The Providence Journal reports the students told police they were sitting at a picnic table in Columbia Park on Monday afternoon when four juvenile males approached them.
The students had their cellphones on the table, and one of the suspects showed a foot-long knife and grabbed the phones.
Police say the suspects fled and someone chased them. It is unclear if the person was one of the students or a bystander.
Authorities say one suspect threw a backpack into a trash can and several phones were found inside.
No injuries were reported.
Public safety officials warn students to be alert, and say students should avoid Columbia Park.
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