There are several ways this could be done.
The easiest one to do would be to simply re-populate the form fields from the previous form submission so that they would already be filled out.
Remove your redirect in the add to cart, and change the button value to "Add Student" and then put another button on the page that is "Done" that takes them to the cart.
Then bind the fields that would likely be the same to the form submit values from the bindings panel.
A fancier solution might use a single form submit and dynamically add rows for new students onto the page, but that would take hand coding of both javascript and php and would be better handled in a premier support ticket.