The BSRs state that a student (aka a non licensed jumper) must always be equipped with a helmet.
You wore one on your tandem to prevent your head from hitting the plane door getting in, out, etc. It also protected your tandem master from getting a head butt to his/her chin.
Every once in a while I'll check out all of the marks and paint chips on my helmet from riser slap, the expected RW contact, and air debris. It makes me appreciate my helmet all the more.
"What's the point of wearing a helmet when you skydive? If that parachute doesn't open, that helmet is now wearing YOU for protection."- Jerry Seinfeld