Maura Flanagan teaches at the Brooklyn Transition Center, a high school for students with emotional disorders. Some students are autistic, others have been kicked out of previous schools.

BTC has a full complement of guidance counselors, therapists and special educators to work with its students, but one of the most promising additions has been a bikeshare program.

Last fall the school was selected for a first-of-its kind experiment from the New York Department of Health. A handful of Flanagan's students were recruited to ride to and from school. They took a bike safety class, were given helmets, and started pedaling around Brooklyn's streets. By this spring, 15 students had bikeshare memberships—as well as a greater sense of independence and confidence.

"When you learn to ride a bike, there's a big pridelowers our costs," said Gabe Klein, co-founder of the transportation consultancy CityFi and former transportation commissioner in Chicago and Washington, D.C.

In many municipalities, it would be cheaper for the government to buy a child a new bike each school year, rather than paying for bus service. In 2013, $914 was spent per U.S. student on transportation. A serviceable bike can be bought for half that figure. And a bikeshare membership could be bought for even less.

Related: The case for bicycles' inevitable triumph over cars

It's a different story elsewhere in the world. Chinese children are welcomed on the country's thriving bikeshare systems at age 12. In Paris, home to Europe's largest bikeshare program, 14-year-olds are allowed. Milan's bikeshare has a set of small bicycles designed to fit children.

The age