It's not always possible to give a complete answer without seeing the floor first hand, but generally you should sand it, oak is a hard wood and as used in a school should be thick enough to take a good sanding use good quality sanders and if the pitting/damage is light start with a reasonable fine grade.
To finish use a quality product and use lambs wool applicators or pads
These jobs take a lot of time if you want a really pukka finish - so price well for time and materials, just remember wood needs to be treated with care, one slip could ruin days of work
Best of luck
Darran