TerraCycle will recycle your old plastic pens (felt tips and other types of plastic pen). 
It simply involves a collection box (any box) and downloading a prepaid label.
To download the free label, you do have to sign up to TerraCycle but it is very easy, only requires basic contact information and, by so doing, you can earn points towards rewards for your school.
You can then arrange a pickup with UPS.
See: https://www.terracycle.com/en-GB/collection-programs#
Parents could also be encouraged to send their used plastic pens into school for recycling.