When experienced analysts explore data in a rich environment, they often transform the dataset. For example, they may choose to group or filter data, calculate new variables and summary measures, or reorganize a dataset by changing its structure or merging it with other information. Such actions background, highlight, or even fundamentally change particular features of the data, allowing different types of questions to be explored. We call these actions data moves. In this paper, we argue that paying explicit attention to data moves, as well as their purposes and consequences, is necessary for educators to support student learning about data. This is especially needed in an era when students are expected to develop critical literacy around data and engage in purposeful, self-directed exploration of large and often complex datasets.