SEATTLE • Three-year-old Desi Sorrelgreen's favourite thing about his pre-school is "running up hills". His classmate Stelyn Carter, five, says she likes to "be quiet and listen to birds - crows, owls and chickadees". And for Joshua Doctorow, four, the best part of pre-school just may be the hat he loves to wear to class (black and fuzzy, with flaps that come down over his ears).

All three children are pupils at Fiddleheads Forest School in Seattle, where they spend four hours a day, rain or shine, in adjacent cedar grove "classrooms" nestled among the towering trees of the University of Washington Botanic Gardens.

The pre-school programme, in its third year, is about 10km from Microsoft, which means some parents sit in front of computers all day inventing the digital future, while Fiddleheads children make letters out of sticks or cart rocks around in wheelbarrows.

Founded in 2012 by certified pre-school teacher Kit Harrington and naturalist and science educator Sarah Heller, Fiddleheads is part of a larger trend across the US that goes beyond Waldorf education, which has long emphasised outdoor play, even in inclement weather.

There is the Chippewa Nature Centre in Midland, Michigan, founded in 2007, where children wear hats and mittens during daily outdoor sessions in the frigid winter months. At the All Friends Nature School in San Diego, California, which became a nature pre-school in 2006, children often spend mornings making sandcastles at the beach. And at the Drumlin Farm Community Preschool in Lincoln, Massachusetts, founded in 2008, children learn to feed farm animals, grow vegetables and explore the farm's wildlife habitat.

Whether the schools are emerging as a reaction to concerns that early education has become increasingly academic or simply because parents think traipsing around in the woods sounds like more fun than sitting at a desk, they are increasingly popular.

The Natural Start Alliance, founded in 2013 in response to demand from a growing number of nature pre-school providers, counts 92 schools that deliberately put nature at the heart of their programmes and where children spend a significant part of each day outside, according to director Christy Merrick. That is up from 20 schools in 2008, when Dr Patti Bailie at the University of Maine at Farmington counted them as part of her doctoral research.

A typical day at Fiddleheads starts at 9am, with Desi, Stelyn, Joshua and fellow pupils zipping up waterproof suits so they can climb on, and sometimes slip off, sopping wet logs; create secret forts under dripping boughs of bright green and examine squirming earthworms in grubby hands.

The children go on "listening walks" with their teachers during which they stand in a circle with their eyes closed and name the things they can hear, like wind and rain, when they don't talk. The children also eat lunch, sing songs and occasionally squabble under the open sky and towering trees.

Desi's mother, Ms Judy Lackey, 34, is pleased. "It's just a magical place," she says. "In indoor spaces, teachers have planned everything. Here, you never know what you're going to see."

While the children are carefully supervised by teachers, the school has a choose-your-own-adventure attitude towards learning. So when pupils first placed one of those closely examined earthworms in an empty toy watering can during a recent visit, it prompted a conversation with a volunteer teacher, Ms Marnie O'Sullivan, about what kind of homes earthworms might most enjoy. (Hint: not a plastic watering can.) "We kind of just think and find what we want to do in our head, and we just do it," Stelyn says.

There are rules, and Stelyn, one of the oldest in the class, is quick to explain them: "If we see a bug, we are careful not to step on it. If we see a pretty leaf, we pick it up and put it in our magic spot."

Walking alone onto the park road (despite its ban on car traffic) and pretending sticks are swords are also forbidden. But such rules and a few others leave room for plenty of adventures. Children can cart around rocks in wheelbarrows, play at being (sword-less) pirates, examine trees split by lightning, dig in wood-chip piles to make child-size "nests", find an unknown seed and dub it a "nothing berry" and run up and down hills.

The most popular word at Fiddleheads is "notice", as in, "What do you notice about this fallen log?" and "I notice mushrooms".

"Some days we're setting up and we hear eagles calling to each other, and we run out and look up," Ms Harrington says. "Kids are the best at sharing in joy and wonder."

Or as Adele Miroite, three, says, her little hands wrist-deep in a wood-chip pile: "I love school."

Fiddleheads is one of at least 18 similar pre-schools founded in the Seattle area since 2005, according to a recent story in ParentMap, a local parenting magazine. And 18 apparently are not enough.

There are 51 kids on Fiddleheads' waiting list and 143 on a list for next year's spots, Ms Harrington says. That's after the school more than doubled its enrolment to 50 pupils in two classrooms this year from about 20 in one classroom last year. And pupils' parents, to judge from a small group picking up their children on a recent afternoon, aren't off-the-grid types.

They include lawyers, chief financial officers and television producers.

"I don't know if we're hitting a tipping point yet, but maybe," says Dr Bailie, who got her start as a teacher in an outdoor pre-school programme at the Nature Centre at Shaker Lakes in Cleveland. At the time, she knew of only about a half- dozen schools in the entire country trying something similar, she says. These days, she teaches a class specifically for would-be pre-school teachers who aim to work outside.

Dr Bailie thinks the pushback against standardised testing and growing concern about young children spending too much time on touch-screen devices have helped the market for outdoor schools. She also credits the best-selling 2005 book, Last Child In The Woods, by Richard Louv, which helped popularise the idea that children should spend as much time as possible in the outdoors.

