iPad Mirroring AND touch interaction

Any info on new technology options to mirror an iPad AND have touch interaction to a touch screen smart TV / classroom Promethean board / Smart Board / etc?

We have classrooms with students who use iOS (AAC) apps for Augmentative & Alternative Communication. Our teachers model/demonstrate using the communication apps on their iPads. Mirroring gives the image, but the interaction is currently done on the iPad. It would be ideal to have the interaction occur on the large touch screen.

Any new insight or equipment set up recommendations?

Thanks so much!!