Final answer:
The email address would not be considered directory information as it often has different privacy rules and requires the student's or guardian's consent to be publicly disclosed.
Step-by-step explanation:
The piece of information about a student that would not be considered directory information is Email address. Directory information typically includes a student's name, address, and phone number. Email addresses, while commonly used for school communications, often fall under different privacy rules and are less likely to be publicly disclosed without the student's or guardian's consent. The protection of such personal information is governed by laws and regulations, like the Family Educational Rights and Privacy Act (FERPA) in the United States, which aim to safeguard student privacy.