The increased availability of computational modeling software has created opportunities for students to engage in scientific inquiry through constructing computer-based models of scientific phenomena. However, despite the growing trend of integrating technology into science curricula, educators need to understand what aspects of these technologies promote student learning. This study used a multi-method research approach involving both quantitative (Paper 1) and qualitative data (Paper 2) to examine student conceptual understanding of astronomical phenomena, relative to two different instructional experiences. Specifically, based on students' understandings of both spatial and declarative knowledge, we compared students who had constructed three-dimensional computational models with students who had experienced traditional lecture-based instruction. Quantitative analysis of pre-interview and post-interview data revealed that construction of three-dimensional models best facilitated student understandings of spatially related astronomical concepts--whereas traditional instruction techniques best facilitated student understandings of fact-oriented astronomical knowledge. This paper is the first in a two-paper set that continues our line of research into whether problem-based courses such as the Virtual Solar System course can be used as a viable alternative to traditional lecture-based astronomy courses.