Xavier Zuniga, 5, shows off his block tower during Kindergarten Prep at Douglas MacArthur Elementary in Alexandria, Va. on Aug. 16. The week-long program helps kids get ready for their first year of school. (Astrid Riecken for The Washington Post)

One day in August, 16 squirmy youngsters at Alexandria’s Douglas MacArthur Elementary School made their way down an empty hallway, some moving haltingly, some running their fingers along the walls.

“Ladies and gentlemen, we’re going to walk quietly to breakfast,” their teacher, Anthony Jackson, bellowed. “I like what I’m seeing today! Good job!”

It was the third day of Kindergarten Prep, a half-day program intended to prepare 4- and 5-year-olds for their inaugural year at the Virginia school. Jackson hoped the children would learn the basic rhythms of the school day and the basic rules of the classroom: Raise your hand when you want to speak, ask the teacher if you need to go to the bathroom, never be afraid to ask for help.

Across the nation, about 3.8 million children will start kindergarten at public schools this fall, some entering classrooms for the first time. In an era when kindergarten is chock full of academic rigor, it can be a moment rife with stress: busy hallways, peculiar routines, unfamiliar faces and long stretches of activity without nap time.

To ease the transition, many schools have introduced boot camps or orientation weeks for young children, hoping to give them a head start so they can be successful.

Kaiden Jackson, 5, gets a little help from teacher Jack Dowd during Kindergarten Prep. (Astrid Riecken for The Washington Post)

“They’re much more comfortable and ready to learn on the first day of school,” said Lisa Piehota, executive director of elementary education for Alexandria City Public Schools. The program, offered to all incoming kindergartners, costs the district about $100 per child.

The programs reflect a move toward more academic rigor in kindergarten, with lessons on reading and math displacing play and free time. Education experts say No Child Left Behind — the federal education law that required more high-stakes testing — spurred the shift, putting pressure on educators to get children ready for standardized exams earlier.

Children from low-income households — who are less likely to attend preschool — are starting off further behind classmates who attended preschool.

At Mount Vernon Woods Elementary in Fairfax County, where 78 percent of the school’s students come from low-income households, some incoming kindergartners show up five weeks before the start of school.

“You have to do whatever you can do to get an early start . . . and do whatever you can to fill the gap,” principal Clint Mitchell said. The school district runs a four-week Bridge to Kindergarten program for at-risk children, and Mitchell uses about $9,000 of school-based money to run another week-long kindergarten transition camp for all children.

Teacher Anthony Jackson shows Jay Fox, 5, how to mold clay into letter shapes. (Astrid Riecken for The Washington Post)

Some of the short-term prekindergarten programs — ranging from a few days to six weeks — are intended to close the gap for children whose families did not have the means to send them to preschool.

Schools in Charlottesville and Des Moines bring children in for about a week during summer to get them accustomed to school buildings. Many schools in California offer four-week prekindergarten academies for at-risk children who have never been to preschool. Fairfax County schools offer a similar program, aimed at giving at-risk children a head start to the school year.

The Pre-Kindergarten Academy in Solano County, Calif., targets children at risk of falling behind because they are English language learners or because they have special needs. More than half of children in the county never attend preschool, and the academy gives a small fraction of them the chance to get a head start.

“We have found that those little ones also critically need the support so they don’t enter school with that gap in their social skills,” said Lisette Estrella-Henderson, the Solano County schools superintendent. She said it also gives teachers the chance to identify children with special needs.

She acknowledged that a summertime of cramming cannot replace a year or more of high-quality preschool. In the absence of money from the state to provide universal prekindergarten, the boot camps can help give a boost to children from families unable to afford preschool.

“I’m really a believer that these pre-K academies could potentially change a child’s developmental trajectory,” Estrella-Henderson said.

Amanda Williford, a University of Virginia professor whose research focuses on academic readiness for children, said a short-term program can help a child feel more comfortable in the classroom, but she was skeptical of the long-term effect.

“That is not designed to get a child ready for kindergarten. It’s really just designed to help kids feel more comfortable,” Williford said.

In Jackson’s Alexandria classroom, students had made plenty of progress toward becoming full-time kindergartners. Nearly all of them rotated politely among activity stations without supervision, making patterns with blocks, creating rubber-band art on peg boards and stretching clay into letters.

Jackson said the week gives him an opportunity to get to know his students: their strengths and weaknesses, their favorite colors and interests. It makes the children more comfortable following his directions, so they can focus on learning.

He gave a small group of students a handout with circles drawn on it and asked them to make their own art using the circles. One girl drew in a face and eyeglasses.

“She’s a spy girl with glasses,” she explained. “These are not ordinary glasses. These are spy glasses — to help her see the bad guys.”

A boy pressed an orange crayon and scribbled indiscriminately over the circle.

“It’s coral!” he said.

That gave Jackson a clue to the boy’s interests and will help him tailor lessons later in the year. If the child is interested in sea creatures, Jackson said he will keep an eye out for books about the ocean, hoping to spur excitement about reading.

At the end of the day, he led students in free drawing. One girl drew an elaborate birthday party scene complete with a cake on which she wrote her name. Another girl scribbled with crayons and handed it to Jackson.

“What is that?” Jackson asked.

“It’s you!” she squealed.

He smiled. “Well, I am just a handsome guy.”