Professor Ober carefully monitors and records the behaviors of children on school playgrounds in order to track the development of their physical skills. Professor Ober is most clearly engaged in

naturalistic observation

Explanation:

In naturalistic observation, researchers will gather data by directly observing the subjects in their natural habitat without making any intervention.

This is what Professor Ober is doing.

Professor Ober wants to collect a data about development of their physical skills among children. This means that the children are his research subjects.

To collect his data, professor Ober observed the children in the playground (which is the children's natural habitat). He also did not told the children to do anything, he just quietly observe and let the children do what they usually do. (not making any intervention)