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Significant research has provided robust task and evaluation languages for the analysis of exploratory visualizations. Unfortunately, these taxonomies fail when applied to communicative visualizations. Instead, designers often resort to evaluating communicative visualizations from the cognitive efficiency perspective: "can the recipient accurately decode my message/insight?" However, designers are unlikely to be satisfied if the message went 'in one ear and out the other.' The consequence of this inconsistency is that it is difficult to design or select between competing options in a principled way. The problem we address is the fundamental mismatch between how designers want to describe their intent, and the language they have. We argue that visualization designers can address this limitation through a learning lens: that the recipient is a student and the designer a teacher. By using learning objectives, designers can better define, assess, and compare communicative visualizations. We illustrate how the learning-based approach provides a framework for understanding a wide array of communicative goals. To understand how the framework can be applied (and its limitations), we surveyed and interviewed members of the Data Visualization Society using their own visualizations as a probe. Through this study we identified the broad range of objectives in communicative visualizations and the prevalence of certain objective types.