It is recommended that teacher-scholars of data science adopt reproducible workflows in their research as scholars and teach reproducible workflows to their students. In this article, we propose a third dimension to reproducibility practices and recommend that regardless of whether they teach reproducibility in their courses or not, data science instructors adopt reproducible workflows for their own teaching. We consider computational reproducibility, documentation, and openness as three pillars of reproducible teaching framework. We share tools, examples, and recommendations for the three pillars.