Hanna has taught the material histories and theories of art and conservation as well as histories of media and technology at the University of Amsterdam, Bard Graduate Center in New York and UCL. 

At UCL Department of History of Art, she has thought the following modules: Intermedia: Art and Materiality in the 1960s and 70s (MA), Theory and History of Conservation (BA), Methodologies of Making (BA), and Methods and Materials of the Artist I&II (BA) and has organized a work placement module Art/Work/Spaces. She has also regularly contributed to the MA Core Course and BA Foundation Course.

Outside her core teaching activities, Hanna has given invited lectures, among others, at Columbia University, New York University, and at the universities in Europe and the UK. She has also contributed to the Summer Institute for Technical Studies in Art (SITSA), a doctoral school at the Harvard Art Museums. 

Hanna has advised and examined MA and PhD students in UK and abroad. She welcomes informal enquiries about studying for a PhD in any of the areas of her research interests. She is especially interested in supervising research that would illuminate new directions for art history and technology studies situated on the intersection of art theory, material culture studies, and the theory of conservation. This might involve projects engaged in a reflective approach to new materialisms, experimental preservation and museology, critical heritage studies and historiographies and epistemes of conservation. Students of a variety of backgrounds, including those underrepresented, are encouraged to contact her.