In this paper we describe a model of the process by which people solve problems using information visualization systems. The model was based on video analysis of forty dyads who performed information visualization tasks in an experiment. We examined the following variables: focused questions vs. free data discovery, remote vs. collocated collaboration, and systems judged to have high and low transparency. The model describes the stages of reasoning and generating solutions with visual data. We found the model to be fairly robust across task type, collaborative setting, and system type, though subtle differences were found. We propose that system transparency can support some stages of the process, and that support is needed in the last stage to help users translate their findings from visual to written representations.