Honolulu is taking its first tentative steps toward a brave new world in which people turn their gaze upward, rather than outward. In a more densely populated urban core centered on a rail transit system, the schoolhouse where young families will send their children is likely to have a vertical design.

This is an approach that makes sense for the state — assuming planners accurately project costs and make sure these schools mesh well with other community assets.

The state Department of Education has changed the way it seeks to finance the construction of new schools to be built within a district extending from Kalihi to Ala Moana — the final stretch of the rail system.

That is where the city expects to encourage transit-oriented development by offsetting much of the infrastructure costs, offering better financing terms and through other inducements.

For their part, developers in this corridor will include more affordable housing units in their plans and be held to a school impact fee, approved in February by the state Board of Education, going into effect Oct. 1. A fee of $3,864 per residential unit will be charged to developers, whose per-unit assessment in other zones amounts to $9,374.

The fee has been an established rule for new developments since 2007. The calculation in this particular district, however, will follow a new formula.

It’s a lower rate of assessment, based on the state’s projection that the vertical schools require much less land and would be less expensive. But the adequacy of that rate to cover costs will need testing and, almost certainly, refinement.

The first test will likely be the development of Pohukaina Elementary School, a $40 million project planned as part of the mixed- use 690 Pohukaina complex in Kakaako.

The project concept has evolved from a school encompassing the lower floors of a high-rise tower that was proposed as an “iconic” structure far exceeding current height limits.

The community opposed that idea, and now the first phase is envisioned as a high-rise residential tower and a separate school that itself could reach about 10 stories in height.

Initial renderings show a school with outdoor terracing providing open-air places for the 750 elementary students expected to attend, although the public Mother Waldron Park is also nearby.

Funds for design and initial construction were approved by the last Legislature. It remains to be seen in the final plans how the school will be laid out, and where the opportunities are to run it efficiently. If this works, Pohukaina can be a model for future vertical schools.

And there are other models, in other cities. New York, to name one, has in the past decade gone vertical to gain needed public schools in areas otherwise cost-prohibitive for new developments.

One is the Spruce Street School, which opened in 2009 in the first five floors of a rental tower. In this deal, the developer built the outer shell while the interior was constructed with the city’s public school funds.

Another example, Beekman Hill International Elementary, admitted students in 2012 to classroom and rooftop garden spaces of the public school. It occupies the brick-clad lower floors of a sleek upscale skyscraper.

Similar projects are rising in cities worldwide. Some share parks and recreational facilities with the larger community; spreading some of these costs among multiple area developments makes perfect sense.

By the time Pohukaina opens, it should become clearer how to make it more energy-efficient, how to save on other operational expenses — and how much vertical schools really will cost.

Ultimately, the new DOE vertical- school financing plan will need tweaks, but the reward should be well-equipped campuses, fitting learning environments for Hawaii’s youth.