Research

The Enterprise receives a communication from a secret research base. They have stored in their computer orders to render any aid the base requires, no questions asked, so they proceed to rendezvous with the planet to pick up some personnel that they have been asked to house for a few days. When they receive the list of personnel, they learn that it is almost entirely composed of children--the children of the scientists on the research base.

It eventually turns out that the scientists are working on a terraforming solution which will transform the poisonous atmosphere of the planet into breathable air, and they wanted the children removed because the next step was dangerous.

Among the children is a Vulcan twin, T'Paalee--who has one mind in control of two bodies. This is explained as being due to the natural telepathic ability of Vulcans, combined with the extended contact in the womb, leading to only a single mind developing:

In the end, Spock and McCoy report that efficiency was up during the period the children were on board, and recommend that further study be done to determine if it would be worth having children aboard starships generally, to improve the morale of the crew.

Notes

A prescient story. The Genesis Device from the film was a similar terraforming tool--with similar concern for its potential for usage as a weapon. And of course by TNG there were children on ships.