask, ‘Why are you doing this?’” she said of parents, students and teachers who have contacted her. “I think playtime fosters the creativity that we need to solve crazy world problems, like global warming, or other issues we need to face as a planet.”

Ms. Dathan is not alone in her observation. Last April, Arizona legislators passed a law that provided two daily recesses for the state’s elementary school students. Teachers have already seen encouraging results, reporting fewer disciplinary actions, enhanced test scores and improvement in children’s overall health. And just last week, youngsters from Arkansas, where a similar move is also being considered, sent letters to state legislators asking they be given a longer recess break.