Karina Orton, 14, sits on the living room couch leafing through her biology textbook while her sister, Sarah Jane, 10, munches on a sandwich at the table and Alison, 12, plays the piano in the next room.  Their brother Eli, 6, is building planes with his favorite Legos and their mother, Emily, reads to Lily, 4, who is drinking milk from a sippy cup.

The relaxed scene resembles a weekend morning, but it’s 11 a.m. on a Thursday.  For the Ortons, this is the norm.  They don’t rush off to school each morning or spend afternoons doing homework. Emily and Erik Orton have been homeschooling their children for more than four years.

“I was really nervous because it’s such a huge responsibility,” Emily, who’s 37,  says about that decision.  “I have my degree in education and I was still nervous because it felt like I would be replicating a classroom in our house.”

The Ortons turned to homeschooling because Karina asked for it, her mother says. Karina doesn’t remember the conversation, but recalls that her public school wasn’t very challenging. “I’m a really fast reader, so if I like a book, I can read it in a day,” she says.  “But in school they usually read it one chapter at a time.”

A decade ago homeschooling was a cutting edge alternative approach to education, but it has become almost mainstream, says Brian D. Ray, president of the National Home Education Research Institute, who has studied homeschooling for 25 years. His 2009 nationwide study, published last spring in Academic Leadership Journal, estimates the number of home-educated students in America at  1.7 million to 2.3 million.

Surveying 11,739 students from 50 states via online and paper questionnaires, including achievement test results, the study also used data from the 13 state education departments, five nationwide homeschooling organizations and other published research to develop that estimate.

More than 2500 New York City students are being homeschooled this year, according to the city’s Department of Education, a number that has fluctuated from 1880 students in 2002-03 to a peak of 3654 in 2006-07.

New York State laws give homeschooling families substantial flexibility, making the administrative procedures surprisingly simple.  Parents must submit a letter of intent to the New York City Department of Education homeschooling office and write an individualized home instruction plan for the year, with a syllabus and textbook for each course.

They must submit quarterly reports to show that children are meeting the plan’s goals, record the number of hours studied and produce a year-end assessment. The law allows parents to choose someone to administer a year-end achievement year-end test — a certified teacher, a peer group review panel, even the parents themselves. The laws also allow homeschoolers to use their district school’s gym, library and other facilities.

Emily Orton says the process proved easier than her family thought, allowed them to spend more time together and simplifying their lives. “We were finally able to get enough sleep,” she says, adding that homeschooling allows Lily, who has Down syndrome, to learn from her siblings.

Erik also thinks that traditional schooling can interfere with learning. “Children are naturally curious and able to figure things out,” he says. “If you give them some freedom, they can learn deeper than when there’s a traditional classroom and a test at the end.”

While Ortons prefer to teach their children themselves, other families hire tutors.  It can be costly, from $85 to $95 an hour, depending on the course and materials, says tutor Jessie Mathisen.  She taught science in New York City public schools for two years before starting a business, Tutor New York City, that coaches members of two uptown homeschool groups.

She says the reasons local families chose to homeschool vary.  “Some parents really enjoy teaching their kids themselves – the closeness, protection against bad influences,” she says.

Nationally, the institute study shows a similar diversity: Some homeschooling parents feel their children accomplish more studying at home with individualized approaches, some cite religious reasons or safety concerns, and others believe it enhances family relationships.

Local families build in a lot of socializing, often with other homeschooled kids, Mathisen points out. The National Home Education Research Institute’s study confirms that “the large majority of home-educated students consistently interact with children of various ages and parents outside their immediate family.”

On the downside, Mathisen thinks many homeschoolers never learn to stand up to bullies, “but for many parents it’s a small price to pay,” she says.  “Other parents can’t even bear to think about their kids bullied.”

The National Home Education Research Institute’s study also shows that homeschooling families are larger, better-educated and higher-earning than the norm:  68.1 percent families have more than three children, 81 percent have an at-home mother and over 60 percent have college-educated parents. The families’ annual incomes average $75,000 to $79,000, of which $400 to $599 is spent on educational materials per student.

The Ortons live in a two-bedroom Washington Heights apartment where the kids’ bedroom has three bunk beds and the parents’ bedroom also serves as an office and piano studi0.

“I cover math, technology and music because I have a degree in music,” says Erik. While he doesn’t give his kids lessons, “they all play multiple instruments and write their own songs.”

Emily, who has a degree in bilingual education, covers almost everything else, except for Karina’s tutoring in biology, which Karina barters for in exchange for babysitting her tutor’s kids.  Karina also studies the Old Testament at the Church of Jesus Christ of Latter-day Saints that the Ortons belong to, a lesson she gets up for at 6:15 a.m.  “I usually go back to bed when I get home,” she admits.

To support the family, Erik does graphics work for an investment bank, working a 3-to-midnight shift. “That’s when Emily and I have a grown-up time, quiet time,” he says, describing their daily routine. “We go to bed around 2 and start our day late.”

That schedule, with Erik at home most of the day, made home schooling even more appealing.  The Ortons disliked the usual morning frenzy, Erik says, lamenting that he barely saw his children. “I’d walk them to school and I’d pass them on the way to work by the subway,” he says, “and that was it.”

Now Erik does work for his theater production company, O Productions, writing and producing plays during the day and essentially keeping a second job while being with his family.

Setting their own schedule gives the Ortons freedom to take day trips and travel.  “We spent a month in Cape Cod in September,” says Erik. “It was quiet and empty.”

The Orton kids are quick to recall favorite educational experiences: they visited a biodynamic farm and forged hooks at a blacksmith shop in Chestnut Ridge, N.Y., took art lessons at the Metropolitan Museum and ski lessons in Utah and learned to sail in New York harbor.

“Sailing is fun,” says Alison. She uses a yacht-shaped Christmas ornament to explain how the sails work.  “I know how to steer. I can raise the jib, but you need more than one person to raise the main sail.”

Except for Eli, who has already decided to become a ninja, the children aren’t sure what they want to do when they grow up.

“It’s such a hard question for me,” Karina says. “I love making things with my hands.”

Alison chimes in. “We’d love to grow our own food, but we don’t know how to do that very well.”

According to the National Home Education Research Institute’s study, homeschooled students test well, with scores 15 to 30 percentile points above public school students’ average of the 50th percentile.

Homeschoolers succeed at college at the same or slightly higher rate than public school kids and fare about as well in adulthood.  However, they  partake more in community services, vote and attend public meetings more frequently than their peers, and internalize their parents’ values and beliefs at a higher rate.

“Our home school isn’t something that happens between certain hours on certain days,” Emily says. “It’s our approach to life.”