The purpose of a study was to explore the link between conceptual understanding, free exploration of hands-on science center exhibits, and Piagetian cognitive developmental levels. In this primarily qualitative study, which is based upon interview and observational data, patterns in children's behavior relating to specific hands-on science center exhibits are described. The data gathering included selecting four exhibits, two that attempted to convey a concrete concept and two that presented a formal concept. Subjects were 45 children between the ages of 5 and 13. Each subject was interviewed and tested using a set of eight Piagetian tasks. The subjects were then divided into three categories: preconcrete, concrete, and postconcrete. After a pretest was given, each subject was given time for individual free exploration of an exhibit. After the subjects had completed as much exploration as they deemed necessary, they were asked to explain how they thought the exhibit worked. The answers of each subject were compared with a concept statement for each exhibit. The level of conceptual understanding of the concrete concept exhibits increased with each developmental group. All groups had difficulty understanding the exhibits requiring formal thought. (18 references) (KR)