Mr Louv, a journalist, argues passionately in his book that children should play and explore the outdoors in the same unstructured ways their parents and their grandparents did before them.

While reducing childhood obesity (8.4 per cent of American two- to five-year-olds are obese) by increasing physical activity is a prime argument in support of outdoor play, Mr Louv suggests that the need goes beyond exercise. Today's children have fundamentally lost touch with nature, he says.

"Nature deficit disorder describes the human cost of alienation from nature," he writes in the book. Among them: diminished use of the senses, attention difficulties and higher rates of physical and emotional illness.

Although they all try to address this "nature deficit disorder", not all of the new nature pre-schools are quite as natural as Fiddleheads, which belongs to a type of school usually described as a "forest kindergarten", characterised by having no indoor space other than an emergency weather shelter.

Many nature pre-schools, like Chippewa in Michigan, do have indoor facilities. Dr Bailie and the Natural Start Alliance both count as nature pre-schools those in which pupils are outdoors for a significant portion of their day and in which the focus of the curriculum is the natural world.

Some pre-school providers still think time indoors can be a valuable addition to an outdoor-focused day (and some children may prefer it). There's also the practical matter of getting licensed. Many states won't allow a school without a building to receive a licence, and unlicensed schools can usually operate for only four hours a day. In fact, that's a requirement in Washington state, and it's one of the reasons Fiddleheads is open only until 1pm.

Then there are the practical requirements of spending all that time outdoors. Children need the right clothing, which can be expensive. And even for the die-hards, sometimes it's just not really safe to have children under five playing outdoors.

At Drumlin Farm Community Preschool, where it can get quite cold, director Jill Canelli uses several overlapping sets of guidelines to determine when it is too cold, windy or icy to go outside.

If the temperature, with wind chill, is below 9 deg C, for instance, the children have an indoor day. That guideline is based on an Iowa Department of Public Health publication, Ms Canelli says. And if the local school district cancels activities because of snow, the pre-school will usually close too.

"Safety is first," she says, adding that parents have asked why their children weren't outside on a given day and she's had to explain Iowa's safe-temperature guidelines to them.

"Children can't learn if they're not safe."

Safety notwithstanding, Dr Deborah Stipek at Stanford University who studies early education is not a booster of the outdoor preschool model. "I have a feeling that this is a flash-in-the-pan idea," she says.

Dr Stipek points out that excellent natural materials can be provided to children indoors and that setting times when they can choose freely between activities such as blocks, art projects and dress-up allows for plenty of self-determined "adventures". And while she is a strong believer in the benefits children get by spending time outside, she is sceptical of the idea that spending the whole day outside is necessarily better.

"I don't see benefits of being outdoors doing the same activity as you'd be doing indoors."

But for the administrators of Fiddleheads, the benefit of children doing the same thing outdoors that they could have done indoors is as clear as a babbling brook.

"When I taught indoors, every material had a learning goal," Ms Harrington says of the various items she would put out for her pupils to play with when she was a Montessori pre-school teacher. "Here, the entire classroom is a material. Certainly, the materials we set out are that way, but this classroom has so much more to offer."

Although there is plenty of evidence that playing outside lowers the risk of obesity, improves balance and agility, calms high-energy children, reduces stress, improves self-regulation, aids healing and soothes the soul, little research specifically on outdoor pre-schools has been conducted in the United States. (There is more in Scandinavia, where they are popular.)

Ms Harrington and Ms Heller hope to help change this by opening their school to researchers. The first study, set to start this month, will look at how much children in outdoor schools move compared to children at home or in traditional pre-schools. The lead researcher is Dr Pooja Tandon, a paediatrician at the University of Washington Seattle Children's Research Institute.

Most nature pre-schools are private; tuition at Fiddleheads is US$760 (S$1,000) a month. But some programmes, like the Chippewa Nature Centre in Michigan, have begun to work with their school districts. Pupils in the nearby Bullock Creek School District can now attend "nature kindergarten" and even "nature first grade" at their regular public elementary school.

And a few city schools have taken up the forest school mantra. Pupils at the Brooklyn New School in the Carroll Gardens neighbourhood of Brooklyn now spend every Wednesday outside in nearby Prospect Park (as long as it's not raining).

In Seattle, Mr Andrew Jay, a former Audubon Centre director and non-profit entrepreneur, thinks it's far past time to take advantage of the low facility costs of outdoor-based programmes and open them up to a broader range of families. He is planning to open nine outdoor schools based in Seattle City Parks in the next two years.

"A city park is the most democratic space" for a school, Mr Jay says. "The nature part is amazing. But what hooked me was making it available to all." He got the go-ahead to operate his schools on city land from the parks department in October, and now he's trying to get approval from the city's education department to qualify for funding as a local public pre-school programme.

Back at Fiddleheads, several children huddle around Stelyn, who is holding a treasure. With her blond hair trailing to the edge of her bright yellow rain jacket, she holds out a "nothing berry" for all to see.

"I want to see the inside," four-year-old Rowan Wessels says.

"OK, but don't break it any more than that," Stelyn says, pointing at a nick someone had made with a rock.

Rowan peers closely at the soft white centre of the mystery berry and exclaims: "It looks like ice cream!"

•This story was published in partnership with The Hechinger Report, a non-profit, independent news organisation focused on inequality and innovation in education.