There's no back-end intelligence that would allow this right now. You could request it as a feature by submitting it here:
That said, here is a possible work-around...
Have at least one field in your form be their student e-mail address. (Making an assumption that you are on a higher ed. campus.)
Upon submission, have the results e-mailed to the student's campus e-mail address, with instructions that their form response is not complete until they forward that e-mail, from their campus e-mail account, to an e-mail address you define.
I include the following language in the Email Submission Receipt for one such form of ours:
Thank you for filling out the <your form name here> form.
You're almost done!
To confirm your identity, please forward this e-mail message, from your <campus> e-mail account, to: email@example.com.
Requests coming from non-<campus> e-mail accounts will not be processed.
This is about the only way to provide a level of assurance as to where the response is truly coming from, and it ensures that Student B is not submitting a response while posing as Student A. Then, in the response table, you can filter out those responses that have not been validated.
One more thing: In the response table, you could add a column where you simply confirm the user has validated their response... making it quick work when the form is closed to simply filter on the "validated response" indicator.
I hope that helps,
Thank you but your idea is unfortunately not applicable in our case. We will submit our case so that it is considered in the context of a possible evolution. Thank you again.