Charles C. Word, 31, of Newark, was arrested for the incident on Sunday morning.
According to Newark Police, Word was driving his silver Dodge Charger on South Chapel Street near Delaware Avenue when he allegedly stopped to ask a 22-year-old woman for directions.
Police say the woman approached the vehicle to find Word's pants were down and his genitals were exposed.
The woman walked away, police say, but Word pulled up a second time and tried to talk to her.
The woman said she was going to call police and that's when Word drove away, investigators said.
Officers used surveillance video to get the registration number of the vehicle and were able to identify Word as the driver.
Police found him at his home on Sandalwood Drive and took him into custody without incident. He was arraigned and released on $4,000 unsecured bail.
Appoquinimink High School posted a message on its website about the incident. The statement said Word has been placed on administrative leave.
Furthermore, school officials say, Word is not allowed to teach, coach or be on school premises.
The statement also made it clear that the charges against Word do not involve any students.