This paper reports on a study that investigated students' metacognitive engagement of in both out-of-school and classroom settings, as they participated in an amusement park physics program. Students from two schools that participated in the program worked in groups to collectively solve novel physics problems that engaged their individual metacognition. Their conversations and behavioral dispositions during problem solving were digitally audio-recorded on devices that they wore or placed on the tables where groups worked on the assigned physics problems. The students also maintained reflection journals on the strategies they employed to manage their own understanding as well as learning processes. Prior to the amusement park physics discourse, the students completed a specially-developed questionnaire instrument. This provided signposts of the students' metacognitive engagement during group problem-solving at the park and subsequent related physics learning tasks back in the classroom. This data, added to field notes arising from observations, and formal and informal interviews during post-visit learning activities provided the data corpus on the students' metacognitive engagement. Analysis of this data revealed three types of metacognitive engagement during group learning tasks: collaborative and consensus-seeking, highly argumentative, and eclectic, resulting from high levels of dissonance. In both cases, evidence of individual students' deeper understandings, which manifested through students' cognitive and social behaviors, demonstrated the invocation of metacognition to varying degrees. The novel physics problems tackled by the students created situations where discrepancies between their prior knowledge and the direct experiences enabled them to explicate their thinking through dispositions of behavior.