Grover, 40, taught for 15 years, the last 10 at D.W. Lunt and Falmouth Elementary schools, and was the 2010 Maine Teacher of the Year. The Greene native taught at Lake Street School in Auburn from 1996 to 2001.
DOE spokesman David Connerty-Marin said Grover collapsed after returning home from a run while visiting family in Rangeley.
In a message to School Department staff members, Co-Principals John Flaherty and Karen Boffa said a memorial service is planned for Saturday, Dec. 1, at Falmouth Elementary School. They said plans will be developed for supporting students and staff.
Grover made service-learning a regular part of his students' school experience, taking them regularly to participate in community service, said Gloria Noyes, president of Maine's Teacher of the Year Association and a mentor to Grover the year he won.
"Kevin is going to be greatly missed," Noyes said. "He was someone who was highly regarded in the world of education and left an impact on all of us. It's a great loss for education and educators in Maine. He made a mark on all his students' lives."
Noyes said Grover was a key element in building and inspiring teachers through the Teacher of the Year Association. He started a Speaker's Bureau within the association, which brought together past recipients of the award to speak at businesses and schools about their expertise, she said.
In school, Grover was a leader in technology and always willing to help inspire other teachers to use it, Noyes said.
"He was a brilliant guy and very creative; he was excellent with technology" she said. "Staff would always go to Kevin for instruction and enhancement of their skills."
Grover graduated from St. Dominic Regional High School in Lewiston. He earned a bachelor's degree from the University of Maine at Farmington and a master's degree from the University of Southern Maine.
Grover and his wife, Rebecca, have two young children. A telephone call to their home in Falmouth on Friday afternoon was not answered.