Natarajan teaches undergraduate and graduate courses in astronomy and physics at Yale. She developed the introductory undergraduate course for non-science majors in cosmology that is regularly taught. She also co-developed the first year graduate course that serves as the foundational course that is required for all students entering the Astronomy PhD program that broadly covers the basics of the physics of astrophysics. She is invested in pedagogy and science education and works closely with the Yale Poorvu Center for Teaching and Learning to improve learning outcomes for her students given the diversity of cognitive styles.
Natarajan has lectured widely in Summer and Winter Schools in various sub-fields in astrophysics including lensing, black hole physics and galaxy formation. In addition, she gives pedagogical talks on many aspects of astronomy and astrophysics, as well as the history of ideas in cosmology.