Opportunities for students to develop problems for scientific investigation have rarely been provided in South Korean science classrooms. The purpose of this study was to examine the nature of elementary students' participation in problem finding in science learning. Specifically, we examined the characteristics of student participation in problem-finding activities in search for productive ways of student engagement in problem-finding and their conditions. Data from six groups of students from two elementary schools were analyzed. Data sources included recordings and transcripts of students' group conversations during problem-finding activities and follow-up interviews, student worksheets completed as a group, and field notes. The findings showed that typical elementary students were able to generate problems for scientific investigation. They kept mostly on task, and enjoyed the activity. We identified three different problem-finding discourse patterns and conditions for productive questioning, which provided ways to facilitate students' problem finding in science learning. Further research questions are discussed.