Participatory sensing is a data collection method in which communities of people collect and share data to investigate large-scale processes. These data have many features often associated with the big data paradigm: they are rich and multivariate, include non-numeric data, and are collected as determined by an algorithm rather than by traditional experimental designs. While not often found in classrooms, arguably they should be since data with these features are commonly encountered in daily life. Because of this, it is of interest to examine how teachers reason with and about such data. We propose methods for describing progress through a statistical investigation. These methods are demonstrated on two groups of secondary mathematics teachers engaged in a model-eliciting activity centered around participatory sensing data. We employ graphical depictions of discrete Markov chains to describe the strategic decisions the teachers follow while analyzing data, and find that this descriptive technique reveals some suggestive patterns, particularly emphasizing the importance of frequent questioning and crafting productive statistical questions.