“She brings new perspective to problems that have existed for a long time,” said Mike Curtis, vice president of engineering at Airbnb. “Almost any problem space — no matter how different it is from the last — she seems to be able to tackle.”

Lumineer Academy opened in January in a former customs house in a wealthy suburb of Melbourne. There are 130 students enrolled and tuition costs around 10,000 Australian dollars, or $8,000.

Unlike most Australian private schools, students at the academy do not wear a required uniform. Instead, students are encouraged to build their own wardrobes within a prescribed palette. (In nautical stripes and khakis, many children resemble those in a J. Crew catalog.)

Classrooms in the school have been rebranded “studios.” There are no desks, but rooms include couches, beanbag chairs and tables to stand at while working.

The Luminaria model claims to balance hard S.T.E.M. subjects, like computer programing, with soft skills like emotional intelligence and teamwork that are increasingly sought by employers. Ms. Wu said the model was based on a concept in physics known as first principles, in which ideas are reduced to their purest form, unencumbered by assumptions, analogies or biases.

Several recent studies have suggested that 30 to 50 percent of Australian teachers leave the profession within their first few years of work. Lumineer Academy has sought to capture some of them with a promise of freedom from strict curriculums.

“When I saw the job advertised, I thought, ‘This can’t be true,’ ” said Kim Staples, a 31-year-old teacher. “I was so frustrated in other systems, because they’re quite prescriptive.”