All datasets emerge from and are enmeshed in power-laden semiotic systems. While emerging data ethics curriculum is supporting data science students in identifying data biases and their consequences, critical attention to the cultural histories and vested interests animating data semantics is needed to elucidate the assumptions and political commitments on which data rest, along with the externalities they produce. In this article, I introduce three modes of reading that can be engaged when studying datasets- a denotative reading (extrapolating the literal meaning of values in a dataset), a connotative reading (tracing the socio-political provenance of data semantics), and a deconstructive reading (seeking what gets Othered through data semantics and structure). I then outline how I have taught students to engage these methods when analyzing three datasets in Data and Society- a course designed to cultivate student competency in politically aware data analysis and interpretation. I show how combined, the reading strategies prompt students to grapple with the double binds of perceiving contemporary problems through systems of representation that are always situated, incomplete, and inflected with diverse politics. While I introduce these methods in the context of teaching, I argue that the methods are integral to any data practice in the conclusion.