This research explores learning in science museums through the most common activity in a science museum--interaction with exhibits. The goal of this study was to characterize the learning behaviors exhibited by students as they engage with interactive exhibits in order to draw insight regarding the design of the exhibits. In order to do so, we used a qualitative method of observation as well as the Visitor Engagement Framework (VEF) model, a visitor-based framework for assessing visitors' learning experiences with exhibits in a science center setting. The combined method produced a framework of nine learning behaviors exhibited during the visitors' interaction with the exhibits, grouped into three categories that reflect increasing levels of engagement and depth of the learning experience. Our research participants consisted of a total 1800 students aged 10-12 (4th, 5th, and 6th graders) who came to the museum with their class for a day visit. We observed nine exhibits, each visited by 200 students. Our observations revealed several design elements that contribute to engagement with exhibits in science museums. For example, exhibits that have familiar activation encourage visitors' interaction, exhibits that facilitate social interaction are more likely to increase engagement, and the highest levels of engagement can be found in exhibits that support large groups.