Designers often collaborate to explore creative ideas, especially during the early stages of conceptual design, and their mental models, as the framework of design tasks, greatly influence the collaborative sketching process. Such models have multiple kinds of differences and each kind might have unique effects, yet previous studies analyzed these differences as a whole and have reported only the effects of overall similarity. Because ideas are the embodiments of mental models, this study referred to the components of ideas to construct the structure of mental models. We constructed a three-level mental model involving goals, functions, and structures and arranged the ideas in sketching accordingly into a three-level idea tree. A collaborative sketching experiment was conducted, and the effects of the three levels of mental models were compared. Participants accepted different goals and produced large numbers of new functions. They stuck with similar functions and continued to generate new structures. Participants had different strategies when exploring the levels of the mental models, providing possibilities for new methods of collaborative sketching.