Students’ activities and difficulties when solving modeling problems with an open goal state

Modeling problems are usually open. Problem solvers must consider which questions need to be answered, which numerical quantities need to be calculated, and which relevant factors need to be taken into account to answer the questions. In the reported study, we examined how students approach modeling problems that include questions with unclear goals. We refer to these problems as modeling problems with open goal states. We aimed to analyze (1) students’ modeling activities and (2) the difficulties they encounter while solving such problems. We conducted a qualitative study with 10 ninth-grade students from German secondary schools. The students solved four modeling problems with open goal states, reported their solution processes by thinking aloud while solving the problems, and took part in two interview phases: first, stimulated recall interviews, and, subsequently, interviews without stimulated recall. The study's findings provide a detailed description of how typical modeling activities, such as simplifying, were enacted with regard to the open goal state. Additionally, we identified difficulties related specifically to the openness of the goal state. For example, several students experienced difficulties in identifying the openness of the problems and in interpreting the results appropriately. This study contributes to a better understanding of how the openness of modeling problems shapes students’ modeling activities and uncovers difficulties in students’ solution processes for problems with open goal states.