The three crystal fragments can be found in three separate locations placed around the first half of the school.
The first crystal fragment can be found inside of the left-most cabinet in the starting classroom where Kaori Hasegawa and Shiho Hasegawa first woke up. The second crystal fragment can be found inside the central cabinet in classroom 2-4. Finally, the third crystal fragment can be found inside of a desk drawer in the infirmary.
After the events at the girls' lavatory where Shiho is trapped, Kaori can give all three crystal fragments to the blue spirit at the stretching hallway. He will combine them all to create a crystal cluster which can be used to free her sister.
If Kaori decides to not combine the crystal fragments, it can be used during the battle against the Vengeful Spirit or Girl's Spirit. It will restore 30 MP to all party members.