J3 Cub flight instructor with student reported a runway excursion on landing.

Narrative

Upon normal three-point landing on the paved runway at ZZZ; student touched down and bounced off of the runway. During the bounce the student failed to properly use his rudder pedals to maintain directional control of the airplane allowing the longitudinal axis of the plane to veer left. I immediately added the correct rudder inputs to align the airplane with the runway. Upon touching down again after the bounce the left wing dipped and we landed on the left main gear. The plane immediately veered hard to the right at nearly a 90 degree angle to the runway. I immediately tried to regain control of the aircraft using rudder pedals and brakes but ultimately failed to do so. We hit the snow bank that divided the paved and parallel grass runway and the plane nosed over causing the prop to strike the ground. Both my student and myself were uninjured. I immediately turned off the fuel; closed the throttle and shut off the magnetos before instructing my student to exit the aircraft. After exiting the aircraft we were met with additional airport personnel who helped us move the plane off the active runway. I think the student; who has spent most of his time in Cessna's; was trying to use the rudders in a similar manner which requires long; constant pressure to control. The Piper Cub requires quick; constantly changing rudder inputs to maintain directional control. I should have recognized the instability of the situation earlier and been quicker on my responses with the rudder pedals. I failed to take control of the situation which resulted in the accident. Additional training on the ground such as practicing taxiing at high speeds could help in the future to demonstrate proper rudder input techniques.